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Research Papers: Techniques and Procedures

Assessing Rotation/Curvature Corrections to Eddy-Viscosity Models in the Calculations of Centrifugal-Compressor Flows

[+] Author and Article Information
G. Dufour1

ISAE, Université de Toulouse, BP 54032 Toulouse Cedex 4, Francegdufour@cerfacs.fr

J.-B. Cazalbou, X. Carbonneau

ISAE, Université de Toulouse, BP 54032 Toulouse Cedex 4, France

P. Chassaing2

ISAE, Université de Toulouse, BP 54032 Toulouse Cedex 4, France

1

Present address: CERFACS, CFD Team, Toulouse, France.

2

Also at INPT-ENSEEIHT-Institut de Mécanique des Fluides de Toulouse, UMR 5502 CNRS, France.

J. Fluids Eng 130(9), 091401 (Aug 11, 2008) (10 pages) doi:10.1115/1.2953231 History: Received April 25, 2007; Revised May 22, 2008; Published August 11, 2008

Rotation and curvature (RC) effects on turbulence are expected to impact losses and flow structure in turbomachines. This paper examines two recent eddy-viscosity-model corrections devised to account for these effects: the Spalart and Shur (1997, “On the Sensitization of Turbulence Models to Rotation and Curvature  ,” Aerosp. Sci. Technol., 1(5), pp. 297–302) correction to the model of Spalart and Allmaras (1994, “A One-Equation Turbulence Model for Aerodynamic Flows  ,” Rech. Aerosp., 1, pp. 5–21) and the correction of Cazalbou (2005, “Two-Equation Modeling of Turbulent Rotating Flows  ,” Phys. Fluids., 17, p. 055110) to the (k,ϵ) model. The method of verification and validation is applied to assess the impact of these corrections on the computation of a centrifugal-compressor test case. First, a review of RC effects on turbulence as they apply to centrifugal compressors is made. The two corrected models are then presented. Second, the Radiver open test case (Ziegler K. U., Gallus, H. E., and Niehuis R., 2003, “A Study on Impeller Diffuser Interaction Part 1: Influence on the Performance  ,” ASME J. Turbomach, 125, pp. 173–182) is used as a basis for the assessment of the two corrections. After a physical-consistency analysis, the Richardson extrapolation is applied to quantify the numerical errors involved in all the calculations. Finally, experimental data are used to perform validation for both global and local predictions. The consistency analysis shows that both corrections lead to significant changes in the turbulent field, in perfect agreement with the underlying theoretical considerations. The uncertainty analysis shows that the predictions of the global performances are more sensitive to grid refinement than they are to RC turbulence modeling. However, the opposite conclusion is drawn with regard to the prediction of some local flow properties: Improvements are obtained with the RC corrections, the best results being observed for the RC-corrected (k,ϵ) model.

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Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

3D view of the Radiver impeller with the computational grid

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Figure 2

Meridional view of the mass-averaged field of turbulent viscosity normalized by the dynamic viscosity (μt∕μ). The two RC corrections reproduce the effect of curvature: Turbulence is increased close to the concave hub surface and reduced near the convex shroud surface. The computational domain is only partially represented, and the color scales are different for the one- and two-equation models. (a) SA; (b) SARC; (c) YS; (d) YSRC.

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Figure 3

Midspan blade-to-blade view of the field of normalized turbulent viscosity μt∕μ. The SARC correction reproduces the effect of rotation: Turbulence is increased close to the pressure side at the trailing edge (area marked by a D) and reduced near the suction side. (a) SA; (b) SARC; (c) YS; (d) YSRC.

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Figure 4

Trailing-edge close-up of a 10% span blade-to-blade view of the field of the normalized turbulent viscosity μt∕μ. Contrary to the blade-to-blade midspan of Fig. 3, here the YSRC correction reproduces the effect of rotation: Turbulence is increased close to the pressure side at the trailing edge. (a) YS; (b) YSRC.

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Figure 5

Numerical errors for the total—total pressure ratio and isentropic efficiency estimated by the Richardson extrapolation. Estimated errors are expressed in percentage of the extrapolated values for the pressure ratio and in efficiency-point decrements with respect to the extrapolated value for the efficiency. The values of the observed order of accuracy are given in the legends. (a) and (d) P1; (b) and (e) M; (c) and (f) S1.

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Figure 6

Comparison of the global performances obtained with the base line and RC-corrected models against experimental values for the Radiver test case. Numerical results obtained on Grid B.

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Figure 7

Comparison of experimental and numerical azimuthally averaged profiles of total pressure. Computational results obtained on Grid B. Experimental- and numerical-uncertainty error bars are smaller than the symbols at the scale of the figure. (a) P1; (b) M; (c) S1.

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Figure 8

Comparison of L2F-experimental and numerical azimuthally averaged profiles for the Operating Point P1. Computational results obtained on Grid B.

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Figure 9

Comparison of predictions and L2F measurements for the relative velocity at the rotor outlet (Operating Point P1). Computational results obtained on Grid B. Color scale given in m/s.

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