assessment of various turbulence models in a high pressure ... · computational fluid dynamics...

Proceedings of ASME TURBO EXPO 2011: Power for Land, Sea & AirGT2011

June 6-10, 2011, Vancouver, CANADA

GT2011-46829

ASSESSMENT OF VARIOUS TURBULENCE MODELS IN A HIGH PRESSURE RATIOCENTRIFUGAL COMPRESSOR WITH AN OBJECT ORIENTED CFD CODE

Luca Mangani∗, Ernesto CasartelliLucerne University of Applied Sciences and Arts

Technik & ArchitekturTechnikumstrasse 21, 6048

Horw, [email protected]

Sebastiano MauriAerodynamics Compressors

MAN Diesel & Turbo Schweiz AGHardstrasse 319, 8005Zuerich, Switzerland

ABSTRACTThe flow field in a high pressure ratio centrifugal compres-

sor with vaneless diffuser has been investigated numerically.Main goal is to assess the influence of various turbulence modelssuitable for internal flows with adverse pressure gradient. Thenumerical analysis is performed with a 3D RANS in-house mod-ified solver based on an object-oriented open-source library. Ac-cording to previous studies from varying authors, the turbulencemodel is believed to be the key parameter for the discrepancybetween experimental and numerical results, especially at highpressure ratios and high mass-flow. Particular care has beentaken at the wall, where a detailed integration of the boundarylayer has been applied. The results presents different compar-isons between the models and experimental data showing the in-fluence of using advanced turbulence models. This is done inorder to capture the boundary layer behavior, especially in largeadverse pressure gradient single stage machinery.

NOMENCLATUREMa Mach, [−]m Mass flow rate, [kg s−1]k Turbulent kinetic energy [m2 s−2]

Pk Turbulence production term = µt

(∂Ui∂x j

+∂U j∂xi

− 23 δi j

∂Uk∂xk

)∂Ui∂x j

−23 ρk ∂U j

∂x j, [kg m−1 s−3]

p Pressure, [kg m−1 s−2]

∗Address all correspondence to this author.

S Strain tensor = 0.5(

∂Ui∂x j

+∂U j∂xi

), [s−1]

T Temperature, [K]U Velocity vector, [m s−1]y+ Non dimensional normal wall distance, [−]

GreeksαΩ,ε Constitutive constants for ω equation in SST modelβ Geometric angles, circumferential direction as reference, [−]η Isentropic efficiency, [−]µ Molecular viscosity, [kg m−1 s−1]µt Eddy viscosity, [kg m−1 s−1]ρ Density, [kg m−3]ω Turbulence frequency, [s−1]Γ Blending function for SST Model

AcronymsAWT Automatic Wall Treatment k−ω SST turbulence modelC.C. Commercial CodeMu Impeller tip Mach numberPS Pressure SideRANS Reynolds Averaged Navier-StokesSS Suction SideSST k−ω Shear Stress Transport Low-Re turbulence modelV 2F v2 − f − k− ε Durbin turbulence model

Subscripts0 Total conditions1 Inlet conditions

1 Copyright c© 2011 by ASME

Proceedings of ASME Turbo Expo 2011 GT2011

June 6-10, 2011, Vancouver, British Columbia, Canada

GT2011-46829

1 Copyright © 2011 by ASME

2 Impeller Outlet

INTRODUCTIONComputational Fluid Dynamics (CFD) is, along with exper-

imental research, an indispensable technique for the design andinvestigation of flow phenomena in centrifugal compressors. Fortwo decades 3D numerical investigations have been included inthe development process of this product. The range of applica-tions and investigations is very large. It starts with the analysisand design of the single components like impellers, vaned dif-fusers, return channels in multi stage machines and volutes [1][2] [3], through the matching of the components up to the inves-tigation of the unstable operating range during rotating stall [4]or the influence of range increasing devices like casing wall treat-ment, flow injection/extraction or recirculation devices at the im-peller inlet [5] [6].

CFD techniques for these applications are to some extentmature and reliable, mainly independent of the code used, beit commercial, in-house or academic. Nevertheless there is adistinct prediction quality of the results when computing ei-ther subsonic or transonic compressors. For the former a verygood agreement between numerical and experimental results canclearly be achieved, thus strongly increasing the confidence inthe simulations. On the latter for high pressure ratio machineswith transonic conditions discrepancies are still present and canbe considerably large [7] [8] [5]. For these types of compres-sors the trends are generally well captured, but critical valueslike choke mass-flow or instability onset are not always accu-rately predicted.

