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1. The Disaglomeration property is dsagglomer ation interval of sizes o A o J Enter the name of the property fFraction_of agglomerates With this property you can evaluate the mass fraction of agglomerates at a given time having a size between a given range Sa Sb S 4 16 Frac fsa sb t oe a Sa Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 116 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu 4 2 4 4 Number of agglomerates of given size Figure 4 47 The Number of agglomerates of given size Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Number of agglomerates of given size xi Number of agglomerates of given size The Disaglomeration property is disaggiomeration interval of sizes o f o J K shape Factor of agglomerates o Ys volume of the sample o x mass fraction of CB in s gt Enter the name of the property number_of agglomerates ox Cancel With this property you can evaluate the number of agglomerates at a given time having a size between a given range Sa Sb Vy Frac N Sa Sb 6 4 17 kS mean where Si S Smean t ee eer 4 18 Sa Sa and Frac sa sb t is defined in Equation 4 16 p 116 V is the volume of a sample able to contain a large number of agglomerates of various sizes
2. 1 4 General Explanation on the Way to Solve a Mixing Task Three major steps must be performed in order to solve a mixing task first we calculate the flow then we calculate a set of trajectories and finally we perform statistics on this set 1 The flow simulation we have to define a finite element mesh via GAMBIT ICEM CFD Patran next we enter in Polydata where a F E M task is defined in order to calculate the flow ONLY With the data file we run Polyflow and finally we obtain a Polyflow result file containing the velocity field the shear rate and other fields of interest If the flow is transient it is recommended that you save the Polyflow Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 4 of ANSYS Inc and its subsidiaries and affiliates General Explanation on the Way to Solve a Mixing Task results files at exacts time steps At However if the flow is piecewise steady with N successive boundary conditions NV small in loop or not it is sometimes easier to perform N Polydata sessions one for each specific set of boundary conditions We will run Polyflow N times one for each data file and we will obtain N result files containing each one a set of fields specific to a particular set of boundary conditions Figure 1 4 The Flow Simulation GAMBIT ICEM Patran etc finite element mesh data file N times if piecewise steady flow
3. Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 161 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 162 of ANSYS Inc and its subsidiaries and affiliates Appendix B The Global Efficiency of Stretching Let s suppose the flow to be 2D steady state in a closed domain We will explain how we can calculate the time evolution of the global efficiency of stretching see chapter 2 for the definition of this parameter For example for the linear stretch at time this efficiency is e M t In 4 d2 I Darao 1 Q 2 0 o o To calculate such a parameter the following steps are necessary 1 In the mixing files are calculated the stretching In 4 and the dissipation rate D along trajectories 2 We have to define in Polystat a new property the cumulated dissipation which is the time integration of the dissipation rate t D lt D X t D X tat 2 0 This new parameter depends on the material point and on time 3 We perform a slicing on the time N slices every At seconds 4 We calculate the sum function of the stretching In Sn 4 M t maaa 3 o 5 We calculate the sum function of the cumulated dissipation D So D dQ ay o 6 Finally we divide the two sum functions to obtain the global efficiency
4. Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 135 The Polystat User s Manual 4 5 2 5 The Probability Function Figure 4 75 The Probability Function Settings for the Create a new function Dialog Box Create a new function Probability Function x Probability Function Select a set of slices new_set_of_slices Select a property temperature Select velocity field velocities Weighting No veloc Normal everywhere veloc Normal if positive Enter the number of values 100 Enter the name of the function new_probability Function OK Cancel To calculate the evolution of the probability function also named distribution function of a property you need to specify which set of slices will be used and to select a property Don t forget to enter the number of values to represent this function and to give it a name If you want to weight the function depending on the local velocity don t forget to select a velocity field see Weighting p 159 for more information You will obtain a probability function for each slice of the set If you visualize this function for a given slice you find on the X axis the property and on the Y axis the probability Figure 4 76 The Probability Function of a Property for a Slice probability for slice S property P Release 15 0 SAS IP
5. If you confirm your order Polystat will calculate successively the new properties the new sets of traject ories the sets of slices and the statistical functions Upon the time a message informs you about the current calculations being done When those calculations are finished we can visualize our results as described in the section that follows 4 1 6 The Draw results Option With this option we can see the results of our calculations we visualize in the flow domain the spatial distribution of a property for a specific slice or for a given trajectory By clicking the Draw results option the Graphic Display window will open the left side has tabs that allow you to specify what to see in the graphics window on the right side One can also find a graphics toolbar above the graphics window this graphics toolbar contains a set of buttons that allows you to manipulate the view see paragraph 2 8 Graphics Toolbar of the Polyflow User s Guide for more information about the use of these buttons Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 79 The Polystat User s Manual Figure 4 9 The Graphic Display Window of Polystat Trajectory 33 of set All_trajectories Property temperature SAARA mad minim A mia die Firstid o Step fi Color set som I Logsrthm scale Enter pixelsize 3
6. Figure 3 30 The Parameters for the tracking Menu Parameters for the tracking Current setup NBELEM the number of steps of integration to cross an element of the mesh EPSPNI the tolerance criterion on a distance EPSVIT the tolerance criterion on a velocity EPSTIM the tolerance criterion on a time 3 1 0000000E 06 1 0000000E 06 1 0000000E 06 Upper level menu Modification of NBELEM Modification of EPSPNT Modification of EPSVIT Modification of EPSTIM You can modify the following parameters Modification of NBELEM NBELEM affects the number of integration steps used to cross one element of the finite element mesh the default value of 3 requests that in the mean any material point crosses one finite element in 3 steps This parameter is important for the accuracy of the calculation of kinematic parameters higher values for NBELEM result in better accuracy It is not necessary to set NBELEM higher than 3 as the intrinsic accuracy of the method is reached with this value and higher values would be expensive in CPU time Modification of EPSPNT EPSPNT is the tolerance on a distance Two points are identical if the distance between these points is smaller than EPSPNT Modification of EPSVIT EPSVIT is the tolerance on a velocity EPSVIT is used to determine if a point is a stagnation point if the local velocity v X is lower than EPSVIT VNORMX then the material point X at time fis a stagnation point M
7. You can select from the following two options Random initial direction of stretching You do not specify a direction the computer will randomly generate an initial direction of stretching This direction will be different from material point to material point Imposed initial direction of stretching You specify a direction dx dy dz every material point has the same initial direction Over time the two options are in fact equivalent from a statistical point of view You can also select from the following to define the way in which tensor F the gradient of deformation tensor is calculated You can choose to leave tensor F unconstrained or you can constrain it such that the determinant of tensor F always remains 1 No constraint over the tensor F Constraint over the tensor F detF 1 2D simulations do not present any problems as the method guarantees that the determinant of F will remain 1 incompressibility it does not matter whether you choose to constrain the tensor or leave it unconstrained For 3D flows on the other hand you cannot be sure that the tensor F will remain 1 along a trajectory of a material point If you do not constrain the tensor F a future analysis of the results in Polystat will show if the calculations were accurate that is if det F remains 1 along the trajectories In the other case unfortunately if you constrain F such that det F remains 1 along trajectories you cannot be sure Release
8. 4 2 3 2 ANx AAx the new property is the property A exponent x you have to select the property A the data to enter the exponent x and to give a name to the new property the result 4 2 3 3 exp A exp A the new property is the exponential of the property A you have to select the property A the data and give a name to the new property the result Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 95 The Polystat User s Manual 4 2 3 4 log A log A the new property is the natural logarithm of the property A you have to select the property A the data and give a name to the new property the result 4 2 3 5 A B7 A B A BY A B the new property is the addition or the subtraction of the properties A and B you have to select the two properties A and B the data and give a name to the new property the result The two properties must have the same type scalar or vectorial 4 2 3 6 A B A B the new property is the division of the property A by the property B you have to select the two properties A and B the data and give a name to the new property the result The property A can be a scalar or a vector but the property B must be a scalar 4 2 3 7 A B A B the new property is the multiplication of two pr
9. All rights reserved Contains proprietary and confidential information 92 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu It is possible to modify or to remove from the list one or several properties note that this is only true for the properties created in Polystat If you want to modify some data of a property select it in the list and then click the Modify button The window that served for the creation of that property will appear then modify some data If you want to store the modified data click OK Otherwise click Cancel To remove one property from the list select it in the list and then click the Delete button To remove all the created properties click directly on the Delete All button In both cases Polystat asks for a confirmation of your choice 4 2 3 Create Properties Based on existing properties it is easy to define new properties First select the CREATE a new property option in the Properties menu of the main window The following window appears Figure 4 21 The CREATE a new PROPERTY Dialog Box x lt Select Type gt v Select property type gt Then click the button J at the right of the combo box presenting lt Select Type gt A drop down list appears showing the properties that can be created Eventually select in this list the appropriate property Release 15 0 SAS IP Inc All rights reserved Contains proprietary and conf
10. Please have your Customer or Contact ID ready UK 0800 048 0462 Republic of Ireland 1800 065 6642 Outside UK 44 1235 420130 Email support uk ansys com Support for University customers is provided only through the ANSYS Customer Portal Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information viii of ANSYS Inc and its subsidiaries and affiliates Contacting Technical Support JAPAN CFX ICEM CFD and Mechanical Products Telephone 81 3 5324 8333 Fax 81 3 5324 7308 Email CFX japan cfx support ansys com Mechanical japan ansys support ansys com Fluent Products Telephone 81 3 5324 7305 Email Fluent japan fluent support ansys com Polyflow japan polyflow support ansys com FfC japan ffc support ansys com FloWizard japan flowizard support ansys com Icepak Telephone 81 3 5324 7444 Email japan icepak support ansys com Licensing and Installation Email japan license support ansys com INDIA All ANSYS Inc Products Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option Telephone 91 1 800 209 3475 toll free or 91 20 6654 3000 toll Fax 91 80 6772 2600 Email FEA products feasup india ansys com CFD products cfdsup india ansys com Ansoft products ansoftsup india ansys com Installation installation india ansys com FRANCE All ANSYS Inc Products Web Go to the ANSYS Customer Port
11. Selection of properties List of selected properties Time always Coordinates always Parameters for the kinematic variables Upper level menu Enable Space integration Enable Rate of stretching Enable Rate of dissipation Enable Direction of stretching Enable Logarithm of stretching Enable Pressure Enable Velocity Enable Temperature Enable Divergence of velocity Enable Determinant of F Enable Viscosity Enable Mixing index Enable First eigenvalue of T In this menu you can start with Parameters for the kinematic variables which allows for the setting of the numerical parameters necessary for the calculation of the mixing parameters evolving along the trajectories see Parameters for the Kinematic Mixing Properties p 59 for details Note that the default numerical parameter settings are appropriate in many applications so this step may not be necessary The next step is to enable the properties you want to store in the mixing result files by clicking the appropriate menu item All enabled properties will be listed at the top of the menu Note that the time and the coordinates are always saved The first property the space integration S ft is the length of the trajectory up to the current time t t S t liver dt 3 1 to The following properties are kinematic parameters that are defined in The Mixing Theory p 11 rate of stretching rate of dissipation direction of stretching and logarithm
12. The stress applied by the matrix on drops or on solid particles is the engine that can lead to dispersion if the stresses are high enough to compete with surface tension of drops or with internal mechanic resistance of solid particles dispersion occurs Dispersion will be better if some elongational effect exists in the flow This information is available by adding some postprocessors while defining the set up for the flow calculation Next it will be possible to evaluate them along trajectories of material points Moreover a model has been included in Polystat to calculate the disagglomeration process along trajectories We have found a general and accurate method to calculate all these parameters in a single simulation The main steps of this method are firstly we calculate the flow as usual secondly we compute the trajectories of a large set of material points initially concentrated in the whole flow domain or not with in complement the calculation along these trajectories of the local deformation of the matter and other relevant properties Finally we analyze these results with statistical tools in order to obtain a global objective and quantitative overview of the mixing evolution 1 3 Classification of Flows Capabilities of the Mixing Module With the mixing module all the kind of flows cannot be studied There exist limitations But first let us define some concepts Open Closed domain a closed domain is a domain where
13. fs OK Cancel With this method you generate automatically a list of ordered slices You have first to select a set of trajectories on which the slicing will be done Second you specify the first slice of the list you select a property a position and a direction for the plane Third you enter the number of slices you want and the distance increment between two successive planes Finally you enter the name of the new set This slicing is based on a single property and all the slices are parallel to each other This is not the case for the manual method 4 4 3 The Manual Slicing Option Figure 4 59 The Create manually a list of slices Dialog Box Create manually a list of slices x Select a set of trajectories All_trajectories z Enter the name of the set of slices new_set_of_slices List of existing slices This list is sorted Up If you want to modify the order select a slice Then click on lt Up gt or lt Down gt to change the position of the selected slice in the list OK Cancel Down Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 126 of ANSYS Inc and its subsidiaries and affiliates The Slices Menu With this method you generate manually one by one a list of ordered slices You have first to select a set of trajectories on which the slicing will be done Second you specify each slice
14. t At By default we define J as T ratio ratio 2 43 List of functions used in the erosion and rupture models and available in the disagglomeration clp file DNSPRB to define the initial mass density distribution function default Gaussian distribution between 15 and 25 um Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 28 of ANSYS Inc and its subsidiaries and affiliates Comment AS EROSION_MODEL to define the function a of erosion model see Equation 2 38 p 26 TRANSFER_RUPTURE to define the transfer function for rupture model CRITICAL_SIZE to define the minimum size of agglomerates that can break for a given shear stress see Equation 2 41 p 27 e RUPTURE_TIME to define the amount of time during which the stress must be above required threshold to get rupture e RUPTURE_RATE to define the fraction of agglomerates that will actually break if rupture criteria are met MODIFY_INDUCTION_TIME to define the function J ratio see Equation 2 43 p 28 2 6 Comment In the presentation of the mixing parameters that we calculate we always define them as evolving with time This kind of representation is well suited if the flow occurs in a closed domain in that case the mixing evolves with time But what if the flow occurs in an open domain such as in a single screw extruder or in a Kenics mixer In such a case the mixing
15. x is the mass fraction of agglomerates included in the sample k is a shape factor k 2 6 if we assume that agglomerates are spheres k 1 if they are cubes Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 117 The Polystat User s Manual 4 2 4 5 Mass of agglomerates of given size Figure 4 48 The Mass of agglomerates of given size Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Mass of agglomerates of given size Mass of agglomerates of given size The Disaglomeration property is disagglomeration interval of sizes fo o Ro volumic mass of pure CB fo Ys volume of the sample fo x mass fraction of CB in s o Enter the name of the property mass _of_agglomerates ox _ caei With this property you can evaluate the mass of agglomerates at a given time having a size between a given range Sa Sb M Sa Sb t VXPegFrac 4 19 h ou Frac sa sb t is defined in Equation 4 16 p 116 V is the volume of a sample able to contain a large number of agglomerates of various sizes x is the mass fraction of agglomerates included in the sample PCR is the density mass per unit volume of pure agglomerates Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential informatio
16. 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 60 of ANSYS Inc and its subsidiaries and affiliates Parameters for the Storage of the Results that this will improve the accuracy of the results for this reason it is recommended that you retain the default setting in which F is not constrained 3 9 Parameters for the Storage of the Results Clicking the Storage of the results menu item in the mixing task menu opens the menu shown in Figure 3 34 The Storage of the results Menu p 61 Storage of the results Figure 3 34 The Storage of the results Menu Storage of the results Generation of several result files named mixing 1 mix to mixing _10 mix These files are formatted ascii The max number of trajectories 100 per file The max CPU time 4 hours per file We store the successive positions of the material points at each time step of 1 0000000E 00 seconds Upper level menu Modify the prefix of result files mixing Modify the number of result files 10 Modify the format of result files ascii formatted Modify the max number of trajectories 100 per file Modify the max CPU time 4hours per file Storage of all the points of the trajectories gt Storage at each time step exactly Storage after each time step minimum Storage at each displacement exactly Storage after each displacement minimum Modify the time step 1 0000000E 00 With this menu
17. 25 ce5 vc sines hoc ects eon Ari EEK tates vo Cai ah ve bade EE EE A selec eae De dae eave tages stv tactl do teses aS 1 TVs Obj QCtives Pcses EET EE E A ted aueda tee Paced tea leetsba te ee ved eanSdeeeta oc OE Gaede ves veaveetaacedt 1 12 How to Characterize MIXING ataiona a aca eultians EEA E E aeaaea eaa NE OaS santana 1 1 3 Classification of Flows Capabilities of the Mixing Module cccccccccessssssneeceeeeesseessneeeeeeeeseeeeees 2 1 4 General Explanation on the Way to Solve a Mixing Task se seeeessseeeeesneeceessceeeeessneeeeessaeeeeessaeeeees 4 1 5 The Numerical Techniques Involved in the Mixing Module csseeeeesseeeeeessneeeeessseeeeeessaeeeseesaeeeeeees 6 TOsEXAM PIGS unene E TA ge tesesaseveveaua nteaacadeves Maun kas E E E eeeaeoehd cee vagy daueee 7 1 6 1 Example 50 The Rectangular Cavity isicscacanzssciscapesseiedayso5 va seacivs sine ibaa pevnavedacas Capeaaees sunnspaadgeciees 7 1 6 2 Example 51 Coextrusion of Polymers in a Square Channel ccccccccsssssssteecceeceesseessneeeeeeeees 7 1 6 3 Example 52 Flat Die ces nere faves a a senate tas vise danse oi duke aids vases c uun adie ESEA S ER ASS bases ENANS 7 1 6 4 Example 46 Periodic Flow Through a Kenics Mixer ssscecesssececeessneeeceessneeceessaneeeeessaeeeeeesaaes 8 1 65 Example 37 Mixer 2 D neiaa Has veined sand E E E has aaa E seamless 8 1 6 6 Example 65 Adaptive Meshing for Moving Parts Mixer 2 D
18. Add a new stopping plane Figure 3 16 Dialog Box for Defining Coefficients k Request from Polydata Update coef A of the new plane Old value 0 New value Ol Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 43 Mixing Tasks in Polydata Figure 3 17 Dialog Box for Specifying Trajectory Question from POLYDATA 83 Q Is it valid for points to cross the stopping plane Se Ges You must be careful when defining a stopping plane in the algorithm of the trajectory calculation after every time step of integration the current position of the material point is entered in each plane equation if the results are all positive then there is no crossing and the calculation continues Otherwise the calculation is stopped and the trajectory is saved Figure 3 18 The Parameters for the stopping planes Menu with Multiple Stopping Planes p 44 shows how the menu looks after the definition of multiple stopping planes Figure 3 18 The Parameters for the stopping planes Menu with Multiple Stopping Planes Parameters for the stopping planes Current setup 2 stopping planes defined plane id B B c D 1 0 100000E 00 O 200000E 00 O 300000E 00 0 400000E 00 2 0 500000E 00 O 600000E 00 O 700000E 00 0 800000E 00 WARNING a trajectory of a point is stopped when its position x y z is such that A
19. E EE EEA EE EESE 105 42316 EXMA U neinei eii enee i e aii a gobs iin eii ieia ene en iiini a 106 rT 26 Yel TAES 0 AA EEA E EE E A SEAE A SE E 107 4 23 18 Instant Eff a a Ghee secs een e Ee sade Wands A aA aden EAE A EARO 108 4 23 19 Time Aver Eff oreinen paii e are ai aeaii e paar KE Na eiO Taari e rea S auaa 109 4 2 3 20 Shear Rate i e Aren ea A EE A T A thee E EAEN eee 110 4 23 21 Melting Index neei eonna thus aa e teoa eon at ane aa aesa a aaa iaa otaa iienaa 111 4 2 4 Disagglomeration Properties sseeesssesessseseessssressssreesssstessseteesssseessssreesssetesssereesssseessssreessee 112 4 2 4 1 Disagglomeration ainireti eiai iaae ia 114 4 2 4 2 Typical size of agglomerates seessseeesssssessssssessssseesssetressssreesssstessssreesssstessssreesseseessse 115 4 2 4 3 Fraction of agglomerates of given size ssessesssssessseressssrerssssreesssrressseresssereessssreesse 116 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information iv of ANSYS Inc and its subsidiaries and affiliates Polystat User s Guide 4 2 4 4 Number of agglomerates of given size 0 0 00 sesseneeecesseceeseeseneeesesseeeeseessaseesesseneeees 117 4 2 4 5 Mass of agglomerates Of given size ss cesseeeseessnceseesenceesessneeescesseseeseesenseeseseees 118 4 3 The Traj ctOnes MENU sisien tounin aa R ALE E AT a E E E Daasere 119 4 3 1 S6e the SEL OF Traj ctoriES nisnin
20. Inc and its subsidiaries and affiliates 37 Mixing Tasks in Polydata Figure 3 7 The Boundary condition along Boundary 1 Menu Boundary condition along Boundary 1 Current choice Non penetrable boundary Upper level menu gt Non penetrable boundary Inflow Outfiow Entry boundary in a spatially periodic flow Exit boundary in a spatially periodic flow arameters to connect spatially periodic boundaries Boundaries are defined as non penetrable by default This type covers the following cases walls axes of symmetry and free surfaces It specifies that a material point cannot cross the boundary If for nu merical reasons a material point does cross the boundary a specific flag attached to it is set and the calculation of the trajectory is interrupted the stopping is ABNORMAL Besides non penetrable boundaries the following types are available for selection inflow An inflow is a part of the boundary where the fluid enters into the flow domain Normally a material point cannot cross an inflow boundary that is a material point cannot go against the flow e outflow An outflow is a part of the boundary where the fluid exits the flow domain When a material point reaches an outflow boundary the calculation is stopped In this case the stopping is NORMAL as opposed to ABNORMAL Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 38 of ANSYS Inc and it
21. Meshing for Moving Parts Mixer 2 D In this sixth example we simulate the 2D transient flow produced by the rigid rotation of two cams in a batch mixer As in example 37 we use the mesh superposition technique to take into account the rotation of the cams Moreover we use adaptive meshing to refine the mesh locally in the neighborhood of the cams in order to get more accurate evaluation of the flow field As the mesh changes with time it cannot be used anymore to perform tracking of material points we have first to save the flow field in a set of csv files that we map onto a new uniformly refined mesh The tracking is eventually performed on this new mesh with the mapped flow field Keywords mesh superposition technique batch mixer time dependent flow adaptive meshing conver sion form CSV files mixing task statistical analysis 1 6 7 Example 91 Dispersion In this seventh example we present the models of erosion and rupture in a simple shear flow By this way we analyze the effect of various functions and parameters of these models Keywords dispersion disagglomeration erosion rupture Polystat 1 6 8 Example 116 Distributive Mixing Analysis in the Mixer GK7N In this eighth example we simulate the 3D transient flow produced by the rigid rotation of two rotors in a batch mixer mixer GK7N As in Examples 37 and 65 we use the mesh superposition technique to take into account the rotation of the rotors Moreover we ev
22. Polydata session and read a mesh to display the top level menu shown in Fig ure 3 1 The Polydata Menu p 31 Figure 3 1 The Polydata Menu File Graphical window Help REFR STOP SAVE EVOL LSEV PMAT LSPM UPDT LSDT FIT Main menu ain menu Polydata SARRA Save and exit Read a mesh fil Mesh decompo Version 15 0 0 Combine mesh Fri 23 08 2013 09 53 54 Windows Convert a mest Convert old res Save and exit Convertod Read a mesh fie Convert a mest p Convert shell m Generate a o Combine mesh fies Filename synta Convert a mesh fie Outputs Convert old result files p Read an old da I Create anew t Convert old csv files Redefine globa Convert a mesh file into a case file Convert shell mesh and results ie Generate a siceable free jet Outputs Read an old data fie Create a new task Redefine global parameters of a task PN N me Polydata in Graphical mode Path to p3rc 2 p3rc Next click Create a new task to open the menu shown in Figure 3 2 The Create a new task Menu p 32 Create a new task Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 31 Mixing Tasks in Polydata Figure 3 2 The Create a new task Menu Create a new task Current setup MIXING task Steady state 2D planar geometry Accept the current setup F E M task gt M
23. Sum B The function Ais sumt The function Bis sumz bd The operator is e os w Enter the name of the Function new_Function With this method it is possible to combine two sum functions with an arithmetic operator addition multiplication division and subtraction Select the two sum functions the operator and enter the name of the new function The calculation will be done like this first we define a list of x values distributed linearly along the X axis and enclosed between the X minimum and the X maximum of the two functions Second for each x value we search for the y value of the two functions y1 function1 x amp y2 function2 x The y value of the result function corresponding to x will be Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 141 The Polystat User s Manual y y1 lt operator gt y2 You will find an example of use of this method in Addendum B 4 5 2 10 The Smoothing Function Figure 4 83 The Smoothing Settings for the Create a new function Dialog Box Create a new function Smoothing xj Smoothing Select a function to smooth Function Type Parameters Equal smoothing Nb of left neighbors 1 Centered smoothing l e D TITER Nb of right neighbors C Downwind smoothing Nb of iterations
24. a EER EEA a Saa Ee ES 16 2 2 35 Hist gra MS sens enen oin ae nioi sa e SEESE S EEEIEE Ea SEEE SEESE TOSI EEEE 16 2 2 3 6 Correlations a onnen ei ae a A A EERE eaa Aa iS 17 2 3 HOMOGENIZATION seini iiaii eE EREE EERE E EAE EREE RS 17 2 3 1 DETIMITION oei E E late E a E a ead E E aioe EA NES EN 17 23 2 N merica Method enn a eaae E EOE EEE E E E EE 19 24 Distrib tive MIXING 2545 scases capes nioran niini i a ai ii i 20 24N Distribution INDOX st cst desaerssssveceasad taei A EEE ENEA RENEE a E E E O Eaa 20 2 4 2 DistributioMih ZoNe Skani ie eaei s ae ire caves E a a EER Ea ia e E E LA E 22 2 4 3 Deviation of Points Concentration eeesssssssessresssssseerereesssssssrreeeesssssseereeesssssseereeeeesssssseereeess 23 2 5 Dis gglomeratioN receure epee nolan ep aE EE ES EKA EAE E EK Ea a eat 25 26 COMM NT arr E ENTEN TEETE A AAE O OTEA ESUN TEREE ACETO E T TRETE 29 3 Mixing Tasks in Polydata 00aeeeeeeeessssesereeesssssseereresssssseereresessssserteeeesssssseereeesesssssereeeeessssssteee 31 3 Creating New Mixing TASK risi erosie ie EEE E E EEEE E E E E EE E 31 3 2 Using the General Menu of a Mixing Task ccccsssesecceesenceesesseeceseesnseesessensessessneeeseeseeseesenseneees 33 3 3 Definition of the Flow Domain ccsesssscccceeceeseessneeeceeecessseesnneeeeeeecesseennnaeecececesseessnaeeeeeseseeeeees 35 3 4 Definition of the Boundary Conditions siiasse cvavevsessvessevindaesdenneasdersuadadtesdie
25. aaa TOT oer unre rc TTT 169 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates v vi Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Using This Manual 1 The Contents of This Manual The ANSYS Polystat User s Guide tells you how to set up a MIXING task in ANSYS Polydata and how to use the ANSYS Polystat module for statistical postprocessing of results Important Under U S and international copyright law ANSYS Inc is unable to distribute copies of the papers listed in the bibliography other than those published internally by ANSYS Inc Use your library or a document delivery service to obtain copies of copyrighted papers 2 The Contents of the ANSYS Polyflow Manuals The manuals listed below form the ANSYS Polyflow product documentation set They include descriptions of the procedures commands and theoretical details needed to use ANSYS Polyflow products The Polyflow User s Guide explains how to use ANSYS Polydata and ANSYS Polyflow to set up and solve a problem The Polyflow Tutorial Guide contains a number of example problems with complete detailed instruc tions commentary and postprocessing of results The Polyflow in Workbench User s Guide explains how to use the ANSYS Polyflow applica
26. allows you to change if necessary the frame of reference one in rotation with respect to the other The data needed are visualized in the following picture Figure 4 25 Rotation Data direction of the rotation axis angular velocity rad s one point of the rotation axis The creation window appears like this Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 97 The Polystat User s Manual Figure 4 26 The Rotate Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY C Rotate A x Rotate The property Ais coordinates Ais a coordinate field Ais another field The TIME is time M enter one point of the axis of rotation 0 0 0 the direction of the axis 0 0 0 angular velocity rad 0 Enter the name of the property C frota If the property A is a coordinate field click the corresponding button The resulting property C will be C t Xo Rot a t A t Xo 4 3 where Xq is one point of the rotation axis and Rot the matrix of rotation at time t However if the property A is not a coordinate field click the A is another field button The resulting property C is C t Rot a t A t 4 4 4 2 3 9 Translate Translate this method allows you to translate a vector
