"user manual"
Contents
1. Fan wake core stator interaction If desired the program will also run the wake vortex flow calculation A tip vortex or preliminary hub vortex calculation may be run with the wake prediction Part 2 of this document discusses what is required to run this program including all program enhancements to date The program may be run in the workstation environment About 10 minutes of time is needed to run a noise prediction on a Sun SPARC 2 Workstation for an average engine condition However a prediction of the only the wake runs extremely quickly The namelist input is used in this program where multiple cases may be run by simply stacking one namelist input above another The code presently requires geometry and performance parameters as a function of radius accross the fan and core stator if applicable 21 2 REQUIREMENTS The Rotor Wake Stator Interaction Program uses Namelist input It gives flexibility to the user entering the data It does not require all possible input be in the data file Variables can be leftout of the input file with ease Thus minimal input from the user is required 21 GENERAL NAMELIST INPUT The following is a general description of how the input file for V072 is set Title this can be up to 80 characters in length and is the title for the case being run If a title isgoing to be entered it must be input before the Namelist data If no title is entered the program will use a2. default title based on the case being run The namelist data section of the input file is to be set up as follows Column 1 of each record must be blank data must start in column 2 The first record of a namelist set of data must contain amp INPUT The data may be entered starting on the same line as the amp INPUT or on the next line If it is to be entered on same line as the amp INPUT a blank space must separate the data from the amp INPUT The data is to be entered separated by commas As much data as fits can be entered on a single line and the order of the variables is irrelevant The form of the data is VARIABLE NAME DATA VALUE ARRAY DATA VALUES Each element separated by a comma The last record of a set of data must contain END Multiple cases can be input in the same data file This is set up as if the cases were in separate files Each case needs its own namelist input Only those items that need to change from the previous case must be defined in the new namelist set Once each case is defined they can be stacked on top of each other in the file For more information regarding the set up of the input data file refer to the Appendix Sample Input 2 2 INPUT DESCRIPTION 2 2 1 Creating a Streamline Input To obtain input to V072 we need to first transform our real engine geometry Fig 12a into a constant area duct geometry Fig 12b To obtain Figure 12b from Figure 12a visualize each streamline
3. 1 Listing of the user s input 2 Wake Characteristic Parameter Output as a Function of Radius 2 1 Streamwise spacing aerodynamic chord 2 2 Airfoil streamline section drag coefficient 2 3 Half wake width rotor pitch 2 4 Wake velocity deficit Freestream relative velocity 2 34 3 Hub Vortex Parameter Output if IHBVTX 1 and IPRINT 1 3 1 Scalar output at the rotor t e 3 1 1 3 1 2 3 1 3 3 1 4 3 1 5 3 1 6 3 1 7 3 1 8 3 1 9 Blade section lift coefficient at the hub Fraction of lift lost to the hub vortex Radius of the hub vortex core hub blade pitch Streamwise velocity deficit of hub vortex core hub freestream velocity Circulation per unit span of hub vortex core 42 5 Angular velocity of hub vortex core hub wheel speed Hub vortex tangential location hub blade pitch Hub blade pitch Hub freestream relative velocity 3 2 Array output as a function of Streamwise Spacing relative to each radius at stator l e 3 2 1 3 2 2 3 2 3 3 2 4 3 2 5 3 2 6 3 2 7 Radius at rotor Le in Streamwise spacing aerodynamic chord Hub vortex core radius hub blade pitch Hub core velocity deficit hub freestream velocity Radial distance of hub vortex from engine center line in Radial distance of hub vortex from engine center line normalized by the rotor tip radius Hub vortex circulation span ft sec 4 Tip Vortex Parameter Output if ITPVTX 1 and IPRINT 1 4 1 Scalar output at the rotor 4 1 1 4 1
4. Ideal Total Pressure at Fan t e Actual Total Pressure at Fan t e Py Total Pressure Fan 1 Static Pressure at Fan l e Other Input Hints Nland TS are only used to calculate the rotor tip mach number e BROTOR MX BETA2D and OMEGA are only used in the rotor wake calculation OMEGA is only used to calculate the rotor drag in the wake calculation Drag is proportional to a value of OMEGA However the wake profile is a weak function of drag Thus only a reasonable estimate of OMEGA is needed e XSPACisonly used to determine the wake shape and determine the wake skew MAS MAC YRD YSD XSD ALPHCH ACLS MRABS are only used in the noise calculation program e YRD and YSD are used in the calculation of radial wake skew YSD and XSD are used to insure that the power levels are properly calculated at the stator leading edge hub axial location in the duct If either of these parameters is important then the noise will not be correctly integrated across the duct BSTATR is utilized in the wake skew vane pressure distribution and chordwise integration calculations e ACLS ALPHCH are only used in the wake skew and vane pressure distribution calculations MRABSis only used to calculate vane pressure distributions RHOS is only utilized to redimensionalize the noise at the end of all other calculations 31 2 3 VORTEX PARAMETER INFORMATION 2 3 1 Tip Vortex Notes Reference 1
5. Input DESH ERRORES dace Caen naw hore a ro 21 2 2 1 Creating a Streamline Inputs 21 2 2 2 Standard Input Data Units 24 2 2 3 Case Descriptive Input 24 2 2 4 Scalar Geometry and Performance 25 2 25 Distributing the Streamlines in V072 26 2 2 6 Streamline Geometry and Performance 24 2 57 Hub Vortex Parameters x ate Ri Re 24 2 2 8 Tip Vortex Parameters eas A eens aaa ale ea gag 24 2 2 9 Program Overiding Parameters 24 2 2 10 Developmental Sa e need A EY Sa a ades 2 2 2 11 Notes On Input Jovia nh EO n ee 34 Figure 10 11 12 13 14 15 16 LIST OF ILLUSTRATIONS Page Sketch of V072 Rotor Stator Geometry 5 Wake Model CUR E C 6 Wake Vortex Flowfield cues a adoro be tendo s a Hec OE cae SO 6 Cascade Unsteady Aerodynamics Geometry 7 Coupling the Unsteady Aerodynamics to the Noise 8 Powered Nacelle Geometry Vs V072 Representation 10 Full Scale Engine Ge
6. accuracy of the answers may be effected Perhaps the least worrisome warning is when the critical mach number does not converge Normally the critical mach number is correct to machine accuracy However the criteria is quite stringent and will sometimes cause this error Note that when this error does occur it isimportant to check the radial mode shape and to check the radial mode power levels for the mode where this occurs This is because while the critical mach number may be good when this error occurs there is usually some computer roundoff error which will effect the radial mode shape In most cases this error is much smaller than the noise which propagates from the important modes This error is most likely to occur when the hub tip ratio is less than 0 4 and seems to be the most significant in rotor core stator interactions See Section 6 of Part 1 the Computational Noise discussion If the stator dipole matrix distribution warning occurs it is important that the engineer and the programmer responsible for this program be contacted This error indicates that the accuracy of this matrix inversion is poor This error occurs because a value along the matrix diagonal is much smaller than one off the diagonal This can effect the program error This error has not occurred for the cases tried However an increase in the matrix condition number has been observed as the BPF harmonic frequency rises FATAL ERRORS will cause the program to aut