This situation in high pressure ratio compressors has shownlittle improvement over the time, if compared to the results ob-tained for the subsonic cases.

The causes of such discrepancies are still a matter of inves-tigation. On one side geometrical discrepancies between the realand the virtual model are mentioned. For example, fillet radiiat the blade root, which are usually not modeled numericallyand blade deformation at high rotational speed or tip clearancesize [9], which in experiments is variable along the blade, dependon the rotational speed and are therefore not easily measurable.

On the other hand additional modeling and numerical rea-sons can hide behind these discrepancies. First on the list arethe turbulence models, additionally followed by numerical tech-niques and parameters. . Also to be noted is Mesh size and theimportance it can play in the accuracy of results.

In this paper we analyze the influence of various turbulencemodels suitable for internal flows with adverse pressure gradient.The idea is to asses if turbulence is a key modeling parametercausing the discrepancy between experimental and numerical re-sults, when dealing with high pressure-ratio radial-compressors.For this, comparisons between numerical results and experimen-tal data are presented, both for global performance data and local

flow field features. Mesh influence is also to some extent inves-tigated.

In addition to the turbulence model assessment, this workalso represents another step towards a more complete develop-ment process aiming to transform the OpenFOAM R© code into acomplete CFD suite for steady and unsteady analyses in turbo-machinery. The development steps to make this code suitable forsuch simulations and to point out its potential as a customizableCFD tool, appropriate for both academic and industrial research,are mentioned below.

In addition to the previous validation efforts, see Manganiet al. [10] based on internal thermo-aerodynamic and conjugatesimulations, this paper represents a further development of thecode in the domain of the centrifugal compressor aerodynamics.

CASE DESCRIPTIONIn order to investigate transonic flow phenomena, a high

pressure ratio centrifugal compressor based on the experimen-tal setup by Krain et al [8] was chosen. The stage has beendesigned and built at DLR. The geometry is representative forhighly loaded compressors, with high specific speed and mass-flow coefficient, which are higher than in typical today’s indus-trial applications. The compressor stage investigated is com-

Table 1. IMPELLER DESIGN DATA SRV2-OInlet Total Pressure P0 101325 Pa

Inlet Total Temperature T0 288.15 K

Shaft Speed n 50000 rpm

Blade Count Full/Splitter z f /zs 13/13 rpm

Mass Flow Rate m 2.55 kg/s

Blade Angle LE Tip β1t 26.5 deg

Impeller Tip Radius r2 112 mm

Blade Angle TE β2 52 deg

Impeller Press. Ratio π12 6.1 −

Efficiency η12 0.84 −

posed of a centrifugal impeller with thirteen main and splitterblades and a vaneless diffuser. The impeller features splitterblades in order to increase the swallowing capacity by remov-ing the blockage near the main blade leading edge.

The impeller also has a level of back-sweep and is un-shrouded with a tip clearance varying from 0.5 mm at the bladeinlet to 0.3 mm at the exit.

The impeller (SRV2-O) key design data are shown in Ta-ble 1. Further details can be taken from [1].



OpenFOAM R©

The OpenFOAM R© (Field Operation And Manipulation)code [11, 12] is an object-oriented numerical simulation toolkitwritten in C++ language. The toolkit implements operator-basedimplicit and explicit second and fourth-order Finite Volume (FV)discretization in three-dimensional space. Efficiency of execu-tion is achieved by the use of preconditioned Conjugate Gradi-ent [13] and Algebraic Multigrid solvers and the use of massivelyparallel computers in the domain decomposition mode.

Being primarily a C++ library ready to create executables,OpenFOAM R© uses an object based programming-language.Meaning programmers can use OpenFOAM R© native classes toboth define their own classes or to build new applications, suchas solvers or utilities, with ease of development. Object ori-ented programming allows data abstraction, object orientation,operator overloading and generic programming. This enablesthe construction of new types of data specific for the problemto be solved, the bundling of data and operations into hierarchi-cal classes preventing accidental corruptions, a natural syntax foruser-defined classes.

OpenFOAM R© native grid engine can handle meshes of ar-bitrary polyhedra bounded by arbitrary polygons, giving a largeflexibility in mesh generation. Switching to OpenFOAM R© wayof thinking, programmers need to approach a field based philos-ophy more than a cell or face based one. Each physical quantity(no matter what dimension, rank or size) is represented by a sin-gle object and treated as a field.

