VorDyn2.0 user manual - Boccelli Engineering
Contents
1. e state matrix export lateral file Lateral State Matrix dat 7 Mesh Esporting you may find useful to create a vortex mesh with VorDyn who knows you can export it a file called Generated Mesh dat is created and it contains the position of control points where flow tangency condition is imposed the components of normal vectors for every control point the area of every panel and the position of the vertices of the vortex on a certain panel Note that the area of the panels is the area of the surface surrounded by the vortex for every panel except for those placed at the trailing edge Since trailing edge rings go to infinity the area of the lifting surface panel must be calculated in a different and fictitious way Every upper case variable causes a call to a certain MODULE called MOD ULE UpperCaseVariableName The MODULE checks the lower case vari ables and if they are set to 1 executes the operations 3 Geometry Construction You can create the geometry by editing the file Geometry m A certain lifting surface can be composed by many segments with different sweep angle dihedral root inclination trailing edge flaps ailerons or not different number of mesh vortices in the spanwise direction and variable pitch A examples of wing geometry may look like this or this kind of car aileron surfs Nc is the number of panels chordwise It is the same for every lifting surface section but of co2. not necessarily a planar surface finding the normal vector of a skew quadrilateral is mostly a question of inventing the normal vectors Several methods are available I use the cross product of the quadrilateral diagonals This also allows me to compute an approximated panel surface The points i to v are implemented in the function surf_geometry_function The vectors tmesh xcv tmesh ycv zcv are filled with coordinates of the control points in global axis 15 tmesh xnv ynv znv are the xyz normals vector components of the normal vectors in the x y and z direction Clearly numel tmesh xnv numel tmesh xcv Vortices are stored in the tmesh xvortic tmesh yvortic tmesh zvortic matrices the size of them is 4 x numel tmesh xcv Every column is a vortex ring the four rows are the coordinates of every vortex corner IMPORTANT the vortex must be percurred in a certain direction al ways the same for every section of every lifting surface of any wing tail or the result will be a complete mess Induced Velocity Calculation For every control point the velocity induced by the vortices is calcu lated using the well known Biot Savart law There are mainly two ways to do that matricial operation of for cycles I ve implemented the sec ond one which is reeeeeally slower I implemented also the first but it was not working properly and unfortunately my spare time is almost over The induced veloc
3. 42 0 006 0 0212 Cra 4 41 5 21 5 019 Cpa 0 182 0 17 0 2409 Cina 0 0409 1 55 1 358 CyB 0 35 0 47 0 287 C 8 0 103 0 008 0 0233 CB 0 0583 0 197 0 1159 Cyp 0 0925 1 87 0 1146 Cip 0 483 0 484 0 2567 Crp 0 035 0 846 0 0278 Cyr 0 175 0 091 0 2652 Cir 0 1 0 03 0 0129 Chr 0 086 0 038 0 0269 a convention is clearly different And now a figure of the Skyhawk geometry created Vortex rings are displayed in green 22 I m afraid something s wrong in my code VorDyn is under GPL licence which isn t pasted here but should be provided along with the code or should not be difficult to be found on the web 10 Thanks to Special thanks to Politecnico di Milano that inter alia provided some of the electric current that powered my laptop Thanks to all the scientists and engineers who discovered and built the aerodynamic knowledge we have today 23
4. VorDyn2 0 user manual Stefano Boccelli May 2014 Fast presentation Hello to everyone My name is Stefano Boccelli and I m a student of Aerospace actually Aeronautical Engineering in Politecnico di Mi lano Italy This version of my Vortex Lattice code for MATLAB is still a spare time project nothing extremely serious Willing to im prove the previous version VorDyn1 0 I ve made some changes the biggest of whom is the possibility of making much more arbitrary ge ometries not bounded anymore to a standard aircraft configuration One can simulate an aircraft as well as an automotive aileron or a paraglider while in the limits of linear aerodynamics You can calcu late aerodynamic forces and stability derivatives with VorDyn2 and more As the previous version this software is surely buggy and odd writ ten but I tried to make it as simple as possible and also to comment strange lines of code There s plenty of software that does the same my softer does and does it better Tornado for example is one of them There are also commercial codes etcetera The goal of my script is supposed to be providing a fast access to geometry modification in a hands on code style Hope you enjoy Stefano Contents 8 9 Introduction to the software Functionalities Geometry Construction Sila Winslet oe bo Oped de pi dei Eg Ea pd Op TU we CA 3 3 Vertical Tail and vertical surfaces Performing an Analysis Program Structu
