NUMERICAL SIMULATION OF CENTRIFUGAL COMPRESSOR

Transcription

1 ARPN Journal of Engneerng and Appled Scences Asan Research Publshng Networ (ARPN). All rghts reserved. NUMERICAL SIMULATION OF CENTRIFUGAL COMPRESSOR Srnvas G. Department of Aeronautcal Engneerng, MIT-Manpal Unversty, Manpal, Udup, Karnataa, Inda E-Mal: ABSTRACT Desgn of 3D-centrfugal mpeller blades s a compromse between manufacturablty and aerodynamcs. The aerodynamc requrement s that edge veloctes along the mpeller channel passage surfaces le hub, shroud, pressure and sucton surfaces vary smoothly wthout sudden deceleratons, whch would otherwse cause flow separaton leadng to losses. The paper ams to study several flow characterstcs between blade channels usng commercal flow solver CFX based on fnte volume technques. From the publc doman lterature, usng the blade data, profles are developed, for whch multbloc hexahedral computatonal meshes are generated. Usng the perodc boundares and defned flow condtons at nflow / ext flow and blade rotatons, the turbulent vscous flow between blade channels are computed. The effcency related parameters usng average quanttes, besdes flow pattern n terms of veloctes, streamlnes and pressure dstrbuton on blade surfaces are graphcally nterpreted. An attempt s also made to study the nfluence of pressure loads on structural deformatons n the chosen blade profle. Ths analyss also provdes nsghts nto the locatons of maxmum prncpal stresses or equvalent stresses on blade surfaces. Ths paper hghlghts aero-mechancal features of centrfugal mpeller obtaned from several numercal smulatons, whch are expected to provde a sound bass for further nvestgatons. Keywords: centrfugal compressor, CFX, multbloc, blades, streamlnes. INTRODUCTION The gas turbne engnes powerng the most passenger and mltary arcrafts are also called et engnes. All et engnes have a compressor to ncrease the pressure of the ncomng ar. There are two compressor desgns found n et engnes as shown n Fgure-1, whch are axal type wheren arflow s parallel and centrfugal type wheren arflow s perpendcular to the axs of rotaton. In centrfugal compressor due to the low effcency and thrust-to weght rato, they are lmted to short range applcatons [1]. However, the nablty for spar gnton engnes to wor at hgh alttude warrants further development to mprove the effcency of these mnature gas turbnes. Furthermore, gas turbnes n the form of turboet or turbofan are capable of provdng propulson at hgher speed, where spar gnton engnes are not applcable wth ar screws. Fgure-1. Jet engne centrfugal compressor MODELING OF COMPRESSOR BLADES Based on publc doman lterature on desgn of compressor blades used n aero engnes, typcal blade profle s constructed usng the template based software module bult n ANSYS worbench-12 verson [2]. The blade gen layout wth constructon features related to wrapper angle, number of blades, angles dstrbuton and blade thcness for generaton of three dmensonal blades was done as shown Fgure-3 n order to carry out structural analyss of the blade surfaces the software provded export optons to generate computatonal mesh accountng blade thcness s also explored n statc structural analyss pacage. The blade profles generated n above software module are mported to template based mult-bloc structured computatonal mesh software module called turbo grd. The nformaton related to machne data, profle curves, several nputs requred for wdth factor perodcty producton, topology freezng for generaton of geometrc representaton n terms of surface mesh generaton wth master and slave control ponts beng generated. default orentaton of master and slave control ponts on the blade surfaces are to be moved to obtan better orthogonally between mesh ponts. After these operatons three dmensonal computatonal mesh generaton process for compressor blade wth boundary patches, perodc surfaces are created. MESHING OF COMPRESSOR BLADES The three dmensonal mesh generated for compressor blade s mported nto the ANSYS Preprocessor usng Turbo setup. In ths process the grd data s read and checed for rght handed coordnate system and scalng the grd data nto SI unts, doman setup wth materal propertes requred are hghlghted. The surface mesh of blade nlet, ext, blade, left and rght perodc and hub and shroud surfaces are vsualzed as shown n Fgure- 2. The compressor mpellor wth multple blades n shaded vew s shown n Fgure