27. be evaluated The difference of the means majed a wk Za Od 2 32 0 e The difference of the standard deviations s t o 0 with se dF papal 2 33 0 Figure 2 11 Real and Optimal Distributions 3 t 1 green_surface As for the segregation scale such parameters have limitations as they are global indices we cannot detect local defects 2 4 2 Distribution in Zones As for the distribution index we want to quantify distributive mixing But with this new method we will be able to detect zones of the mixer where material points are missing and where there is an excess of points As usual we distribute a cluster of particles initially concentrated in a small box see figure below Figure 2 12 Distributing Particles from a Small Box box As a function of time the flow will distribute this set of points We define a set of adjacent and non overlapping zones covering all the flow domain Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 22 of ANSYS Inc and its subsidiaries and affiliates Distributive Mixing In the figure below we have four zones Figure 2 13 Zones of the Flow Domain GED Next we distribute randomly in all the flow domain the same number of points N we assume that such a distribution is the optimal one At time for each zone for the two distributions we will determine the number of points included
28. coordinate field a time field a threshold distance A point is stagnant if the distance between its initial position Xo and some of its successive positions Xt are less than this threshold distance a period P If one wants to detect stagnation points close to a fixed wall we impose the period P to zero all suc cessive positions Xt will be tested from t 0 until t stagnation time ts If one wants to detect stagnation points close to a rotating wall of a moving part for example we have to specify the period P of rotation of the moving part all positions Xt Xo nP will be tested from t 0 until t stagnation time ts a stagnation time ts This stagnation time ts must be in the range 0 max residence time a squeezing factor sx Sy Sz Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 123 The Polystat User s Manual It is a way to weight specifically some components of the coordinates when computing distance between Xo and Xt distance Xo Xt sqrt sx xo xt A2 sy yo yt A2 sz zo zt A2 By default the squeezing factor is set to 1 1 1 4 4 The Slices Menu Figure 4 55 The Slices Menu Options MEPOLYSTAT i x File Properties Trajectories Slices Statistics Help SEE MOD DEL sets of slices Automatic Slicing Manual Slicing Sub Slicing Af
29. eeessseeeeessneceeeesseeeeeessneeeeeaaee 8 1 6 7 EXample O1 Dispersion vs 2 sscece csd aceet EE E E E E E E A EEE a 8 1 6 8 Example 116 Distributive Mixing Analysis in the Mixer GK7N eesseeeceessneeeeeesneeeceesneeeeeeaaee 8 1 7 Known Limitations in ANSYS Polystat 15 0 siivississsiessecenssatessanaedeedpenosoadvewoadevssapiqnesuausteciuenmalvynentianeenees 9 2 The Mixing TheOry isere ces ecuicraststns reei in kakiri Ea V AET IEE lesan dv EEEo V ERRERA TEENE Ea Aa TEETE aa 11 gt V INtrod cti Nessas asa aiaee e E A A AE E A ae a E aaae aa EAA oeiia 11 2 2 Ki nematic ParameteTS ennari ininsert aaa SEAE Sess GASTAR ANS EAEE EEEO NE AC AEE nea EEAS 12 2 2 1 Kinematic Parameters for 2D FIOWS cssssccccccccessesssneceeceeeeeeeeesnaeeeeeeeceseessenaeeeeeeeeseneesnnaeess 12 2 2 2 Kinematic Parameters for 3D FIOWS cssscccccccccessesesnecececeeeeseeesneeeeeceecessesenaaeececeeeeeeeesnnaeees 13 2 233 Statistical ANALYSIS cz 2522 s cessnei n ceed olive Sade d ods coaetea a Ea ved Sbdeg A saleadaddieedenveahded she neadeevest 14 2 2 3 1 Mean and Standard Deviation ccccseescccccecceeeeeesncecceeeecsesesnnueeeececeseseeesnneeeeeeeeeeees 15 2 2 3 2 Cumulated Probability Function or Distribution Function ceeeeeeseeteeceeeeeeeeeeeneees 15 22 3 3 Density OF Probability FUNCION 6 uicscairrdicucnasyatnng es iosita eeir aaiae a E Eien 15 2 2 3 4 Percentile Sensi esonera cai etar niea aa n ieena teed eS
30. every ticked curve is sent to Polycurve a chart is automatically created to present them as can be seen in the next figure If you want now to visualize curves of another function in another chart then in the Polycurve window click the button New Chart Next click the button Statistics the Draw Statistical Results window opens and you can select another statistical function and another set of curves as explained above The Close button allows you to close the Polycurve window and to go back to the main Poly stat window Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 84 of ANSYS Inc and its subsidiaries and affiliates The File Menu Figure 4 12 The Polycurve Window 0 Percentile 10 0 of bpgarithe_of_stretching 1 Percentile 50 0 of garth of_siretcring 2 Percentile 90 0 of bga Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 85 The Polystat User s Manual 4 1 8 The WRITE Trajectories Option Figure 4 13 The Save Set of Trajectories Dialog Box Save Set of Trajectories In this window you will select the set of trajectories you want to save in formatted files First you select one set in the upper list Then you click the gt button The next window appears Figure 4 14 Setti
31. ez T where D 4trD 2 7 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 12 of ANSYS Inc and its subsidiaries and affiliates Kinematic Parameters The values of this instantaneous efficiency are always included in the interval 1 1 We can easily show that m Dm e X M t 2 8 D We note that e is a local measure along the path of a material point the time averaged efficiency is defined as t e X M t faama 2 9 0 However there exists another way to define a mean efficiency over time t ji dt 0 In A e1 X M t 2 Dar oar 0 0 2 10 The physical interpretation of Equation 2 10 p 13 is the following for one material point at time ez is the ratio of what we get the final stretching obtained at time over what we put the total mechanical dissipation until time 2 Eventually we can define a global efficiency over all the material points distributed initially in the flow fia 2 dQ e Mt 2 2 11 par ae Q 0 o This global efficiency is the ratio of the output the mixing obtained the total stretching of the matter until time over the input the energy we get the total mechanical dissipation until time t 2 2 2 Kinematic Parameters for 3D Flows For 3D flows we will calculate the local stretching of infinitesimal surfaces by the mean of the area stretc
32. in it Based on these numbers we can evaluate a relative error of distribution for each zone Z nbr Z nbo Z e Z N 2 34 where nbr is the number of points of the real distribution included in zone Z at time and nbo is the number of points of the optimal distribution included in the same zone If is zero for a zone the right number of points is found in that zone If is negative for a zone there is a lack of points in that zone compared to optimum If is positive for a zone there are too many points in that zone compared to optimum Eventually we can define a global index based on all the zones 1 nb zones Eg 7 le z 2 35 r The number of points and the zones partitioning can influence dramatically the indices described above When comparing two different mixers it is recommended that you keep constant the ratio number of points zone In order to have relevant results this ratio should be higher than 100 2 4 3 Deviation of Points Concentration As for the distribution index we want to quantify distributive mixing However compared to that parameter we do not need to compute a perfect points distribution we just need the actual one As usual we distribute a cluster of particles initially concentrated in a small box see figure below Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affilia
33. in Figure 3 12 The Updated Boundary condition along Boundary 1 Menu p 41 40 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Definition of the Boundary Conditions Figure 3 12 The Updated Boundary condition along Boundary 1 Menu Boundary condition along Boundary 1 Current choice Entry of a spatially periodic flow Boundary connected to Boundary 2 exit This boundary can be crossed 1 times Xexit i A i j Xentry j where A i j 0 0000000E 00 0 0000000E 00 0 0000000E 00 and B i 0 0000000E 00 0 0000000E 00 0 0000000E 00 Upper level menu Non penetrable boundary Inflow Outflow T BI 0 0000000E 00 0 0000000E 00 0 0000000E 00 0 0000000E 00 0 Q0000000E 00 0 0000000E 00 gt Entry boundary in a spatially periodic flow Exit boundary in a spatially periodic flow Parameters to connect spatially periodic boundaries You must now specify how the coordinates of the points in the entry section should be transformed in order to relate to the corresponding coordinates in the exit section The general relation between points in the two sections is Xexit A Xentry B Click the Parameters to connect spatially periodic boundaries menu item and then specify the coefficients of the rotation matrix A and the translation vector B in the dialog boxes that open see Figure 3 13 The Dialog B
34. logarithm of stretching If you add concentration to the property list you must define zones where the concentration field is set to 1 If a material point has its starting position in one of these zones it will be assigned a unit concentration otherwise it will be assigned a null concentration The initially assigned concentration value is transported unchanged along the trajectory for every point and the diffusion and the chemical reactions are not taken into account You will be prompted to define the concentration zones when you add concentration to the list You also have the option of defining zones at a later point by clicking Define zones where concentration 1 in the Management of properties for the KINEMATIC analysis menu Note that a zone is a box defined by the coordinates of its two extreme corners Xmin Ymin Zmin and Xmax Ymax Zmax 3 12 Definition of the Distribution Analysis If you have set the task type to DISTRIBUTION analysis in the mixing task menu by clicking the Modify task type menu item repeatedly until the task type is defined as shown in Figure 3 41 A Distri bution Analysis Mixing Task p 69 you can click the Definition of a DISTRIBUTION analysis menu item to open the menu shown in Figure 3 42 The Definition of the DISTRIBUTION analysis Menu p 70 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 68 of ANSYS Inc and its subsidiaries and affili
35. one by one Each slice must have a different name You can modify or delete existing slices You can also modify the order of the slices it is important to notice because the statistical functions are also ordered in function of the slices on which they are based Finally you enter the name of the new set This slicing is not based on a single property each slice can be defined on a different property The slices are not necessarily parallel to each other This method is more general but is more time consuming for you 4 4 4 The Sub Slicing Option Figure 4 60 The Generate a subslicing on a set of slices Dialog Box Generate a subslicing on a set of slices x Select a set of slices new_set_of_slices Select a property time v M Periodic Yes C No Enter the First position in 20 3 the direction 400 5S fe the increment Po the number of subslices slice PB Enter the name of the set of slices new_set_of_subsices 0000 OK Cancel Suppose that you have a 3D unsteady flow and that you want to visualize the spatial repartition of the stretching in a plane cutting your flow domain Suppose that you define a slice whom the selected property is the coordinates the instants in this slice can have various time What you want to do is to distribute those instants among a list of time intervals and look at the spatial repartition of the stretching for one time interval What you have done abo
36. points There are two ways which can be combined to limit this problem decreasing the time step between two successive flows and refining the mesh of the flow domain ANSYS Polystat does not support mixing tasks if the mesh of the flow domain changes with time changes in coordinate position of the mesh vertices and or number and shape of mesh elements This does not include the use of the Mesh Superposition Technique with moving parts on a transient flow field because the underlying mesh remains constant Boundary conditions ANSYS Polystat does not support mixing tasks on flow fields defined by non conformal boundaries In some cases material points massless particles may stop on a non penetrable boundary wall free surface plane of symmetry due to stagnation of the flow field in close proximity to these boundaries This can have a dramatic effect on the flow statistics particularly if you are analyzing an open flow field with entry and exit of fluid When slicing from entry to exit you should confirm that the number of samples in each slice remains constant If the concentration of samples decreases by more than 10 15 it may be necessary to refine the mesh e Material properties ANSYS Polystat does not support mixing tasks on compressible fluids Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 9 Releas
37. process let us suppose that initially we place a set of particles in a small zone in the flow domain as a function of time these particles move in the flow and distribute Our parameter 6 measures the deviation of the current distribution with respect to a perfect distribution of particles in the flow domain Another technique similar to the previous one is now available we divide the flow domain in a set of adjacent and non overlapping zones Initially we place a set of particles in a small box in the flow domain and they distribute progressively Then for a given time we count the number of points in Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 1 Introduction each zone We get a good distributive mixing if each zone contains a number of points proportional to its surface volume A third option to estimate distributive mixing is to evaluate the local points concentration in various locations in the flow domain and to compare it with a perfect points concentration corresponding to the case where we find the same number of points per unit volume everywhere in the mixer Eventually a new parameter Op measures the deviation in points concentration The dispersive mixing is another important aspect of the mixing it concerns the break up of drops into small droplets or the disagglomeration of solid particles in a matrix
38. quality evolves from the entry of the machine to the exit To analyze this process we generate a set of points in the plane section of the entry then we calculate their trajectory through the machine until they reach the exit For the statistical analysis we will generate a set of slicing planes uniformly distributed from the entry to the exit For each slice we determine the intersections with the trajectories Then at these intersections we interpolate the values of the kinematic parameters For each slice we can then calculate the mean value of a field a or the distribution function of a field and so on As the slices are sorted from the entry to the exit we can analyze the evolution of the mixing slice by slice Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 29 30 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Chapter 3 Mixing Tasks in Polydata 3 1 Creating a New Mixing Task In order to create a mixing problem you must have defined and solved the Navier Stokes equations on the flow domain in a previous session You will therefore have one or more result files containing the velocity field In this session you will use these velocity fields as data for solving a mixing problem To begin launch a
39. that if you plan to use the distribution analysis to generate a statistical analysis of the mixing you must create only one generation zone which must be shaped like a box if the domain is closed the box must be located inside the flow domain if the domain is open the box must be located on the inflow boundary and have no thickness in the direction of flow As soon as more than one generation zone is defined a new property is added to the list of properties evaluated along the trajectories and enabled in the Selection of properties menu see Selection of Properties p 57 This new property named label is constant along each trajectory and indicates the zone ID of the material point s origin Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 49 Mixing Tasks in Polydata When you have generated one or more zones as shown in Figure 3 25 The Generation of material points Menu with Multiple Zones p 50 you can modify the parameters of zones or delete zones Figure 3 25 The Generation of material points Menu with Multiple Zones Generation of material points Current setup index intensity generation zone type 1 1 Generation Zone 1 box 2 4 Generation Zone 2 flow domain initial time 0 for every material point Create a new topo object Modify the name of a topo object Delete a topo object Uppe
40. the material point reaches in the absolute system the given plane see Figure 3 14 2 5D Flow with a Stopping Plane p 42 Figure 3 14 2 5D Flow with a Stopping Plane stopping plane absolute trajectory relative trajectory plane Z 0 containing the mesh and the flow domain Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 42 of ANSYS Inc and its subsidiaries and affiliates Definition of the Boundary Conditions Clicking the button next to the Add modify or remove stopping planes label in the Boundary con ditions menu will open the menu shown in Figure 3 15 The Parameters for the stopping planes Menu p 43 Add modify or remove stopping planes Figure 3 15 The Parameters for the stopping planes Menu Parameters for the stopping planes Current setup no stopping planes defined WARNING a trajectory of a point is stopped when its position is such that A x B y C z D is negative Upper level menu Add a new stopping plane Modify a stopping plane Remove a stopping plane af ot If you click Add a new stopping plane you have to respond to the dialog boxes that open entering the coefficients that define the plane for example see Figure 3 16 Dialog Box for Defining Coeffi cients p 43 and specifying whether it is valid for points to cross the stopping plane see Figure 3 17 Dia log Box for Specifying Trajectory p 44
41. the name of the result file that stores this field and whether it is formatted Finally you enter the time of use of the current velocity Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 48 of ANSYS Inc and its subsidiaries and affiliates Parameters for the Generation of the Material Points field If the lifetime of the material points is greater than the sum of all times of use the succession of velocity fields will be used in a loop Note The manual selection mode is not practical if many such as a dozen result files must be specified 3 6 Parameters for the Generation of the Material Points Clicking the Generation of the material points menu item in the mixing task menu opens the menu shown in Figure 3 24 The Generation of material points Menu p 49 Generation of the material points Figure 3 24 The Generation of material points Menu Generation of material points Current setup no generation zones initial time 0 for every material point Create a new topo object Modify the name of a topo object Delete a topo object Upper level menu Add a new generation zone Modify a generation zone ration zone Delete a gene Enter a time interval Tmin Tmax This menu allows you to define zones where the material points are initially positioned In order to have a well defined mixing problem you must have at least one generation zone Note
42. there is no entry and no exit of fluid An open domain is the opposite Figure 1 1 Open and Closed Domains oe p gt gt gt 5 iy x y gt z gt n c gt K 3 a N c 4 the square cavity a closed domain the channel flow an open domain Steady state Time dependent flow a steady flow is a flow that does not change with time The general case of a time dependent flow is a flow that evolves continuously with time our mixing module can study these two kinds of flow However for transient flows the flow domain must not change with time except for flows with moving parts simulated with the mesh superposition technique If the flow is transient we have to calculate and store the current flow at successive time steps let s note them flow t flow t2 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 2 of ANSYS Inc and its subsidiaries and affiliates Classification of Flows Capabilities of the Mixing Module However in order to calculate particles path we have to know the velocity field at intermediate times two techniques are implemented In the first case the piecewise steady case we assume the flow is steady between two time steps tl t2 with t1 lt t2 and is equal to flow t 1 This assumption is valid if inertia is neglected and if the boundary conditions change abruptly One example is the oscillating square cavity Fig
43. type selection the following menu items become available these additional options allow you to customize the analysis to suit your problem as described in Definition of the Kinematic Analysis p 64 and Definition of the Distribution Analysis p 68 Definition of a KINEMATIC analysis Definition of a DISTRIBUTION analysis 3 3 Definition of the Flow Domain Clicking the Definition of the flow domain menu item in the mixing task menu opens the menu shown in Figure 3 4 The Flow domain Menu p 35 Definition of the flow domain Figure 3 4 The Flow domain Menu Flow domain The mixing task will be defined on the union of the next subdomains Subdomain 1 Subdomain 2 Subdomain 3 Subdomain 4 Subdomain 5 Subdomain 6 Remove Remove All The remaining subdomains are Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 35 Mixing Tasks in Polydata With this menu you can remove or add subdomains of the whole mesh in order to define the flow domain as shown in the example below Figure 3 5 Fluid and Solid Subdomains The flow domain is the union of the subdomains s2 s3 and s4 The subdomains s1 s5 and s6 which are solid parts of the problem should be removed from the upper list of the menu 3 4 Definition of the Boundary Conditions Clicking the Definition of the bo
44. way to use Polystat we will now explain in detail every menu option and window 74 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates The File Menu 4 1 The File Menu Figure 4 3 The File Menu Options MEPOLYSTAT x Fie Properties Trajectories Slices Statistics Help Open Options Read Data Read mesh Run Draw results Draw Stats WRITE Trajectories WRITE Slices WRITE Stat Save Save as Quit The Open option allows you to read an old Polystat session file The Options allow you to specify some parameters for reading trajectories for slicing and for visualiz ation The Read Data option allows you to read the files containing the trajectories calculated by Polyflow All the trajectories and the kinematic parameters calculated along those trajectories are stored in Poly stat The Read mesh option allows you to read the file containing the finite element mesh Polyflow format used to calculate the flow and the trajectories This mesh is used only by the option Draw results to visualize a property in a slice through the flow domain By clicking the Run option you ask for the calculation of all the objects defined earlier new properties new sets of trajectories new sets of slices new statistical functions With the Draw results opti
45. will be a surface We assume that each slice as the same perfect points concentration that is equal to the number of points in a slice S divided by the area of the part of the slice S that cuts the flow domain For a 3D closed flow domain we perform a slicing in time therefore each slice will be a volume We assume that each slice as the same perfect points concentration that is equal to the number of points tracked divided by the volume of the flow domain For a 2D open flow domain we perform a slicing in space in the direction of the flow therefore each slice will be a line We assume that each slice as the same perfect points concentration that is equal to the number of points in a slice S divided by the length of the part of the slice S that cuts the flow domain For a 2D closed flow domain we perform a slicing in time therefore each slice will be a surface We assume that each slice as the same perfect points concentration that is equal to the number of points tracked divided by the area of the flow domain Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 151 The Polystat User s Manual In order to evaluate the points concentration in each slice around each point one must specify the radius of the sample all points in the neighborhood of point x at a distance smaller than this radius will be taken to evaluate t
46. x reduces the scaling of the view in the x dimension by half Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 83 The Polystat User s Manual Ctrl y reduces the scaling of the view in the y dimension by half Ctrl z reduces the scaling of the view in the z dimension by half e Resize r removes the scaling factors and fits the display into the window R fits the display into the window while retaining the scaling factors 4 1 7 The Draw Stats Option Figure 4 11 The Draw Statistical Results Dialog Box Draw Statistical Results x Select a function 0 10 0 th Percentile of logarithm_of_stretching v 1 50 0 th Percentile of logarithm_of_stretching 2 90 0 th Percentile of logarithm_of_stretching In this window you will select the functions you want to visualize with Polycurve Polycurve is a charts editor linked to Polystat its main goal is to allow you to create and visualize charts see the chapter 8 of the Polymat User s Guide for a complete description of Polycurve A chart can contain several curves We can add and remove a curve change a title a color the range of the axes First you select one function in the upper list The corresponding set of curves are displayed in the lower list Then tick the curves you want to display Eventually click the Ok button Then
47. x B y C z D is negative Upper level menu Add a new stopping plane Modify a stopping plane Remove a stopping plane gP Mh Note that you can Modify a stopping plane or Remove a stopping plane as necessary 3 5 Definition of the Flow Field 3 5 1 Steady State Flow Clicking the Definition of the velocity fields menu item in the mixing task menu for a steady state flow simulation opens the menu shown in Figure 3 19 The Flow definition Menu for Steady State Flow p 45 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 44 of ANSYS Inc and its subsidiaries and affiliates Definition of the Flow Field Definition of the velocity fields Figure 3 19 The Flow definition Menu for Steady State Flow Flow definition Current choice filename res Ascii formatted file Upper level menu Enter the result filename Enter the time of use Switch to binary unformatted file Click the Enter the result filename and specify the name of the result file containing the velocity field in the Polyflow result file format If the file is unformatted click the Switch to binary unformatted file menu item the note at the top of the menu will reflect your choice and the menu item will change to Switch to ascii formatted file 3 5 2 Time Dependent Flow Clicking the Definition of the velocity fields menu item in the mixing task menu for a time dependent flow simulati
48. you will specify how the calculated trajectories and evolution of different properties are stored These results can be stored in several files in order to be analyzed by Polystat The menu items allow you to revise the settings for the following e result files You can modify the prefix of the result files that are created which is set to mixing by default The full name of the result files will be of the following form prefix _x mix where x varies from 1 to the total number of files which you can specify You can also specify whether the files are formatted ASCII or not binary Despite the fact that the unformatted files are smaller in size and so take up less memory space the default option is formatted e trajectories and CPU time Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 61 Mixing Tasks in Polydata You can specify the maximum number of trajectories that are stored in a single result file as well as the maximum CPU time in hours that is spent before the current file is closed and results begin to be stored in the next file In this way files are continuously generated you can begin the statistical analysis on a short popu lation of material points while at the same time Polyflow continues to work If you are happy with the results you can interrupt Polyflow You have the option of running Polyflow a
49. 0000E 01 Evaluation of axial distribution index YES Modify axis direction Z Evaluation of Left Right transfer X dir YES Evaluation of Upper Lower transfer Y dir YES Evaluation of Back Front transfer Z dir YES Modify surrounding box for transfer functions XYZ min 0 0000000E 00 0 0000000E 00 0 0000000E 00 XYZ max 0 3000000E 01 0 3000000E 01 0 9000000E 01 Hide advanced options Enable automatic settings Modify slicing type function of time Modify slicing coordinates standard coord Modify 2nd generation zone all the flow domain Modify number of values for dist distr fct 100 Modify number of values for axial distr fct 100 Modify number of values for transfer fct 100 If you want to make major modifications to the slicing method you can Disable automatic settings This action will make menu items available that allow you to modify the slicing type the slicing coordin ates and second generation zone Note that such modifications are not recommended unless you have extensive expertise in the subtleties of Polyflow The remaining menu items allow you to modify the number of values used to represent the various functions Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 72 of ANSYS Inc and its subsidiaries and affiliates Chapter 4 The Polystat User s Manual After the calculation of a large set of trajectories performed with Polyflo
50. 0E 01 Show advanced options The Definition of the DISTRIBUTION analysis menu allows you to modify the default settings of the distribution analysis as described in Using the General Menu of a Mixing Task p 33 in order to cus tomize the preset statistical analysis of the mixing to fit your problem Note that at any time you can revert to the default settings by clicking Reset to default values To begin you can modify the parameters for the slicing of the trajectories including the number of slices the starting position for an open domain the starting time for a closed domain the increment between slices and the direction of slicing For a closed domain the slices represent moments in time For an open domain the slices represent parallel spatial planes that are perpendicular to a coordinate axis which begin at the inflow boundary and proceed to the outflow boundary Next you can select and define the indices and transfer information you want to evaluate These values are calculated using the position data of the material points that originate in two separate generation zones The first generation zone is the single box zone you created for the mixing task the points that originate in this zone are tracked as they become distributed throughout the flow region as the solution progresses The second generation zone is created internally by Polyflow by taking the same number of points as are in the first zone and randomly distr
51. 1 Enter the number of values 100 Enter the name of the Function new_smoothed_function OK Cancel First select the function to smooth Then select the kind of smoothing you want and specify some parameters we will explain that below You must also enter the number of values to represent the smoothed function a good practice is to use the same number of values that represent the data function You have also to give a name to the new function The type of the result function will be the same as that of the data function Note that it is impossible to smooth a function that is already a smoothed function The method of smoothing is the following to calculate one value of the result function we calculate the mean of values that surround it in the data function This process can be iterated several times The calculation of the mean can be weighted in different ways type of smoothing With an equal smoothing the current Y value and every neighbor have the same weight Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 142 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu Figure 4 84 Equal Smoothing X cur With a centered smoothing the current Y value has the highest weight and the weight decreases linearly as the distance to the current X value increases Figure 4 85 Centered Smoothing y w