7. shows the Pratt amp Whitney Powered Nacelle APN fan rig geometry while Figure 6b illustrates how the APN geometry is represented in V072 using a constant wy Ze 8 yy TP IM lt lt BLADES VANES a Powered Nacelle Geometry CLOLLLLLLLLLLLLL LALLA LLAMA A AA AM MM hhh MMMM MM hh hh Ld BLADES VANES b 072 Powered Nacelle Geometry M44468 3 920608 Figure6 Powered Nacelle Geometry Vs V072 Representation To choose a constant area duct we must consider its effect on the modal content of the noise and its influence on the rotor wake and stator pressure distribution calculations The effect of the choice of duct radii on the wake calculation occurs in the computation of the drag coefficient to obtain wake width and velocity deficit and in the computation of the tip vortex In the pressure distribution the choice of duct radii effects the calculation of vane solidities and certain streamline performance such as wheel speeds The noise propagation calculation is influenced by radius in the calculation of the cutoff ratio which sets the number of propagating modes and calculates mode dipole alignment 10 Therefore chosen location for constant area annular duct should occur near the stator where the noise is generated but not far from the rotor where the wake is generated and where the wheel speed is set As a result the rotor leading edge is recommended for most configurations unless the change inradi
8. wake variations along the span These variations are handled in terms of harmonics inmuch the same fashion as the chordwise variations where the number of pressure variations increases with each higher harmonic i e if there are four actual wakes in contact with a given vane then at 3BPF there will be 12 spanwise phase variations in upwash velocity Thus a parameter called the wake phase lag is used to set the number of radial variations The phase lag is a form of reduced frequency which has the form NRAD 2 x PI x No of spanwise wake disturbances on the stator span Wake Phase lag relative to the hub The required number of radial integration stations is now calculated by simply choosing the highest calculated value from the two NRAD criteria either NRAD or NRAD To insure reasonable accuracy minimum values have been set based on the type of run For a rotor wake stator interaction without any vortices NRAD must be at least 11 To insure reasonably accurate vortex representation the minimum is raised to 21 when a vortex is calculated This is done to deal with the evenly spaced radial integration stations utilized by the program Due to the program s structure one NRAD value is then employed corresponding to the highest harmonic being calculated To calculate NRAD for the rotor wake core stator interaction a variation on this criteria was introduced As was suggested before the core stator only generates noise along its real span se
9. 2 4 1 3 4 1 4 4 1 5 4 1 6 4 1 7 4 1 8 4 1 9 Blade section list coefficient at the tip Fraction of lift lost to the tip vortex Radius of the tip vortex core tip blade pitch Streamwise velocity deficit of tip vortex core tip freestream velocity Circulation per unit span of tip vortex core Angular velocity of tip vortex core tip wheel speed Tip vortex tangential location tip blade pitch Tip blade pitch Tip freestream relative velocity 5 Array output as a function of Streamwise Spacing relative to the radius at stator 1 5 1 Radius at rotor l e in 5 2 Streamwise spacing aerodynamic chord 5 3 Tip vortex core radius tip blade pitch 35 5 4 velocity deficit tip freestream velocity 5 5 Radial distance of tip vortex from engine center line in 5 6 Radial distance of tip vortex from engine center line normalized by the rotor tip radius 5 7 Tip vortex circulation span ft sec Velocity Profiles if IPRINT 1 6 1 Relative velocities fixed to the rotor at specified axial locations ft s 6 2 Absolute velocities fixed to the stator at specified axial locations ft s 63 Upwash velocities fixed to the stator at specified axial locations ft s 6 4 Harmonic Content of Rotor Wake Vortex Flow 6 5 Wake Harmonic Magnitude Noise Output 7 1 Radial mode power levels dB for each Circumferential mode and BPF harmonic in the inlet and aft 72 Circumferential mode power levels dB for each harmo
10. 23 57 53 53 66 49 91 47 47 43 73 38 41 32 61 25 75 0 02317 0 05942 0 06431 0 07369 0 11269 0 09059 0 07378 0 09270 0 21135 MRABS 0 389 0 410 0 418 0 419 0 426 0 414 0 403 0 400 0 447 MX 0 493 0 449 0 445 0 450 0 442 0 447 0 431 0 394 0 306 ACLS 41 71 41 13 37 77 34 13 32 61 29 75 27 35 25 59 26 74 XSD 0 0 0 010 0 080 0 092 0 094 0 094 0 095 0 031 0 0 IHBVTX 0 SBNH 0 5 DHUB 55 74 BRHUB 7 555 MXHUB 493 BETAIH 38 78 BETA2H 61 23 ITPVTX 0 SBNT 0 5 TAUG 0 01 BRTIP 9 79 0 306 1 19 21 2 25 75 IPRED 3 TEST CASE amp INPUT NRADS 9 NCHRS 8 NRADC 7 NCHRC 6 IHBVTX 1 ITPVTX 1 amp END IPRED 3 TEST CASE amp INPUT NRADS 9 NCHRS 8 NRADC 7 NCHRC 6 IHBVTX 0 ITPVTX 1 amp END 41 IPRED 3 TEST CASE amp INPUT NRADS 9 NCHRS 8 NRADC 7 NCHRC 6 IHBVTX 1 ITPVTX 0 amp END ud o QX How 199 Q9 42
11. KCN CAUSES UNSTEADY PRESSURE wj ones REGION OF THE CHORD FIRST WAKE FLOW DIRECTION SECOND WAKE FIRST WAKE DISTURBANCE lt ET SECOND WAKE Econo WAKE DISTURBANCE THIRD WAKE M4 4468 7 920608 Figure 8 Wake Convection Along the Cascade The criteria which was formed to represent this variation is NCHORD 2x PI x Number of convected disturbances on the vane where NCHORD number of points on the chord at which unsteady pressures are calculated This criteria is found to be equivalent to setting NCHORD equal to two times the reduced frequency of the convected wakes in the chordwise direction e g NCHORD 2 x Reduced Frequency 2 x 2 where harmonic Number of Rotor Blades 2 rotational speed revolutions sec 2a ec 40 U flow velocity in stator fixed coordinates ft sec b 1 2 stator aerodynamic chord ft QI SOL tp Because the program Simpson s rule integration requires an even number of data points this criteria is then raised to the nearest even number To insure reasonable accuracy at low reduced frequencies a minimum value of 8 is used To increase program running efficiency a different NCHORD value is utilized for each wake BPF harmonic In addition the maximum NCHORD value is set to 60 5 2 RADIAL DIRECTION Obtaining a radial integration station criteria was found to be significantly more involved than the chordwise case T
12. PRED EQ 1 OR IPRED EQ 3 OR IPRED EQ 3 3 NONDIM IPRED1 IPRED2 6 IF 0 MER d 1 50 mes BB not available 7 WKEVTX 50 BESY BESY 3 FILLOV 1 1 5 VORTXIJ I KERNE 2 DRAGQ BES Y 1 If IPLOT EQ 1 WPLT78 3 2GES 4 TURB note plotting not available The numbers next to subdirectory names denote the order in which they are called by the calling routine Figure 16 Flow Chart for the V072 Rotor Wake Stator Interaction Program lt vA asked The 2 NL 3 5 6 8 br ar y 9 e 10 dicital version ava e I0 10 REFERENCES Majjigi R K et al Development of a Rotor Wake Vortex Model NASA 174849 June 1984 Ventres 5 et al Turbofan Noise Generation 167952 July 1982 Dongarra J J et al LINPACK User s Guide Published by SIAM 1979 Danda Roy I et al Improved Finite Element Modeling of the Turbofan Engine Inlet Radiation Problem submitted to NASA Lewis August 1992 Strazisar A J et al Laser Anemometer Measurements in a Transonic Axial Flow Fan Rotor NASA TP 2879 Nov 1989 J M Development of Unsteady Aerodynamic Analyses for Turbomachinery Aeroelastic and Aeroacoustic Applications NASA Contractor Report 4405 October 1991 Whitehead D S Vibration and Sound Genera
13. ROTATIONAL HUB DIRECTION ENGINE CENTERLINE Ysp is positive in the direction opposite rotor rotation Yrp is positive in the direction of rotor rotation Figure 13 Definition of Ygp and Ysp Schematic View of a Rotor Blade TE and Stator Vane LE Looking Perpendicular to the Rotor Axis RADIAL LINE RADIAL LINE ROTOR LE STATOR LE HUB ENGINE X CENTERLINE XSD is positive in the direction of reducing the axial spacing relative to the hub streamline Figure 14 Definition of Xsp 2 2 7 Hub Vortex Parameters Use Only When IHBVTX 1 These are scaler quantities 2 2 8 Tip Vortex Parameters Rotor hub diameter Tangential distance of vortex center from rotor wake pressure side divided by the rotor pitch at the hub default 0 5 Hub rotor aerodynamic chord Axial mach no rotor l e hub streamline Relative flow angle rotor l e hub streamline Relative flow angle rotor t e hub streamline Use Only When ITPVTX 1 These are scaler quantities uae INCHES DEGREES DEGREES Rotor tip clearance gap Tangential distance of vortex center from rotor wake pressure side divided by the rotor pitch at the tip default 0 5 Tip rotor aerodynamic chord Axial mach no rotor l e tip streamline Relative flow angle rotor l e tip streamline Relative flow angle rotor t e tip streamline 12 9 Program Overiding Parameters These a