5. an do that by simply compiling the inversion vector 11 3 2 Winglets If you want to create a vertical surface you make a segment with a 90 dihedral The limitations that were present in VorDyn1 0 have now been removed you can choose the dihedral you like and playing with epsilon0 you can give the desired inclination to your surface 3 3 Vertical Tail and vertical surfaces As stated in the Winglets section to create a vertical surface you just have to set to 90 the dihedral SYM flag will create a symmetrical surface behind the XZ plane The Geometry m file is an input for other scripts like Geometry Creator m but just let it do the job for you 12 Performing an Analysis Create the Geometry by editing the default Geometry m file or if you already have call your Geometry file Geometry m and replace the original Set inertial properties in the Various Properties m file Tell the program what to do set the flags in the What To Do m file Do you want to perform some aerodynamic force analysis Then set the upper case variable ON 1 Now which one of the available analysis do you want to perform Set the lower case variable You can perform more simulations at once Don t you like the plots because they are out of range Open the General Settings m file and set axisvalues as you like Oh I forgot set the initial conditions Edit the Initial Conditions m file Set Ving rho alpha0 and beta be
6. d Diagram a plot of the magnitude and the phase of the states involved in a certain mode ATTENTION The results are clearly strongly affected by the inertial properties to be set in the Various Geometry m file and by the CG position static margin Also I m not that sure of having well compiled matrices and all so you better be careful with my results 20 9 Validation I shall now compare the results of my code with other data First of all a naif and very crude validation have been made comparing the lift computed on a finite wing geometry to the theoretical lift generated by a wing immerged into bidimensional current L pV7SC_ Cr is 2ra as stated by the small perturbances theory Creating four wings with increasing aspect ratios I ver ified that the relative error between numerical Lift and theoretical 2D Lift decreased Of course a real validation would have passed through Prandtl finite wing model 24 T T T 22r 7 error o 0 5 10 15 20 25 30 35 40 45 50 Wing Aspect Ratio The software Tornado is the result of a Magistral Thesis work In one of the final chapters of the thesis stability derivatives of a Cessna 172 Skyhawk are calculated and compared with experimental data I add here my results calculated like Tornado in a reference point located at 31 9 of the wing mean aerodynamic chord 21 Derivative Experimental Tornado VorDyn Cr 0 386 0 386 0 3812 Cp 0 0
7. eed Aerodynamics by Joseph Katz and Allen Plotkin It s basically a text about numerical panel meth ods for solving the incompressible flow and it s a kind of holy textbook for aerodynamics students Ok let s talk about VorDyn As you can see the created geometry is not thick at all as a matter of fact the code is a lifting surface method You can create a thick wing by creating two surfaces one which is the top and one the bottom of the wing As explained in Geometry paragraph you can tell VorDyn whether your surface is an airfoil midline or top or bottom by setting the surfs airfkind vector properly The implemented method consists in some steps 1 Preparing the geometry i dividing the surface into panels ii finding the quarter chord line and the 3 4 line of every panel iii placing a vortex ring of unknown intensity I on the panels start ing from the quarter chord line of a panel and ending to the quarter chord of the next panel in chordwise direction The vortex of the trailing edge panels is a horseshow vortex a ring vortex with an arm placed at infinity running in the direction of the stream I set this lone arm at 300 chords away iv locating control points one for each panel placed in the middle of the 3 4 chord line As a result the control point will be situated in the middle of the vortex ring v creating normal vectors and surfaces Unfortunately a quadrilat eral one of our panels is