Differential operators can be treated like finite volume cal-culus (fvc) or finite volume method (fvm) operators. The firstapproach performs explicit derivatives returning a field, the sec-ond is an implicit derivation converting the expression into ma-trix coefficients. The idea standing behind it is to think aboutpartial differential equations in terms of a sum of single differ-ential operators that can be discretized separately with differentdiscretization schemes. Differential operators such as gradient,divergence, laplacian and curl have been overloaded for the dif-ferent types of field, giving each of them the most suitable mean-ing.

Implementing different types of equations is therefore onlya matter of combining in a different way the same set of basicdifferential operators. Just to give an example of the capabil-ity of such a top-level code, a standard equation like momentumconservation

∂ρU∂t

+∇ · (ρUU)−∇(µ∇U) =−∇p . (1)

can be implemented in an astonishingly, almost natural lan-guage which is ready to compile source C++ code.

solve(

fvm::ddt(rho, U)+ fvm::div(phi, U)- fvm::laplacian(mu, U)

==- fvc::grad(p)

);

Another important feature allowed by object programming is thedimensional check. Physical quantities objects are in fact con-structed with a reference to their dimensions and so only validdimensional operations can be performed. This avoids errors andallows for easier understanding.

Although OpenFOAM R© can be used as a standard simula-tion package, its tools are in general too rough to well predictcases of industrial interests. Its strength does not lie in its abil-ity to behave as ready-to-use code but more so in being open interms of source code and in its inner structure and hierarchicaldesign, thus giving the user the opportunity to fully extend itscapability.

COMPUTATIONAL DETAILSCFD Solver

A pressure-based finite volume solver using a co-locatedvariable approach suitable for calculating steady-state flows at allspeeds was developed based on the OpenFOAM R© framework.To make it robust, fast and reliable for 3D RANS simulations inturbomachinery, it was necessary to implement additional sub-modules. The package coded by the authors within the environ-ment includes a suitable algorithm for compressible steady-stateanalysis. A SIMPLE-C like algorithm was specifically devel-oped to extend the application fields to a wider range of Machnumbers, especially for transonic and supersonic conditions.

Full second order upwind scheme for convection discretiza-tion together with several Low-Reynolds number eddy-viscosityturbulence models, chosen among the best performing in wallbounded flows, were developed and implemented: for further de-tails, see Mangani [14]. The code has recently been used also forheat transfer analysis [10] [15] [16] [17] and conjugate simula-tions [18] [19] for gas turbine applications.

Automatic Near Wall TreatmentAll previously cited Low-Reynolds models require a fine

grid at the walls (y+ ∼ 1), but for cases of a certain complex-ity this becomes quite a strict constraint. Unfortunately one ofthe most common issues in the preparation of accurate calcula-tion meshes for wall bounded flows of complex geometries isthe assurance of a proper y+ distribution, particularly when theflow field is characterized by a wide range of flow Mach number.Therefore, in order to increase grid independence, a mixed ap-proach between wall-function and Low-Reynolds was added to



the k−ω SST model. The idea, see [20], is to blend the two ap-proaches via a blending function Γ calculated algebraically fromthe non-dimensional wall distance. Both turbulent productionand turbulent specific dissipation are imposed on the first nodemixing the effects of the Low and the High Reynolds contribu-tions. Starting from the transport equation for ω:

∂(ρω)∂t

+∂(ρωU j)

∂x j− ∂

∂x j

[(µ+µtαΩ)

∂ω∂x j

]=

ρC1Pk

µt−ρC2ω2 +

2ραε(1−F1)

ω∂k∂x j

∂ω∂x j

, (2)

both contributions are formulated as follows,

Pawt,p = PLR,pe−Γ +PHR,pe−1Γ , (3)

ωawt,p = ωLR,pe−Γ +ωHR,pe−1Γ , (4)

where Γ is calculated with an algebraic expression for y+ de-fined with uτ = max(uτ,LR,uτ,HR) . The same blending is appliedto thermal quantities following Kader universal law [21]. Forfurther details concerning Automatic Near Wall Treatment thereader is referred to [20].

Turbulence ModelingThree turbulence models are used in the present work,

namely Low-Reynolds formulation k − ω Shear Stress Trans-port (SST) in the revised form of Menter [22] with Dirichlettype boundary condition for ω at the wall, its automatic walltreatment version (AWT) and the four equation turbulence modelv2 − f − k− ε (V2F) [23] with realizability constraint [24].