14. Rotor Wake Stator Interaction Noise Prediction Code Technical Documentation and User s Manual David A Topol and Douglas C Mathews United Technologies Corporation Pratt amp Whitney East Hartford CT April 1993 Prepared for Lewis Research Center Under Contract NAS3 25952 Task 10 NASA National Aeronautics and Space Administration TABLE CONTENTS yg RC c ETC Page SUMMARY e e CU BE VO HR WO e 1 PART I TECHNICAL DOCUMENTATION 2 1 INTRODUCTION A ee 2 2 P amp W ENHANCEMENTS CAD AO RA d RR 3 3 PHYSICAL DISCUSSION OF PROGRAM CALCULATIONS 5 4 PROGRAM ASSUMPTIONS s ose ees ape Red Gao wes d 10 5 PROGRAM INTEGRATION STATION CRITERIA 13 2 1 eonun date ice EE M ata P RR cod S 13 5 2 Radial Direction NER IO ERE RE CR 14 6 COMPUTATIONAL NOISE tros ex edo dde CS gd pr s 18 T CONCLUDING REMARKS 525 ctas ete daa T ea 2 PART 2 USER S MANUAL 2 de HNIRODUGCTION ado e dud tati Mri ied epis 21 Ze INFUTREOUIREMENES 2 21 General Name Cae dU ERES 21 2 2
15. T 32 SBNT is also never known nor can we estimate it However we know the effect of the placement of the vortex on the harmonic content of the stator upwash If SBNT 0 5 then the vortex is half way between two wakes Consequently two velocity deficits are created per passage in the tip region one from the vortex and the the other from the wake This will cause any tip generated 2BPF noise to dominate If SBNT 0 0 then the vortex velocity deficit adds on top of the wake velocity deficit This causes a rise in all harmonics where BPF noise 2BPF noise 3BPF noise Reference 1 studies this effect in detail 2 3 2 Hub Vortex Notes It is important to realize that the hub vortex model is only partially developed from the technical standpoint Reference 1 will give details but essentially the empirical correlations for this vortex do not exist so the NASA program either uses tip vortex relations or it sets values equal to a constant Because of the preliminary nature of this option extreme care should exercised when it is used 33 3 3 1 NOISE AND WAKE OUTPUT The Rotor Wake Stator Interaction program creates 3 output files The Noise output file is a mandatory output file but the IPRINT input option allows for this file to be either a long output file short one The Eversman Radiation code output file is the second file It outputs the real and imaginary part of each of the radial mode amplit
16. When this occurs the rotor wake core stator results should be suspect for that mode and a radial mode plot should be made to check the results While these numbers add no noise to the total result they do mislead the user into incorrectly concluding that some tone noise was generated by this mode when in fact there was none 18 AMPLITUDE HUB TIP RADIUS a Mode Shapes 38 0 MODE HUB SPLITTER RADIUS b Enlargement of Core Stator Region Figure 11 Radial Mode Shapes Hub Tip Ratio 0 38 19 7 CONCLUDING REMARKS Two NASA computer codes were combined and improved to form a new rotor wake stator interaction code Program capabilities include the ability to run noise predictions from the following noise sources Rotor wake stator interaction in a low pressure compressor stage Fan wake core stator interaction Fan wake FEGV interaction in a fan stage A semi empirical tip vortex calculation and a partial hub vortex calculation are also available Finally under certain circumstances the program will insert computational errors of its own giving rise to computational noise Thus when running rotor wake core stator interaction noise predictions care should be taken to check mode power levels for this effect PART 2 USER S MANUAL 1 INTRODUCTION The BBN PW code has been designed to calculate noise from the following sources e Compressor rotor wake stator interaction Fan wake FEGV interaction
17. ading edge the generated For a fan wake core stator interaction assume that the noise decays by an insignificant amount when it reaches the rotor leading edge so that MAC is used at the rotor leading edge However if the engine performance shows a need these values may be specified anywhere in the duct Note that as MAS or MAC are increased the number of propagating radial modes will increase 4 ALPHCH The stator stagger angle may be expressed using a number of different parameters The method chosen here is to use the stagger angle defined as follows tan stagger tan B F 2 ALPHCH cal where stagger angle the chord of the stator airfoil section makes with the circumferential direction alpha chord Stator leading edge metal angle relative to the circumferiential direction This angle is chosen becuase it is effectively the angle of the airfoil at the quarter chord point Stagger may be approximated by 1 1 em stagger 2 4 where 85 Stator trailing edge metal angle relative to the circumferiential direction 30 5 TAUG SBNT SBNH These parameters are not readily available However estimates of their values can be made See Section 6 2 on Vortex Parameter Information for more information 6 OMEGA Rotor Loss Coefficient see Reference 10 in the relative reference frame fixed to the rotor where _
18. ane in an annular duct Pressure distributions on the other vanes may be calculated knowing the phase relationships that are a function of theblade and vane number Physically we can say that we now have an annular duct which contains chordwise pressure distributions along every stator in the cascade and across the vane span see Figure 5 STATOR CALCULATE POWER LEVELS ALONG SECTION A A DENOTE PRESSURE DISTRIBUTION POINTS BY EACH IS COUPLED TO EACH RADIAL MODE USNG A DUCT ACOUSTIC METHOD GREENE S FUNCTION AND IS COMBINED AT SECTION A A THIS FORMS THE DUCT ACOUSTIC PRESSURE FIELD FOR EACH RADIAL MODE AT SECTION ON 1 PRESSURE DISTRIBUTIONS ON EVERY VANE IN THE DUCT _ Figure 5 Coupling the Unsteady Aerodynamics to the Noise Assuming a mean axial flow in a constant area annular duct we can now calculate the radial mode amplitudes for each propagating circumferential radial mode To understand this calculation we can look at an axial location in Figure 5 At this location we can evaluate the effect of the unsteady pressures propagating from the cascade and then sum up these effects to calculate the amplitude of each propagating mode in the duct termed the Greene s function approach outlined in Ref 2 or Ref 9 The calculation is done preserving all magnitudes and phases of every pressure in the pressure distributions including how those pressures couple to each circumferential and ra
19. art 2 of this document only streamlines for flow through the core stator need to be specified in the program Then to create the fan inlet duct the program will ask for the fan outer diameter Therefore the core stator duct has been created In applying these assumptions to the fan wake FEGV interaction only streamlines associated with the fan bypass duct need be specified This plus the fan outer diameter which will be the same as the radius of the most outer streamline will form the constant diameter duct When doing both predictions simultaneously the splitter diameter is simply input twice at the point where the fan core stator interaction input ends and the fan FEGV interaction input begins Then both ducts will be automatically specified See Part 2 of this document for more information on the mechanics of the input 11 As result we have defined our constant area ducts for all three configurations of interest Figure 7 STATOR a Full Scale Engine Geometry CORE PRMARY STATOR DUCT FAN NLET SPLITTER DUCT STREAMLINE FAN BYPASS DUCT FEGV CORE STATOR EXTENSION USED IN FAN CORE STATOR INTERACTION b V072 Full Scale Engine Geometry 44468 4 920608 Full Scale Engine Geometry Vs V072 Representation 5 PROGRAM INTEGRATION STATION CRITERIA As was discussed earlier the program chooses how many points it needs along the stator span and stator chord to effectively calculate the total power levels T