2 ARPN Journal of Engneerng and Appled Scences Asan Research Publshng Networ (ARPN). All rghts reserved. was checed and the grd data was found to be wthn tolerances. The mesh has been exported as.gtm fle for further pre-processng n the Ansys CFD pre and solver software pacage. Fgure-2, 3. Surface grd sngle Blade, Shaded vew of 3d compressor blades. The blade geometry desgned has been saved as. bgd fle for future modfcatons and shape optmzaton. For further analyss, the.bgd fle can be exported as hub, shroud, profle and perodc curves to Turbogrd module where space dscretzaton can be carred out whch n turn can be exported to CFD flow smulaton. In addton to ths, ths software also exports as IGES fle for dscretzaton of computatonal mesh wth structured mult bloc mesh for blade thcness for structural analyss. Thus for rapd analyss, ths software module provdes detaled 3D sold modelng geometry components for maxmum accuracy when assessng a partcular desgn. COMPUTATIONAL MESH FOR STRUCTURAL ANALYSIS Most flud flow smulaton technology uses completely dfferent meshng, loadng and solvng methods compared to structural smulaton. And ths s where the true power of Worbench 12.0 comes nto play. When the user s connectng up the dalogs wthn the schematc layouts, many of these are handled automatcally, smply by draggng a connecton between the outputs of one analyss system and the nputs of another. When and f there s mappng to be done, ths s handled n a very smple dalog that maes the process smple, rather than the often-tortuous methods tradtonally assocated wth ths type of wor [2]. There are no geometry creaton tools n the Mechancal applcaton and so geometry must be attached to the Mechancal applcaton. The geometry from ether of the CAD Systems and Blade Gen Model can be connected to smulaton model before setup opton s actvated. Fgure-4. Compressor blade surface wth mproved control ponts. The control ponts on the perodc lne should be postoned, e.g. n the mddle of the blade passage. Selectng the optons-show-duplcate blade opton wll gve gudance to locate the md passage ponts. The O-grd at leadng and tralng edge control ponts should be postoned at the approxmate 45 degree poston around the leadng and tralng edge radus. The O-grd mdchannel control ponts should be postoned to mae mdchannel control curve perpendcular to the O-grd. The near blade upstream and downstream control curves should bsect the angle between the O-grd and the channel boundary. After the modfcatons to control ponts to mprove mnmum face angles and selectng the mesh sze optons the resultng topology for blade hub and shroud surfaces are shown n Fgure-4 wheren t s observed that percentage of bad elements s zero Volume mesh has been generated and shown for the sngle blade row n the Fgure-5. The mesh qualty n terms of sew angles, aspect rato and rght-handed ness Fgure-5. Three dmensonal mesh for sngle compressble blade row. The next step s to generate the meshng sold body for whch several methods are provded n ANSYS Worbench these tools have the beneft of beng hghly automated along wth havng a moderate to hgh degree of user control. Upon startup of the meshng applcaton meshng optons panel dsplays, whch allows you to qucly and easly set your meshng preferences based on the physcs you are preparng to solve. For sold bodes, the software uses meshng technques based on algorthms and element shape. One of the technque extensvely used are called patch ndependent meshng for the part usng tetrahedral element. The default value selects meshng control parameters and provdes a successful automated mesh. By default, the applcaton attempts to use auto sweepng for sold models and quadrlateral element generaton for surface body models. If a model s not sweepable, the Patch Conformng mesher under Tetrahedrons s used. 640