52. 1 Gee In the Graphic Options window there exist two zones in the first one two buttons Draw and Close are placed in the second one we can see three tabs Slice Prop and Mesh First let s explain the use of every button The button Draw this button allows you to update the drawing with the current set of options you se lected The button Close with this option we close the Graphic Display window the current graphic options are saved Now let s explain the three tabs of the Graphic Options window Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 80 of ANSYS Inc and its subsidiaries and affiliates The File Menu Figure 4 10 The Graphic Display Window Tabs Oraw Close Sice Jrrop Mesh Set of dices or traj ae ee eee Export Animation C Image Series Save Frame Rate E sec Options r Color set M Show F Log Enter pixel size 3 Enter pause fi sec Logo I Show Logo Color C flak Yhite Go in the three tabs in the following order 1 In the Mesh tab you have to specify the parts of the mesh you want to see In the upper part of the Mesh tab the list of existing domains is shown A domain is a topological object based on the mesh The following objects are built automatically a the domains b an in tersection of a domain with another domain f
53. 16 Discretized Mass Density Function f s t ds 1 0 So S S San S The mass fraction of agglomerates of size in interval S Sp is iF s ds a Of course this mass fraction distribution will change with time as the volume Vx attached to the point X moves in the mixer because of erosion and rupture taking place during mixing We assume there is no transfer of agglomerates between adjacent volumes due to the high viscosity of the matrix Erosion is a slow and continuous process observed for all admissible sizes of agglomerates This process generates a lot of small particles Rupture occurs when a critical stress is reached and is observed for large particles This process generates two or more agglomerates Erosion and rupture depend on the size of agglomerates the shear rate and the shear stress In the following text we distinguish two types of solid particles the aggregates and the agglomerates The Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 25 The Mixing Theory first ones are the smallest particles that cannot be eroded or broken anymore The second ones are larger particles formed of a number of aggregates linked together by cohesive forces Figure 2 17 Disagglomeration Processes rupture erosion Erosion The erosion model implemented in Polystat is based on the work of Collin and P
54. Chaos and Transport Cambridge University Press 1989 7 J M Ottino W E Ranz and C W Macosko A Framework for Description of Mechanical Mixing of Fluids AIChE Journal 27 4 565 577 July 1981 8 Tadmor and Gogos Principles of Polymer Processing John Wiley and Sons 1979 9 T H Wong and I Manas Zloczower Two Dimensional Dynamic Study of the Distributive Mixing in an Internal Mixer Intern Polymer Proc IX 1 3 10 1994 10 H H Yang and I Manas Zloczower Analysis of Mixing Performance in a VIC Mixer Intern Polymer Proc IX 4 291 302 1994 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 169 170 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates
55. Concentration Deviation FUNCTION esssssessssssessssserssssrrsssereesssrressssreessee 151 45 3 New disagglomeration functions 5 asasaicosecaveanavenvmsserantarnaiecvansoveleanadeduetetenleuntnavenbantas tiaras 152 4 5 3 1 The See disagglomeration along a single trajectory FUNCTION eeeeeeeeeeeseeeeeeeeenees 154 4 5 3 2 The Mean disagglomeration function sssccesserseeeesseceeseesseseesenseneessesseeeeseesenees 155 4 5 3 3 The Probability FUNCtION esseesid esiri aner ri aA n iee E aaa eiue a seans 157 4 6 Th Help MENU s ee asan raanei E E bs E EE ODER E SENOPATI SES ENN EAO E ENOS Toa o ENES 157 4 7 Additional Definitions srren Ti ay ceed ub ca E A E aea ad a a Res 158 ATV H a Ee E EOE E BT aN a ER ves 158 472 Mhe ZNE Sinnen a a a gabe e a tac aa ON E aaa E E A a aAA 159 BTS Weighting eae eiere e e REEE KEA RE E a Re KE E RTE e 159 A The Simulation of the Distribution s s ssccsndseasovecrdcasenriqncrbanstecssnouhadesueatadisensannsbonsdutevoaveadaeds uansavsauarvacy ees 161 B The Global Efficien y of Stretching s src uaisti i e ia ei 163 C Adaptive Meshing and Mixing Task ssssssseeeeessssssssreressssssssrereressssserereeesssssssereressssssseeeeeesssssseeeeeessssse 165 D Sliding Mesh Technique and Mixing Task sssesssssessssssesssseesssssesssssressssressssttessssreessssresssereesseeesssseeesssene 167 Bibliography siiis aa ONE Sen Pri eea aa EEK Peer aa E E Rr E e rr Te
56. IXING task gt Steady state problem s Time dependent problem s Evolution problem s Volume Of Fluid problem s Optimization problem s Rigid rotation gt 2D planar geometry 2D axisymmetric geometry 2D 1 2 planar geometry 2D 1 2 axisymmetric geometry 1 Specify that it is a mixing task MIXING task N N D D A ot O D O oF ot gt D O Q ot O al ke D A a ot gt D ot lt xe D O o ot gt D z O o Qa ot fe ot w Nn xe ond a gt lt O C v lt a v A Z fe ot D Qa Steady state problem Time dependent problem 3 Select one of the following to specify the nature of the geometry of the problem Note that mixing tasks are not available for 2D or 3D blow molding simulations 2D planar geometry 2D axisymmetric geometry 2D 1 2 planar geometry Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 32 of ANSYS Inc and its subsidiaries and affiliates Using the General Menu of a Mixing Task 2D 1 2 axisymmetric geometry 4 Click Accept the current setup to open the mixing task menu which is described in Using the General Menu of a Mixing Task p 33 3 2 Using the General Menu of a Mixing Task Clicking the Accept the current setup menu item in the Create a new task menu opens a menu like the one shown in Figure 3 3 The MIXING Task 1 Menu p 33 Figure 3 3 The MIXI
57. Inc All rights reserved Contains proprietary and confidential information 136 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu 4 5 2 6 The Auto Correlation Function of the Concentration Function Figure 4 77 The Auto Correlation Function of the Concentration Settings for the Create a new function Dialog Box Create a new function Auto Correlation Function of the Concentration x Auto Correlation Function of the Concentration Select a set of slices new_set_of_slices Select a concentration field Concentration _C Select coordinate field coordinates z Enter the number of values 100 Enter the name of the function new_autocorrelation_functio To calculate the evolution of the auto correlation function of the concentration you need to specify which set of slices will be used You must select a coordinate property that will serve to calculate the distance between pairs of points in a slice and you must also select a concentration field Don t forget to specify the number of values necessary to represent the auto correlation function You have also to give a name to the new function You will obtain an auto correlation function for each slice of the set If you visualize this function for a given slice you find on the X axis the distance and on the Y axis the auto correlation function of the concentration Figure 4 78 The Auto Correlation Fun
58. Mean Standard Deviation Function ssessssssesssssesssssessssereessseresssereesssreessssreesse 134 AS 2A Th Correlation FUNCOM sieri eperra neiederas naida eei anceteas 135 452 5 The Probability BUNCHON cis eosiasecoupunvaqesaseccrnesabiatibearsacs aeuatve aia arisa a a aE itana einkis 136 4 5 2 6 The Auto Correlation Function of the Concentration Function eeessseseesssseesseerersssree 137 4 5 2 7 The Distance distribution Function s ssessssssssssssessseseressssressssrtessseresssereessssressssreessse 138 4 5 2 8 The Distribution in zones Function essssssssssssssssssseesssreessssresssseessssresssereessssreesssees 139 4 5 2 9 The Sum A lt op gt Sum B Function sssssssssesessssssssserreesssssesereeeeesssssseereeeesssssserreeeesssseeee 141 4 5 2 10 The Smoothing Function esssssessssssesssssessssseessssseesssstessseresssstesssestesssetessseresssssresss 142 4 5 2 11 The Density of Probability Function ssssesssssssssssseesssseessssressssseesssereesssreessseressssrees 144 4 5 2 12 The Percentile FUnCtiOnN iseci aiieieo eia 145 4 5 2 13 The Hist gram FUNCOM 5 sys cusiossccadonupaieasnusadoianermosdaosseeeieaesiealonaadaianersuonauaeeninieste 147 4 5 2 14 The Segregation Scale Function esssssessssssssssssesssssressseressssreessssreessseresssetessssreessseees 148 4 52 15 The Deviation FUNCION nisinsin ea e Ye a Aa TA O A AAEE 149 4 5 2 16 The Points
59. N successive steady states result file velocity field shear rate etc The mixing simulation in a second step we enter back in Polydata to define a MIXING task We specify the mesh the velocity fields to use and the initial position of the material points and other properties to evaluate along trajectories Next we run Polyflow with this data file Polyflow generates randomly the initial position of a set of material points and calculates their trajectory in the flow domain Along these trajectories Polyflow calculates also the evolution of some properties and kinematic parameters temperature viscosity stretching rate of stretching rate of dissipation And finally Polyflow generates files containing these results Figure 1 5 The Mixing Simulation POLYDATA POLYFLOW data file result file s velocities shear rate etc result files trajectories properties kinematic parameters The statistical postprocessing finally we use the postprocessor Polystat to analyze all these trajectories We will calculate the time evolution of global mixing parameters such as the segregation scale or the evolution of the mean stretching and so on Polystat has been built in such a way that we can define new parameters and test them New parameters In such a way a nee d are created by combining existing parameters in various ways Il Il vee Polystat can also be used to analyze other proc
60. NG Task 1 Menu MIXING Task 1 Modify task type generic task Upper level menu Definition of the flow domain Definition of the boundary conditions Definition of the velocity fields Generation of the material points Parameters for the tracking Selection of properties Storage of the results Definition of moving parts Definition of a KINEMATIC analysis Definition of a DISTRIBUTION analysis Perform the following steps in this general menu 1 Define the flow domain not necessarily the complete domain defined by the mesh as described in Definition of the Flow Domain p 35 Definition of the flow domain 2 Define the type of boundaries of this domain as described in Definition of the Boundary Conditions p 36 There are several kinds of possible boundary conditions for example a material point can cross an entry but not a wall Definition of the boundary conditions Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 33 Mixing Tasks in Polydata Define the velocity fields necessary to calculate the trajectory of the material points as described in Definition of the Flow Field p 44 Definition of the velocity fields Define the zones of the flow domain where the initial positions of the material points are generated as described in Parameters for the Generation of the Material Points p 49 The ini
61. Select object 1 Note that an object like Subdomain 1 Boundary 5 refers to the intersection of Subdomain 1 and Boundary 5 Then select an operator intersection or union enter a name for the new topo object and click create Important When using the intersection operator you must be sure that the resulting object is not empty as there is no check to avoid such a situation Running Polyflow with this kind of degenerated generation zone will lead to a fatal error Modify the name of a topo object You can Modify the name of a topo object by clicking this menu item and then using the Modify name of topo objects menu that opens You should select an existing object in the list click Select object enter a new name and then click modify Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 54 of ANSYS Inc and its subsidiaries and affiliates Parameters for the Tracking Delete a topo object You can Delete a topo object by clicking this menu item and then using the Delete topo objects menu that opens You should select an existing object in the list click Select object and then click delete 3 7 Parameters for the Tracking In order to calculate the trajectory of a material point you have to specify a set of numerical parameters These parameters have different purposes such as deciding when to stop the calculation or when there is a problem Clicking the Parameters fo
62. Slices If you select the option SEE MOD DEL sets of slices in the Slices menu of the main window you will see the list of the existing sets of slices Figure 4 57 The See Modify Delete existing sets of slices Dialog Box See Modify Delete existing sets of slices x Select a set of slices new_set_of_slices OK Modify Delete Delete All If you want to modify some data of a set select it in the list and then click the Modify button The window that served for the creation of that set will appear then modify some data If you want to store the modified data click OK Otherwise click Cancel To remove one set from the list select it in the list and then click the Delete button To remove all the created sets click directly on the Delete All button In the two cases Polystat asks for a confirmation of your choice Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 125 The Polystat User s Manual 4 4 2 The Automatic Slicing Option Figure 4 58 The Create Automatically a list of slices Dialog Box x Select a set of trajectories all_trajectories Select a property time bd Enter the name of the set of slices new _set_of_slices Enter the First position in iz sd Booo the direction ee is 6 the increment 7 0 the number of slices
63. University customers is provided only through the ANSYS Customer Portal Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information x of ANSYS Inc and its subsidiaries and affiliates Chapter 1 Introduction 1 1 Objectives In industry the mixing process is widely present it occurs in different kind of machines in a continuous or batch process like in Banburry mixers Kenics mixers extruders stirred vessels and so on The object ives are various too distribution of pigments or other compatibilizers generation of interfaces between different fluids in order to enhance chemical reactions The main objective of this module is to offer you the ability to quantify the mixing in the process of your interest We will define later a set of objective parameters that are relevant for different situations But we tried to go a step further there is at this time always a certain evolution in the way scientists are quantifying mixing That s why we developed software that uses existing parameters and allows you to also define new parameters This module simulates mixing for various flows but the situation is in general so complex that numer ical simulation cannot take into account all the real phenomena existing in such processes In a next section of this chapter we will explain the needed assumptions and hypotheses 1 2 How to Characterize Mixing There are various ways to de
64. aiwadnatar dee eastavayaterdeatsasegien 36 3 4 1 Specification of the Boundary Type ssesssssesssssessssssesssssressssressssreesssseessssrtessseressssressssreessssees 37 3 4 2 Specification of a Stopping Plane ssssssseessesssssssssereesssssssseeeeesssssseereressssssesrereeeesssssseereeeeesssseet 42 3 5 Definitlon of the Flow Field niniaren nonin tena E ATA E EEN A Gini R as 44 3 521 Steddy State FlOW se csess es sstaneeceacacscussdwtvan sdeaa EA AE E RE AE E AE EEE 44 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates iii Polystat User s Guide 3 5 2 Time Dependent FOW s ccicssseivessecsccdasacossescestacedsacsedeesonsecdecacadssesassecedaacasdevsssdeseedaceeccessesudeeaanncd 45 3 6 Parameters for the Generation of the Material Points cccessesccccccceeeseeenneeeeeeeeseseeesnaneeeeeeeeseees 49 3 7 Paralneters TOP TMG Tracking een eroras salencntanyavtatnay EEEE RE EER EE EEEE REE KOE 55 3 8 Sele tion of Propertie Sisa saena aena aese Eea ds osbivs visit deve Adib ENESE eN er deoe TAa sab ete 57 3 8 1 Parameters for the Kinematic Mixing Properties scccssssreesessescescesseseesesseeeessesseseeseses 59 3 9 Parameters for the Storage of the Results aciacissecctisstesdadoavaapeio oueeaniond cents ceaanoanaagann ecaaatineneonneeenaaes 61 3 10 Definition Of MOVING Parts 34 cs sacsncossdas visa
65. al http support ansys com and select the appropriate option Toll Free Telephone 33 0 800 919 225 Toll Number 33 0 170 489 087 Email support france ansys com BELGIUM All ANSYS Products Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates ix Using This Manual Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option Telephone 32 0 10 45 28 61 Email support belgium ansys com Support for University customers is provided only through the ANSYS Customer Portal SWEDEN All ANSYS Products Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option Telephone 44 0 870 142 0300 Email support sweden ansys com Support for University customers is provided only through the ANSYS Customer Portal SPAIN and PORTUGAL All ANSYS Products Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option Telephone 34 900 933 407 Spain 351 800 880 513 Portugal Email support spain ansys com support portugal ansys com Support for University customers is provided only through the ANSYS Customer Portal ITALY All ANSYS Products Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option Telephone 39 02 89013378 Email support italy ansys com Support for
66. al interpretation of Equation 2 20 p 15 is the following for one material point at time 7 ey i is the ratio of what we get the final stretching obtained at time t over what we put the total mechanical dissipation until time Like for 2D kinematic parameters we can define a global efficiency over all the material points distributed initially in the flow c t E barado Q 0 2 19 2 2 3 Statistical Analysis Let us assign to the M material points an initial orientation M which does not need to be identical for all points While tracking the material points as a function of time we also calculate successive values of e and e A global representation of e and e is again obtained by associating a ma terial point with a small rectangle of size dx X dy the color of the rectangle is associated with the value of the field to be represented The quality of the representation increases with the number of points N Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 14 of ANSYS Inc and its subsidiaries and affiliates Kinematic Parameters When the number of material points is sufficiently large we may proceed with a statistical treatment of the calculated quantities Several statistical tools have been implemented in the new software Poly stat 2 2 3 1 Mean and Standard Deviation For any scalar kinematic parameter a we can calculate th
67. aluate the distributive mixing capability of the mixer Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 8 of ANSYS Inc and its subsidiaries and affiliates Known Limitations in ANSYS Polystat 15 0 Keywords mesh superposition technique batch mixer time dependent flow distributive mixing mixing task preset statistical analysis Polystat 1 7 Known Limitations in ANSYS Polystat 15 0 This section lists limitations that are known to exist in ANSYS Polystat Where possible suggested workarounds are provided Mesh ANSYS Polystat does not support mixing tasks on CutCell meshes ANSYS Polystat does not support mixing tasks on meshes with subdivided elements See Ap pendix C p 165 for a method to circumvent this limitation ANSYS Polystat does not support mixing tasks if the flow field is meshed using the sliding mesh tech nique See Appendix D p 167 for a method to circumvent this limitation When using the Mesh Superposition Technique MST with moving parts with or without slippage along the moving parts the trajectories and kinematics of the deformation may be affected when material points massless particles are close to the surface of the moving parts When using MST with moving parts it may happen that some of the material points get overlapped by a moving part This is due to the accumulation of small errors along the trajectory of the material
68. an of a property prefix _mean crv standard deviation of a property prefix _stdv crv deviation of points concentration prefix _pcd crv operator on functions prefix _opr crv auto correlation on concentration field prefix _crc slice index crv probability prefix _prb slice index crv Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 90 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu density of probability prefix _dns slice index crv distance distribution prefix _dsp slice index crv histograms prefix _hst slice index crv percentiles prefix _pct percentile index crv distribution in zones global deviation prefix _zonGlI crv deviation for zone i prefix _zon zone index crv zones partitioning points concentration prefix _ slice index csv as a set of csv files The crv files that are generated are ASCII files that can be plotted in ANSYS Polymat and ANSYS Polycurve see Defining and Plotting Curves in the separate Polymat User s Guide for details or viewed in other spreadsheet applications The files have the following format The optional header is the first 5 lines line 1 lt empty line gt line 2 title or name of the current curve line 3 lt empty line gt line 4 lt empty line gt line 5 lt empty line gt The next lines are the set of points defining the curve On each li
69. and f t2 in ordinate an analysis of the graph reveals a possible correlation between the fields Figure 2 5 Correlations Graph B time t2 a time t1 2 3 Homogenization 2 3 1 Definition Suppose we want to mix two fluids A and B both fluids occupy at time t 0 two separated zones of the flow domain see figure below Figure 2 6 Mixing Fluids fluid A fluid A Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 17 The Mixing Theory Let c X t denote the concentration of fluid A throughout the mixing process Since no diffusion occurs between fluids A and B we conclude that c equals either 0 or 1 and remains constant along the trajectory of a material point Its evolution is governed by the transport equation c 0 2 25 The concept of concentration allows us to introduce the notion of segregation scale 5 p 169 8 p 169 At time consider a set of M pairs of material points separated by a distance r For the j pair and j and cj denote the concentrations at both points of the pair moreover let denote the average concentration of all points and c the standard deviation At time f the correlation coefficient time let c R r t for the concentration is defined as follows M 2 lt e Ca z 2 26 R r t 5m Oc The function R r t gives the probability of finding a
70. ard deviations Enter the name of the function new_deviation OK Cancel This function will allow you to calculate the gap existing between two density of probability functions The second one is supposed to be an optimal function Three different methods exist to evaluate this deviation integral abs f f_opt 2 co idx gt vide f s idx ds 4 25 e difference of the means idx 5 3 P 4 26 e difference of the standard deviations idx a a 4 27 where co idx f s idx sds 4 28 and Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 149 The Polystat User s Manual z idx idx s 3 7ds 4 29 This distribution index defined in chapter 2 corresponds to the result of the first method In all cases you have to specify the density of probability function of the real distribution and the density of probability function of the optimal one Next you select a method and eventually you give a name to the new function You will obtain the evolution of the deviation along the slices If you visualize this function on the X axis you have the index of the slice and on the Y axis the value of the deviation Figure 4 97 The Deviation along the Slices deviation index of the slices To simulate and analyze t
71. ask to save them in files readable by your graphic postprocessor The concentration of real points will be evaluated like this for each point X of the optimal distribution we determine the number of points of the real and optimal distributions included in a sphere of radius Rand center _X The concentration at point X will be BO es GD E105 0 4 23 nbr nbo Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 140 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu where nbr number of points of the real distribution C sphere X R and nbo number of points of the optimal distribution C sphere X R If the sample size method you chose is the automatic evaluation the radius of the sphere is evaluated as follows First we determine the smallest box that surrounds all the points of the optimal distribution Next we calculate its volume V A typical distance between points is d V nbi where nbi is the number of instants Eventually the radius of the sphere is set to 3d However if the sample size method you chose is the User specified one you can impose its own value for the radius that must be a positive real 4 5 2 9 The Sum A lt op gt Sum B Function Figure 4 82 The Sum A lt op gt Sum B Settings for the Create a new function Dialog Box Create a new function Sum A lt op gt Sum B x Sum A lt op gt
72. at Fo apt p 2 24 Ay t indicates that at time t p of the material points have a value of a lower than a t as you see on the figure below Figure 2 3 Percentiles Graph a ap t time t With the percentiles we can study the evolution of the mixing for specific fractions of the population of material points it s interesting for example to know the value of the length stretch reached by the 5 or 10 of the points with the lowest stretching these percentiles can easily show local defects in the stretching 2 2 3 5 Histograms Another way to represent the frequency of values of a field is to define histograms you specify a set of intervals of values of a and he obtains the percentage of the points population that have a value of a in each interval at time see figure below Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 16 of ANSYS Inc and its subsidiaries and affiliates Homogenization Figure 2 4 Histograms Graph time t a1 a2 a3 a4 an Ons We see that p of the points population has a value of a between 1 and a2 at time t 2 2 3 6 Correlations Finally once the number of material points is sufficiently large it is possible to examine the correlation between fields either at the same or at different times We have to define two times tl and t2 and two fields a and p For every material point we plot a tl in abscissa
73. ates Definition of the Distribution Analysis Figure 3 41 A Distribution Analysis Mixing Task MIXING Task 1 Modify task type DISTRIBUTION analysis Upper level menu Definition of the flow domain Definition of the boundary conditions Definition of the velocity fields Generation of the material points Parameters for the tracking Selection of properties Storage of the results Definition of moving parts Definition of a KINEMATIC analysis Definition of a DISTRIBUTION analysis Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 69 Mixing Tasks in Polydata Figure 3 42 The Definition of the DISTRIBUTION analysis Menu Definition of the DISTRIBUTION analysis Reset to default values Upper level menu Modify number of slices 21 Modify starting time 0 0000000E 00 Modify increment between slices 0 5000000E 03 Modify direction of slicing to the future Evaluation of global distribution index YES Modify max distance between points 0 1000000E 01 Evaluation of axial distribution index NO Modify axis direction Z Evaluation of Left Right transfer X dir YES Evaluation of Upper Lower transfer Y dir YES Evaluation of Back Front transfer Z dir NO Modify surrounding box for transfer functions XYZ min 0 0000000E 00 0 0000000E 00 0 0000000E 00 XYZ max 0 3000000E 01 0 3000000E 01 0 900000
74. be initially concentrated in a small volume We have to calculate their trajectory for a given time interval We store these trajectories in files named real_0001 to real_000X for example We calculate in the mixing task 2 the optimal distribution We suppose the material points to be initially distributed in all the flow domain We have to calculate their trajectory for a very short time interval infinitesimal amount of time We store these traject ories in files named opti_0001 to opti_000X In Polystat we read the files real_0001 to real_000X and the files opti_0001 to opti_000X We define two sets of trajectories the first one named real_set contains all the trajectories from the real_ files the second one named opti_set contains all the trajectories from the opti_ files We define two sets of slices the first one named real_slicing is a slicing on the time N slices every At seconds for the real_set set of trajectories The second one named opti_slicing is one slice defined for time t 0 and on the opti_set set We define two Distance Distribution functions the first one named real_distribution is based on the real_slicing set of slices The second one named opti_distribution is based on the opti_slicing set of slices We define one Deviation function to calculate the deviation of the real distribution real_distribution function from the perfect distribution opti_distribution function
75. ce see The Slices p 158 Second you specify a list of zones see The Zones p 159 In this slice the instants included in a zone have a concentration value of 1 The instants external to all the zones have a concentration of 0 Figure 4 33 Defining Concentration Using a Slice slice trajectory 1 trajectory 2 To define such property the following window appears Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 104 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 34 The Concentration Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY C Concentration xj Concentration X List of zones moa In order to define an initial concentration field you have first to define a slice Next in this slice you will define zones where the concentration is 1 elsewhere the concentration is 0 Define a slice Enter the name of the new property Concentration _C Every zone must have a different name To define a new zone click the Add button If you want to modify an existing zone select it in the list and then click the Mod button If you want to delete an existing zone select it in the list and then click the Del button 4 2 3 15 Min Max This method allows you to calculate the minimum or the maximum of a property A along trajectories The follo
76. ction for a Slice for slice S distance Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 137 The Polystat User s Manual 4 5 2 7 The Distance distribution Function Figure 4 79 The Distance distribution Settings for the Create a new function Dialog Box Create a new function Distance Distribution x Distance distribution Select a set of slices new_set_of_slices Y Select coordinate field coordinates M Evaluate distance distribution between all pairs of points C between pairs of neighboring points For distance between 0 and 0 Enter the number of values 100 Enter the name of the function new_distribution_function OK Cancel To calculate the evolution of the distribution function of distances between material points you need to specify which set of slices will be used You must select a coordinate property that will serve to cal culate the distance between pairs of points in a slice Don t forget to enter the number of values to represent the distribution function You have also to give a name to the new function Finally you have the possibility to choose between two methods e the first determines the distance distribution between all pairs of points The maximum distance measured will be about the size of the flow domain if
77. ctions by adding or removing them from the list See Management of Properties p 67 for details You also have the ability to select the statistical functions that will be evaluated for a specified set of properties You can choose to evaluate the mean and standard deviation functions the percentile functions which are 10 50 and 90 by default the probability functions and the density of probability functions with or without smoothing Note that if you added concentration to the list of properties using the Management of properties menu item the previous functions mean and standard deviation functions etc will not be calculated for concentration as they are for the other properties instead you have the option of enabling the Evaluation of the segregation scale which will only be calculated for concentration Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 65 Mixing Tasks in Polydata You can click Show advanced options to add menu items to the menu see Figure 3 39 Advanced Options for the Definition of the KINEMATIC analysis Menu p 66 These additional menu items allow you to modify some of the numerical parameters involved in the evaluation of the statistical functions Show advanced options Figure 3 39 Advanced Options for the Definition of the KINEMATIC analysis Menu Definition of the KINEMATIC analysi