20. ascade geometries and steady as well as unsteady lift Whitehead and Smith are older but are more like what the program utilizes In both of these cases the authors assume two dimensional compressible flow over a cascade of unloaded flat plates at zero incidence to the incoming flow see Figure 4 In each case the annulus of vanes was unwrapped to form an infinite cascade along each streamline or strip For this rotor wake stator interaction program a procedure outlined by Goldstein Ref 9 utilizing the same assumptions as Smith and Whitehead was employed so that according to Ventres Ref 2 all three formulations give the same results 5 PRESSURE DISTRIBUTION f GEOMETRY IS DEFINED FOR EACH STREAMLINE OR STRIP Upwash Velocity U Freestream Absolute Velocity Vane Stagger Angle Figure 4 Unsteady Aerodynamics Geometry The program extends the strips formed during the wake calculation along the stator cascade and proceeds to calculate unsteady pressure distributions on a reference vane of the cascade at a program specified number of chordwise stations for the P amp W developed criteria see section 1 1 The program assumes that all the vanes in the cascade are of the same geometry and are equally spaced in the circumferential direction At this point the program rewraps strips to re form an annular duct We now chordwise pressure distributions along the span of a reference v
21. des from this noise source will occur in the fan bypass duct Therefore the rotor leading edge radii are chosen for this interaction from the splitter streamline to the tip streamline with all mode propagating in the fan bypass duct For rotor wake core stator interaction many more assumptions are needed the core stator leading edge isless than a wavelength at 3BPF from the splitter leading edge then we can reasonably assume that decay will not be significant in the inner duct forward of the core stator and that all noise propagation and decay will occur in the fan inlet duct Thus the fan inlet duct is the core stator s constant area duct However no noise may propagate radially through the splitter until the stator leading edge Consequently while only noise will be generated on the core stator itself we must effectively extend the core stator across the entire inlet duct see Figure 7b effect of these assumptions is that any wave reflections off the splitter leading edge at the entrance to the primary duct are neglected In addition these assumptions have effectively removed the splitter from the problem The application of these assumptions to the computer program input can now be explained For the fan wake core stator interaction there is no wake impinging on the core stator extension shown in Figure 7 Thusin applying the above assumptions the program need only integrate across the real core stator As will be found in P
22. describes the tip vortex model which is a simple semi empirical model There are two important parameters in this model which are not easily determined SBNT Circumferential location of the tip vortex relative to the pressure side of the wake of a nearby blade divided by the blade pitch TAUG Rotor blade tip clearance TAUG is quite important as it determines the vortex strength and contributes to determining the vortex radius A couple of notes Inareal engine TAUG varies around the circumference Inareal engine TAUG varies with engine condition In V072a constant TAUG is assumed at a given engine condition SBNT refers to the circumferential location of the tip vortex relative to the pressure side of the wake of a nearby blade normalized by the blade pitch see Figure 15 We can explain the development of this parameter as follows Wakes from each blade are convected downstream along some path Fig 15 Near the tip at or near the blade leading edge a vortex develops as a result of the interaction between the blade and tip leakage This vortex convects along some path toward the stators Fig 15 As it convects it moves away from the suction side of the blade where it was generated and toward the pressure side of the neighboring blade wake WAKE PATH 7 SENT aid 2 M44468 6 920608 Figure 15 Vortex Location SBN
23. dial mode These pressures are then integrated for each mode thus giving us an inlet and aft power level and complex radial mode amplitude for each propagating mode This process is repeated for every propagating mode and the power levels are then summed up to give the circumferential mode power levels and total power levels for each harmonic It should be noted that these noise calculations give inlet and aft mode amplitudes phases and power levels which are at an axial location associated with the stator hub leading edge section A A in Figure 5 Thus this axial location should be used as a starting point for propagating the modes upstream and downstream in the duct Further details of this method may be found in Reference 2 4 PROGRAM ASSUMPTIONS The previous section physically discussed the program assumptions and calculation procedures for a rotor wake stator interaction occurring in a constant area duct Figure 1 Real life configurations of concern are however somewhat more complicated than this geometry The real duct configurations of interest include the following applications 1 Compressor rotor wake stator interactions 2 Fan wake FEGV interactions 3 Fan wake core stator interactions To calculate noise using V072 it is necessary to simplify the real duct geometry by making some reasonable assumptions To best visualize the problem let us look at the rotor wake stator interaction configuration of Figure 6 Figure 6a
24. e Section 4 and Figure 7 Therefore we need only integrate along the core stator span itself i e we need not integrate over the entire inlet duct So to determine NRAD for this case we simply take the value calculated for the total inlet duct and multiply it by the percentage of the total span which is occupied by the core stator This criteria significantly reduces computational time without affecting program accuracy For this case the minimum NRAD value is set to 7 The present maximum for NRAD is set at 79 After formulating these criteria a battery of test runs were initiated using the APN and full scale engine data input Results indicated that the criteria were effective in giving accurate results 2 STATORL E WAKE TRAJECTORY AX ROTOR TO STATOR T AXIAL SPACING CIRCUMFERENTIAL r DISTANCE BETWEEN THE TWO WAKES ATSTATORL E TIP WAKE TRAJECTORY a Cascade View STATORL E TWO WAKES ALONG THIS STATORSPAN b End View of Wakes at Stator Leading Edge 42468 2 920608 Figure 10 Wake Time Phase Lag Due to Rotor Blade Twist 17 6 COMPUTATIONAL NOISE In numerical analysis applications such as this program the potential exists for the computer to add noise of its own due to computer roundoff or truncation error This is particularly true the BBN PW code for a rotor wake core stator interaction This is because many mode shapes concentrate themselves at the tip whe