8. emented LOW SUBSONIC CODE If you like you can do it by hand The code can return some different outputs see functionalities para graph mainly e aerodynamic forces e control surfaces deflection e stability derivatives e mesh exporting e longitudinal and lateral modes e etc Which geometries can I create process You can create as many lifting surfaces as you want flat or curved in the x direction to follow a NACA 4 digit airfoil You can create an aircraft just like VorDyn1 0 would do and much more To create a bent wing one can put one aside another a number of wing sections In the same way a paraglide can be drawn Every Lifting surface can be composed by more segments each one with control surfaces or trailing edge flaps I will refer to a wing like entity as a lifting surface and to the components that create the lifting surface as lifting surface segments or sections Before proceeding a couple of examples of geometries Vortex Rings on a paraglider Vortex Rings on a weird geometry 2 Functionalities To tell the program what to do you set 1 or 0 flags in the What To Do m file See the Performing an Analisys Paragraph Let s now see what the code can do by analizing the variables in the What To Do file Open it and you will find the following 1 Geometry Various calculated data is stored as many more vari ables in the structure surfs e surfaces_and_aerodynamic chords the s
9. ity calculation is performed by the Vortex Lattice INDUCEDVELOCITYFUNCTION function The function internally imports the geometry and returns the MAT matrix Only the constant term is now needed to solve the linear system and find the circulations MAT I ff I don t know how I could forget to include a cutoff factor in VorDyn1 0 Anyway it have been implemented now and has a value of 10 That means that induced velocities bigger than this one are cut off to zero since they probably come from a vortex overlapping a control point and thus induce an infinite not physical velocity To modify the cutoff term take a look at the Vortex Lattice INDUCEDVELOCITY FUNCTION m file The Constant Term The constant term is where the main variables come in ff is basically the dot product of the free stream velocity and the normal vector of every panel By modifying the 5 and a angles we can calculate the results in that a 6 condition We can find the stability derivatives by solving two times the main linear system the first time with a certain ff and the second one with a constant term ff evaluated with incremented angles 16 4 Forces and Moments From T we can easily obtain aerodynamic loads thanks to the Kutta Joukowski theorem Moments are obtained multiplying the forces by the distance from the center of mass of the vehicle Lift Drag and Sideforce are calculated as geometrical projection of the total Force in
10. re Vortex Lattice Method Stability Derivatives 7 1 Angle Derivatives cosa E en A a eh E la 7 2 Roll Pitch Yaw Rate Derivatives 7 3 amp Derivatives eae Geet od a a ter Be chord ea hed AO a 7 4 Adimensionalization sog ek li SR S Gab Bobs Sa Hh Sd 7 5 Adiustments srt ie Ste ee ae ERA e Flight Dynamics modes Validation 10 Thanks to 13 14 15 18 18 18 18 18 18 20 21 23 1 Introduction to the software VorDyn is basically a vortex lattice method actually a vortex ring method that can evaluate aerodynamic properties of a given geometry The reference conditions are stored in the Initial_Conditions m file Why the name VorDyn Because my idea was originally to implement a vortex lattice method to obtain stability derivatives and solve the aircraft dynamical system Then since it always takes longer than you expected I ran out of time and havn t tested the dynamical part very much This is a Vortex Lattice method which gives a solution of the potential flow that s why the initial linearization condition must be in the linear aerodynamics field the method won t take stall or any kind of flow separation into account Also boundary layer can t be seen from the potential flow point of view Aeromodelists must take care because the lower the Reynolds number i e small wing chord and low velocity the bigger the boundary layer A Prandtl Glauert correction is still not impl