Computational DomainAs reported also by previous authors in Krain et al. [7] [8],

in the present work the analysis of the radial compressor wasperformed assuming periodicity of the solution thus leading to areduction of the computational domain, limiting the calculationof the thermodynamic variables to only one thirteenth of the realcomputational domain. The computational domain covers there-fore a single flow passage. Such an approach allows CPU mem-ory and computational time saving. In this case cyclic type 1-to-1 boundary condition was used in order to accurately capturethe periodicity of the flow in pitch-wise direction (see Fig. 1).

The inlet of the domain was taken upstream of the impellerand normal to the axis, so total conditions based on pressure andtemperature with an axial direction of the absolute inlet velocitywere imposed, see Figure 2. For the walls no slip and adiabaticconditions were defined.

Figure 1. OVERALL CENTRIFUGAL COMPRESSOR DOMAIN.

Figure 2. COMPUTATIONAL DOMAIN.

Computational Mesh

The impeller computational domain was divided into a typ-ical I&H-type grid to obtain better mesh quality with multisplit-ters configuration. Clustering of the mesh along the span-wisedirection was also used, Figure 3.

Two meshes were selected for AWT and Low-Reynolds tur-bulence models. Each mesh was based on hexahedral elements,and the total number of grid points was 979,884 and 2,335,968respectively. The value of y+ for the first grid point above thewall at design conditions was below one with an average of 0.356for the finer grid, as required by Low-Reynolds models con-straints, and below 16 with an average of 8 for the AWT model.

The impeller tip clearance was fully analyzed for both mainand splitter blade using Generic Grid Interface boundaries, withconservative mass-based interpolations. For the coarse mesh theminimal skewness angle was 33.30 with a maximum aspect ra-tio of 2802, while for the finest grid the average was 13.02 and204970 respectively.



(a) IMPELLER GRID.

(b) SPAN-WISE GRID DETAIL.

Figure 3. COMPUTATIONAL GRID FOR AWT TURBULENCE MODEL.

(a) MAIN BLADE

(b) SPLITTER BLADE

Figure 4. MODELED TIP GAP FOR AWT TURBULENCE MODEL.

RESULTSGeneral Results and Validation

In this section the compressor flow field at design condi-tions are analyzed and compared to measurements performed byKrain et al. [7] and [8], in order to perform a validation of theresults obtained with this code. This case is challenging becauseof the three-dimensional shock structure, shock-boundary layerinteraction, flow separation, tip clearance flow, radial mixing andwake development resulting in a highly non-uniform flow. Ad-ditionally, due to strong compressibility effects, an incorrect es-timate of the loss productions could affect the gas density, thusleading to errors in the velocity triangles.

The first comparison is with the compressor global data, i.e.pressure ratio and efficiency vs. mass-flow, as shown in Figure 5and 6. The comparison of the pressure ratio shows a very goodagreement at low rotational speed (30,000 rpm), matching ex-actly the experimental data over the whole mass-flow range. At40,000 rpm the agreement is similar but only for one part of thecharacteristic. Toward the choke regime the CFD and experimen-tal results grow slightly apart, leading to an overestimated chokemass-flow for the simulation. At design rotational speed only

0,50 0,75 1,00 1,25 1,50 1,75 2,00 2,25 2,50 2,75 3,00 3,25 3,501,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

5,5

6,0

6,5

7,0

30000RPM,Mu=1.03

40000RPM,Mu=1.37

m

EXP AWT V2F SST C.C.

50000RPM,Mu=1.72

Figure 5. PRESSURE RATIO OVER MASS-FLOW RATE FOR THREEROTATIONAL SPEEDS.

the shape of the characteristic is well captured, but there is a shiftof the computational results compared to the measurements to-ward higher mass-flow and pressure. This kind of shift has beendetected also by other authors [1].

From the comparison at 40,000 rpm it can be deduced thatas soon as the compressor is working at high transonic condi-tions (relative Ma > 1.3), the CFD does not match the measure-ments anymore. In order to assess the results obtained with thepresent code a few selected points were computed with a largely



0,75 1,00 1,25 1,50 1,75 2,00 2,25 2,50 2,75 3,00 3,250,60

0,65

0,70

0,75

0,80

0,85

0,90

0,95

1,00

40000RPM,Mu=1.38

30000RPM,Mu=1.03

50000RPM,Mu=1.72

m

EXP AWT V2F SST C.C.