25. e a physical discussion of how the new code works will be introduced The program assumptions will be introduced next including the rotor core stator interaction and duct assumptions The program s P amp W developed automatic radial and chordwise integration station criteria used in calculations will then be presented Lastly calculation inaccuracies due to program computational noise will be introduced so the user will be aware of where it is important A number of additions and improvements were made to two NASA programs which now form 2 P amp W ENHANCEMENTS TO V072 V072 since their receipt from NASA The resulting code has the following capabilities These capabilities were achieved by initially combining the two NASA decks In addition the program The program will now run The wake model by itself at any radii Acompressor rotor interaction or fan wake FEGV interaction fan wake core stator interaction Both a fan wake FEGV interaction and fan wake core stator interaction Additional wake model capabilities Preliminary hub vortex model Atip vortex model Achoice of three wake profiles Gaussian or Hyperbolic Secant or Loaded Rotor choice of two wake width and velocity deficit correlations Original GE NASA correlation or the P amp W high tip speed rotor correlation Multiple run capability program input can be stacked Input is based on output from a 2D or axisymetric streaml
26. ere created is documented in a separate document The rolor caleolstien Oto e noise responce calculation ich 3 PHYSICAL DISCUSSION OF PROGRAM CALCULATIONS The V072 program as originally received from NASA in the mid 1980 s was designed by Bolt Beranek and Newman Ref 2 to handle standard rotor wake stator interactions in an infinitely long constant area annular duct Figure 1 Later the wake model of Ref 1 was added to the code to form the present code Discussions in this section will concentrate on how the program as updated by P amp W calculates noise from a rotor wake stator interaction noise source In Section 4 the method utilized to set up the constant area duct will be covered In addition the extension of this procedure to include rotor wake core stator interactions will be discussed Figure 1 Sketch of V072 Rotor Stator Geometry The rotor wake stator calculation is divided into two parts the rotor wake calculation and the stator noise response calculation The performance input to this program will need to come from a two dimensional or axisymetric streamline type steady aerodynamic prediction code To expedite the noise calculations the new program dimensionalizes all input geometry and performance Then before any calculations done the program linearly interpolates the streamline radially distributed non dimensional parameters to a p
27. he program as received from NASA lacked this capability Consequently it was necessary to create these criteria In each case we need to ask how rapidly in space the important parameters relating to the noise will change in the spanwise and chordwise direction These criteria were developed based on a total power level accuracy of plus or minus 1dB 5 1 CHORDWISE DIRECTION Let us first look in the chordwise direction As the rotor wakes reach the stator they cause an upwash to convect along the stator Figure 8 This upwash varies along the chord causing an unsteady pressure distribution to form along the chord Figure 8a As the wake continues travelling down the stator chord another wake reaches the stator at a later time Figure 8b This wake will cause an upwash velocity at an upstream location on the chord while the earlier wake is disturbing a downstream section In our case we are looking at a specific harmonic of the wake so that the wake disturbance on the chord will be a sinusoidal shape For BPF this sine wave will have as many cycles on the vane as there are wakes on the vane for 2BPF there will be twice as many for 3BPF three times as many etc In other words the more variations we have on the chord at once the more points we will need to accurately calculate the chordwise pressure distribution on the vanes and to later integrate these chordwise pressures during the duct noise calculation WAKE CONVECTION FROM FIRST WAKE
28. i from the rotor to the stator is very large Itshould be noted however that all geometry and performance at the rotor leading edge and downstream should be selected along the streamlines starting at the rotor leading edge The method for creating the input to the code using this method may be found in Part 2 of this document the program user s manual What do these assumptions mean Effectively what we have done is to choose streamlines at radii at the rotor leading edge We have then followed those streamlines to the stator using the geometry and performance along each streamline with the exception of the effects of changing radii We then effectively treat the streamline like a string which goes from the rotor leading edge to the stator trailing edge with geometry and performance except the radii which vary according to the real streamline geometry We can think of this string as being pulled taught to form streamlines in our constant area duct in Figure 6b Now consider the more complicated case of a real fan stage like that shown in Figure 7a The simplification of this configuration is shown in Figure 7b obtain to Figure 7b from Figure 7a we made a number of reasonable assumptions First as we concluded in the rotor wake stator interaction case discussed above the rotor leading edge radii could be used In the case of the fan wake FEGV interaction FEGV s are usually far enough back from the splitter so that the propagation or decay of mo
29. ine type steady aerodynamic prediction code Program criteria setting the number of spanwise and chordwise integration points This option my be replaced with user input integration station values was modified so that The code is no longer dependent on any external subroutines such as the matrix inversion routine except to obtain today s date User is notified of any program errors Programis nowin double precision necessary when working with small numbers like acoustic pressures Bessel function subroutines were changed or replaced The J Bessel function subroutine was replaced with one that is more reliable and calculates the J Bessel function and its derivative simultaneously The Y Bessel function subroutine was changed so that it will calculate the Y Bessel function and its derivative simultaneously These changes were intended to increase program speed and accuracy The matrix inversion routine was changed from IMSL routine to a routine created by SIAM called LINPACK Ref 3 This makes the code independent of specific packages which my not be available on other computer systems The code will run on both Sun and Silicon Graphics Workstation platforms and should be portable enough to run on other platforms The Loaded Rotor wake profile and and the P amp W high tip speed rotor correlation were createdusing Rotor 67 data under Task 10 of contract NAS3 25952 The details of how these items w
30. l complex radial mode amplitude normalized as required by the Eversman Radiation Code Ref 4 are output Originally the BBN PW code had its own partial wake model which P amp W replaced with the more complete GE NASA model However the wake phase lag or wake skew calculation in the original code was retained to account for the greater distance that a wake at one radius must travel relative to the distance that another wake must travel at another radius This feature allows for the real effects of wake vane slicing to occur rather than the simultaneous wake slapping limitation that was imposed by earlier theories In addition to the wake width and velocity deficit developed by General Electric in Ref 1 P amp W has developed high tip speed wake width and velocity deficit correlations under NASA Lewis funding Also skewed loaded wake profile based on Rotor 67 high tip speed wake data Ref 5 was developed These additions to the wake model are included in the present code The development of these correlations are discussed in a separate document Given this unsteady wake vortex flow we must now calculate the unsteady chordwise pressure distributions on the vanes along the stator span This type of calculation has been developed by a number of authors including Verdon Ref 6 Whitehead Ref 7 and Smith Ref 8 Verdon s case is the most recent in which he developed a two dimensional cascade calculation which includes real c