11. rement of few degrees 1 in my case in the MODULE Stability Derivatives but angular rate derivatives are a little more touchy A nice way to set them would be starting from the stream velocity composing a velocity triangle and setting 18 the angular rate increment so that tan 1 dt the angular rate causing the incidence of the tail to vary of 1 19 8 Flight Dynamics modes The flying aircraft is subject to different aerodynamic forces as a first ap proximation some are almost proportional to an angular position like angle of attack or sideslip we can see them as stiffnesses others to the velocity and in the end we have inertial terms As a result the aircraft is a dynamical system subject to well known flight modes Phugoid short period and the third mode are linked to the longitudinal plane while the roll mode the spiral mode and the dutch roll mode are latero directional modes Knowing the damping ratio and the natural frequency of those modes is important to ensure proper flight qualities ensuring the modes are stable or not too much unstable is a fundamental requirement for succesful and safe flight By filling a couple of matrices with proper stability derivatives VorDyn accepts the Hypothesis of small perturbations and studies separately the longitudinal and the latero directional planes solving two separated linear systems Eigenvalues are plotted on the Gauss plane and Eigenvectors on the Ar gan
12. ta is the sideslip angle positive when the aircraft velocity has a component in the positive Y body direction Run VorDyn2 m And possibly yell Go Go Gadget VorDyn 13 5 Program Structure Everything starts from VorDyn2 m which imports the geometry Geome try m file and the flight conditions Initial Conditions m file then the geom etry is created Geoemtry_Creator calls some functions surf_geometry_function for every single lifting surface segment collecting data and building big vec tors and matrices Data related to a single surface is stored in the surfs struct while total data is resumed and collected in the struct tmesh the name standing for total mesh Those are the infos needed for plotting mesh exporting or further processing Then a sequence of 1f statements starts checking the flags set in the What_To_Do m file When a flag is found to be 1 a MODULE is called I call MODULE a script that collects the op eration of the same type For example the MODULE_Aerodynamic_Forces contains the following operations e print on a file the total forces e print on a file the forces generated by every lifting surface e print forces generated by every single panel How do I activate those sub tasks By setting the relative sub flag in the What_To_Do file In the MODULEs you can find some more if statements to check that 14 6 Vortex Lattice Method First of all I strongly suggest the book Low Sp
13. urface value of every lifting surface segment is calculated and printed on a file Mean aerodynamic chords are calculated too The file is called Sur faces and Chords dat e plot normal vectors geometry and panel normal vectors are plotted 2 Aerodynamic Forces computed aerodynamic forces are stored in the structure forces e plot cp vectors plots geometry and the A Pressure Coefficient acting on every panel Cp top Cp bottom e total_aerodynamic_forces writes on the file Calculated_Total_ Aerodynamic_Forces dat the aerodynamic forces Lift Drag Side force Fx Fy Fz Mx My Mz generated by the whole configura tion e component_aerodynamic_forces the same but separating ev ery lifting surface contribute Filename Calculated_ Compo nent Aerodynamic Forces dat e panel aerodynamic forces writes on a file the forces Fx Fy Fz generated by every single panel and also the relative Coefficient of Pressure Cp The panels coordinates are printed too 3 Component Aerodynamics e neutral point computation calculates the position of the neu tral point by evaluating the pitching moment in two different ref erence points e aerodynamic centers lifting derivatives computes the aero dynamic center of every lifting surface and the derivatives La and Ma of stand alone surfaces The position of aerodynamic centers is plotted and printed on a file called Aerodynamic Centers dat while a derivatives are a
14. urse it can differ from one lifting surface to another surfs coord are the coordinates of the leading edge of the root section ordinated in a raw or column vector xA yA zA surfs SYM if you set this flag to one the lifting surface will be mirrored around the XZ plane otherwise you will have only the right wing surfs airfoil allows you to choose the airfoil you wish to use It s possible only to choose NACA 4 digit airfoils If you want to load your coordinates or modify it you should start from the Geometry_Creation m file that calls the function surf_geometry_function Making a flat surface is pretty easy you choose a symmetric airfoil lika NACA0012 airfoil surfs airfkind is a vector of two elements Let s start with the first element The way VorDyn2 operates is through lifting surfaces which have no thickness for definition BUT you can create a thick surface if you like just keep reading When you create a lifting surface you also create the variable surfs airfkind which is intended to tell VorDyn what kind of surface you want 0 stands for mid line 1 for upper surface 2 for lower surface Let s say you choosed a NACA4415 airfoil if you choose 0 the function naca4digit will return you the mid line of the NACA4415 if you choosed 1 the top and if 2 the bottom To create a thick airfoil you simply create the top and the bottom as two different lifting surfaces Second element of the vector