Figure 6. EFFICIENCY OVER MASS-FLOW RATE FOR THREE ROTA-TIONAL SPEEDS.

used commercial code using AWT turbulence model and the re-sults are reported in Figure 5 and Figure 6. The pressure ratiois nearly identical for both codes. The efficiency with the com-mercial code is slightly underestimated, while for the presentedcode a slight overestimation is detected. For this discrepancydifferent reasons can be assumed. In the present work the focushas been set on the turbulence model used, since already Eisen-lohr [1] and Krain [25] presumed the discrepancy being due tothe turbulence model. This will be addressed in the next section.

The overall efficiency has also been compared with the ex-perimental data, see Figure 6. The behavior is well captured bythe simulations. Here the comparison with the measurementsshows that at low speed there is a constant shift of the simulationresults of about +2%. At high speed the maximum efficiency isthe same for computations and measurements.

The validation has been performed also with local data,comparing the relative Mach number distribution at the impellerinlet, Figure 7, and exit, Figure 8, as well as at different span-wise locations, Figure 9. These comparisons present an overallgood agreement with the measurements, showing that the code isable to capture the flow field details present, under both subsonicand transonic conditions.

Please note that for Figure 8 the measurements for the exper-imental results show blade with lean because the cutting surfaceat the blade TE was chosen conical. Since in the literature no de-tails on this analysis surface are given, the present authors havechosen a cylindrical for the CFD results. According to the re-sults obtained by previous authors, [25], the main flow featuresare still well captured.

In this section few points are addressed in detail. The shockin front of the main blade LE at 90% span is quite sharp asshown in the measurements, but close to the blade SS it is slightly

(a) EXPERIMENTAL DATA.

(b) NUMERICAL RESULTS.

(c) LEGEND.

Figure 7. LEADING EDGE PLANE ROTATING MACH CONTOURS ATDESIGN CONDITION (AWT).

smeared. The bend in flow direction of the shock is captured aswell as the highest reached Mach number occurring and its po-sition along the main blade SS. The extension of this high speedregion is larger in the CFD than in the experiments. Compared topreviously obtained numerical results( [7], [8] and [1]), where themain discrepancies with respect to measurements were indicatedto lay in the mesh resolution, it can be stated that the present re-sults with considerably larger meshes are for some details better,but still present differences compared to the experimental data,



(a) NUMERICAL RESULTS.

(b) EXPERIMENTAL DATA.

Figure 8. IMPELLER EXIT ROTATING MACH CONTOURS AT DESIGNCONDITION (AWT).

both globally and locally.

Turbulence Models AssessmentAs stated above, three models with increasing resolution and

complexity have been used in order to investigate the influenceof the turbulence model on the discrepancy at high pressure ra-tios. The turbulence models were selected with the focus on theboundary layer resolution and their performance for internal flowwith adverse pressure gradients. A detailed comparison is pre-sented for selected points at 30,000 rpm and 40,000 rpm. At50,000 rpm only global data is shown. At design speed the con-vergence of the computations with both Low-Reynolds modelswas difficult to achieve, mainly due to the extremely high aspectratio necessary in order to resolve the boundary layer accord-ingly. The overall results with the more detailed turbulence mod-els do not present differences from the AWT model, also towardchoking conditions where a discrepancy between measurementsand CFD was detected, see Figure 5 and 6. Please note that theSST and V2F results are overlapping for certain operating pointsand are therefore difficult to distinguish from each other. Thesmall differences between the used turbulence models suggestthat the more detailed resolution of the boundary layer is proba-bly not the main reason for the mismatch at high flow rates. Thisis also valid for the choke regime at design speed, see Figure 5.

In this section the results of the three turbulence models usedare compared in detail. From the global data it can be seen thatlittle differences should be expected, over the whole operatingrange. The detailed comparison is presented in the Figure 10 and

(a) NUMERICAL RESULTS,SPAN 30%.

(b) EXPERIMENTAL DATA, SPAN 30%.

(c) NUMERICAL RESULTS,SPAN 50%.

(d) EXPERIMENTAL DATA, SPAN 50%.

(e) NUMERICAL RESULTS,SPAN 90%.

(f) EXPERIMENTAL DATA, SPAN 90%.

(g) LEGEND.

Figure 9. BLADE-TO-BLADE SECTION ROTATING MACH CON-TOURS AT DESIGN CONDITION (AWT).

Figure 11 for an operating point close to the instability limit at40,000 rpm (see Figure 5 for the exact operating point location).