3 ARPN Journal of Engneerng and Appled Scences Asan Research Publshng Networ (ARPN). All rghts reserved. Then one needs to change the default values sutably n the Mesh opton panel. Fgure-6. Three dmensonal mesh on the blade wth thcness. Patch ndependent mesh are defned by max element sze and number of elements. The default value s calculated from the dagonal length of the boundng box whch s based on the ntal seed settngs of mesh obect folder. When curvature and proxmty refnement optons enabled, the mesh automatcally refned based on geometry. Ths wll result n larger elements on flat planar faces and smaller elements n areas of hgh curvature or wthn small gaps. However proecton to geometry and smoothng may push the sze even smaller for some of the elements as observed n blade leadng edges. OVERVIEW OF FLUID MECHANICS FOR TUBOMACHINERY All The transport of flud comprses gases/lqud from one component to other n power/process equpment are descrbed through mass, momentum and energy conservaton prncples. The Naver Stoes (transport) equatons are derved from these prncples and are dscussed by Hoffman, K.A (1993) whch are represented mathematcally as: ρφ + t dv ( ρφu r ) = dv ( Γgradφ ) + q φ The terms on Left Hand Sde (LHS) defnes acceleraton of flow over tme wth nerta depends on the sum of the external forces, dffuson and sources actng on the flud element. If the value of ϕ s 1, the equaton (1) results n contnuty equaton. If the value of ϕ s ether u or v or w, the above equaton descrbes momentum equaton n x, y, z drectons. If the value of ϕ s h then the above eqn. yelds to energy equaton. Two mportant materal propertes of flud.e., densty and vscosty, whose rato tmes characterstc flow velocty and length are defned as Reynolds number. Ths non-dmensonal quantty s the rato of nertal forces to vscous forces, whose magntude depends upon flow dsturbances, can change the flow from lamnar to turbulent. In other words, f the Reynolds Number s small, then the flow wll be lamnar, meanng that the flow progresses n layers [6]. If the Reynolds Number s large then the flow wll be turbulent, meanng there wll be a mxng of flow layers and the creaton of large eddes. The flow conssts (1) of a spectrum of dfferent scales n turbulent flow, largest eddes are the order of geometry scales and breas nto smaller as tme progress. At the other end of the spectra, the smallest eddes by vscous forces dsspated nto nternal energy. Even though turbulence s chaotc, ts characterstcs are determned through Naver-Stoes equatons. The turbulence s dsspatve, whch means that netc energy n the small eddes are transformed nto nternal energy. The small eddes receve the netc energy from slghtly larger eddes. The slghtly larger eddes receve ther energy from even larger eddes and so on. In order to resolve wde spectrum of scales n turbulent eddes, normally two approaches are employed Ths requres dense mesh ponts for proper resoluton and ts soluton depends on heavy computatonal resources that are expensve, tme consumng process and therefore very rarely used smulaton technque. The other approach generally used for most of the applcatons are Reynolds averagng process wheren flow varables are decomposed nto mean and fluctuatng components as: u u + = u (2) ' Where =1.2, 3 denotes n x, y, z drecton [7]. Lewse the pressure and other scalars can be expressed as: φ + ' = ϕ φ (3) Substtutng flow varables n ths form nto the nstantaneous contnuty and momentum equatons and tang a tme (or ensemble) average (and droppng the over bar on the mean velocty) yelds to: ( ρ ) = 0 ρ + u t x ρu + ρu u = t x u p u + 2 u µ x x δ x x 3, x l l ρ + ρu' u' x (4) (5) Equaton (4), (5) are called RANS equatons. The ' ' u u term n the equaton (5) results from averagng process and s called Reynolds Stress. Wth the help of Boussnesq hypothess to relate the Reynolds stresses, ' ' choosng Kronecer delta δ=1 f = and u u = 2 the Reynold s stress term n the equaton (5) s rewrtten as: u u u ' u u ' 2 ρ = µ t + ρ + µ t δ x x 3 x, (6) 641