15. vailable as internal variables stored in the structure stab_der 4 Stability Derivatives Stability derivatives are stored in the structure stab_der e longitudinal derivatives longitudinal stability derivatives are evaluated around the linearization condition set in the Initial Conditions file The output is written to a file called Stabil ity Derivatives Longitudinal dat e lateral derivatives the same as for lateral derivatives 5 Longitudinal Modes A dynamical system simplified to take only longitudinal variations into account is created and solved Inertial properties are stored in the Various Properties m file Be careful because I haven t tested this module much ATTENTION the derivatives Cra and Ca are not supported any more since their expression in VorDyn1 0 was analitical and based on the classical aircraft geometry assumptions Results of dynamical simulation are not that sure e eigenvalue plot longitudinal plots the 4 eigenvalues of the lon gitudinal plane e eigenvectors plot longitudinal plots two of the longitudinal plane eigenvectors on an Argand diagram e state matrix export longitudinal you may be interested in the state matrix for various purposes like studying an automatic control system for example The matrix is written on a file named Longitudinal State Matrix dat 6 Lateral Modes the same as Longitudinal Modes e eigenvalue plot lateral e eigenvectors plot lateral
16. wind axis 17 7 Stability Derivatives 7 1 Angle Derivatives Calculating an estimation of a and derivatives is pretty easy the software performs a couple of force and moment evaluations with 2 different angles the stability derivative is simply Force Forces angle angle Attention stability derivatives are evaluated in the linearization condi tions so the angle is in reality an increment 7 2 Roll Pitch Yaw Rate Derivatives The computation of angular rate derivatives is easy too although requiring some small adjustment by you if the calculated derivative values are odd or the flow velocity is much different from the default 50m s see Adjustments paragraph a triangular velocity profile centered in the CG is added to the stream velocity 7 3 Derivatives derivatives are not calculated anymore VorDyn1 0 used an analitical ex pression based on the tail volume ratio but since VorDyn2 is much more general the configuration is not intended to be strictly and classically aero nautic this way can t be followed anymore I decided to set it to zero Please don t do the same if you are studying aircraft dynamics P 7 4 Adimensionalization To provide adimensional coefficientsm forces and angular rates are divided by the following factors p a d fp f where p q and r are the roll pitch and yaw rate 7 5 Adjustments Angular derivatives are easy to be found you just set an inc
17. you could also want to have an airfoil which is cambered upside down like my automotive aileron to do that you set the second element of surfs airfkind to 1 You want to keep it normal Then set 0 In figure a thick wing 10 After setting those parameters you create the geometry the length of the following vectors is the number of the lifting surface segments you create Each element is a surface section if you want your surface to have 57 hope you don t segments and the 56 to have an aileron you add 57 elements in the following vectors and put FCR zero to any of them and the right flap chord ratio on the 56 element of the vector If you look at the vectors one upon the other each column of the matrix you created represents a surface segment In the aircraft picture above the wing is made of 3 segments the horizontal tail 1 and the vertical tail 2 one is pretty small 3 1 Aileron or Flap Once you have set the Flap Chord Ratio FCR of a segment you choose the deflection angle by placing in the vector its value in RADIANS Note that in the default Geometry m file the value between the brackets is in DEG dimensions but is converted to radians by multiplying to pi 180 If you flagged SYM 1 then the symmetric surface segment will be created To tell the software that your surface is an aileron for example you set the inversion flag to 1 the deflection of the symmetric flap will be inverted You c
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