78. ctions click directly on the Delete All button In both cases Polystat asks for a confirmation of your choice 4 5 2 Create Statistical Functions If you select the option CREATE a new function in the Statistics menu of the main window the fol lowing window appears Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 129 The Polystat User s Manual Figure 4 65 The Create a new function Dialog Box Create a new function xj lt Select Type gt T select function type Then click the 7 button at the right of the combo box presenting lt Select Type gt A drop down list appears showing the functions that can be created Finally select the appropriate statistical function from this list Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 130 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu Figure 4 66 Types of Functions that Can Be Created Create a new function x lt Select Type gt gt Property along a trajectory Correlation Function Sum Mean Standard Deviation Probability Function 4uto Correlation Function of the Concentration Distance distribution Distribution in zones Sum lt op gt Sum B Smoothing Density of Probability Function Percentile Histogram Segregation Scale Deviat
79. d points that are outside the flow domain will be rejected Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Mixing Tasks in Polydata Figure 3 27 Equidistant Distribution of Points in a 2D Box This zone is all the inflows of the flow domain In a previous menu you have defined the boundaries that are the inflows of the flow problem With this option the initial positions of material points are randomly generated in these inflows this option is well suited for flows in an open domain This zone is a topo object With this option you can define a zone by selecting a topo object from a list If the list does not have appropriate topo objects it is possible to add new ones as described in a later step This zone is one inflow of the flow domain In a previous menu you have defined the boundaries that are the inflows of the flow problem With this option you select one of these inflow sections The initial positions of material points are randomly generated in the selected boundary This option is well suited for flows in an open domain This zone is a CSV slice included in the flow domain With this option you can specify your own initial distribution of points saved in a comma separated values CSV file After selecting this option use the dialog box that opens to specify the name of the CSV file A question dialo
80. dex of the slices Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 133 The Polystat User s Manual 4 5 2 3 The Mean Standard Deviation Function Figure 4 71 The Mean Standard Deviation Settings for the Create a new function Dialog Box Create a new function Mean Standard Deviation xi mean Standard Deviation Select a set of slices new_set_of_slices Select a property time wei Select velocity Field velocities Weighting No veloc Normal everywhere veloc Normal if positive Enter the name of the mean Function new_mean OK Cancel To calculate the mean and the standard deviation of a property you need to specify which set of slices will be used and to select a property You have also to give a name to the new function If you want to weight the mean and the standard deviation in function of the local velocity don t forget to select the velocity field Additional information on weighting is available in Weighting p 159 You will obtain two curves one for the evolution of the mean of a property along the slices and the second for the evolution of the standard deviation If you visualize these functions you find on the X axis the index of the slice and on the Y axis the property a Figure 4 72 The Mean and Deviation of a Property al
81. e available are referred to as the following e the kinematic analysis The kinematic analysis is focused on the kinematic parameters of the material points and can calculate results for a variety of functions such as probability functions and density of probability functions on a set of properties such as shear rate and stretching that you select e the distribution analysis The distribution analysis is focused on the spatial distribution of the material points and can calculate the global distribution index the axial distribution index and the transfer rates between different parts of the mixer Note that the distribution analysis requires that you have only one generation zone which must be shaped like a box if the domain is closed the box must be located inside the flow domain if the domain is open the box must be located on the inflow boundary 34 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Definition of the Flow Domain and have no thickness in the direction of flow See Parameters for the Generation of the Material Points p 49 for details on creating the generation zone To enable a preset statistical analysis repeatedly click Modify task type at the top of the menu until the text of the option shows that the task type is set to the kind of analysis you want Modify task type Depending on your task
82. e www ansys com under Support gt Customer Portal The direct URL is support ansys com One of the many useful features of the Customer Portal is the Knowledge Resources Search which can be found on the Home page of the Customer Portal Systems and installation Knowledge Resources are easily accessible via the Customer Portal by using the following keywords in the search box Systems Installation These Knowledge Resources provide solutions and guidance on how to resolve installation and licensing issues quickly NORTH AMERICA All ANSYS Inc Products Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option Toll Free Telephone 1 800 711 7199 Fax 1 724 514 5096 Support for University customers is provided only through the ANSYS Customer Portal GERMANY ANSYS Mechanical Products Telephone 49 0 8092 7005 55 CADFEM Email support cadfem de All ANSYS Products Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option National Toll Free Telephone German language 0800 181 8499 English language 0800 181 1565 Austria 0800 297 835 Switzerland 0800 546 318 International Telephone German language 49 6151 152 9981 English language 49 6151 152 9982 Email support germany ansys com UNITED KINGDOM All ANSYS Inc Products Web Go to the ANSYS Customer Portal http support ansys com and select the appropriate option Telephone
83. e 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Chapter 2 The Mixing Theory 2 1 Introduction In polymer blending a minor component is generally present as drops or filaments in a continuous phase of a major component Mixing is a process of deformation and rupture of the drops but also a process of distribution of those drops in the whole flow domain A good mixing is characterized by small and identical drops distributed uniformly in the all flow domain Deformation of drops is promoted by the viscous stress T exerted on the drops by the flow field and counteracted by the interfacial stress R where a is the interfacial tension and R the local radius The capillary number Ca is useful to characterize mixing For a given pair of polymers a critical Capillary number may be found It corresponds to the situation where the viscous stress competes with the interfacial stress the drop is extended and finally breaks up into smaller droplets We name this process dispersive mixing Let us note that an extensional flow field is more efficient to break up drops into droplets than a shear flow If the capillary number is much higher than the critical capillary number then the viscous stress overrules the interfacial stress and the drop is extended but does not break up this process is called distributive mixing On the cont
84. e correlation coefficient scale t may then be easily calculated by numerical integration on the basis of Equation 2 27 p 18 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 19 The Mixing Theory Figure 2 8 Calculated Values of the Correlation Coefficient R r t distance 0 d 1 a i d nbval dmax There exists a limitation to this method as the number of points is finite the mean size of the pixels is finite too we cannot calculate accurately a segregation scale that is smaller than this characteristic size If the segregation falls below that size that means that the mean thickness of the striations in the flow is smaller than the size of the pixels the concentration field will appear like a random distribution of pixels of the two colors there are no more continuous lines of one color Another problem of the segregation scale is that it cannot detect a local defect in the flow it is a global index of the quality of mixing Finally the segregation scale depends on the size of the flow domain The parameters of this method are e The initial distribution of the zones of fluid A and B d max the maximum possible distance between two points in the flow domain e nbpair the number of pairs of points necessary to calculate one value of the correlation function nbval the number of values of the co
85. e id Switch to binary unformatted result files Modify the list of result files You must specify one by one the list of Polyflow result files that define the flow To begin click Modify the list of result files to open the menu shown in Figure 3 22 The Flow definition list of result files Menu p 48 Modify the list of result files Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 47 Mixing Tasks in Polydata Figure 3 22 The Flow definition list of result files Menu Flow definition list of result files Current setup the velocity fields are included in the following files Index Time of use Filename 1 1 00000E 20 res Upper level menu Add a velocity field Remove a velocity field Modify a velocity field Change the order of the velocity fields In this menu you can add remove and modify the result files as well as change the order The parameters for a particular velocity field are summarized in a menu like the one shown in Figure 3 23 The velocity field 1 Menu p 48 Figure 3 23 The velocity field 1 Menu velocity field 1 Current choice filename res Ascii formatted file time of use 1 0000000E 20 Upper level menu Enter the result filename Enter the time of use Switch to binary unformatted file You define a new velocity field in this menu by specifying
86. e properties are correct This window appears like this Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 109 The Polystat User s Manual Figure 4 39 The Time Aver Eff Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Time Averaged Efficiency of Mixing x Time Aver Eff Rate of stretching Jrate_of_stretching x Rate of dissipation rate_of_dissipation m wwe Enter the name of the property C time_aver_eff 4 2 3 20 Shear Rate This method allows you to create the instantaneous local shear rate based on the rate of dissipation D defined in The Mixing Theory p 11 For 2D and 3D flows the shear rate is defined as y J 2D 4 11 This property is accessible only if the rate of dissipation has been calculated along the trajectories In the creation window the default values for the properties are correct This window appears like this Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 110 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 40 The Shear Rate Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Shear rate D x Shear Rate Rate of dissipation rate_of_dissipation bd Enter the name of
87. e time evolution of its mean and its standard deviation N dai 1 2 20 a t t 1 N a t a t 2 21 og t H E N 2 2 3 2 Cumulated Probability Function or Distribution Function Let us now define the distribution function F associated with the scalar field a The quantity F P t is defined as follows Fa Pt P a t f 2 22 where the right hand side is the probability that the field be smaller than at time t A new graph of the distribution function is calculated at every time see figure below Figure 2 1 Distribution Function Graph probability 0 B 2 2 3 3 Density of Probability Function Based on the distribution function F of a scalar field a we can define the density of probability function f B t as follows dF a da 2 23 The function f t is the frequency with which we find a value of a in the range 4a P 4a at time A new graph of the density of probability function is calculated at every time see figure below Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 15 The Mixing Theory Figure 2 2 Density of Probability Function Graph density of probability 0 2 2 3 4 Percentiles An easier representation of the mixing progress is based on the time dependence of percentiles For the field a let us define a t such th
88. e trajectory whom its initial position is the closest to the specified position If we choose Independently of the moment we don t specify any peculiar moment The selected property is not necessarily a coordinate property We can for example select the trajectory that has an initial velocity the closest to the value 1 2 3 If the selected property is a scalar enter the position in the rectangle 1 the rectangles 2 and 3 are set to zero 4 3 5 The SEARCH stagnation points Option By selecting this option the following window appears Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 122 of ANSYS Inc and its subsidiaries and affiliates The Trajectories Menu Figure 4 54 The Search stagnation points Dialog Box Search stagnation points x Select a set of trajectories all_trajectories Select a coordinates field coordinates Select a time field time Enter the threshold distance fo Enter period fo Enter stagnation time fo Enter squeezing Factor fp Poo Poo Enter the name of the set stagnation Points OK Cancel With this method we will select points having a specific behavior the points remaining close to their initial position or those coming back after a specific period close to their initial position We have to specify the following data a set of trajectories in which we will search stagnation points a
89. ea Raeann 88 4 1 10 The WRITE Stat Option socsccsscdcidecesessadesacetetuveneenstius cadevesetanghsuedhebevevsonstsacetdbeseeunedhsavetedaeseents 90 AL ATEING Save Optlonasess cic cdscteessdeceisaa Sis is Sai ecto Set ease elias tea eed ea ee ees 91 AD ANE Properties MONU ss sexcusseeid cee essevedhds cad e E ed dae s8 Site cneedede des Sevancestel cine Seveded ab E E aS 91 AD Ve Definitio Anean narea e E e a oea ea ues E EN E CodiwebeaUagiessdhaneds EE 91 4 22 See Properties shor scsavesnecidecadscnauedeces TEESE EE E E EE AN EOE caves TES aeS 92 42 3 Create Properties was sevsieeccesacticesuws ve i en E E n E a i a A E a E ERE 93 Wer Ea TE aan eee ec EE T E EEEE TE E 94 AD PA a O AENEA AE O EEA EAA E AEN E EE 95 PIERS N O E E OAE E A E NE T AE 95 FIZA GCA anann ER TN A E ARETA i AURATA 96 ADB DOA HE e W A a AEAT A NE N E A A NT 96 4230 AA B Lae E EE TRN E eee eee eer 96 4237 AF Bi rionn iiio nai EAE E E L OA E E E E AE E E a 96 4 23 87 Rotate pinen eE a e i R E i a a a a a a a aia 97 4 2 3 9 Translate in aiea i a e a araa aa a e a a a aas ia aeS 98 4 23 10 D rivate meisson e aeaiia ereere eeann e thes adeavesducabecesdecevoiadedbeten ss 99 4 23 11 IME GKALe ninen a A a R E A AA TEA EEEE 100 ALII lt a 601 1 1 10 eein OP 101 A233 NIVA SCEN oora aa a EAE cea EEE EA a E e ear a AEA A EA A SDE 102 4 2 3 14 C ncentration oeeie iiae AE e Eeee sds Eae EEATT EEEE EAEE EEEE ENEA EE AEE Eea 104 4 23 15 MN MaX een E EEE EEE E EE E
90. ectories that belong to the two sets If we select the Minus operator the new set C will contain the trajectories of the set A that do not belong to the set B If we select the Difference operator the new set C will contain the trajectories of the set A that do not belong to the set B and the trajectories of the set B that do not belong to the set A We can write this operation as C A Minus B Union B Minus A Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 121 The Polystat User s Manual 4 3 4 The SELECT one single trajectory Option By selecting this option the following window appears Figure 4 53 The Select a single trajectory Dialog Box Select a single trajectory x Select a set of trajectories Jall_trajectories Select a coordinates field coordinates Define a position 1 2 3 We will select the trajectory which is the closest to this position Initially Independantly of the moment Enter the name of this trajectory single_trajectory OK Cancel With this method we will select a single trajectory from a set that is the closest to a specified position We have to specify the following data a set of trajectories in which we will search one trajectory a property a position an option for the selection If we choose Initially we select th
91. eeii iai eiie a aiaa iair aeii oai iaie 119 4 3 2 The CREATE a new set of trajectories Option ssessssssssssssesssssesssssessssrresssrressseressssreeesssees 120 43 3 The COMBINE sets of trajectories OPtlonijassiceunisiarennisredeynavcecdgnorseapauseractaueseceiniaeianennees 121 4 3 4 The SELECT one single trajectory Option ce eeseeseesseseeseeeesseeceseesseseesenseeseesesseneeseesonees 122 4 3 5 The SEARCH stagnation points Option cssssccccccceeesesesnececceceeeseeesnneeeeceeeessessnnseeeeeseess 122 AA The SliGes MONO amp xa veccssnce caves cacovte sey EA E EE E E ces tenes sveandceee covers ERES 124 4 4 1 See the Set Of Slices ineno ai E ceeds tak scecadecssehevatdcdeneaeseuawedacensaeeeds 125 AA2 The AULO MALE SUING OPTION cj ans aypnasvacesananedygunieraiersenysigneswaiysveaiera patio EEE ENE E Ei 126 4 4 3 The Manual Slicing Option sirasini e e ii a a a i e 126 AAA The Sub Slicing ORUON seenen aea a Saa RA a Caratamiantitnanuanaurana 127 4 5 The Statistics Men nrerin i sE A EE E EE o AAEE AE E E AA EENE ERS 128 4 5 1 See the Statistical FUNCIONS eenei eaenesni i aa a a e E A E A E EE eai 128 AS 2 Cleave Statistical FUNCIONS ansieae ienai aatia e geie aeoe ka aeaaea e aeaa aeai 129 4 5 2 1 The Property along a trajectory FUNCTION ssssseesssssesssssesssssesssssreesssrressseressssreessssreesse 132 A522 The SUI FURETION norce nea i ia i a e Eia a ia 133 4 5 2 3 The
92. eight X cur With the upwind smoothing we look first at the Y value of the farthest neighbor We weight more the size to the left or the right size of the current X value with the highest Y value Figure 4 86 Upwind Smoothing With the downwind smoothing we look first at the Y value of the farthest neighbor We weight more the size to the left or the right size of the current X value with the lowest Y value Figure 4 87 Downwind Smoothing In general we obtain a good result with a centered smoothing and with the following parameters 2 neighbors at left 2 at right and 2 iterations Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 143 The Polystat User s Manual 4 5 2 11 The Density of Probability Function Figure 4 88 The Density of Probability Function Settings for the Create a new function Dialog Box Create a new function Density of Probability Function xj Density of Probability Function z Select a distribution function Function Enter the number of values 100 Enter the name of the Function new_density_Function To calculate the evolution of a density of probability function you need to specify which probability function to use You must enter the number of values to represent such a function a good practice is to use half the number of value
93. el To calculate the evolution of percentiles you need to specify which probability function to use You must define a list of percentiles and also give a name to the new function Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 145 The Polystat User s Manual To add a percentile to the list ranged from 0 to 100 enter a value in the box in the line tagged lt enter new value gt and then click lt CR gt To delete one percentile select it in the list and then click the Del button As there exists a list of probability functions one for each slice of a sorted list you will obtain the evolution of a percentile along the slices one curve for each percentile If you visualize all the percentiles on the X axis you have the index of the slice and on the Y axis the value of the property chosen earlier when the probability function has been defined Figure 4 91 Percentiles along the Slices property P percentile p1 percentile p2 percentile p3 index of the slices Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 146 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu 4 5 2 13 The Histogram Function Figure 4 92 The Histogram Settings for the Create a new function Dialog Box Create a n
94. end of this step we have a new mesh and a set of res files 1 res file per time step compatible with this new mesh In Polydata we define a mixing task based on the new mesh and the new results files In Polyflow we compute the trajectories of a set of material points In Polystat we perform a statistical analysis on these trajectories Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 165 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 166 of ANSYS Inc and its subsidiaries and affiliates Appendix D Sliding Mesh Technique and Mixing Task When sliding mesh technique is used two limitations of the mixing module forbid the use of the computed flow field to perform tracking of material points Firstly in the case of transient simulations the mesh can will change with time position of the nodes Secondly the mesh is non conformal As the tracking of material points does not allow such cases we propose the following procedure In your mesher application define a mesh constituted of different subdomains for the flow domain one subdomain is fixed while the other s is are rotating In the figure below the flow domain is composed of disconnected subdomains 1 to 3 The subdomain 1 is fixed while subdomain 2 is rotating with the left cam and subdoma
95. erates decreases because of their reduction in size their number staying constant This can be seen in the next figure where we see the effect of erosion on an initial set of agglomerates with sizes ranged between 15 and 25 microns They are mixed in a matrix with a viscosity of 11000 Pa s We applied a constant shear rate of 10 s and we plot the mass distribution function every 25 seconds We observe the shift to left the widening and flattening of the Gaussian curve centered initially at 20 microns as erosion develops But we observe also an in creasing peak at extreme left of the graph in the small sizes corresponding to the generation of ag gregates Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 26 of ANSYS Inc and its subsidiaries and affiliates Disagglomeration Figure 2 18 The Effect of Erosion on the Mass Distribution Function over Time shear rate 10 1 s 0 0 5 0 10 0 15 0 20 0 25 0 size microns Rupture For the model of rupture also based on 4 p 169 we assume that the rupture into a few fragments occurs if an agglomerate is submitted to a shear stress higher than a critical shear stress during a given amount of time called rupture time This critical shear stress for rupture function of size S can be written Cot S Omin 2 40 Indeed we are more interested by the inverse relation we have to know which agglomerates can break fo
96. ere V is the volume of the mixer With this set of distances we can calculate the density of probability function on the distance f d the probability to find a pair of points chosen randomly such that their inter distance is included in range d d Ad at time t is f d Ad Figure 2 10 Density of Probability over Distance density of at time t probability area probability distance 0 d dmax Suppose on the other hand that you have distributed randomly a same number of points in all the flow domain we can assume that such distribution is ideal With the same tools we can calculate the function f d for this optimal distribution It is noted f d The distribution index 6 is defined as the deviation of the function f d real distribution from the function fe d optimal distribution co 6 t 2 ro f 1 dl de 0 1 2 31 As the distribution improves the index decreases This index is dimensionless it is independent of the size of the flow domain The evolution of 6 depends of course on the initial position of the box Another important parameter not to forget is the number or material points to distribute a careful analysis must be done to measure its influence Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 21 The Mixing Theory Two other parameters can also
97. erved Contains proprietary and confidential information 156 of ANSYS Inc and its subsidiaries and affiliates The Help Menu 4 5 3 3 The Probability function Figure 4 104 The Probability function Settings for the Create a new function Dialog Box Create a new function Probability Function x Probability function Select a density of probability Function mean_disagglo_function_ Enter the name of the Function new_probability_Function you have to select a density of probability function and to give a name to the new function With this function one evaluates for each slice idx a probability function P as the integral of a density of probability function f on a property a P a idx f caid da 4 37 4 6 The Help Menu Three options are available in the Help menu The Polystat User s Guide option opens the ANSYS help viewer to the table of contents of the Polystat User s Guide The Accessing PDF Help option can be used to open the ANSYS help viewer to the section of the Polyflow User s Guide that describes how to access PDF files of the documentation Accessing the PDF Files of the Documentation The About option opens a window that displays installation details including the version numbers of the ANSYS products you have installed Release 15 0 SAS IP Inc All rights reserved Contains proprietary and conf
98. erview of the process With such a method we can have an objective and quantitative evaluation of the mixing of any process we can for example find areas in the domain where the mixing is poor low stretching instead of exponential increase For 3D flows we generalize the concept the interface is now a surface and we will calculate the stretching of infinitesimal surfaces attached to material points Let Q and Q denote the domain occupied by the homogeneous fluid at time 0 and respectively The motion of the fluid is described by the relationship x 7 X 7 2 2 where X denotes the position of a material point P in Q and x in Q The symbols F and C denote the deformation gradient and the right Cauchy Green strain tensor between both configurations The velocity gradient and the rate of deformation tensor at time are denoted by Land D respectively For later use we note that F LF 2 3 where a dot denotes the material time derivative 2 2 1 Kinematic Parameters for 2D Flows Consider in 2 a material fiber dX with a unit orientation M which deforms into a material fiber dx with a unit orientation m at time Let denote the length stretch dx dX It is easy to show 6 p 169 that A X M t 4JM CM 2 4 while m is given by FM A A good mixing quality requires high values of A throughout time and space A local evaluation of the efficiency of mixing 7 p 169 is given by the ratio pe X M t 2 6
99. esses than mixing for example the quality of a molten glass exiting a furnace Eventually we calculate statistical functions of these parameters these functions can be visualized inside Polystat Excel Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 5 Introduction It is also possible to visualize with Polystat the spatial distribution of a kinematic parameter at a given time or in a cutting plane or along a given trajectory Figure 1 6 The Statistical Postprocessing data files trajectories kinematic parameters POLYSTAT POLYCURVE result files statistical curves 1 5 The Numerical Techniques Involved in the Mixing Module Generally the trajectories are calculated by the time integration of the equation X V with an Euler explicit scheme it s enough if we are only interested in the successive positions of material points But if we need to know precisely the deformation accumulated along these trajectories a very accurate numerical technique is required We chose to combine two techniques first we use an explicit Runge Kutta scheme of the fourth order second instead of integrating the motion of a particle in the real space we perform a coordinate transformation We calculate the trajectory in the parent element we integrate with the Runge Kutta method f v 1 3 To know the
100. euvrel Disdier 4 p 169 on the dispersive mixing of carbon black agglomerates N234 in a SBR matrix Of course due to the large variety of models and raw materials it is possible to adapt or modify the implemented model accessible in the CLIPS file disagglomeration clp that can be found in POLYFLOW bin directory the corresponding functions are interpreted by Polystat at run time We consider hereafter the case of low concentration of carbon black pellets meaning that we neglect erosion due to friction between pellets we only consider erosion due to hydrodynamic forces During erosion small particles are removed continuously from the agglomerates that diminish in size erosion i This removal can occur if the shear stress is above a given threshold ogy In this case if we assume that agglomerates are roughly spherical the variation of size As of the agglomerate after At seconds can be described as follows erosion As _ 8a 0 crit y 2 38 At 382 where is a coefficient of proportionality 7 the local shear rate and S the size of the agglomerate at time and AS will be the new size of the agglomerate at time t At Based on the assumption of mass conservation the mass distribution function becomes 3 Ft s As t At ser 5 2 2 39 S Moreover as the total mass of solid particles is constant in the control volume Vx the mass fraction of aggregates increases has the mass fraction of agglom
101. ew function Histogram 7 x Histogram List of values Del All 25 Del zenter new value gt a Select a distribution Function Function Enter the name of the Function new_histogram OK Cancel To calculate the evolution of histograms you need to specify which probability function to use You must define a list of intervals by introducing a set of values one by one enter a value in the box in the line tagged lt enter new value gt and then click lt CR gt To delete one value select it in the list and then click the Del button You have also to give a name to the new function As there exists a list of probability functions one for each slice of a sorted list you will obtain a histogram function for each slice If you visualize this function for a given slice on the X axis you have the specified intervals of values the corresponding property has been chosen earlier when the probability function has been defined and on the Y axis the percentage of instants of the slice having a property value in each interval Figure 4 93 The Histograms for a Slice for slice S p1 p2 p3 p4 p5 property P Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 147 The Polystat User s Manual 4 5 2 14 The Segregation Scale Function Figure 4 94 The Segregation Sca
102. example let s suppose that we analyze the flow through a cylinder like shown on the next picture Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 73 The Polystat User s Manual Figure 4 2 A Cutting Plane Through a Flow Domain inflow outflow cutting plane To analyze this flow we place a set of material points in the inflow section and we calculate their trajectory until they reach the outflow section We will cut the trajectories with planes disposed regularly from the entry to the exit this is the slicing step In each plane we will calculate statist ical functions Those functions will evolve from entry to exit and show the way the mixing changes Remark if the flow occurs in a closed domain we want to know the time evolution of statistical functions and the slicing will be done on the time In the menu Statistics we define the set of statistical functions we want to calculate on the defined set of slices Finally we go back to the File menu and click the Run option By clicking this option we order Polystat to calculate actually all our desiderata new properties the subset of trajectories the set of slices the set of statistical functions This calculation can last for a while When the calculation is over we can analyze visualize and store our results After this brief description of the
103. f trajectories and sets of slices you have to define the statistical functions you want to calculate on these objects By default no function exists General ones can be created by selecting CREATE a new function while functions specific to the disagglomeration model can be found in NEW disagglomeration functions Figure 4 63 The Statistics Menu Options 15 x File Properties Trajectories Slices Statistics Help Create a new function New disagglomeration functions 4 5 1 See the Statistical Functions If you select the option SEE MOD DEL functions in the Statistics menu of the main window you will see the list of the existing functions Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 128 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu Figure 4 64 The See Modify Delete existing functions Dialog Box See Modify Delete existing functions x Select a function OK Modify Delete Delete All If you want to modify some data of a function select it in the list and then click the Modify button The window that served for the creation of that function will appear then modify some data If you want to store the modified data click OK Otherwise click Cancel To remove one function from the list select it in the list and then click the Delete button To remove all the created fun
