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Research Papers

# Assessment of Turbulence Model Predictions for an Aero-Engine Centrifugal Compressor

[+] Author and Article Information
Jason A. Bourgeois

Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Drive Northwest, Calgary, AB, T2N 1N4, Canadajabourge@ucalgary.ca

Robert J. Martinuzzi

Department of Mechanical and Manufacturing Engineering, University of Calgary, 2500 University Drive Northwest, Calgary, AB, T2N 1N4, Canada

Eric Savory, Chao Zhang

Department of Mechanical and Materials Engineering, University of Western Ontario, 1151 Richmond Street North, London, ON, N6A 5B9, Canada

Douglas A. Roberts

Compressor Aerodynamics, Pratt and Whitney Canada, 1801 Courtney Park Drive, Mississauga, ON, L5T 1J3, Canada

These are normalized by the SST complete diffuser values to protect the proprietary data.

J. Turbomach 133(1), 011025 (Sep 27, 2010) (15 pages) doi:10.1115/1.4001136 History: Received September 25, 2008; Revised January 06, 2010; Published September 27, 2010; Online September 27, 2010

## Abstract

The accurate prediction of mean flow fields with high degrees of curvature, adverse pressure gradients, and three-dimensional turbulent boundary layers typically present in centrifugal compressor stages is a significant challenge when applying Reynolds averaged Navier–Stokes turbulence modeling techniques. The current study compares the steady-state mixing plane predictions using four turbulence models for a centrifugal compressor stage with a tandem impeller and a “fish-tail” style discrete passage diffuser. The models analyzed are the $k-ε$ model (an industry standard for many years), the shear stress transport (SST) model, a proposed modification to the SST model denoted as the SST-reattachment modification (RM), and the Speziale, Sarkar, and Gatski Reynolds stress model (RSM-SSG). Comparisons with measured performance parameters—the stage total-to-static pressure and total-to-total temperature ratios—indicate more accurate performance predictions from the RSM-SSG and SST models as compared to the $k-ε$ and SST-RM models. Details of the different predicted flow fields are presented. Estimates of blockage, aerodynamic slip factor, and impeller exit velocity profiles indicate significant physical differences in the predictions at the impeller-diffuser interface. Topological flow field differences are observed: the separated tip clearance flow is found to reattach with the SST, SST-RM, and RSM-SSG models, while it does not with the $k-ε$ model, a larger shroud separation at the impeller exit seen with the SST and SST-RM models, and core flow differences are in the complex curved diffuser geometry. The results are discussed in terms of the production and dissipation of $k$ predicted by the various models due to their intrinsic modeling assumptions. These comparisons will assist aerodynamic designers in choosing appropriate turbulence models, and may benefit future modeling research.

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## Figures

Figure 1

Centrifugal compressor stage

Figure 2

Computational domain and stage nomenclatures

Figure 3

Computational grid for the blade, hub, and diffuser wall surfaces

Figure 4

Comparisons of predictions with different resolution grids of relative meridional and tangential velocity profiles at arbitrarily chosen streamwise locations

Figure 5

Normalized pressure ratio versus (a) inlet and (b) net exit corrected flows

Figure 6

Normalized impeller total pressure ratio versus (a) inlet and (b) net exit corrected flows

Figure 7

Normalized temperature ratio versus (a) inlet and (b) net exit corrected flows

Figure 8

Aerodynamic slip factor versus (a) inlet and (b) net exit corrected flows

Figure 9

Efficiency change versus (a) inlet and (b) net exit corrected flows

Figure 10

Mass flow averaged production and dissipation of the turbulence kinetic energy on either side of the mixing plane for constant radius isosurfaces. The radius r is scaled by the mixing plane radius rmp.

Figure 11

Mean eddy-viscosity comparison of the upstream (solid lines) and downstream (dashed lines) sides of the mixing plane

Figure 12

Impeller mean exit radial velocity profile at the design net exit corrected flow rate. Dotted lines about experimental points indicate experimental uncertainty.

Figure 13

Blade-to-blade relative Mach number contours at 50% span for the (a) k-ε model, (b) SST model, (c) SST-RM model, and (d) RSM-SSG

Figure 14

Blade-to-blade relative Mach number contours at 95% span for the (a) k-ε model, (b) SST model, (c) SST-RM model, and (d) RSM-SSG

Figure 15

Trailing edge tip clearance flow viewed by the blade surface and projected streamlines at the surface shown in (a) and colored by the relative velocity for the (b) k-ε model, (c) SST model, (d) SST-RM model, and (e) RSM-SSG

Figure 16

Pressure contours and surface limiting streamlines (shear stress lines) on the impeller trailing edge and hub surfaces for the (a) k-ε model, (b) SST model, (c) SST-RM model, and (d) RSM-SSG

Figure 17

Diffuser pipe Mach number contours of cuts normal to the pipe centerline for the (a) k-ε model, (b) SST model, (c) SST-RM model, and (d) RSM-SSG model models

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