4 ARPN Journal of Engneerng and Appled Scences Asan Research Publshng Networ (ARPN). All rghts reserved. where µ t s turbulent vscosty. To resolve turbulence vscosty and Reynolds stresses, eddy vscosty models based on Boussnesq hypothess wll leads to zero, one and two equaton turbulence models and Reynolds s Stress Models (RSM). The strength and weaness of these models for predcton of turbulence effects are extensvely studed. Whenever non-sotropc effects are mportant use of hgher models le v 2 fs preferable to predct separaton near the wall. When the flud flow s subected to rotatng components, Large Eddy Smulaton (LES) or Detached Eddy Smulatons (DES) s employed to evaluate flow characterstcs as a functon of turbulence vscosty and energy dsspaton. These models are based on fltered equatons, whch stll requre fner meshes to solve RANS calculatons n transent mode. In the smulaton of turbulent flows, accurate estmaton of pressure drop nfect hghly dependent on usage of turbulence model wth smooth/rough wall functons. STRUCTURAL DEFORMATIONS DUE TO FLOW PRESSURE LOADS - FSI The mathematcal formulatons to smulate structural deformatons and stresses on the component surfaces are extensvely dscussed n the lterature. To determne the deformatons, the governng equatons are mathematcally represented as: ρ u & = σ + b (10) where u& & s dsplacement, σ s stress feld that depends on stran, nternal varable, b - body force. The expresson for stran n terms of dsplacement can be expressed as: T ( u & + u& ) 1 ε = (11) 2 The fnte volume form and after ntegraton by parts, the equaton (19) can be wrtten as: In order to compute the stress tensor ε on the centrods of the faces, t s requred to establsh the dscrete form of the stran tensor and the deformaton gradent u& &. The deformaton gradent s computed at cell centers based on the dfference n dsplacement between neghborng ponts. The approxmaton of stffness matrx can be accumulated over all faces are: r f K = = N() (14) u f ( ) u, Wth the help of Newton method to correct dsplacement equaton (14) further smplfes to: K u&, = n r ; n n u&& u&& + 1 = u& (15) To obtan structural deformatons, pressure/heat flux loads are normally obtaned from CFD solver usng fnte volume approxmatons and deformatons/stresses are obtaned through fnte element technques. However, n the current versons of few flow solvers, flow and thermal stress based on fnte volume technques can provde FSI characterstcs of ndustral components. FLOW SIMULATION IN CENTRIFUGAL COMPRESSOR BLADE The three dmensonal mesh generated for compressor blade s mported nto the ANSYS Preprocessor usng Turbo setup. In ths process the grd data s read and checed for rght handed coordnate system and scalng the grd data nto SI unts. Among several boundary condtons appled for flow smulaton blade wall rotaton about Z-axs wth specfed revoluton per mnute s accounted. The boundary condtons determne to a large extent the characterstcs of the soluton you obtan. Therefore, t s mportant to set boundary condtons that accurately reflect the real stuaton to allow you to obtan accurate results. ρ udv & = σ + V A ds V bdv (12) For all cells n the doman V, the dscrete form of the momentum equaton become: ρ u& V = f + b V where f = σ s ; f () s surface vector (13) Droppng nertal terms and consderng some of the forces actng on the body are zero for a statc case, the equaton (13) can be re-wrtten as: r = f f () + b V (13) Fgure-7. Boundary condtons (Flow Solver). Boundary condtons must be appled to all the boundng regons of the computatonal doman. Boundary condtons can be nlets, outlets, openngs, walls and 642

5 ARPN Journal of Engneerng and Appled Scences Asan Research Publshng Networ (ARPN). All rghts reserved. symmetry planes as shown n Fgure-7. For a gven computatonal doman, boundary condtons can be gven that over-specfy or under-specfy the problem. Ths usually results n non-physcal solutons or falure of the soluton to converge. To predct vscous losses ndustry standard two equaton turbulence model has been employed. Wth sutable ntal guess and under relaxaton parameters, flow and energy equatons are terated tll the resdual errors are dropped to the order of 1e-04 shown n fgure from After completon of flow smulaton a macro bult n the software for generatons of report s actvated to obtan performance and effcency calculatons. The varatons n the rotatonal speed of the blade has been accounted to predct total pressure rato and Isentropc effcency of the blade s estmated and plots generated to understand the phenomena of chong and surgng. Fgure-8. Momentum and mass converged resdual plot. The nfluence of pressure loadng on the blades for structural ntegrty s examned usng lnear statc structural analyss module bult n