31. like string with geometry and performance varying along the string Now pull the string soit is taught where the radius of the string from the engine centerline corresponds to the rotor leading edge radius of this streamline Thus each streamline is located at the rotor leading edge radius to create the constant area duct We then follow along each streamline back to the stator to obtain engine geometry and performance parameters 22 For example Looking at Figure 12 streamline 2 to get from Figure 12a to 12b look at the streamline radius at point A in Figure 12a This radius will be the radius of the streamline in the program Therefore utilize geometry and performance at points Identify the rotor chord along point A to B and the stator chord from point C to D respectively this is the aerodynamic chord Do not use the axial chord Use the aerodynamic chord as defined on a streamline Use the stator stagger angle at an airfoil cross section starting at point C Identify the axial spacing as the streamline distance from points to C STREAMLINE 1 STREAMLNE 2 STREAMLINE 1 PRMARY DUCT STREAMLINE 2 55 b V072 Full Scale Engine Geometry 44468 8 Figure 12 Full Scale Engine Geometry Vs V072 Representation 23 For more information the choice of radial locations see Section 4 of Part 1 of this document Note that if the radial change on the engine from
32. n to stator fixed coordinates is then performed to calculate the flow upwash perpendicular to the mean flow direction in stator fixed coordinates From these upwash velocity profiles wake harmonic magnitudes and phases are calculated at the stator leading edge for each harmonic at each radial strip location 4 XN WAKE AT m n 3 STATOR Flow oy j p 5 4 ET INCOMING FLOW Figure 2 Wake Model TIP VORTEX Figure 3 Wake Vortex lowfield At this point we arrive at the second part of the calculation the calculation of noise due to the unsteady flow upwash on the stators For this calculation a program developed by Bolt Beranek and Newman BBN under contract to NASA Ref 2 was used Essentially this program calculates the total harmonic power levels travelling forward and aft in the duct To do this the program individually calculates the circumferential radial mode power levels for every propagating mode resulting from this interaction It then sums up all of the circumferential radial mode power levels to obtain inlet and aft total power levels for each harmonic Two different sets of radial mode amplitudes and phases are also calculated and output by the program In the main output file the dimensional amplitude and phase of the complex radial mode amplitudes normalized using the method outlined in Ref 2 are output In a separate file the real and imaginary parts of the dimensiona
33. nic in the inlet and aft 7 3 Total power levels dB for each harmonic in the inlet and aft 36 4 ERROR MESSAGES OUTPUT The program will output a number of different types of error messages to signal possible problems with the program answers The two important areas where this is done are during the various aspects of the radial mode shape calculation and during the matrix inversion of the stator dipole strength calculation In the mode shape calculation errors the problem will be identified along with the absolute value of the circumferential mode number m and the radial mode number muofthe effected radial mode In large part these errors signal where minor errors have occurred and in most cases the user should simply check the answers for the mode shapes for the modes where these errors occur to see that these errors are in fact insignificant There are three types of errors NOTES WARNINGS and FATAL ERRORS NOTES notify the user that bessel function subroutine has calculated an answer which has gone to plus or minus machine infinity according to these subroutines These errors are just there to inform the user of this fact These errors do not in and of themselves signal a real problem WARNINGS are more serious They relate to one of two things The critical mach no radial mode eigenvalue calculation did not converge or the stator dipole distribution matrix inversion is ill conditioned In these cases the
34. ofile 3 Loaded fan wake profile default m oH W ITPVTX Tip Vortex option 0 Tip Vortex not included in calculation default Calculation includes a Tip Vortex IHBVTX Hub Vortex option O Hub Vortex not included in calculation default 1 Calculation includes a Hub Vortex oi IPRINT Print option 0 Short output file Does not print detailed wake profile and vortex information 1 Long output file Prints wake profile details and vortex information n t IPLOT Plot option 0 Plotting file not created default Create plotting file 2 2 4 Scalar Geometry and Performance Input Variable Needed as Variable Type Description Name IPRED option X X X X No of rotor blades No of stator vanes or FEGV s No of core stators Outer duct diameter at rotor L e Uncorrected rotor speed Mass averaged static temperature rotor Massed averaged static density rotor t e Mass averaged axial mach no FEGV or stator l e Mass averaged axial mach rotor hauc te pngrove 2 2 5 Distributing the Streamlines In V072 Once the streamline radii are located the geometry and performance may be obtained Streamlines must include the wall streamlines and must be specified as follows IPRED Number of Streamlines Being Input Wall Streamlines Where Input Must Be Specified EXE NDATS 1 NDATS Stator hub streamline Stator tip streamline 2 NDATC Fan h
35. oise Both of the rotor core stator answers however due to computational noise Figure 11a shows the actual mode shapes These mode shapes look quite correct with the mode shapes having zero value across part or all ofthe core stator span and azero slope atthe hub and tip However we need to look at the mode shape in the region where the core stator is located Figure 11b In Figure 11b it is seen that the 38 0 mode still is near zero accounting for the 14dB power level result In the 38 1 mode case there is a tail near the hub which is not in fact at zero slope to the hub with error showing up in the third decimal place of the radial mode shape This tail is due to the fact that both J Bessel function and its derivative go to zero while the Y Bessel function goes to minus infinity The Bessel function calculation develops errors in calculating these results correctly and thus a develops in the results in the hub region This 81dB result is representative of a worst case scenerio using the improved J Bessel Function subroutine The routine originally supplied with the BBN code Ref 2 allowed computational noise at the core stator to rise as high as 120dB which is unacceptable when the real noise is at this level This type of problem shows up for high circumferential mode lobe numbers with low radial mode orders and is at its worst when a critical mach number not converged warning is seen in the printout
36. omatically end execution They suggest a drastic problem with the input to one of the bessel function subroutines It may also indicate that the matrix inversion routine LINPACK has detected a singular matrix Under these circumstances the responsible program engineer and programmer should be contacted promptly to correct the problem 37 5 SYSTEM EXECUTION To execute the V072 system 1 Insure that the 070 v072 executable created in v070sys v070src v072 subdirectory has been sourced Enter 070 v072 on the command line in the directory where you have an input file At this point the following message will occur input file must be on your current directory Enter the filename or carrage return control d to quit Enter the file name and press enter The following output will be created 4 1 Output file with the superset name equal to the input file name with an extension v0720ut e g if the input file was called file1 the output file would be 1 072 4 2 Output file with the superset name equal to the input file name with an extension raddata This file has in it the input to the Eversman Radiation code 4 3 If IPLOT 1 then another file would be created called by the input file name with an extension plotdat This file would be used for plotting if there were a plotting routine A flowchart of how the computer program is given in Figure 16 38 A ADATE 8 IF I