Some slight differences in the flow field and in the flow dis-tribution at impeller exit, see Figure 11, can be detected. Butthese do not seem to be substantial and do not have an impact onthe global data. This suggests that the boundary layer resolution(from high, i.e. y+ ∼ 10, to very high, i.e. y+ ∼ 0.1)) and the tur-bulence model (from 2 to 4 equations) do not play a major role



(a) AWT MODEL, BLADE-TO-BLADE.

(b) V2F MODEL, BLADE-TO-BLADE.

(c) SST MODEL, BLADE-TO-BLADE.

(d) BLADE-TO-BLADE LEGEND.

Figure 10. CONTOUR PLOTS OF ROTATING MACH AT 90% OF SPAN:40,000 RPM.

as presumed in previous publications.Furthermore a comparison between AWT and V2F close to

(a) AWT MODEL, HUB-TO-SHROUD.

(b) V2F EXIT MODEL, HUB-TO-SHROUD.

(c) SST EXIT MODEL, HUB-TO-SHROUD.

(d) HUB-TO-SHROUD LEGEND.

Figure 11. CONTOUR PLOTS OF ROTATING MACH AT IMPELLEREXIT: 40,000 RPM and M=2.62.

the stability limit at 30,000 rpm has been performed. Here alarge, axisymmetric separation zone along the shroud was de-tected, reaching from the inlet duct into the impeller channels,with an extension to about 70% span. For this analysis the vec-tors at 70% span are plotted in Figure 12. The local flow fieldpresents in this region large separation zones and is clearly dif-ferent for both turbulence models. On the other hand the flowdistribution at impeller exit presents the same overall behaviorand only little local differences, thus leading to practically iden-tical global data (pressure ratio and efficiency).

The recirculation zone and the difference in flow field is alsoshown with the help of streamlines, see Figure 13, started in frontof the impeller at 70% span. The streamlines show that withthe V2F model stronger swirling structures are detected in thepassage between the main blade PS and the splitter blade SS.This is believed to be due to the higher resolution of turbulencestructures with the V2F model.

CONCLUSIONSA high specific speed and high pressure ratio centrifugal

compressor has been numerically investigated. In the presentwork the focus has been set on the turbulence models used, inorder to verify the commonly observed disagreement betweenexperiments and the numerical results at high pressure ratios.Since previous authors presumed the discrepancy was due to theturbulence model, advanced models were assessed. The k −ω



(a) AWT RESULTS.

(b) V2F RESULTS.

(c) LEGEND.

Figure 12. 70% SPAN VECTORS AND IMPELLER EXIT CONTOURMAPS: 30,000 RPM.

SST model with AWT is taken as reference. Moreover a detailedboundary layer integration with Low-Reynolds approach was in-vestigated with a two-equations model (SST) as well as with a

(a) AWT RESULTS.

(b) V2F RESULTS.

Figure 13. IMPELLER STREAMLINES: 30,000 RPM.

more complex four-equations model (V2F).The finite volume three dimensional Navier-Stokes code

used was based on an open source framework namedOpenFOAM R©. In particular in-house improvements of the li-brary were developed in order to analyze steady state highly com-pressible flows for turbocharger applications.

The three turbulence models, presenting increasing resolu-tion and complexity, have been then implemented in the code.The object oriented libraries for continuum mechanics, have re-vealed to be an efficient solution framework, showing the largeflexibility of the open source environment.

The obtained results were compared and validated againstglobal and local experimental data present in the literature, show-ing a good agreement for both the global results and local flowfield features, and showing that the code is able to capture theflow field details present, under both subsonic and transonic con-



ditions.The overall results with the more detailed turbulence mod-

els do not present differences from each other, also toward thechoking conditions and high pressure ratios where the largest dis-crepancy between measurements and CFD is mainly present, asindicated by other authors in the past. The results suggest that themore detailed resolution of the boundary layer is probably not themain reason for the mismatch at high flow rates in high pressurecentrifugal compressors, at least not for modern impellers withvery sound flow over the largest part of the operating range.

Locally, slight differences in the flow field were detected forthe turbulence models investigated, but these do not affect theoverall behavior of the machine. The additional computationalefforts needed for the use of Low-Reynolds models is thereforenot reflected in the overall accuracy of the numerical prediction.The authors could show that for the performance prediction theautomatic wall modeling is accurate enough, leading to a signif-icant reduction in computational costs.

ACKNOWLEDGMENTThanks go to Dr. Ribi Beat from MAN Diesel & Turbo

Schweiz AG for the support given to this work.

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