ANSYS worbench. The process of tang blade geometry n structural smulaton s connected frst and later CFX result fle was mported. Setup s actvated so as to obtan the geometry of the blade along wth flud-sold surfaces n structural smulaton module. Fgure-10. Heat transfer converged resdual plot. Automatc methods to generate computatonal mesh for blade along wth thcness are used and appled to get mported pressure load on blade surface. Blade s constraned through fxed support and usng nertal opton wall rotatons are defned. Wth ths physcs setup and materal propertes smulatons has been carred out for Total dsplacement and equvalent stresses. The results obtaned for blade deformatons and maxmum and mnmum stress levels are nterpreted graphcally. RESULTS AND DISCUSSIONS The mpellor blades are rotatng wth rpm s subected to mass flow g/s wth the worng pressure s of order 1 atm. The pressure loadng over stream wse drectons for the span of 20%, 50% and 80% are shown n the Fgures The pressure profles on the surfaces near hub mean and tp regon provdes detals of boundary layer separaton wth steep adverse pressure gradents [5]. Fgure-11. Pressure loadng over stream wse loadng span of 20%. Fgure-9. Turbulence converged resdual plot. Fgure-12. Pressure loadng stream wse loadng span of 50%. 643

6 ARPN Journal of Engneerng and Appled Scences Asan Research Publshng Networ (ARPN). All rghts reserved. Fgure-13. Pressure loadng over stream wse loadng span of 100%. Both Fgures show the pressure and effcency curve features of typcal centrfugal compressors, where pressure and effcency pea at a certan flow rate. Increasng or decreasng the flow rate from ths optmum pont results n a reducton n both pressure and effcency. Fgure-16. Stage effcency curves. CONCLUSIONS The applcaton of centrfugal compressor wth bacward sweep twsted blade n turbofan and ts performance of ar moton from upstream components are descrbed based on publshed lterature. Smulaton for dfferent rotatonal speeds wth the varatons n mass flow, the pressure and effcency curve features of typcal centrfugal compressors, show that the pressure and effcency have pea at a certan flow rate. Fgure-14. 3D streamlnes from the nlet of mpellor around the blades. Fgure-17. Equvalent stress under blade surface. Fgure-15. Pressure rato mass flow curve of the compressor. Pressure drops rapdly wth the ncrease n mass flow rate and ths wll lead to chong at a certan pont. On the other hand, pressure also drops accordngly as the mass flow rate s reduced from that optmum pont and the stage wll qucly start to surge. The exact ponts for surgng and chong would not be predcted. Increasng or decreasng the flow rate from ths optmum pont results n a reducton n both pressure and effcency. Pressure drops rapdly wth the ncrease n mass flow rate and ths leads to chong at a certan pont. On the other hand, pressure also drops accordngly as the mass flow rate s reduced from that optmal pont and the stage qucly starts to surge. It s observed that maxmum stress s tang place at the hub surface tralng edge and mnmum stress s notced on shroud surface when pressure load obtaned from CFD soluton s specfed on the blade surfaces s shown n Fgure-17. As mass flow vares at constant rotatonal speeds the magntude of maxma and mnma of stresses decrease. Smlarly, the total deformaton also decreases at constant speed at dfferent mass flow rates. REFERENCES [1] D. Japse Centrfugal Compressor Desgn and Performance. Concepts ETI Inc. 644

7 ARPN Journal of Engneerng and Appled Scences Asan Research Publshng Networ (ARPN). All rghts reserved. [2] R. Aunger Centrfugal Compressors: A Strategy for Aerodynamc Desgn and Analyss. ASME. [3] D. Flaxngton and E. Swan Turbocharger Aerodynamc Desgn. Proc. Instn Mech Engrs. 213(Part C): pp [4] P. Dalbert, B. Rb, T. Kmec and M.V. Casey Radal Compressor Desgn for Industral Compressor. Proc Instn Mech Engrs. 213(Part C): [5] P.M. Came and C.J. Robnson Centrfugal Compressor Desgn. Proc. Instn of Mech. Engrs. 213(Part C): [6] A. Lohmberg, M. Casey and S. Ammann Transonc Radal Compressor Inlet Desgn. Proc Instn of Mech Engrs. 217(Part A): [7] J.D Denton and W.N. Dawes Computatonal Flud Dynamcs for Turbomachnery Desgn. ProcInstn of Mech. Engrs. 213(Part C):