104. fine the process of mixing Dankwertz in the 50s analyzed the mixing as a homogenization process of a concentration field initially two different fluids are separated in two adjacent zones as the time goes on the local concentration of each fluid evolves everywhere in the fluid and if the mixing is perfect the concentration must tend to the same value everywhere in the flow to quantify this homogenization process Dankwertz defined two parameters firstly the segregation scale is the average thickness of the striations existing in the flow domain Secondly the intensity of segregation is the standard deviation of the concentration around its mean These parameters are used when there are only two fluids to mix and when their proportion in the flow domain is more or less equivalent Later in the 80s Ottino defined other parameters based on the Continuum Mechanics Theory He showed that mixing is a process increasing the interface existing between fluids But instead of meas uring the surface of the interface that is almost impossible in complex flows he prefers to measure local increases of infinitesimal surfaces distributed everywhere in the flow But these parameters are not very useful if we analyze the distribution of a small amount of pigments tracers and so on in the flow domain small percentage in volume of the total flow domain Based on the work of Manas Zloczower we have defined a new parameter in order to measure this
105. flow is rigid M 0 a shear flow M 0 5 or an extensional flow M 1 Moreover the first eigenvalue of the extra stress tensor T indicates the local stress which is an im portant parameter for the evaluation of the capillary number You should enable only the properties that are necessary in order to save time and memory 3 8 1 Parameters for the Kinematic Mixing Properties Clicking the Parameters for the kinematic variables menu item in the Selection of properties menu opens the menu shown in Figure 3 33 The Parameters for the kinematic variables Menu p 60 Parameters for the kinematic variables Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 59 Mixing Tasks in Polydata Figure 3 33 The Parameters for the kinematic variables Menu Parameters for the kinematic variables Current setup Random initial direction of stretching No constraint over the tensor F Accept the current setup gt Random initial direction of stretching Imposed initial direction of stretching gt No constraint over the tensor F Constraint over the tensor F detF 1 As a material point moves in the flow a small volume of matter attached to it will deform To calculate its stretching and rate of stretching you need to specify the direction in which this stretching is measured as explained in the theoretical background
106. function the filename containing this curve is built like this prefix _zon zone index crv nbc Z _ nbo Z zone Z nbtotal nbtotal with 5 Z C 1 1 4 21 where nbc Z nbo Z is the number of points of the real optimal distribution included in zone Z and nbtotal is the total number of points in the real distribution If zone Z is zero that means that the right number of points is included in zone Z If zone Z is negative that means that the number of points included in zone Z is smaller than the optimum there is a lack of points in that zone If zone Z is positive that means that the number of points included in zone Z is larger than the optimum there is an excess of points in that zone e the evolution of the global deviation of the real distribution compared to optimal distribution If one wants to save the function the filename containing this curve is built like this prefix _zonGl crv nbzones 5 Z with c 0 1 4 22 1 1 E 9 Z additional properties Additional properties are also evaluated but only available through the save functions option We will save in csv files one file per slice_index the zones partitioning the deviation from optimal dis tribution and the concentration of points in each area of the flow domain If you want to see those fields enter Polydata read the mesh and select convert old csv files enter the name of csv file and
107. g Box Create a new function Mean disagglomeration function x Mean disagglomeration Function bi Select a set of slices new_set_of_slices Y Select a diagglomeration property disagglomeration Select type of statistical treatment Mean Enter the name of the mean function new_disagglo_function you have to select a set of slices and a disagglomeration property Different types of treatment are available minimum maximum mean standard deviation standard deviation for values below the mean and standard deviation for values above the mean Eventually the use gives a name to the new function With this function and the min treatment selected one evaluates for each slice a min disagglomeration function based on the disagglomeration property known at each point included in the slice fain 1dx min f s pointi V point cslice idx 4 31 With this function and the max treatment selected one evaluates for each slice a max disagglomeration function based on the disagglomeration property known at each point included in the slice Snax 194x max f s pointi V pointicslice idx 4 32 With this function and the mean treatment selected one evaluates for each slice a mean disagglom eration function based on the disagglomeration property known at each point included in the slice n Feit YFG Yonek 4 33 ni 0 Release 15 0 SAS IP Inc All rights rese
108. g box will then ask if you agree to have all fields reinitialized to default values Click Yes if you just want the coordinates of the points to be read from the CSV file The other properties will be reinitialized to their default values time 0 logarithm_of_stretching 0 space_integration 0 and so on Click No in the question dialog box if you want Polyflow to read not only the coordinates of the points in the CSV file but also some other properties If they are found they will be used to initialize the property otherwise the default values will be used for initialization The properties that are 52 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Parameters for the Generation of the Material Points read in the CSV file are as follows note that the coordinates must be the first property written in the file COORDINATES in upper case always with three components time logarithm_of_stretching space_integration direction_of_stretching label All the points defined in the CSV file that are included in the flow domain will be tracked The other points will be rejected Another use of this option is the following assume that you divided your flow simulation into several sections to simplify and reduce the size of the problem The flow in each section is evaluated separately If yo
109. gain with the same data file it will begin to generate a new result file without erasing the result files from an old session storage You have to select one of the five available ways to store trajectories You can store all of the calculated points of the trajectories Note that this can be very expensive in terms of memory space You can store the positions of the material point every dt seconds exactly where dt is the time step specified in a later step You can specify that successive stored positions have a minimal time step of dt seconds where dt is the time step specified in a later step You can store a position every time the length of the trajectory has increased a distance of dl where dl is the displacement specified in a later step You can store a new position if the increase in the trajectory length is greater than dl where dl is the displacement specified in a later step The increase in this case is the difference between the trajectory length for the current stored position and the trajectory length for the previous stored position time step If you specified that you wanted the material point positions stored based on dt as described previ ously you can modify the exact or minimum time step e displacement If you specified that you wanted the material point positions stored based on dl as described previ ously you can modify the exact or minimum displacement 3 10 Definition of Moving Pa
110. h 7 In the initial configuration Qg consider an infinitesimal surface dA with a normal direction N With time this surface deforms at time this surface is noted da with a new normal direction fi The area stretch y is the ratio of the deformed surface da at time t over the initial surface dA da n X N t 2 12 n n ET If the fluid is incompressible we obtain 7 p 169 x E F n C j 2 13 If the fluid is incompressible the normal direction to the surface da is Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 13 The Mixing Theory 1 A P a 2 14 gt Il 4i A good mixing quality requires high values of 7 throughout time and space A local evaluation of the efficiency of mixing 7 p 169 is given by the ratio i ln X N t 2 15 The values of this instantaneous efficiency are always included in the interval 1 1 After some trans formations it is easy to show that A eA A n Dn ey X Nit _ 2 16 D We note that en is a local measure along the path of a material point the time averaged efficiency is defined as t e X N 1 ae X r d 2 17 4 to 4 However there exists another way to define a mean efficiency over time t las dt n XN i ae nC 2 18 Dar Ddt 0 0 Like for Equation 2 10 p 13 the physic
111. he distribution of matter a series of steps are necessary to perform Those are explained in detail in addendum A Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 150 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu 4 5 2 16 The Points Concentration Deviation Function Figure 4 98 The Points Concentration Deviation Settings for the Create a new function Dialog Box Create a new function Points Concentration Deviation x Points Concentration Deviation Select a set of slices new_set_of_slices Select coordinate field coordinates Perfect points concentration booo Sample radius fo Minimum number of neighboring points Bo The points in a given slice surface f are distributed ina Enter the name of the function new_deviation_function OK Cancel This function will allow you to calculate the deviation of points concentration in a slice compared to a perfect points concentration This deviation will be evaluated for each slice of the selected set of slices You must select a set of slices and a coordinate field Moreover you must introduce the points concentration for a perfect distribution in each slice This perfect distribution may be evaluated as follows For a 3D open flow domain we perform a slicing in space in the direction of the flow therefore each slice
112. he local points concentration at position x This radius must be chosen carefully if it is too small no points will be found and the local concentration will not be relevant if it is too large we will evaluate a global concentration that will be identical for all points in the slice and that will not change from slice to slice A first estimation is to take as the radius a tenth of a typical distance in the slice diameter of a rotor or of a screw for example you can also specify the minimum number of points needed to evaluate the points concentration at a position x the default is set to 3 If the number of neighboring points is smaller than this minimum we increase progressively the radius for that position x only until we have that right number of neighbors Next you must not forget to specify the dimensionality of the samples If the samples are straight line segments dim 1 surfaces dim 2 or volumes dim 3 This is needed to evaluate the local points concentration x as explained in Deviation of Points Concentration p 23 The deviation On in a slice S is evaluated as follows N 2 Lo x 4 4 30 N t dp S where N is the number of points in the slice S the x correspond to the location of points 7 in the slice S and b is the perfect points concentration Eventually you can give a name to the function 4 5 3 New disagglomeration functions If you select the option New d
113. ial property you have to select the property A to translate and the time the data some data specifying the translation direction and amplitude of the translation velocity and to give a name to the new property the result This property allows you to change if necessary the frame of reference one in translation with respect to the other The creation window appears like this Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 98 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 27 The Translate Settings in the CREATE a new PROPERTY Dialog Box xi Translate The property Ais coordinates Me Ais a coordinate field Ais another field The TIME is time enter the direction of the translation 0 0 0 the amplitude of the velocity 0 Enter the name of the property C trans _A If the property A is a coordinate field click the corresponding button The resulting property C will be C t A t Virans 4 5 where Virans is the translation velocity and the time However if the property A is not a coordinate field click the A is another field button The resulting property C is C t A t Virans 4 6 4 2 3 10 Derivate Derivate this method allows you to derivate a property along the trajectories you have to select the property A
114. iated a concentration depending on its situation in a zone of fluid A c 1 or a zone of fluid B c 0 When time progresses we calculate the new location of each point it is easy to visualize the current state of the concentration field for each point we plot in the domain a small pixel if 2D flow with the appropriate color Once the successive coordinates of material points are stored a minor effort is needed to calculate at time the concentration corresponding to another set of initial conditions The limitation of the method lies of course in the size of the material point identified by the pixel but the number of points can be increased at will together with the computation time Let us now assume that we have tracked N material points It is easy to calculate the average and the standard deviation of the concentration N ae lt y a 2 29 i iw 1 2 0c ae c T 2 30 where c is the concentration 0 or 1 of the material point 7 Let d max be the maximum distance between two material points in the flow domain We will calculate nbval values of the correlation function for distances uniformly distributed between 0 and dmax To calculate one value of correlation function for a distance d we select randomly nbpair pairs of points dmax dmax 2nbval 2nbval R r t is completed by a linear interpolation through the discrete calculated values The segregation if their relative distances are in the interval d Th
115. ibuting them throughout the whole flow region if the domain is closed or the whole entry section if the domain is open these points are also tracked as their distribution changes as the solution progresses You have the option of enabling the calculation of the global distribution index This index compares the distribution of the first generation zone with that of the second generation zone by using the in tegral method of the Deviation function described in The Deviation Function p 149 The distribution Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 70 of ANSYS Inc and its subsidiaries and affiliates Definition of the Distribution Analysis calculation only considers points that are within a certain distance of each other the Modify max distance between points menu item allows you to define this distance For a closed flow domain you should set this distance to be greater than the maximum distance possible as defined in Equa tion 4 20 p 138 For closed domains you can enable the calculation of the axial distribution index This index compares the point densities of probability associated with the two generation zones along a particular axis by using the integral method of the Deviation function described in The Deviation Function p 149 When the evaluation of this index is enabled you can set the axial direction Note that for a mixer wi
116. iccaxeds ded eaan ia E EEE I AEE ened AE aa e 62 3 11 Definition of the Kinematic Analysis sis sizevt cs sa dendacsevsnta eia csaned sonsthsa Gib reduatuewtiasads tease wbla se det auexentaate 64 3 11 1 Management of Properties iiss caeseageoucaratang uae vasteyaat ade ethedrea ereesauaaa maa eegaade Maadulnstensaangeies 67 3 12 Definition of the Distribution Analysis siiccjsssevecsssouseapessanesdssbestagesatessdesouvaceseonvaadeaaes bares nbvesavaaanesyes 68 4 The Polystat User Ss Manuals cne anii i a a ii aa aa as ieii 73 4l ThetFilet Men s enit hyhi iadnn aes aieia a a aa E a E Ea A tia aE E E e ae ia Ei Rea 75 4 1 1 The Opens O Pt ices cee sve ai Soana AE EAE sac TE TAERAA cua cae seceldaesaieitacdscecheasicnts 76 4 1 2 The Options OptioMse sereen e a e K Ea Ea a A a Aa ARS Ee ERES 76 4 1 3 The Read Data Option siiicar ni a a A A E A Hider E Aaa alain he 77 4 1 4 The Read mesh Option ccccccsssssscccceceesseeesnneeeceeecesseessneeeeeeeceeseeesnaeeeeeeesseeeesnaeeeeeeseeeeees 78 4 1 5 THE RUN OPTION ascen eie dace she EEE EEE EEE sags OE REE E EE E 79 4 1 6 The Draw results Option isorine erei E EE e a a aian 79 4 1 7 The Draw Stats ODON ccsscicciwsveect cade cost E E EE EE AE NEEE E ETE 84 4 1 8 The WRITE Trajectories Option ssessssssesssssesssssesssssresssereesssstessssressssstessseteesssstessseressseseessses 86 4 1 9 The WRITE Slices Option i tsiere iirrainn eenas ea a oia iae reiia ea
117. idential information of ANSYS Inc and its subsidiaries and affiliates 157 The Polystat User s Manual Figure 4 105 The Help Menu Options T2 i polystat ST Fie Properties Trajectories Slices Statistics Help 4 7 Additional Definitions 4 7 1 The Slices A slice is the set of instants of the trajectories that respect some specified condition A condition is for example the time t must be equal to 30 seconds or the position x must be included in the plane 10x 2y 3z 6 0 etc The general way to define a condition is the following for a property P the value of P must be included in a plane this plane is defined by a position and a normal direction To define a slice the following window appears Figure 4 106 The Define a slice Dialog Box xi Select a property coordinates For this property enter a value 1 2 3 enter a direction 4 5 6 Enter the name of this slice new_slice OK Cancel First you select a property on which the condition will apply Second you specify the plane to respect To define it enter the position in the rectangles 1 to 3 and the normal direction in the rectangles 4 to 6 Finally enter the name of the slice If the selected property is a scalar the value to respect is specified in the rectangle 1 the rectangles 2 and 3 are set to zero The normal direction must be set to 1 0 0 Release 15 0 SAS IP Inc All rights reser
118. idential information of ANSYS Inc and its subsidiaries and affiliates 93 The Polystat User s Manual Figure 4 22 Types of Properties that Can Be Created CREATE a new PROPERTY x 4 2 3 1 A This method allows you to calculate the amplitude of a property the velocity for example or more precisely the evolution of the amplitude of a property along all the trajectories After selecting the item A the following window appears Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 94 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 23 The A Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY C Amplitude A S x ILA Il z The property Ais velocities Enter the name of the property C amplitude_c The following data is necessary in this case 1 You select a vectorial or scalar property the data 2 You give a name to the new property the result There cannot be two properties with the same name 3 If you agree with the data click OK the new property will be stored in the list of existing properties If you click Cancel there is no storage of this property For the other methods the process is always the same What changes is the number and the type of the data needed to calculate the new property Now let s define each method
119. in 3 is rotating with the right cam The internal part of the cams are not be meshed Figure 1 Disconnected Subdomains subdomain 1 subdomain 2 subdomain 3 In Polydata during the definition of the flow task we use the sliding mesh technique we define motion of the rotating subdomains Connected boundary conditions are needed between tangential boundaries of fixed and rotating subdomains Moreover we ask for the output of CSV results files In Polyflow we evaluate the transient flow using sliding mesh technique at each time step a CSV file is generated that contains the current flow field In your mesher application define a new mesh where the flow domain is conform and with new subdo mains overlapping the flow domain and corresponding to the moving parts as if we had to define sub domains for the mesh superposition technique The position of the moving parts must correspond to the initial position of the moving parts used for the simulation of the flow field Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 167 Sliding Mesh Technique and Mixing Task Figure 2 Overlapping Subdomains subdomain 1 subdomain 2 subdomain 3 In Polydata we perform a conversion of the csv files into new Polyflow results files onto this new mesh the mesh of the flow domain will remain constant in time at the e
120. ion Points Concentration Deviation If you want to go back to the main window click the Cancel button There exist three kinds of functions the first one are functions based directly on the instants of slices The second one are functions based on other functions Eventually the last one are functions based on a set of trajectories To create a new function click the corresponding item in the list Let s have a look now to every function in detail Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 131 The Polystat User s Manual 4 5 2 1 The Property along a trajectory Function Figure 4 67 The Property along a trajectory Settings for the Create a new function Dialog Box Create a new function See property along trajectory x Property along a trajectory Select a single trajectory All_trajectories Select a property rate _of _dissipation z Select time time v Enter the name of the function new_Function With this function you will see the time evolution of a given property calculated along any trajectory he wants You have to specify which set of trajectories will be used to select the property to see and the time One has also to give a name to the new function If you visualize this function you find on the X axis the time and on the Y axis the property
121. isagglomeration functions in the Statistics menu of the main window you will see a window showing the list of functions that can be calculated on properties derived from properties linked to disagglomeration model Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 152 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu Figure 4 99 Types of New Disagglomeration Functions Create a new function my x lt Select Type gt F lt Select Type gt See disagglomeration along a single trajectory Mean disagglomeration function Probability function Histogram Percentile Smoothing The first three functions are specific to disagglomeration model and are explained in the next sections while the last three functions are identical to general statistics functions see explanations in The Smoothing Function p 142 The Percentile Function p 145 and The Histogram Function p 147 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 153 The Polystat User s Manual 4 5 3 1 The See disagglomeration along a single trajectory Function Figure 4 100 The See disagglomeration along a single trajectory Settings for the Create a new function Dialog Box Create a new function See disagglomeration along a
122. ith 2 components vector with 3 components to specify its value and to give a name to the new property the result Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 101 The Polystat User s Manual Figure 4 30 The k constant Settings in the CREATE a new PROPERTY Dialog Box CT x Ik constant Select the type of the constant K e Scalar C vector 2 comp vector 3comp enter the value of the constant K 1 2 3 Enter the name of the property C constant K 4 2 3 13 A Slice A Slice this method allows you to transport the value of a property along the trajectories you have to select the property to transport to define a slice see The Slices p 158 and to give a name to the new property the result Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 102 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 31 The A Slice Settings in the CREATE a new PROPERTY Dialog Box xi la Slice The value of a property in a slice will be transported unchanged along the trajectories Define a slice Select the property to transport time x Enter the name of the new property Transport_Al The next picture exp
123. ive coordinates exist or if you defined your own coordinates or time The selected property for the COORDINATES will be named COORDINATES and will appear as the first property in the file Useful if you need to read a CSV file as a generation zone see Parameters for the Generation of the Material Points p 49 for additional information You have now the ability to save slices in two different formats The default format is CSV format One saves the selected set of slices in a set of CSV files The CSV file format see the Polyflow User s Manual is a common format for tabulated data that can be read into spreadsheet programs such as Excel Polystat will generate one file per slice their names are built like this prefix _ slice index csv The other format is the FV format One saves the selected set of slices in a single FVP file that can be loaded in FieldView This option is useful if your simulation is transient and if you want a better graphic treatment of your trajectories for steady state simulations see The WRITE Trajectories Option p 86 Polystat will generate one file with the name prefix fvp After the writing the set of slices already written appear in the list named Selected set of slices of the window Save Set of Slices When you have finished click the OK button in this window to go back to the main window Release 15 0 SAS IP Inc All rights reserved Contain
124. l if you want a better graphic treatment of your tra jectories Polystat will generate one file with the name prefix trk Enter now the prefix of the files to generate or select it with the browser click the browser button After the writing the set of trajectories already written appear in the list named Selected set of traject ories of the window Save Set of Trajectories When you have finished click the OK button in this window to go back to the main window Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 87 The Polystat User s Manual 4 1 9 The WRITE Slices Option Figure 4 15 The Save Set of Slices Dialog Box Save Set of Slices a xi m x ea In this window you will select the set of slices you want to save in formatted files First you select one set in the upper list Then you click the gt button The next window appears Figure 4 16 Setting Up the Writing of Slice Data coordinates E fime evrom zl pensasse mower x ea Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 88 of ANSYS Inc and its subsidiaries and affiliates The File Menu You have now the ability to choose the coordinates and time to be used useful in some case where absolute and relat
125. lains the concept defined above Figure 4 32 Transporting a Property from a Slice a slice intersection i of the trajectory and the slice i one trajectory transport of A i to all the other instants of the trajectory value of the property A at the intersection i In general we want to visualize the current value of a property for example the temperature attached to a material point at the current position of this point But for the study of mixing it may be useful to see results differently For example if we study the stretching of a set of particles in a Kenics mixer it may be useful to see at the initial position of the particles their final stretching By this way we can detect zones of the inlet from which the stretching is bad or good Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 103 The Polystat User s Manual 4 2 3 14 Concentration Concentration you can define any concentration field in an initial configuration As the concentration field is constant for a material point no diffusion no chemical reactions we transport the value of the concentration along the trajectories without making any change you have to define the initial config uration and give a name to the new property the result The initial configuration is composed of two things first you have to specify a sli
126. le Settings for the Create a new function Dialog Box Create a new function Segregation Scale x Segregation Scale Select an auto correlation Function new_autocorrelation_Function nd Enter the name of the function new_segregation_scale To calculate the evolution of the segregation scale you need to specify which auto correlation on concentration function to use You have also to give a name to the new function As there exists a list of auto correlation functions one for each slice of a sorted list you will obtain the evolution of the segregation scale along the slices If you visualize this function on the X axis you have the index of the slice and on the Y axis the value of the segregation scale Figure 4 95 The Segregation Scale along the Slices segregation scale index of the slices Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 148 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu 4 5 2 15 The Deviation Function Figure 4 96 The Deviation Settings for the Create a new function Dialog Box Create a new function Deviation x Deviation z Select a function new_distribution_Function Select the optimal Function Jopt_distribution_Function m Select a method integral abs f FLopt 2 C difference of the means C difference of the stand
127. lso you have to choose correctly the first slice the first moving parts position step slice and moving parts step Note that the default values are rarely correct You can save the visualized slices or trajectories using the controls in the Export group box To save a series of individual images select Image Series and click Save In Windows you also have the option of saving an animation select Animation specify the Frame Rate and then click Save The Options group box at the bottom of the Slice tab provides the following options for the graphics window In the Color set group box you can enable the Show option to display the color scale and change the intervals of the scale from linear to logarithmic using the Logarithmic Scale option 82 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates The File Menu The Enter pixel size number entry box allows you to specify the pixel size The Enter pause number entry box allows you to specify the waiting time between two successive drawings displayed when you click Animate In the Logo group box you can specify whether the ANSYS logo is displayed by using the Show Logo option and you can specify whether the color of the logo is black or white by making a selection from the C
128. lyflow result files one particular file for each flow the number of result files to be read and the number ID of the first flow For example in Figure 3 20 The Flow definition Menu for Time Dependent Flow p 46 the flow is defined in 10 files named res 1 res 2 etc until res 10 The prefix is res The first file is res 2 The time step is 1 second between successive flows Note that all these files must exist there cannot be missing result files from the specified sequence If the lifetime of the material points is greater than time_step number_of_res ult_files the succession of velocity fields are used in a loop Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 46 of ANSYS Inc and its subsidiaries and affiliates Definition of the Flow Field Manual selection of result files If Manual selection of result files is selected the menu items change as shown in Figure 3 21 The Flow definition Menu with Manual Selection p 47 Figure 3 21 The Flow definition Menu with Manual Selection Flow definition Continuous transient flow Manual selection of result files No result file defined Upper level menu Piecewise steady flow gt Continuous transient flow Automatic selection of result files gt Manual selection of result files Modify the time step Modify the prefix of the result files Modify the number of result files Modify the first result fil
129. mation about these functions and how to interpret the curves that result from a distribution analysis see Example 116 in the ANSYS Polyflow Examples Manual Note that if the domain is open you cannot evaluate the transfer of points in the direction of slicing If any of the transfer evaluations are enabled you must define the coordinates for the extreme corners of the smallest box that could surround the mixer by using the Modify surrounding box for transfer functions XYZ min and or XYZ max menu items You can click Show advanced options to add menu items to the menu see Figure 3 43 Advanced Options for the Definition of the DISTRIBUTION analysis Menu p 72 These additional menu items allow you to modify some of the numerical parameters involved in the evaluation of the statistical functions Show advanced options Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 71 Mixing Tasks in Polydata Figure 3 43 Advanced Options for the Definition of the DISTRIBUTION analysis Menu Definition of the DISTRIBUTION analysis Reset to default values Upper level menu Modify number of slices 21 Modify starting time 0 0000000E 00 Modify increment between slices 0 5000000E 03 Modify direction of slicing to the future Evaluation of global distribution index YES Modify max distance between points 0 100