37. ometry Vs V072 Representation 12 Wake Convection Along the Cascade 13 Radial Mode Shapes cese Rd eh RU i arde db d 15 Wake Time Phase Lag Due to Rotor Blade Twist 17 Radial Mode Shapes Hub Tip Ratio 0 38 19 Full Scale Engine Geometry Vs V072 23 Definition of YRD and YSD Me 27 Definition of XSD ede eR ep iba 27 Tip Vortex Location SBNT EE 32 Flow Chart for the V072 Rotor Wake Stator Interaction Program 39 iii SUMMARY This report documents the improvements and enhancements made by Pratt amp Whitney to two NASA programs which together will calculate noise from a rotor wake stator interaction The code is a combination of subroutines from two NASA programs with many new features added by Pratt amp Whitney To do a calculation V072 first uses semi empirical wake prediction to calculate the rotor wake characteristics at the stator leading edge Results from the wake model are then automatically inputinto a rotor wake stator interaction analytical noise prediction routine which calculates inlet and aft sound power levels for the blade passage frequency tones and their harmonics along with the complex radial mode amplitudes The code allows f
38. or a noise calculation to be performed for a compressor rotor wake stator interaction a fan wake FEGV interaction or a fan wake core stator interaction This report is split into two parts the first part discusses the technical documentation of the program as improved by Pratt amp Whitney P amp W The second part is a user s manual which describes howinput files are created and how the code is run PART 1 TECHNICAL DOCUMENTATION 1 INTRODUCTION In 1982 and 1984 two codes were developed the GE NASA semi empirical rotor wake vortex model Ref 1 and the BBN NASA analytical rotor wake stator interaction noise prediction computer program Ref 2 These codes together calculate noise in the duct from a rotor wake stator interaction Pratt amp Whitney under independent research and development funding has combined and improved these codes Additional improvements to the code s wake model were made under Task 10 of contract NAS3 25952 along with the ability to run the code on a Silicon Graphics Workstation This section of the report documents the technical improvements to this new computer code from here on called V072 or the BBN PW code Documentation of the wake model improvements are not discussed here but are instead discussed in the documentation of the above referenced contract The remainder of this part of the report is organized as follows First there will be a brief discussion of P amp W program enhancements From ther
39. peed default 0 0 Multiplier for wake width correlation WAKEWTH WKEFAC WAKEWTH default 1 0 Multiplier for velocity deficit correlation VELDEF VELFAC VELDEF default 1 0 29 2 2 11 Notes On Input 1 ISHAPE The wake profile shape is defined by the variable ISHAPE The best value for this shape is a function of the streamwise spacing to chord SSOC in the output file The Loaded Wake profile ISHAPE 3 is best used for streamwise spacing to chords of less than 4 For streamwise spacing to chords of greater than 4 the Hyperbolic secant wake profile ISHAPE 1 is the best profile to use 2 RADIUS RADIUS defines the streamline radii which will identify the constant area duct to be utilized by the program RADIUS has been defined at the rotor leading edge However if the fan duct shows significant convergence or radius change from the rotor to the stator then it may be desirable to redefine the RADIUS at another axial location See Section 5 of Part 1 of this document Program Assumptions for a more complete discussion of this parameter Note If RADIUS is defined at an axial location other than the fan l e then DDUCT must be set equal to the tip radius at the location used 3 MAS MAC The mass averaged axial mach numbers MAS and MAC are utilized in the calculation of the cutoff ratio and are used to specify the nature of the duct acoustics FECVoREnieti n MAS is specified stator le
40. re scaler quantities Needed as input for Default Value ipred option Variable Description Convergence criteria to calculate my in Tyler Sofrin No of radial integration stations Rotor FEGV or Rotor Stator interactions Must be an odd no maximum 79 No of radial integration stations Rotor Core stator interaction Must be an odd no maximum 79 No of chordwise integration stations Ro tor FEGV or Rotor Stator interactions Must be an even no maximum 60 No of chordwise integration stations Ro tor Core stator interaction Must be an even no maximum 60 Note Experience shows that Run Time NRADS x NCHRS and NRADC x NCHRC When the above parameters are set near their limits runs of up to 1 5 hrs per case have been found to occur on a Sun SPARC2 workstation CALCULATED USING A CRITERIA CALCULATION IN THE PROGRAM If this variable is used in a multi case run it must be input for all cases separately Otherwise the code will automatically override 1 2 10 Developmental Parameters These parameters may be used to effect the wake harmonic magnitudes May be input for Description IPRED option CRM X X X X Rotor inviscid velocity gradient rotor wheel speed negative value accounts for rotor loading default 0 0 Wake flow angle variation parameter default 0 0 CRP parameter rotor 2 fan speed rotor 1 fan s
41. re the noise generated at the core stator is not a factor To minimize this problem the program has been designed to detect very small numbers in the J Bessel function subroutine so as to minimize computational noise However even with this improvement some computational noise is likely to occur when the Bessel function goes to zero This computational noise is normally worse when the calculation of the critical mach number also does not converge see Part 2 Section 4 The improvements made to the code have rendered computational noise insignificant for the Fan FEGV interaction noise predictions and most Fan core stator noise predictions However it does have an effect on Fan core stator predictions where the expected noise is relatively low There are sometimes instances where judgement is required to ascertain if the generated noise for a particular radial mode is actually due to computational noise An example of this occurs in a full scale engine for example Figure 11 where a rotor wake core stator interaction generates the m 38 mode Figure 11 illustrates the 38 0 and 38 1 modes as they are generated in the present code In this situation the expected power levels for BPF for these modes are near zero dB However real predictions give power levels at BPF for these modes are 14dB and 81dB respectively Note that the associated Fan FEGV noise prediction for this case is much higher closer to 120dB and is not effected by computational n
42. rogram determined number of spanwise locations or radial integration stations for the P amp W developed criteria see section 1 2 From there the program proceeds to the wake model calculation To calculate the rotor wake a program originally developed by General Electric under contract to NASA was utilized Ref 1 Essentially this program divides the annulus into streamlines or strips It then unwraps each strip to form a two dimensional flow in the circumferential and axial directions see Figure 2 No radial flow is permitted A two dimensional mean flow is calculated analytically along each streamline with the assumption of incompressible flow across the rotor This incompressible flow assumption allows for the application of an analytical expression for the drag coefficient which was utilized in creating the rotor wake empirical relationships used in the program A series of rotor wakes combined with hub and tip vortices if desired are then superimposed on the mean flow to describe the flow field see Figure 3 The streamwise wake widths and velocity deficits are calculated empirically at the stator leading edge The resulting wakes are then combined with hub and tip vortices which are also calculated semi empirically at the stator leading edge Details ofthese calculations may be found in Reference 1 Thus a combined wake vortex profile is developed inrotor fixed coordinates at the stator leading edge A coordinate transformatio