130. mentation 1 6 1 Example 50 The Rectangular Cavity This example is the tutorial of the mixing module In this first example we will compare the mixing efficiency of a steady state flow with a piecewise steady flow It is 2D planar and isothermal flow problem We explain in detail how to use Polystat a how to create new properties b how to define a slicing on time and c how to define the statistical functions needed for the comparison of the two cases Moreover we explain how to extract useful information from those statistical curves Keywords piecewise steady flow distributive mixing reorientation process mixing efficiency Polystat statistical analysis 1 6 2 Example 51 Coextrusion of Polymers in a Square Channel In this second example two viscoelastic fluids are injected in a channel They have identical rheological properties but different colors We analyze the axial evolution of the interface between those fluids in the square channel we calculate the axial evolution of the segregation scale in order to quantify the progressive deformations of the interface in the channel Keywords 2D 1 2 planar flow viscoelasticity coextrusion secondary motion Polystat concentration field segregation scale 1 6 3 Example 52 Flat Die In this third example we will analyze a 3D steady state non isothermal flow through the die section of an extruder We are specially interested by the residence time distribution and the mel
131. n 118 of ANSYS Inc and its subsidiaries and affiliates The Trajectories Menu 4 3 The Trajectories Menu Figure 4 49 The Trajectories Menu Options MEPOLYSTAT x File Properties Trajectories Slices Statistics Help SEE MOD DEL trajectories CREATE a new set of trajectories COMBINE sets of trajectories SELECT one single trajectory SEARCH stagnation points The SEE MOD DEL trajectories option allows you to manage the list of existing sets of trajectories With the CREATE a new set of trajectories option you will define a new set as a subset of an existing one based on a selection criterion With the COMBINE sets of trajectories option you will define a new set by selecting trajectories with boolean operations between two existing sets Eventually with the SELECT one single trajectory option you can select a single trajectory from an existing set based on a selection criterion 4 3 1 See the Set of Trajectories After the creation of new properties you have the ability to select the set of trajectories on which you will do some statistical treatment Before any creation of such sets if you select the option SEE MOD DEL trajectories in the Trajectories menu of the main window you will see the list of the existing sets of trajectories Figure 4 50 The See Modify Delete existing sets of trajectories Dialog Box See Modify Delete existing sets of trajec
132. n in the disagglomeration clp file The transfer function for rupture can be seen in the following figure with a rupture rate of 1 Figure 2 19 The Transfer Function for Rupture f size before rupture after rupture 0 0 8S S size Let us briefly enter in the details of implementation of the rupture model We associate to each discretized agglomerate size S an induction time 7 initialized to zero As we progress along the trajectory we evaluate the shear stress g based on Equation 2 41 p 27 we get immediately all the classes where rupture can occur For classes S lt Sg their induction time 7 is reset to zero For the other classes their associated induction time is increased by the local time step At For all classes where the induction time is above the rupture time the rupture occurs and the corresponding induction time is reset to zero also for agglomerates that do not break phenomenon occurring when the rupture rate is not 100 Regarding now classes with S 2 So but with an induction time below the rupture time they can receive fragments but does not break Their mass frequency increases but their induction time T must be modified because we assume that incoming fragments come with their own zero induction time We apply the following rule LG f t At t t At q t At I 2 42 where J is a function of the ratio of mass frequency f of class S at previous time f and current time
133. n of the percentile functions YES Evaluation of the probability functions YES Evaluation of the density of probability functions NO Smoothing of the density of probability functions NO Evaluation of the segregation scale NO Show advanced options The Definition of the KINEMATIC analysis menu allows you to modify the default settings of the kin ematic analysis as described in Using the General Menu of a Mixing Task p 33 in order to customize the preset statistical analysis of the mixing to fit your problem Note that at any time you can revert to the default settings by clicking Reset to default values To begin you can modify the parameters for the slicing of the trajectories including the number of slices the starting position for an open domain the starting time for a closed domain the increment between slices and the direction of slicing For a closed domain the slices represent moments in time such slicing allows you to analyze the time evolution of the stretching distributions in a batch mixer for example For an open domain the slices represent parallel spatial planes that are perpendicular to a coordinate axis which begin at the inflow boundary and proceed to the outflow boundary such slicing allows you to analyze the spatial evolution of the residence time distributions in a static mixer for ex ample The Management of properties menu item allows you to specify which properties are evaluated in the fun
134. nd affiliates The Properties Menu Figure 4 36 The Extract Settings in the CREATE a new PROPERTY Dialog Box xi Extract The property Ais coordinates v Enter the component to extract ji Enter the name of the property C extract 4 2 3 17 Step This method allows you to create a new property C defined as follows in H mode in H mode C ti Amplitude if property A at time ti 2 threshold value C ti 0 if property A at time ti lt threshold value in 1 H mode C ti 0 if property A at time ti threshold value C ti Amplitude if property A at time ti lt threshold value The following parameters must be defined the property A e the H or 1 H mode Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 107 The Polystat User s Manual an amplitude a threshold value the name of the resulting property Figure 4 37 The Step Settings in the CREATE a new PROPERTY Dialog Box xi step The property Ais temperature Enter the amplitude f Enter the threshold value jo Enter the name of the property C step_A 4 2 3 18 Instant Eff This method allows you to create the instantaneous efficiency of mixing based on the rate of dissipation and the rate of stretching As seen in Chapter 2
135. nd of this step we have a set of res files 1 res file per time step compatible with the new mesh In Polydata we define a mixing task based on the new mesh and the new results files In Polyflow we compute the trajectories of a set of material points In Polystat we perform a statistical analysis on these trajectories Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 168 of ANSYS Inc and its subsidiaries and affiliates Bibliography 1 B Alsteens Mathematical Modelling and Simulation of Dispersive Mixing PhD thesis Universit Catholique de Louvain Louvain le Neuve Belgium 2005 2 B Alsteens and V Legat A Model for the Disagglomeration of Carbon Black in Rubber Matrix Proceed ings of the 6th Conference Eurheo Erlangen Germany September 2002 3 R G C Beerkens T van der Heijden and E Muijsenberg Possibilities of Glass Tank Modeling for the Prediction of the Quality of Melting Processes Ceram Eng Sci Proc 14 3 4 139 160 1993 4 V Collin and E Peuvrel Disdier Dispersion Mechanisms of Carbon Black in Elastomers Conference on European Rubber Research Practical Improvement of the Mixing Process Paderborn Germany 2005 5 P V Dankwertz The Definition and Measurement of some Characteristics of Mixtures Applied Science Research 3 279 296 1952 6 J M Ottino The Kinematics of Mixing Stretching
136. ne there is one pair of x y values the format is 14 characters per value with 7 digits after the dot A white space separates the two numbers next lines 0 0000000E 00 0 0000000E 00 0 0000000E 00 0 0000000E 00 4 1 11 The Save Option This option allows you to save in a file with a sav suffix your current Polystat session In the session file are saved all information regarding properties those existing in the mixing files but also the created ones set of trajectories set of slices and of course statistical functions Let us note that this session file does not contain information regarding mesh and result files used only for graphical purpose 4 2 The Properties Menu 4 2 1 Definition Figure 4 18 The Properties Menu Options MEPOLYSTAT x File Properties Trajectories Slices Statistics Help SEE MOD DEL properties CREATE 4 new property NEW Disagglomeration properties Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 91 The Polystat User s Manual With this menu you have the ability to define new properties by combination of the existing ones Along each trajectory we have stored a list of values for a small set of parameters also named properties like explained in the next drawing Figure 4 19 Positions along a Trajectory t2 3 trajectory For each particle f
137. ng Up the Writing of Trajectory Data Exporting All_trajectories fime xl fra Prones or Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 86 of ANSYS Inc and its subsidiaries and affiliates The File Menu You have now the ability to choose the coordinates and time to be used useful in some case where absolute and relative coordinates exist or if you defined your own coordinates or time You can also select the format of writing The default format is CSV format One saves the selected set of trajectories in a set of CSV files The CSV file format see the Polyflow User s Manual is a common format for tabulated data that can be read into spreadsheet programs such as Excel Polystat will generate one file per trajectory their names are built like this prefix _ trajectory index csv The second format is the FV format One saves the selected set of trajectories in a single FVP file that can be loaded in FieldView This option is useful if your simulation is steady state and if you want a better graphic treatment of your trajectories for transient simulations see The WRITE Slices Option p 88 Polystat will generate one file with the name prefix fvp The last format is the CFD Post format One saves the selected set of trajectories in a single TRK file that can be loaded in CFD Post This option is usefu
138. ns of our module are the following Geometrical limitations the domain must not change with time we have to find a frame of reference where the domain occupied by the flow does not vary For example if one wants to analyze mixing in a single screw extruder we assume the screw to be fixed and the barrel to be rotating If there are moving internal parts the mesh superposition technique must be used to simulate their motion For a piecewise steady flow there must be no inertia The flow must always be incompressible There is no void formation in the flow The flow domain is completely filled with the same fluid if we want to mix two or several fluids they must have the same rheological behavior no diffusion nor chem ical reactions between them and no interfacial tension It is thus clear that despite the fact that we calculate a mixing problem the flow calculation is identical to that of a single homogeneous fluid We will examine the time dependence of a set of mixing para meters without making any distinction between the fluids we want to mix However there is no limitation on e the model of fluid generalized Newtonian or visco elastic models are available e the dimensional complexity of the problem 2D planar 2D axisymmetric 2D 1 2 planar 3 components for the velocity field 2D 1 2 axisymmetric swirling flows 3D e the thermal complexity of the problem isothermal or non isothermal simulations are possible
139. ntial information of ANSYS Inc and its subsidiaries and affiliates 77 The Polystat User s Manual It is possible to remove from the list one several or all the files To remove one file from the list select it in the list and then click the Del button To remove all the files click directly on the Del All button In both cases Polystat asks for a confirmation of your choice If there are no file in the list it is impossible to do anything with Polystat of course If the current list seems complete to you click the OK button and you will go back to the main window 4 1 4 The Read mesh Option When you click this option the following window appears Figure 4 7 The Read a mesh file Dialog Box Read a mesh file x Initial mesh frst Browser Formatted C Unformatted M Moving parts motion C Yes No Prefix of result files fres Browser First index 1 Last index fi Formatted C Unformatted OK Cancel In the upper part of the window just enter the name of the mesh file Polyflow mesh format and its format If the file is not on the current directory click the Browser button a file browser appears in order to search the location of the file In the lower part of the window you can enter specific data in order to visualize later the motion of moving parts calculated with the mesh superposition technique in a previous Polyflow run Fir
140. o KINEMATIC analysis in the mixing task menu by clicking the Modify task type menu item repeatedly until the task type is defined as shown in Figure 3 37 A Kinematic Analysis Mixing Task p 64 you can click the Definition of a KINEMATIC analysis menu item to open the menu shown in Figure 3 38 The Definition of the KINEMATIC analysis Menu p 65 Figure 3 37 A Kinematic Analysis Mixing Task MIXING Task 1 Modify task type KINEMATIC analysis Upper level menu Definition of the flow domain Definition of the boundary conditions Definition of the velocity fields Generation of the material points Parameters for the tracking Selection of properties Storage of the results Definition of moving parts Definition of a KINEMATIC analysis Definition of a DISTRIBUTION analysis Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 64 of ANSYS Inc and its subsidiaries and affiliates Definition of the Kinematic Analysis Figure 3 38 The Definition of the KINEMATIC analysis Menu Definition of the KINEMATIC analysis Reset to default values Upper level menu Modify number of slices 21 Modify starting position 0 0000000E 00 0 0000000E 00 0 0000000E 00 Modify increment between slices 0 4500000E 00 Modify direction of slicing 0 0000000E 00 0 0000000E 00 0 1000000E 01 Management of properties Evaluation of the mean and standard deviation functions NO Evaluatio
141. o position the pixels or the segments in the domain and a property to draw Once a property is chosen you can see the range of values for this property in boxes named Min value and Max value If it is a vector field the range is based on the norm of the field You have the ability to change this range of values if needed The Clip to Range option is enabled by default so that areas in which the value is outside of the specified range are left empty If you disable this option values below the Min value will be displayed in the color that represents the lowest value on the color scale and values above the Max value will be displayed in the color that represents the highest value on the color scale In the Slice tab you have to specify the set of slices or trajectories you want to visualize You can also specify a possible link between successive slices and successive positions of moving parts First select a set of slices or a set of trajectories second a first slice or trajectory index of this set If you want to see successive slices or trajectories enter also a positive increment step Then click the button First the first slice or trajectory is drawn in the graphics window Now each time you click the Next button the current slice or trajectory is increased by the step so that we can analyze easily the complete set If we want to avoid to click again and again on the Next b
142. odification of EPSTIM EPSTIM is the tolerance on a time step A time step smaller than EPSTIM is considered to be zero it will be used to stop the iterative Newton Raphson procedure that finds the time step needed to reach the border of the current finite element containing the point 56 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Selection of Properties Figure 3 31 The Trajectory of a Material Point element 1 element 2 successive positions of a material point element 4 Remember that the trajectory of a material point is calculated piece by piece the velocity is integrated in a finite element until the border of this element is reached Then the adjacent element where the calculation is to continue is identified and so on It is therefore important to precisely determine the time step needed to reach the border of the current element containing the material point 3 8 Selection of Properties Clicking the Selection of properties menu item in the mixing task menu opens the menu shown in Figure 3 32 The Selection of properties Menu p 58 Selection of properties Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 57 Mixing Tasks in Polydata Figure 3 32 The Selection of properties Menu
143. of interest In this graph you have a new function y f x for each trajectory Figure 4 68 The Time Evolution of a Property for Two Trajectories property trajectory T1 trajectory T2 time Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 132 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu 4 5 2 2 The Sum Function Figure 4 69 The Sum Settings for the Create a new function Dialog Box Create a new function Sum x Sum Select a set of slices Inew_set_of_slices Select a property time Select velocity field velocities Weighting No veloc Normal everywhere veloc Normal if positive Enter the name of the sum function new _sum OK Cancel To calculate the sum function of a property you need to specify which set of slices will be used and to select a property You have also to give a name to the new function If you want to weight the sum in function of the local velocity don t forget to select the velocity field Additional information on weighting is available in Weighting p 159 You will obtain the evolution of the sum of a property along the slices If you visualize this function you find on the X axis the index of the slice and on the Y axis the property a Figure 4 70 The Evolution of the Sum Function of a Property along the Slices a sum a in
144. of stretching For 2D flows The rate of stretching is equal to Al The rate of dissipation is equal to D Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 58 of ANSYS Inc and its subsidiaries and affiliates Selection of Properties The direction of stretching is the vector m The logarithm of stretching is the natural logarithm of A e For 3D flows The rate of stretching is equal to 7 7 The rate of dissipation is equal to D The direction of stretching is the vector n The logarithm of stretching is the natural logarithm of 7 The following properties are based on the fields stored in the result files needed for tracking pressure velocity and temperature These properties come from the flow calculation If these fields are not in the result files they are initialized to zero The following properties are useful to evaluate the accuracy of the calculation divergence of velocity and determinant of F The following properties are based on fields stored in the result files needed for tracking viscosity mixing index and first eigenvalue of tensor T These properties are postprocessors defined as additional sub tasks to the flow calculation If these fields are not in the result files they are initialized to zero These three fields are especially useful for the analysis of the dispersive mixing The mixing index M in dicates whether locally the
145. of stretching e M t Sin ay M t S py t 5 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 163 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 164 of ANSYS Inc and its subsidiaries and affiliates Appendix C Adaptive Meshing and Mixing Task Example 65 explains the procedure to follow in the case adaptive meshing has been used to evaluate the flow field Indeed two limitations of the mixing module forbid to use meshes whom some parts have been sub divided Firstly in case of transient simulations the mesh of the flow domain can will change with time new elements and new nodes are created deleted Secondly as the mesh is refined locally non conformity appears sub divided elements are adjacent to non sub divided elements As the tracking of material points does not allow such cases we propose the following procedure e In Polydata during the definition of the flow task we ask for the output of CSV results files e In Polyflow we evaluate the transient flow using adaptive meshing at each time step a CSV file is gener ated that contains the current flow field In Polydata we perform a conversion of the CSV files into new Polyflow results files onto a new uniformly refined mesh the mesh of the flow domain will remain constant in time at the
146. olor list Moreover there exists a series of shortcuts that can be used for modifying the graphics window Typically they can be invoked for modifying the appearance of object the axes the background color and the view point They can be easily invoked when the graphics window is active The list of keys is the following e Appearance s displays topological objects in shaded mode w displays topological objects in wireframe e Axes a removes axes from display A adds axes to display Background b sets background color to light blue B sets background color to black W sets background color to white G sets background color to grey e Views x changes the view to be perpendicular to the yz plane from a positive x coordinate repeatedly pressing this key will cause the view to alternate with the view from a negative x coordinate y changes the view to be perpendicular to the xz plane from a positive y coordinate repeatedly pressing this key will cause the view to alternate with the view from a negative y coordinate z changes the view to be perpendicular to the xy plane from a positive z coordinate repeatedly pressing this key will cause the view to alternate with the view from a negative z coordinate Scaling X doubles the scaling of the view in the x dimension Y doubles the scaling of the view in the y dimension Z doubles the scaling of the view in the z dimension Ctrl
147. on If one looks carefully at this definition you must be aware that we evaluate points concentration only at positions where there are points There is no points concentration evaluation in zones of the mixer empty of material points If distributive mixing improves the points concentration deviation should decrease At perfect distribution we should have same points concentration in any location in the cluster and the deviation 6 should be zero Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 24 of ANSYS Inc and its subsidiaries and affiliates Disagglomeration 2 5 Disagglomeration We wish to evaluate the dispersive mixing of solid particles in a fluid matrix in studying the evolution of the size of the agglomerates 2 p 169 1 p 169 Let us consider a set of agglomerates of different sizes at the start of the mixing in an internal mixer In each point of the volume of the mixer we define a little volume Vx called representative volume that contains agglomerates of different sizes as illustrated here below Figure 2 15 A Representative Volume time If the number of agglomerates is large enough in volume Vx this distribution of agglomerates sizes can be summarized in a mass density function f s where is the time and s the size mean dia meter of the agglomerate Its unit is 1 um It is discretized by a piecewise linear curve Figure 2
148. on you can visualize one selected slice trajectory in the flow domain you will see the spatial repartition of any property in this slice trajectory The drawings can be saved in Postscript files With the Draw Stats option you can visualize the calculated statistical functions and save them in Postscript files With the WRITE Trajectories option you select a set of trajectories to save on files in the csv file format see the Polyflow User s Manual for more details With the WRITE Slices option you select a set of slices to save on files in the csv file format see the Polyflow User s Manual for more details With the WRITE Stat option you select statistical functions to save on files in the crv file format see the Polymat User s Manual for more details Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 75 The Polystat User s Manual The Save option allows you to save your current Polystat session Finally to quit the program click the Quit option and confirm your choice 4 1 1 The Open Option This option allows you to read a file with a sav suffix containing a previous Polystat session By this way it is possible to pursue an interrupted session on the same set of mixing files or to apply same statistical treatment on a new set of mixing files in this case the mixing files mu
149. on of solid particles presented in chapter 2 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 112 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 42 Types of New Disagglomeration Properties CREATE a new PROPERTY x lt Select Type gt ation Typical size of agglomerates Fraction of agglomerates of given size Number of agglomerates of given size Of course it is not possible to evaluate size fractions number of agglomerates without having first define a property of type disagglomeration Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 113 The Polystat User s Manual 4 2 4 1 Disagglomeration Figure 4 43 The Disagglomeration Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Disagglomeration g xi Disagglomer ation Select time time Select rate_of_dissipation rate_of dissipation 7 Initial size distribution of agglomerates Erosion and Rupture rate functions Select viscosity viscosity ZJ are included in file Discretization disaggomeration cip browser number of intervals eee max aggretates size bpo o o j max agglomerates size e j Enter the property name disagglomerationl With this property Disagglomeration we
150. on opens the menu shown in Figure 3 20 The Flow definition Menu for Time Dependent Flow p 46 Definition of the velocity fields Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 45 Mixing Tasks in Polydata Figure 3 20 The Flow definition Menu for Time Dependent Flow Flow definition Continuous transient flow Automatic selection of result files time step 0 1000000E 01 the res files are ascii formatted files res files from res 1 to res 10 first res file res 2 Upper level menu Piecewise steady flow gt Continuous transient flow gt Automatic selection of result files Manual selection of result files Modify the time step Modify the prefix of the result files Modify the number of result files Modify the first result file id Switch to binary unformatted result files Modify the list of result files Perform the following steps 1 Select one of the following to specify the kind of flow Piecewise steady flow Continuous transient flow 2 Specify the list of result files that contain the successive flow fields There are two ways to specify this Automatic selection of result files If Automatic selection of result files is selected the default you use the menu items at the bottom of the menu to specify the time step constant between two successive flows the prefix and the format of the Po
151. one is one inflow of the flow domain This zone is a CSV slice induded in the flow domain Modify the intensity of the generation of points You have the following options e You can modify the name of the generation zone this is optional and local to Polydata Modify the name of this generation zone You can make a selection from the following to specify how the zone is generated This zone is all the flow domain The generation zone is the entire flow domain The initial positions of material points are randomly generated in the flow domain This option is well suited for flows in a closed domain This zone is a box included in the flow domain You define a box by its two corners xmin ymin zmin and xmax ymax zmax This box must have a non empty intersection with the flow domain Two modes of generation are available With the first mode the initial positions of the material points are randomly generated in the box With the second mode referred to as the equidistant distribution the material points are initially dis tributed at equal distance d which you specify between neighboring points If the flow domain is 2D the points are distributed at vertex positions of a lattice of identical equilateral triangles see Figure 3 27 Equidistant Distribution of Points in a 2D Box p 52 If the flow domain is 3D the points are distributed at locations corresponding to the centers of close packed equal spheres The generate
152. ong the Slices mean g deviation index of the slices Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 134 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu 4 5 2 4 The Correlation Function Figure 4 73 The Correlation Function Settings for the Create a new function Dialog Box Create a new function Correlation Function x Correlation Function Select a set of trajectories Jall_trajectories Define a first slice and a second slice Select a property For the 1st slice rate_of_stretching Select a property for the 2nd slice rate_of_dissipation Enter the name of the Function new_correlation_Function To analyze a possible correlation between two properties in two slices you have first to select excep tionally a set of trajectories Second you define two slices by clicking successively on the a first slice and a second slice buttons Third you specify the properties associated to each slices Finally you give a name to this new function If you want to visualize this function on the X axis you have the property associated with the first slice and on the Y axis the property associated with the second slice Figure 4 74 Exploring the Correlation Between Properties in Two Slices Field_2 slice_2 Field_1 slice_1 Release 15 0 SAS IP Inc All rights reserved
153. operties A and B you have to select the kind of multiplication and the two properties A and B the data and give a name to the new property the result Figure 4 24 The A B Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY C A B xj m Select the kind of product Scalar vectorial Other The property Ais velocities bd The property B is coordinates Enter the name of the property C _TIMES_ Three cases are possible Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 96 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Scalar product dot product both properties A and B are vectors The result property c is a scalar c ayb aby a3b3 4 1 e Vectorial product cross product both properties A and B are vectors The result property c is a vector c az2b3 a3b2 C a3b ayb3 4 2 C3 ayb gt azb Other product you can multiply one scalar by another scalar the result is a scalar or one vector by a scalar the result is a vector 4 2 3 8 Rotate Rotate this method allows you to rotate a vectorial property you have to select the property A to rotate and the time the data some data specifying the rotation rotation axis angular velocity and to give a name to the new property the result This property
154. or each position stored at time t 0 t1 t2 t5 etc we can store in the mixing files from Polyflow several of the following properties the current time the position coordinates the space integration length of the trajectory from the initial position e the natural logarithm of stretching note that the words stretching and elongation are equivalent In or Inn the direction of stretching 1m or fi the rate of stretching g A or amp 7 7 the rate of dissipation D the pressure the velocity the temperature the determinant of the tensor F the divergence of the velocity Both parameters give information about the accuracy of the calculation as the flow is supposed to be incompressible the determinant of F must remain equal to one and the divergence of the velocity equal to zero e the mixing index the first eigenvalue of tensor T the vorticity 4 2 2 See Properties After the reading of the mixing files if you select the option SEE MOD DEL properties in the Properties menu of the main window you will see the list of the existing properties Figure 4 20 The See Modify Delete existing properties Dialog Box See Modify Delete existing properties x Select a property time coordinates rate_of_stretching rate_of_dissipation logarithm_of_stretching velocities temperature viscosity OK Modify Delete Delete All Release 15 0 SAS IP Inc
155. or example the intersection between the domains 1 and 2 is written Domain1 Domain2 c an intersection of a domain and a boundary for example the intersection between the domain 1 and the boundary 3 is written Domain1 Boundary3 d the perimeter of the previous objects the perimeter of Domain1 Boundary3 is written Domain1 Bound ary3 If you want to visualize a domain of this list click its name Then click the Add button the selected domain will disappear from this list and appear in the list named Domains to draw In this list you can see the set of domains to visualize If you want to change the color of one domain click its name in the list of domains to draw selection its name now appears in the box Selected do main as well as its current color in the box Color This color can be changed by clicking the button J Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 81 The Polystat User s Manual If you don t want to see a domain click its name in the list of the domains to draw selection then click the button Del If you click the button Del All all the domains will disappear If you want to see all the domains then click the button Add All In the Prop tab you have to specify the property you want to see on the slices or along the trajectories Select a coordinate field used t
156. ox for the Spatially Periodic Boundary Parameters p 42 for an example Parameters to connect spatially periodic boundaries Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 41 Mixing Tasks in Polydata Figure 3 13 The Dialog Box for the Spatially Periodic Boundary Parameters Request from Polydata Update the coefficient A 1 1 Old value 0 New value 1 Note When you choose the exit boundary connected to the entry boundary of a spatially peri odic flow the boundary type of the exit boundary is automatically updated It is not ne cessary to define it again 3 4 2 Specification of a Stopping Plane You can define stopping planes so that the calculation is stopped when the material point reaches a defined spacial plane The purpose of adding stopping planes is to save CPU time when you are only interested in the mixing in a fraction of the domain Another situation in which you might want to use stopping planes is for 2 5D planar flows where the mesh is 2D but the velocity field has 3 components Vz is perpendicular to the mesh For such flows there are two systems of coordinates the relative coordinates for the trajectory in the plane of the mesh and the absolute coordinates in the real flow domain 3D A stopping plane allows you to continue to calculate the trajectory until
157. pair of random points with a relative distance r and with the same concentration Figure 2 7 The Correlation Coefficient for Concentration over Distance R r t distance The previous figure shows a typical graph of R as a function of r Let be such that R t 0 when r we cannot predict whether the members of the pair have the same concentration or not The segregation scale S t is defined as ei S t sires 2 27 0 It is easy to understand that S is a measure of the size of the regions of homogeneous concentration S t decreases when mixing improves Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 18 of ANSYS Inc and its subsidiaries and affiliates Homogenization While quantities such as A e and e are proper to the flow irrespective of the initial concentration the segregation scale S t is a quantity that is affected by the flow but depends strongly upon the initial distribution of concentration Note Dankwertz defined another parameter the intensity of segregation oi t I hn 2 28 K oz 0 Because of our assumptions the concentration attached to any material point remains con stant with time this parameter does not change with time and will not be calculated 2 3 2 Numerical Method We distribute uniformly but randomly a set of material points in all the flow domain at time t 0 To each point is assoc
158. r a given shear stress o The Equation 2 40 p 27 becomes b Sn 2 41 i 0 amin All agglomerates with a size greater than S can break for a shear stress o In our model we assume that the rupture time is a constant the default value is set to 0 1 seconds in the disagglomeration clp file and that only a fraction of all particles of a given size will break if rupture criteria are met Indeed we can understand easily that all particles of a given size do not have same cohesion or same impregnation level infiltration of the matrix inside the agglomerate due to diffusion That is why we can specify the rupture rate the fraction of particles that break when rupture criteria are met however the default value is set to 1 in the disagglomeration clp file meaning that all agglom erates break Eventually we have to model how a set of agglomerates of size will break in numerous fragments of various sizes We assume here that the volumes of the fragments follow a Gaussian distribution between 0 and the parent agglomerate volume In average the parent agglomerates of size S are cut into two fragments of equal volume leading to a mean size of 0 85 Of course once again this behavior can be Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 27 The Mixing Theory modified by changing the corresponding functio
159. r level menu Add a new generation zone Modify a generation zone Delete a generation zone Enter a time interval Tmin Tmax The following are definitions for the terms used in the menu shown in Figure 3 25 The Generation of material points Menu with Multiple Zones p 50 e The index is the identification number of the zone For example in the previous figure the second zone that is ID 2 is the flow domain The intensity identifies the relative number of points that are generated in the various zones The previous figure shows two defined zones every time 4 points are generated in the second zone flow domain only 1 point is generated in the first zone a box in the flow domain You can add a new generation zone by using the menu shown in Figure 3 26 The Generation Zone 1 Menu p 51 opens Add a new generation zone Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 50 of ANSYS Inc and its subsidiaries and affiliates Parameters for the Generation of the Material Points Figure 3 26 The Generation Zone 1 Menu Generation Zone 1 Current choice NAME INTENSITY TOPO OBJECT Generation Zone 1 1 All the flow domain E a Upper level menu Modify the name of this generation zone gt This zone is all the flow domain This zone is a box induded in the flow domain This zone is all the inflows of the flow domain This zone is a topo object This z
160. r the tracking menu item in the mixing task menu opens the menu shown in Figure 3 29 The Parameters for the tracking Menu p 55 Parameters for the tracking Figure 3 29 The Parameters for the tracking Menu Parameters for the tracking Current setup TIMAX the lifetime of the material points VNORMX the maximum velocity in the flow field 1 0000000E 04 1 0000000E 00 Upper level menu Modification of TIMAX Modification of VNORMX Options You must modify the following two parameters Modification of TIMAX TIMAX is the lifetime in seconds of the material points Their trajectories will be calculated until that time is reached In order to lower the CPU time of your simulation do not use unnecessarily large Modification of VNORMX VNORMX is the maximum velocity magnitude in the flow field and is used to detect stagnation points in the flow A stagnation point is a point that has a negligible velocity in comparison with the max imum velocity By default negligible is defined as one millionth of the maximum velocity You can modify some numerical parameters acting on the accuracy of the integration scheme by clicking Options and using the menu shown in Figure 3 30 The Parameters for the tracking Menu p 56 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 55 Mixing Tasks in Polydata Options
161. rary if the capillary number is much lower than the critical capillary number then the interfacial stress dominates and the drop is only slightly deformed In general mixing begins with a distributive step drops are deformed passively followed by a dis persive one drops break up into droplets and finally by the distribution of the droplets in the flow In the paragraphs below we concentrate mainly on distributive mixing Kinematic Parameters p 12 and Homogenization p 17 and on distribution of material points into the flow domain Distributive Mixing p 20 However dispersive mixing can also be analyzed you can add postprocessors to the flow calculation a the mixing index or flow number indicates if the flow is locally a rigid motion mixing index 0 a shear flow mixing index 0 5 or in extension mixing index 1 b the eigen values of the extra stress tensor T with this field we have access to the main component of the stress which stretches and breaks the drops Once the flow and those postprocessors are determined we can calculate the evolution of the mixing index and the main stress along the trajectories of material points With those data we can evaluate the fraction of the matter experiencing a given stress value and then evaluate the efficiency of the dispersive mixing We call also dispersive mixing the process where solid particles are broken by erosion or rupture in smaller parts due to st
162. resses applied on them by the matrix carbon black or silica in a rubber matrix for example A new model has been developed by B Alsteens and V Legat 2 p 169 to simulate this process of disagglomeration thanks to them this model is already available in Polystat The description of the model can be found in Disagglomeration p 25 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 11 The Mixing Theory 2 2 Kinematic Parameters A first way to measure mixing is to quantify the capacity of the flow to deform matter and to generate interface In the theory presented below we neglect interfacial forces the interface is passive and no break up into droplets can occur For 2D flows the interface between fluids is a line in order to avoid to calculate the evolution of this interface a very complex and impossible task to perform because of the exponential growth of the interface we prefer to calculate the stretching of infinitesimal vectors attached to a large number of material points distributed in all the flow domain As the points move in the flow the vectors are stretched The stretching and the rate of stretching of these vectors are interesting properties that vary from place to place in the flow domain and that evolve with time Finally we perform a statistical analysis of the set of results in order to have a global ov
163. rrelation function to calculate 2 4 Distributive Mixing 2 4 1 Distribution Index Suppose we want to distribute a cluster of particles initially concentrated in a small box see figure below We suppose that the particles do not affect the flow field and that there is no interaction between them Their number is supposed to be large Figure 2 9 Distributing Particles from a Small Box Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 20 of ANSYS Inc and its subsidiaries and affiliates Distributive Mixing As a function of time the flow will distribute this set of points It is important to define a distribution index 6 to quantify this process Its definition is based on the work performed by Manas Zloczower and her colleagues 9 p 169 10 p 169 At time we have N points distributed more or less in the flow domain Option 1 These points can form N N 1 2 pairs of points For each pair of point x and X j we calculate their inter distance dij x x The maximum inter distance will be of the order of the diameter of the mixer Option 2 For each point x we search its closest neighbor Xj and we store their inter distance d x x We have thus only N distances With this method of calculation we are able to better discriminate distributive capacities of similar mixers The maximum inter distance will be of the order of NV N wh
164. rts Clicking the Definition of moving parts menu item in the mixing task menu opens the menu shown in Figure 3 35 The Define moving parts Menu p 63 Definition of moving parts Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 62 of ANSYS Inc and its subsidiaries and affiliates Definition of Moving Parts Figure 3 35 The Define moving parts Menu Define moving parts Deletion of a moving part Upper level menu Creation of a new moving part With this menu you specify the moving parts if any overlapping the flow domain This data is used to remove particles that are randomly generated in the flow domain and also included in a given moving part Important You must specify the moving parts in the same order as in the previous flow task First click the Creation of a new moving part menu item to open the menu shown in Figure 3 36 The moving part 1 Menu p 63 Creation of a new moving part Figure 3 36 The moving part 1 Menu moving part 1 Upper level menu Definition of the moving part domain Modification of title For this moving part you specify its domain and its title Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 63 Mixing Tasks in Polydata 3 11 Definition of the Kinematic Analysis If you have set the task type t
165. rved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 155 The Polystat User s Manual Figure 4 103 The Mean Disagglomeration Function for a Slice f size for a given slice agglomerates size f size agglomerates size With this function and the standard deviation treatment selected one evaluates for each slice a standard deviation disagglomeration function based on the disagglomeration property known at each point included in the slice n ae 2 of s idx LF point i J si V point icslice idx 4 34 ni 0 With this function and the standard deviation for values below the mean treatment selected one evaluates for each slice another standard deviation disagglomeration function based on the disagglom eration property known at each point included in the slice 4 2 ite ly tee ote ee ae of s idx f s pointi f s idx VY point i cslice idx ni 0 4 35 with f s pointi f s idx With this function and the standard deviation for values above the mean treatment selected one evaluates for each slice a last standard deviation disagglomeration function based on the disagglom eration property known at each point included in the slice n a 2 2r 1 of s idx D f s pointi f s idx V point i cslice idx n i 0 4 36 with f s point i T s idx Release 15 0 SAS IP Inc All rights res
166. rved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 159 The Polystat User s Manual a slicei Lajo Lo J J oq slice i a 2 o Lo J ji where the index j indicates the J instant of slice 7 a is the value of a at instant j and jis the weight at instant jJ J To calculate the probability function P a we sort the set of pairs a 0 witha Sa 44 forj 1 to nbi where nbi is the number of instants in slice 7 Finally the probability to find a value a below a J nbi P a lt a L wgl Ox k 1 k 1 The value of the weight is if no weighting Oj e if weighting everywhere Oj if weighting when vje is positive where v e is the dot product of the velocity at instant 7 by the normal of the slice 7 J J S vje if vje gt 0 0 otherwise 4 39 4 40 4 41 4 42 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 160 of ANSYS Inc and its subsidiaries and affiliates Appendix A The Simulation of the Distribution Let s suppose the flow to be 3D steady state in a closed domain To perform the analysis of the distribution the following steps are necessary Lis 2 We calculate the flow velocity and pressure We calculate in the mixing task 1 the real distribution We suppose the material points to
167. s Reset to default values Upper level menu Modify number of slices 21 Modify starting position 0 0000000E 00 0 0000000E 00 0 0000000E 00 Modify increment between slices 0 4500000E 00 Modify direction of slicing 0 0000000E 00 0 0000000E 00 0 1000000E 01 Management of properties Evaluation of the mean and standard deviation functions NO Evaluation of the percentile functions YES Evaluation of the probability functions YES Evaluation of the density of probability functions YES Smoothing of the density of probability functions YES Evaluation of the segregation scale YES Hide advanced options Enable automatic settings Modify slicing type function of space Modify slicing coordinates standard coord Modify number of values for probability fct 100 Modify number of values for density fct 50 Modify number of values for smoothed fct 50 Modify number of values for auto corr fct 100 Modify number of percentiles 3 Modify list of percentiles 1 00000E 01 5 00000E 01 9 00000E 01 If you want to make major modifications to the slicing method you can disable the automatic settings This action will make menu items available that allow you to modify the slicing type and the slicing coordinates Note that such modifications are not recommended unless you have extensive expertise in the subtleties of Polyflow The remaining menu items allow you to modify the number of values used to represen
168. s you should begin by clicking the boundary that is the entry of the flow domain in the Boundary conditions menu Next select Entry boundary in a spatially periodic flow in the menu that opens Entry boundary in a spatially periodic flow The dialog box shown in Figure 3 10 Dialog Box for the Entry Boundary p 40 will then open Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 39 Mixing Tasks in Polydata Figure 3 10 Dialog Box for the Entry Boundary Request from Polydata Update the number of crosses Old value 0 New value J Here you will enter the number of loops that the material points can do in the flow domain the cal culation of a trajectory is stopped when the material point reaches the exit after this number or if the lifetime of this particle has expired After you click OK in the previous dialog box the menu in Figure 3 11 The Corresponding boundary Menu p 40 will open where you can select the exit boundary that is connected with the entry Figure 3 11 The Corresponding boundary Menu Corresponding boundary ia Upper level menu Select in the following list which boundary is connected to Boundary 1 Boundary 1 current entry Boundary 2 Boundary 3 Boundary 4 Boundary 5 Boundary 6 Finally you will return to the previous menu which has changed as shown
169. s proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 89 The Polystat User s Manual 4 1 10 The WRITE Stat Option Figure 4 17 The Save Statistical Results Dialog Box Save Statistical Results x Select a function P log_stretching perc log_streting Es Selected functions In this window you will select the functions you want to save in formatted files First you select one function in the upper list Then you click the gt button A file browser appears enter now the file name or the prefix of the filename to generate After the writing the functions already written appear in the lower list When you have finished click the OK button in order to go back to the main window Depending on the type of function to write Polystat can generate one or several files for example if you select a probability function there exists a function of the type y f x for each slice and Polystat will generate a file for each one The name of these files are built like this you specify the prefix of the files and Polystat add an index if necessary and a suffix depending on the kind of result you want to save see a property along a trajectory prefix _see trajectory index crv correlation between two fields prefix _corr crv segregation scale prefix _seg crv deviation from an ideal distribution prefix _dev crv sum of a property prefix _sum crv me
170. s subsidiaries and affiliates Definition of the Boundary Conditions Figure 3 8 Inflow and Outflow Boundary Conditions stopped trajectory outflow Spatially periodic flow options The remaining options are specific to spatially periodic flows Remember that a problem is spatially periodic if there exists an elementary module on which the flow field can be calculated and where the velocity field in the inflow section is equal exactly to the velocity field in the outflow section The flow field is repeated infinitely in space With this kind of flow when a material point reaches the outflow the calculation can continue by injecting this particle back into the inflow the particle will travel several times through the same module There are therefore two systems of coordinates the first is relative to the coordinates in the module the second is absolute and is attached to the real trajectory in the real infinitely repeated domain See Figure 3 9 Relative and Absolute Trajectories p 39 for an illustration Figure 3 9 Relative and Absolute Trajectories flow domain module relative trajectory absolute trajectory In order to calculate trajectories in spatially periodic flows the inflow must be connected with the outflow Note that due to a limitation of the program the geometrical dimensions and the mesh distribution in the inflow and the outflow must be equal To define the spatially connected boundarie
171. s that represent the probability function You have also to give a name to the new function As there exists a list of probability functions one for each slice of a sorted list you will obtain a density of probability function for each slice S Fas _ P 4 5 4 24 da If you visualize this function for a given slice you find on the X axis the property values the property has been chosen earlier when the probability function has been defined and on the Y axis the density of probability Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 144 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu Figure 4 89 The Density of Probability Function of a Property for a Slice density of probability for slice S property a In order to avoid wiggles it is a good practice to smooth the probability function before the calculation of the density of probability And in general it is also necessary to smooth the density of probability function before visualization 4 5 2 12 The Percentile Function Figure 4 90 The Percentile Settings for the Create a new function Dialog Box Create a new function Percentiles x Percentile hd List of percentiles Del All Del zenter new value gt Ba Select a distribution Function Function Enter the name of the function new_percentile OK Canc
172. single trajectory x See disagglomeration along a single trajectory Select a single trajectory single_trajectory x Select a disagglomeration property disagglomeration gt Select time or displacement lime o Storage every Dt or DI fo Enter the name of the Function new _function With this function you will see the time or displacement evolution of the disagglomeration property calculated along any trajectory he wants you have to specify which single trajectory will be used to select the disagglomeration property to see and the time or displacement you must also specify the time or space interval where the disagglom eration property will be stored Eventually the use gives a name to the new function If you visualize this function you find on the X axis the size of agglomerates and on the Y axis the density of probability to find agglomerates of a given size In this graph you have a new function y f x for each time or displacement step Figure 4 101 Disagglomeration Functions for Two Time Steps f size t2 gt t1 agglomerates size Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 154 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu 4 5 3 2 The Mean disagglomeration function Figure 4 102 The Mean disagglomeration function Settings for the Create a new function Dialo
173. size of agglomerates xi Typical size of agglomerates The Disaglomeration property is disagglomeration calculation of mean size v Warning calculation does not take into account aggregates Enter the name of the property typical_sizel With this function it is possible to evaluate the minimum mean or maximum size of agglomerates without taking into account the aggregates To do that we evaluate a new distribution function ranged between the maximum size of aggregates a and the maximum size of agglomerates b oe b Inrange a b f s t f s t Ar s t ds 4 13 Otherwise f s t 0 The mean size of agglomerates is the following b D Mean size t aly ajea s t ds 4 14 a a where b ly s t ds 1 4 15 a The minimum and maximum sizes are evaluated as shown in the picture below They corresponds in fact to the 5 percentile and os percentile of the f function Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 115 The Polystat User s Manual Figure 4 45 Minimum and Maximum Sizes a min max b size 4 2 4 3 Fraction of agglomerates of given size Figure 4 46 The Fraction of agglomerates of given size Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Fraction of agglomerates of given size Fraction of agglomerates of given size
174. st answer yes to the question Moving parts motion Next enter the prefix of the result files Polyflow result files in which are stored the successive flow fields enter also the number N of those files in the last index input area Finally specify the format The result file names will be built like this prefix id where id ranges from 1 first index to n last index Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 78 of ANSYS Inc and its subsidiaries and affiliates The File Menu The OK button is used to close the window and read the files The Cancel button closes the window without any reading The Reset button reinitializes the internal data structure containing the mesh and the successive positions of the moving parts Note Be careful not to make any mistake in the format of the files because a wrong answer can interrupt your session definitively Note It is absolutely necessary to read a mesh before any visualization of your results 4 1 5 The Run Option By selecting the Run option you want to actually calculate all the objects you defined elsewhere properties trajectories But it takes time That is why firstly you will have to confirm your choice Figure 4 8 The RUN Dialog Box MM i amp Do you really want to perform the calculation on the current mixing database
175. st have same name same type ASCII or binary and with the same number of mixing files See The Save Option p 91 for additional information on the list of objects saved or not saved in the Polystat session file 4 1 2 The Options Option Figure 4 4 The Options Dialog Box Options hl ie Maximum number of instants per trajectory 1000 Method of intersection between trajectory and slice Find all intersections SS OK Cancel Default This option allows you to specify some parameters The maximum number of instants per trajectory default value 1000 If a trajectory has more instants than this maximum we interpolate the properties along the trajectories in order to limit the instants to that number It may be useful to increase this number if one knows that some trajectories are very long and have much more instants stored in the mixing file The method of intersection between a trajectory and a slice by default we compute all the intersections This may cause some bias in the statistical functions if one performs a slicing in a space direction and if there are backflows In that case it is mandatory to use the Find first intersection method Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 76 of ANSYS Inc and its subsidiaries and affiliates The File Menu 4 1 3 The Read Data Option Figure 4 5 The Read Mixing files Dialog Bo
176. successive positions of the particle in the real space we use x Lx 8 1 4 L x x 6 The algorithm is the following 1 initialization a find an element E containing the initial position x b find the local coordinates amp of x in this element E 2 while no problem amp no required stop a we integrate Equation 1 3 p 6 until we cross a boundary of the element E b if a boundary of E is crossed we adapt the time step of integration in such a way that the position is on the boundary Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 6 of ANSYS Inc and its subsidiaries and affiliates Examples c if we are on a boundary of E in x i we search the element adjacent to E where to continue the integration let s note this element E ii find the local coordinates in element E of the current position x iii go to step 2 a We explained this because some important numerical parameters used by this algorithm must be defined by you in Polydata see Chapter 3 Parameters for the tracking for example we must define the coefficient NBELEM that indicates the mean number of integration steps necessary to cross an ele ment 1 6 Examples Here below one can find a short description of the Polyflow examples devoted to mixing Refer to the documents corresponding to those examples for their full description in the Polyflow docu
177. t property You can Remove a property from the list if there is a property that is not useful for your analysis You can also Add a property to the list Besides the properties selected by default as shown in Fig ure 3 40 The Management of properties for the KINEMATIC analysis Menu p 67 you can add the following e space_integration e direction_of_stretching pressure temperature e divergence_of_velocity Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 67 Mixing Tasks in Polydata e determinant_of_tensor_F e viscosity mixing_index e first_eigenv_of_tensor_T melting_index concentration e min shear_rate e min first_eigenv_of_tensor_T max first_eigenv_of_tensor_T min mixing_index e max mixing_index Note that in order to be evaluated the following properties must exist in the Polyflow result file s used to perform the computation of the material points trajectories velocities pressure temperature viscosity mixing_index and first_eigenv_of_tensor_T Other properties are derived from these For example the melting index is a function of time viscosity and temperature therefore these last three properties must exist in the Polyflow result file s if you want to evaluate the melting index Still other properties are evaluated during the computation of the trajectories such as the
178. t the slicing For the optimal distribution Jopt_set_of_slices x Select a coordinate field coordinates x Sample size method Automatic evaluation x Radius of Sample jo Enter filename containing center of zones feones crv Browser Enter the name of the function new_distribution_in_zones OK Cancel Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 139 The Polystat User s Manual To calculate the evolution of the distribution of material points initially concentrated in a box you need to specify two set of slices the first one contains points coming from the real distribution the second one contains points coming from an optimal distribution Next you must select a coordinate property used to evaluate in which zones are included the points Eventually you must specify in an ASCII file the coordinates of the center of the zones The format of this file is as follows on each line there are the three coordinates X Y Z of one center If the flow domain is 2D the Z is set to zero 0 0000000e 00 0 0000000e 00 0 0000000e 00 0 0000000e 00 0 0000000e 00 0 0000000e 00 0 0000000e 00 0 0000000e 00 0 0000000e 00 With this function we will obtain for each slice e for each zone the evolution of the deviation of the real distribution compared to optimal distribution If one wants to save the
179. t the various curves as well as the number and values of the percentiles Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 66 of ANSYS Inc and its subsidiaries and affiliates Definition of the Kinematic Analysis 3 11 1 Management of Properties Clicking the Management of properties menu item in the Definition of the KINEMATIC analysis menu opens the menu shown in Figure 3 40 The Management of properties for the KINEMATIC analysis Menu p 67 Management of properties Figure 3 40 The Management of properties for the KINEMATIC analysis Menu Management of properties for the KINEMATIC analysis Define zones where concentration 1 Remove a property from the list Upper level menu Add a property to the list Evaluate time stats Evaluate rate_of_stretching Evaluate rate_of_dissipation Evaluate Jlogarithm_of_stretching stats Evaluate velocities Evaluate instantaneous_efficiency stats Evaluate time_averaged_efficiency stats Evaluate shear_rate stats Evaluate max shear_rate stats This menu shows the list of properties that will be evaluated as part of the kinematic analysis The ad dition of the phrase stats indicates that for that property statistical functions will be evaluated for each slice otherwise the properties are just evaluated along the trajectories To add or remove stats simply click the menu item associated with tha
180. ter the creation of new sets of trajectories you must select one set on which you will perform some statistical treatment Before this step you have first to define a list of slices that cut the trajectories This list is necessary to analyze the evolution of the mixing from one slice to the next from the beginning of the process to its end By default no set of slices exists Based on an existing set of trajectories it is easy to define a set of slices Three possibilities exist e the automatic creation of a list of slices e the manual definition of each slice one by one e the subslicing which is the generation of a new list of slices based on each slice of an other list Remember that a trajectory is a set of instants ordered in time Each slice will contain a set of instants that are the intersections of the slice and the trajectories If the intersection of a trajectory and a slice is not a stored instant we create a new instant by interpolation with the previous and the next instants that surround the intersection as explained below Figure 4 56 Interpolating a New Instant slice previous O stored instants of the trajectory E intersection of the trajectory and the slice new instant created by interpolation Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 124 of ANSYS Inc and its subsidiaries and affiliates The Slices Menu 4 4 1 See the Set of