43. the rotor leading edge to the stator leading edge is significant a program streamline radial location other than the rotor leading edge may be desirable 2 2 2 Standard Input Data Units Standard Input Data Units Lengths Inches Rotor speed RPM Temperatures Degrees Rankin Densities lbm ft3 Angles Degrees air and stagger angles are defined relative to the circumferential direction 2 2 3 Case Descriptive Input Parameters IPRED type of prediction 0 Compressor rotor wake prediction only Rotor Stator or Fan FEGV interaction only default 2 Fan Core stator interaction only 3 Both Fan FEGV and Fan Core stator interactions Ho H NDATS No ofstreamlines where streamline information will be input for a rotor stator rotor FEGV interaction use when IPRED 0 1 or 3 NDATC No of streamlines where streamline information will be input for a rotor core stator interaction use when IPRED 2 or 3 ICASE Thenumber of cases being run default 1 NHT number of harmonics where noise is being calculated default 3 IWAKE Chooses Wake width and velocity deficit correlations to be used 1 Loaded fan wake profile default 2 Linear rational function for rotor wake profile rea un ge wt fo ISHAPE Wake Tangential profile option This elec is ally F 1 Hyperbolic Secant profile elc 12 Gausian pr
44. tion in a Cascade of Flat Plates in Subsonic Flow R amp M No 3685 1972 Smith S N Discrete Frequency Sound Generation in Axial Flow Turbomachines R amp M 3709 1973 Goldstein M E Aeroacoustics McGraw Hill International Book Co New York 1976 Lieblein S et al Diffusion Factor For Estimating Losses and Limiting Blade Loadings in Axial Flow Compressor Blade Elements NACA 53 01 June 8 1955 CASI pital ei le ils ble Order thie document APPENDIX et e o Sample Input This is the test3 test case in the ws test IPRED 3 TEST CASE amp INPUT IPRED 3 ICASE 4 IPRINT 1 IPLOT 0 N1 2760 1 NHT 3 WKEFAC 5 VELFAC 5 NDATS 5 NRADS 9 NCHRS 8 NDATC 4 NRADC 7 NCHRC 6 NBLADE 38 NVANES 72 NVANEC 80 MAS 0 331 MAC 0 335 DDUCT 92 510 TS 564 RHOS 0 0770 RADIUS 27 87 30 0 33 0 36 0 38 0 40 0 42 0 44 28 46 255 XSPAC 12 704 12 734 12 719 12 725 12 760 12 948 13 251 13 692 14 028 BROTOR 7 555 7 665 8 042 8 338 8 542 8 839 9 173 9 512 9 79 4 52 4 538 4 563 4 563 4 562 4 563 4 561 4 487 4 462 74 368 74 926 75 547 75 862 75 859 76 453 77 41 75 362 74 846 80 0 0 126 0 294 0 465 0 491 0 601 0 704 0 648 0 568 0 0 186 0 412 0 624 0 772 1 010 1 352 1 687 1 900 10 38 78 36 10 33 24 30 48 28 49 26 39 24 09 21 31 19 21 20 61
45. ub streamline Fan inner splitter dia streamline 3 NDATC NDATS Fan hub streamline Fan inner splitter dia streamline Fan outer splitter dia streamline Fan tip streamline Note that all input radii must be specified starting at the inner most radius given above and ending with the outer most radius shown above 2 2 6 Streamline Geometry and Performance Input These parameters should be input at the number of streamlines described by the previous section Section 2 2 5 i Variable Needed as input for Variable Description Name IPRED option X X V RADIUS Radius of streamline rotor l e BROTOR Rotor aerodynamic chord V v XSPAC x x x REAL tostator le axial spacing v vVYRD lx ix Tx Non radial variation Rotor t e see Figure 13 BSTATR Stator aerodynamic chord YSD x Non radial variation stator e see Figure 13 Axial variation stator l e see Figure 14 Stator stagger angle Relative flow angle rotor l e Relative flow angle rotor t e Rotor loss coefficient See Note 6 Axial mach no fotor Relative flow angle stator Le V x X X X X X X X X Absolute mach no stator 2029 1 Schematic View of a Rotor Blade and Stator Vane LE Looking Down the Turbofan X AXIS in Stator fixed Coordinates RADIAL LINE RADIAL LINE ROTORLE STATOR LE
46. udes in pound force per square inch for each propagating radial mode This output may then be non dimensionalized for input into the Eversman Radiation Code The Plot Data output file is the final output file and is optional The user controls the creation of this file through the IPLOT input option For information on the use of IPRINT and IPLOT refer to section on Case Descriptive Input Parameters of this manual The output files will be of the following format Output File Output File Output File What is in it Name Extension Noise output file Same v072out Wake and noise output from the as user s program including power levels input file and complex radial mode amplitudes using radial mode shape as defined by Ref 2 Peak complex mode amplitudes Ib in normalized to the Eversman Radiation Code To use this output in the radiation code non dimensionlize it by pc where far field freestream air density and c far field freestream speed of sound Note These are peak levels and not RMS levels Plotting output file not used Same name plotdat Data for a plotting routine that output only output if as user s was never completed IPLOT 1 input file 3 2 NOISE OUTPUT FILE DESCRIPTION Same name as user s input file Radiation output file The Noise output will be written to a file of the form user input file name v072out
47. ult the criteria becomes NRAD 2 1 1 2x No ofradial mode zero crossings 2 1 2 3 where NRAD Number of Radial strips required based on acoustic radial mode shape MU Highest order radial mode which propagates at a given harmonic for an m 0 circumferential mode Also equal to the number of radial mode zero crossings 14 045 0 8 AMPLITUDE RADIUS a 4 0 Mode HUB TIP RADIUS b 4 21 Mode 0 AMPLITUDE Figure 9 Radial Mode Shapes 15 The second parameter we need to consider relates to the number of wakes slicing along the stator span at any one time best explain this aspect we consider Figure 10 which illustrates the rotor stator geometry relative to the wake flow geometry obtain maximum aerodynamic efficiency standard high bypass ratio fans are highly twisted along the span This twist from hub to tip causes the wakes at the tip to travel further than the wakes at the hub Figure 10a The result is that the circumferential locations of the wakes from hub to tip create a line which is highly canted where the cant angle increases as the wakes travel downstream Consequently at any one time the stator may experience more than one rotor wake on its span at once Figure 10b resulting in pressure variations along the span At any one time on a high bypass ratio engine there may be up to four spanwise
48. wo parameters are important in this case The first one relates to the number of Zero crossings a radial mode shape makes across the span An example of this is shown in Figure 9 for the 4 0 and the 4 21 modes We know that the radial mode shape of the 4 0 mode has nozero crossings while the radial mode shape of the 4 21 mode has 21 sign changes along the span As can be seen the number of radial stations needed to effectively represent the 4 21 mode shape is going to be many more than are needed to represent the 4 0 mode shape The problem then becomes one in which we cannot efficiently calculate which modes will be cuton and cutoff before we enter the program for every circumferential and radial mode and effectively use this information However we can do this calculation for one mode per harmonic i e the m 0 mode which if generated would have the highest number of propagating radial modes Since we can calculate how many radial modes will propagate from this circumferential mode for each harmonic then we can efficiently utilize this information to choose a conservative estimate for the number of radial integration stations we need Consequently it was determined that we need at least two points along the span i e the hub and the tip points plus two more points for every time the radial mode shape crosses zero In addition the specialized integration procedure in the program requires an odd number of radial integration points As a res
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