181. tes 23 The Mixing Theory Figure 2 14 Points Within a Cluster box radius As a function of time the flow will distribute this set of points At time t we have N points distributed more or less in the flow domain For each point x we search its neighbors x that stay at a distance smaller than a sample radius Depending on the dimensionality dim of the cluster of points at time we can evaluate the local points concentration x Fordim 1 x Nx 2radius si H ae Fordim 2 x Ne zradius a6 For dim 3 x Nx reais where Nx is the number of points of the cluster around x at a distance smaller than the radius On the other side at perfect distribution we expect that the points are distributed equally in all the flow domain we should find everywhere the same number of points per unit volume Then we can easily determine the perfect points concentration y it corresponds to the number of points divided by the volume of the flow domain For other situations the reader can easily adapt the method of evaluation of the perfect points concentration as explained in The Points Concentration Deviation Function p 151 Eventually the standard deviation p of points concentration at time is evaluated as follows 2 37 where N is the number of points in the cluster at time 7 the x correspond to the location of points i at time and is the perfect points concentrati
182. th moving parts it is recommended that you set the axis to be the axis of rotation of the moving parts You can evaluate the transfer of the points of the second generation zone as they move from one half of the domain to the other This information is particularly useful for 3D batch mixers with closed flow domains You can divide the domain into halves relative to the coordinate axes the positive x direction corresponds to the direction from left to right the negative y direction corresponds to the direction from the upper half to the lower half and the positive z direction corresponds to the direction from back to front For each direction two functions are calculated Each function represents a fraction with respect to time or axial position depending on whether you have a closed or open domain respectively For example the fractions associated with the Evaluation of the Left Right Transfer X dir menu item include the left left fraction that is the fraction of the points that originate in the left half of the domain and still remain there and the left right fraction that is the fraction of the points that originate in the left half of the domain and move to the right half Because the fluid is incompressible and the mixer is fully filled only the left left and left right fractions are calculated because the right right and right left fractions are complementary this statement holds true for all three transfer directions For more infor
183. the flow domain is closed e the other determines the distance distribution only for pairs of points that are close neighbors The max imum distance measured for a closed flow domain will be Max distance 2 V n 4 20 where V is the volume of the flow domain and n the number of material points The search of neighboring points will be done only for distance between 0 and a value you specified It is recom mended that you choose a value greater than the maximum distance evaluated above In all cases it is recommended that you have V n identical if you want to compare different flow domains or set ups on a same flow domain You will obtain a distribution function for each slice of the set Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 138 of ANSYS Inc and its subsidiaries and affiliates The Statistics Menu If you visualize this function for a given slice you find on the X axis the distance and on the Y axis the distribution function Figure 4 80 A Distribution Function of Distances Between Material Points f d distance between pairs of points 4 5 2 8 The Distribution in zones Function Figure 4 81 The Distribution in zones Settings for the Create a new function Dialog Box Create a new function Distribution in zones Distribution in zones Select the slicing For the current distribution new_set_of_slices Selec
184. the property C shear_rate 4 2 3 21 Melting Index This method allows you to create the melting index based on the viscosity 7 and the temperature T The concept of a melting index has been introduced by Beerkens et al 3 p 169 to characterize the quality of the glass melting in a furnace The melting index evolves along a given trajectory starting at point X as a function of temperature viscosity and time For 2D and 3D flows it is defined as t m X t ae 4 12 on P T This property is accessible only if temperature and viscosity have been calculated along the trajectories In the creation window the default values for the properties are correct This window appears like this Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 111 The Polystat User s Manual Figure 4 41 The Melting Index Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Melting Index xj Melting Index Temperature temperature v Viscosity viscosity m Time time z Enter the name of the property C melting_index 4 2 4 Disagglomeration Properties Select the NEW Disagglomeration properties option in the Properties menu In the specialized window that opens it is possible to create properties directly related to the model of disagglomerati
185. the sum of the intensities Important If some of the generation zones are defined as boxes with equidistant distribution it is difficult to estimate the exact number of points that will eventually be generated in those zones That is why an approximation an upper bound of the number of points that will be generated is provided to you when defining the box generation zone This number can be used to appropriately define the intensity of generation the number of result files and the maximum number of trajectories per file as described in the previous note Note that the management of topo objects is done in the Generation of material points menu Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 53 Mixing Tasks in Polydata Create a new topo object You can Create a new topo object by clicking this menu item and using the menu shown in Fig ure 3 28 The Add topo objects Menu p 54 Figure 3 28 The Add topo objects Menu Add topo objects Upper level menu List of existing topo objects Subdomain 1 Boundary 1 Subdomain 1 Boundary 2 Subdomain 1 Boundary 3 Subdomain 1 Boundary 4 Subdomain 1 Boundary 5 Subdomain 1 Boundary 6 Subdomain 1 To define a topo object first specify two objects by making a selection from the list and then clicking the appropriate button for example
186. this efficiency is defined as e jin 2D flows _ Tate of stretching e O 2 D rate of dissipation in 3D flows ly rate of stretching 4 8 a a TS ATT UE D rate of dissipation This property is accessible only if the rate of stretching and the rate of dissipation have been calculated along the trajectories In the creation window the default values for the properties are correct This window appears like this Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 108 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 38 The Instant Eff Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Instantaneous Efficiency of Mixing x Instant EFF Rate of stretching rate_of_stretching Rate of dissipation rate_of_dissipation z Enter the name of the property C instant _eff 4 2 3 19 Time Aver Eff This method allows you to create the time averaged efficiency of mixing based on the time the rate of dissipation and the rate of stretching As seen in Chapter 2 this efficiency is defined as in 2D flows t e sled 4 9 in 3D flows t e F feya 4 10 This property is accessible only if the time the rate of stretching and the rate of dissipation have been calculated along the trajectories In the creation window the default values for th
187. tial positions can be randomly generated or distributed in an equidistant manner inside each generation zone Generation of the material points Specify the numerical parameters necessary for the precision of the trajectory calculation in the flow as described in Parameters for the Tracking p 55 Parameters for the tracking You have the option of selecting the properties such as mixing parameters or pressure temperature etc you want to calculate along the trajectories as described in Selection of Properties p 57 Selection of properties Specify how to store the results of the simulation as described in Parameters for the Storage of the Results p 61 You will use the created result files to make a global analysis of the mixing with Polystat Storage of the results You have the option of defining moving parts that overlap the flow domain as described in Definition of Moving Parts p 62 This step can be necessary if the mesh superposition technique has been used previously to calculate the flow field Definition of moving parts After you have defined the mandatory information needed for the mixing task that is performed steps 1 5 and 7 you can enable and customize a preset statistical analysis These analyses generate typical sets of statistical results and allow you to proceed directly to postprocessing in ANSYS Poly stat after the solver has completed the calculation The two preset statistical analyses that ar
188. ting character istics of the matter leaving the die Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 7 Introduction Keywords 3D steady state flow non isothermal flat die Polystat residence time distribution melting index preset statistical analysis 1 6 4 Example 46 Periodic Flow Through a Kenics Mixer In this fourth example we analyze the distributive mixing generated by a Kenics mixer As the complete flow domain is too large to be used we reduce the flow calculation to a single mixing element of the mixer We assume the flow field to be spatially periodic We analyze the generation of striations through successive mixing sections and the efficiency of the process Keywords 3D steady state flow periodic boundary conditions static mixer Polystat distributive mixing preset statistical analysis 1 6 5 Example 37 Mixer 2 D In this fifth example we simulate the 2D transient flow produced by the rigid rotation of two cams in a batch mixer Moreover we evaluate the dispersive mixing capability of the mixer Forces and torque along the cams are also evaluated Keywords mesh superposition technique batch mixer transient flow problem forces and torque dis persive mixing mixing index eigen values of the stress tensor shear rate vorticity Polystat preset statistical analysis 1 6 6 Example 65 Adaptive
189. ting laws warranties disclaimers limitations of liability and remedies and other provisions The software products and documentation may be used disclosed transferred or copied only in accordance with the terms and conditions of that software license agreement ANSYS Inc is certified to ISO 9001 2008 U S Government Rights For U S Government users except as specifically granted by the ANSYS Inc software license agreement the use duplication or disclosure by the United States Government is subject to restrictions stated in the ANSYS Inc software license agreement and FAR 12 212 for non DOD licenses Third Party Software See the legal information in the product help files for the complete Legal Notice for ANSYS proprietary software and third party software If you are unable to access the Legal Notice please contact ANSYS Inc Published in the U S A Table of Contents Using This Mari Wall cossisiisnsayeeets suvex inkatenennieaivass sudnthy ded a E A uncd naaeany ped eel dr ei a T N ee aa vii LeThe Gontents of THIS Manuals sessie nieo nren desea tea acecedsddeeecdeasactedchdesousubedteedadsoosddevseneeteddenvbeenss vii 2 The Contents of the ANSYS Polyflow Manalsis c ccdicciteyacrasvenccnensaicisana cosets oer ussecanitauhdh eteusevGveaniaeeeay vii 3 Contacting Technical SUpport cceeeesseeccecceceeeesnsneeeeeeceesseesenseeeeeeeeseseesnnaeeeeeeeseseeeseaeeeeeeseseeenenaaes vii 1 IMRFOCUCUION 2 25 2
190. tion within ANSYS Workbench The Polymat User s Guide explains how to use the ANSYS Polymat module for material property evaluation e The Polystat User s Guide explains how to set up a MIXING task in ANSYS Polydata and how to use the ANSYS Polystat module for statistical postprocessing of results The GAMBIT manuals teach you how to use the GAMBIT preprocessor for geometry creation and mesh generation The CFD Post User s Guide explains how to use CFD Post to examine your results The ANSYS Polyflow Examples Manual provides overviews of solutions to a variety of problem types For details on how to access the ANSYS Polyflow manuals see ANSYS Polyflow Documentation in the separate Polyflow User s Guide 3 Contacting Technical Support Technical Support for ANSYS Inc products is provided either by ANSYS Inc directly or by one of our certified ANSYS Support Providers Please check with the ANSYS Support Coordinator ASC at your company to determine who provides support for your company or go to www ansys com and select Contact ANSYS gt Contacts and Locations Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates vii Using This Manual If your support is provided by ANSYS Inc directly Technical Support can be accessed quickly and effi ciently from the ANSYS Customer Portal which is available from the ANSYS Websit
191. to derivate and the time the data and to give a name to the new property the result Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 99 The Polystat User s Manual Figure 4 28 The Derivate Settings in the CREATE a new PROPERTY Dialog Box xi Derivate The property Ais logarithm_of_stretching Si The TIME is time x Enter the name of the property C derivate_A 4 2 3 11 Integrate Integrate this method allows you to integrate a property along the trajectories in time you have to select the property A to integrate and the time the data and to give a name to the new property the result Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 100 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu Figure 4 29 The Integrate Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY C Integrate A i x integrate The property is fiogarithm_of_stretching The TIME is time x Enter the name of the property C integrate_A 4 2 3 12 k constant k constant this method allows you to create a property that is constant along all the trajectories You have to select the type of the constant scalar vector w
192. tories that have always the determinant of F between 99 and 1 01 we reject inaccurate trajectories A trajectory is selected if along this one the property has never values in the specified interval A trajectory is selected if along this one the property has one time at least a value in the specified interval For example we can select the trajectories that cross a specified box in the flow domain If the selected property is a scalar the interval is defined in the rectangles 1 and 4 the others are set to zero 4 3 3 The COMBINE sets of trajectories Option If we select this option the following window appears Figure 4 52 The set C set A lt operator gt set B Dialog Box set C set A lt operator gt set B x The set Ais all_trajectories z The set Bis interrupted_trajectories M the operator is Union Intersection C Difference Minus Enter the name of the set C A_op_B OK Cancel With this option we can combine logically two sets of trajectories A and B in order to create a new set C For example in the window above we selected the sets All_trajectories and Interrupted_trajectories and the Intersection operator That means that the new set C will contain the trajectories that belong to the two sets A and B If we select the Union operator the new set C will contain all the trajectories of the two sets A and B there is no duplication of the traj
193. tories x Select a set of trajectories All_trajectories set_mixing_5S mix_ 4 OK Modify Delete Delete All In this list you can see three different types of sets of trajectories The All_trajectories set contains all the trajectories read in the mixing files The Interrupted_trajectories set contains all the trajectories the calculations of which have been inter rupted for different possible numerical problems and read in the mixing files Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 119 The Polystat User s Manual The set_from_filename sets contain the trajectories stored in the mixing file filename We cannot modify or delete those sets If we remove a mixing file in the window Read Data the list of existing sets is adjusted automatically If new sets of trajectories have been created it is possible to modify or to remove them from the list If you want to modify some data of a set select it in the list and then click the Modify button The window that served for the creation of that set will appear then modify some data If you want to store the modified data click OK Otherwise click Cancel To remove one set from the list select it in the list and then click the Delete button To remove all the created sets click directly on the Delete All button In the t
194. u then want to track material points across all the sections you would begin by defining a first tracking through the first flow section Next with the generated mixing files perform a slicing in Polystat at the exit of the first flow domain and save the slice in a CSV file You can then define a second mixing task in Polydata on the second flow section the generation zone will be the CSV file you created in Polystat In this way you will continue the tracking in the second flow section In such a case it is useful to click No in the question dialog box in order to keep the history of deformation and stretching throughout the whole flow domain e You can modify the intensity of the generation of points in order to generate a higher frequency of points in one zone in comparison with the others Clicking this menu item opens a dialog box which you can use to modify the intensity factor of the created zone A higher intensity value results in a higher frequency of point generation in that zone Modify the intensity of the generation of points Important If some of the generation zones are based on CSV files you must set the intensity of each zone equal to the number of material points starting from that zone Then be sure to set the number of result files and the maximum number of trajectories per file in the Storage of the results menu as described in Parameters for the Storage of the Results p 61 such that their product is equal to
195. undary conditions menu item in the mixing task menu opens the menu shown in Figure 3 6 The Boundary conditions Menu p 37 Definition of the boundary conditions Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 36 of ANSYS Inc and its subsidiaries and affiliates Definition of the Boundary Conditions Figure 3 6 The Boundary conditions Menu Boundary conditions fa Upper level menu Select one by one the following boundaries Boundary 1 is non penetrable Boundary 2 is non penetrable Boundary 3 is non penetrable Boundary 4 is non penetrable Boundary 5 is non penetrable Boundary 6 is non penetrable m C Add modify or remove stopping planes With this menu you can do two things you can select each boundary and specify the type as necessary such as wall entry or exit as described in Specification of the Boundary Type p 37 and you can use the button next to the Add modify or remove stopping planes label to add stopping planes as described in Specification of a Stopping Plane p 42 3 4 1 Specification of the Boundary Type Selecting a boundary from the list in the Boundary conditions menu and clicking the Modify button opens a menu like the one in Figure 3 7 The Boundary condition along Boundary 1 Menu p 38 Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS
196. ure 1 2 Example of a Piecewise Steady Flow state 1 DT1 sec state 2 DT2 sec fluid fluid In this case two velocity fields alternate The first state lasts for DT1 seconds the upper wall moves to the right while the other walls are at rest The second state lasts for DT2 seconds the lower wall moves to the right while the other walls are at rest With such a flow we can obtain a far better mixing than with a steady state flow In the second case the more general the flow changes continuously between t1 and t2 the flow at time will be a linear combination of flow tl and flow t2 flow t 1 a flow tl aflow t2 1 1 where t2 tl and tl lt lt t2 t24tl Spatially periodic flows the flow is spatially periodic if there exists an elementary module on which we can calculate the flow field and where the velocity field in the inflow section is equal exactly to the velocity field in the outflow section A spatially periodic flow is necessarily a flow through an open domain Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 3 Introduction Figure 1 3 Example of a Spatially Periodic Flow flow domain module inflow The flow field is repeated infinitely in space the flow field in the next module is the same as in the current module and in the previous module and so on The limitatio
197. utton click the Animate button all will be automatic In that case do not forget to define the pause in seconds in the Options group box which corresponds to the waiting time between two successive drawings Once the animation is started the button Animate changes to Stop if selected the animation is interrupted If the mesh superposition technique has been used in Polyflow to calculate a flow with moving parts it is possible to see the location of those moving parts at different time steps To do so select yes to the question Set into motion Then select the first position of the moving parts corres ponding to the first slice of your set of slices Enter also an increment step for the successive po sitions of the moving parts you want to look at Then click the button First the first slice and the first position of the moving parts are drawn in the graphics window Now each time you click the next button the current slice is increased by the slice step and the current moving parts position is increased by the moving parts step The motion of the moving parts is now linked to the suc cessive slices of the current set You have the responsibility to define the correct set of slices cor responding to the motion of the moving parts you have to define an automatic slicing on time with an increment corresponding to the time step existing between two successive positions of the moving parts A
198. v t y ll w a DA JL Fluid Dynamics Structural Mechanics Electromagnetics Systems and Multiphysics a ANSYS Polystat User s Guide ANSYS Inc Release 15 0 Southpointe November 2013 275 Technology Drive Canonsburg PA 15317 ANSYS Inc is ansysinfo ansys com certified to ISO http www ansys com 9001 2008 T 724 746 3304 F 724 514 9494 Copyright and Trademark Information 2013 SAS IP Inc All rights reserved Unauthorized use distribution or duplication is prohibited ANSYS ANSYS Workbench Ansoft AUTODYN EKM Engineering Knowledge Manager CFX FLUENT HFSS and any and all ANSYS Inc brand product service and feature names logos and slogans are registered trademarks or trademarks of ANSYS Inc or its subsidiaries in the United States or other countries ICEM CFD is a trademark used by ANSYS Inc under license CFX is a trademark of Sony Corporation in Japan All other brand product service and feature names or trademarks are the property of their respective owners Disclaimer Notice THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFID ENTIAL AND PROPRIETARY PRODUCTS OF ANSYS INC ITS SUBSIDIARIES OR LICENSORS The software products and documentation are furnished by ANSYS Inc its subsidiaries or affiliates under a software license agreement that contains provisions concerning non disclosure copying length and nature of use compliance with expor
199. ve is called subslicing you defined a list of slices on another list of slices To define a subslicing you select first an existing set of slices Next you define your slicing data as for an automatic slicing What differs is the number of subslices for each slice and if the subslicing is periodic or not Let s define N the number of subslices by slice After subslicing the subslice indices will be for the slice 1 the subslices are numbered from 1 to N e for the slice 2 the subslices are numbered from N 1 to 2N Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 127 The Polystat User s Manual e for the slice 3 the subslices are numbered from 2N 1 to 3N etc If we select the Periodic option we gather the instants in the following way for a given slice the in stants included in the series of intervals named i are gathered in the subslice Figure 4 61 Periodic Subslicing number of sub slices slice 3 time interval of sub slice 2 time If we do not select the Periodic option we gather the instants in the following way for a given slice the instants included in the interval named i are gathered in the subslice Figure 4 62 Nonperiodic Subslicing number of sub slices slice 3 time interval of sub slice 2 time 4 5 The Statistics Menu After the creation of properties set o
200. ved Contains proprietary and confidential information 158 of ANSYS Inc and its subsidiaries and affiliates Additional Definitions 4 7 2 The Zones A zone is an interval of values for a specified property For example for a vector property as the position we have to define the two extreme corners of a box Figure 4 107 Defining a Position Zone xmax ymax zmax xmin ymin zmin If the property is a scalar we define the minimum and the maximum values of the interval To define a zone the following window appears Figure 4 108 The Define a zone Dialog Box xi Select a property coordinates enter the minimum value 1 2 3 the maximum value 4 5 6 Enter the name of this zone Jnew_zone OK Cancel First you select a property on which we define the zone Second you specify the interval enter the minimum value in the rectangles 1 to 3 and the maximum value in the rectangles 4 to 6 Finally enter the name of the zone If the selected property is a scalar the minimum value is specified in the rectangle 1 and the maximum value is specified in the rectangle 4 the rectangles 2 3 5 and 6 are set to zero 4 7 3 Weighting The slicing must been defined on a coordinate field in order to weight a property by the velocity The general formula for the sum the mean and the standard deviation are L slice ajo 4 38 a J Release 15 0 SAS IP Inc All rights rese
201. w we have to use Polystat in order to treat and or visualize those results to obtain a global overview of the mixing process in the current flow To perform such statistical treatment several steps must be performed in a specific order the main menu of Polystat appears as follows Note that the Help option summarizes this analysis process and gives information on the way to contact us if necessary telephone Email and fax number Figure 4 1 The Polystat Window MEPOLYSTAT x File Properties Trajectories Slices Statistics Help The major steps are the following 1 In the menu File we read the results generated by Polyflow the data necessary to Polystat 2 In the menu Properties we can ask the program to calculate new parameters evolving along the tra jectories For example we can define any concentration field or a new mixing index These new para meters are always a combination of existing parameters those calculated in Polyflow and stored in the mixing result files We will see later the different possibilities accessible to you 3 In the menu Trajectories we have the ability to select a subset of trajectories on which we will perform the statistical treatment For example we can eliminate all the trajectories that terminated abnormally on a wall for example We will see later the different possibilities accessible to you 4 Inthe menu Slices we determine the way to slice the selected trajectories For
202. will know the time evolution of the mass fraction distribution for a set of agglomerates of various sizes As explained in chapter 2 the mechanisms of erosion and rupture depends on time shear rate and viscosity of the matrix Those properties must be defined first Let us note that the Polyflow solver evaluates the rate of dissipation D instead of the shear rate which is in fact equal to 2D Next you must specify the number of classes of agglomerates he wants to evaluate He must specify the size of the largest agglomerates and the maximum size of the aggregates particles that cannot be broken in smallest pieces anymore Next you must specify in which CLIPS file are defined transfer function for erosion and rupture mechanisms the kinetics of erosion and rupture function of shear rate viscosity size of agglomerates and of course the initial distribution function of agglomerates size As this file is interpreted during the calculation it is very easy to modify those functions as the understanding of the disagglomeration improves or to test new ideas Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 114 of ANSYS Inc and its subsidiaries and affiliates The Properties Menu 4 2 4 2 Typical size of agglomerates Figure 4 44 The Typical size of agglomerates Settings in the CREATE a new PROPERTY Dialog Box CREATE a new PROPERTY Typical
203. wing parameters must be defined a the property A of interest b if we want the minimum or the maximum of the property c the name of the resulting property d if we want the absolute ex treme value of property P along the whole trajectory option 0 gt t_end or a time evolving extreme value of property P option 0 gt t option 0 gt t_end for a given trajectory T min max A at any time min max A ti for ti t_o to t_end option 0 gt t for a given trajectory T min max A at time t min max A ti for ti t_o to t Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 105 The Polystat User s Manual Figure 4 35 The Min Max Settings in the CREATE a new PROPERTY Dialog Box xi Min l Max The property Ais viscosity 7 0 gt t_end O gt t Max C MIN Enter the name of the property C max_ 4 2 3 16 Extract This method allows you to create a new scalar property by extracting a component of a vectorial property A The following parameters must be defined a the vectorial property A b the component x y or z to extract 1 x 2 y 3 z c the name of the resulting property Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 106 of ANSYS Inc and its subsidiaries a
204. wo cases Polystat asks for a confirmation of your choice Based on existing sets of trajectories it is easy to define new sets Four possibilities exist e the creation of a new set based on a condition to respect the combination of two sets to create a new one the selection of a single trajectory based on a criterion of proximity e the selection of trajectories of stagnant points 4 3 2 The CREATE a new set of trajectories Option By clicking this option in the main window the following window appears Figure 4 51 The Add a new set of trajectories Dialog Box Add a new set of trajectories q x Select a set of trajectories Jall_trajectories Select a property time ka Enter the minimum value 1 2 3 the maximum value 4 5 6 To construct this new set we will keep the trajectories that have always the values of the selected property between the minimum and the maximum Enter the name of the new set Jnew_set OK Cancel Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confidential information 120 of ANSYS Inc and its subsidiaries and affiliates The Trajectories Menu With this method we will select a subset of trajectories that respect a condition Three kinds of condition are possible A trajectory is selected if along this one the property has always values in the specified interval For ex ample we can select the trajec
205. x Read Mixing files created with Polyflow x List of files to read This window shows the list of mixing files already read If you want to add several mixing files to the list in a single command click the Add all button the following window will appear Figure 4 6 The Read mixing files Dialog Box Read mixing files xi Prefix of mixing files fixing Browser First index fi Last index 10 Formatted C Unformatted OK Cancel In this window you have to specify the prefix of the mixing files their first and last indexes and their format If the mixing files are not in the current directory click the Browser button to search their location with a specific file browser The names of the mixing files are built like this prefix 000i where i is the current index Once those data are entered click the OK button to close the window and ac tually read the mixing files Click Cancel to close the window without any reading If you want to add just one file click the Add button a file browser will appear in which you have to select the file It is not possible to read the same file twice When a file has been selected a new window appears asking if this file is formatted or not don t make any mistake because a wrong answer can unfortunately interrupt definitively your session Release 15 0 SAS IP Inc All rights reserved Contains proprietary and confide

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