Large eddy simulation of unsteady rotor-stator interaction in a centrifugal compressor

A proof of concept, LES computation of the flow through a centrifugal compressor is carried out. The large cost of such a computation limits its use to flows such as the jet-wake flow in a centrifugal compressor for which more economical approaches are unsuitable. We solve the 3D, unsteady, compressible Navier-Stokes equations numerically on an unstructured, tetrahedral grid in a time accurate manner using a finite volume formulation. Convective fluxes at the cell interfaces are computed using the fluctuation splitting concept. A Galerkin formulation is used for the viscous terms. A multi-level generalization of the dynamic subgrid stress model is used. The code uses adaptive grids and a multigrid acceleration procedure with a four stage Runge-Kutta smoother. A hierarchical, octree organization of the data is employed with a single tetrahedron division rule. This is shown to allow significant reductions in memory usage. Comparisons with rotating channel experimental, LES and DNS data are carried out. A comparison with the Eckhardt compressor measurements show qualitative agreement in the quasi-steady state case. The unsteady rotor-stator interaction results are preliminary and await a parallel and as yet uncompleted experimental program validation.

[1]  A. Jameson Solution of the Euler equations for two dimensional transonic flow by a multigrid method , 1983 .

[2]  A statistical formulation of the dynamic model , 1996 .

[3]  P. Moin,et al.  On the Effect of Numerical Errors in Large Eddy Simulations of Turbulent Flows , 1997 .

[4]  B. V. Leer,et al.  Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method , 1979 .

[5]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[6]  S. Ta'asan,et al.  Multilevel turbulence simulations , 1993 .

[7]  U. Piomelli High Reynolds number calculations using the dynamic subgrid‐scale stress model , 1993 .

[8]  S. A. Eide,et al.  Turbulent Boundary Layers on Centrifugal Compressor Blades: Prediction of the Effects of Surface Curvature and Rotation , 1976 .

[9]  D. Michalek,et al.  Grid-independent upwind scheme for multidimensional flow , 1993 .

[10]  A. Jameson Time dependent calculations using multigrid, with applications to unsteady flows past airfoils and wings , 1991 .

[11]  C. Hirsch,et al.  Characteristic decomposition methods for the multidimensional euler equations , 1986 .

[12]  Danesh K. Tafti,et al.  A numerical study of the effects of spanwise rotation on turbulent channel flow , 1991 .

[13]  H. Paillere,et al.  MULTIDIMENSIONAL UPWIND RESIDUAL DISTRIBUTION SCHEMES FOR THE CONVECTION-DIFFUSION EQUATION , 1996 .

[14]  Kenneth Jansen,et al.  Preliminary large-eddy simulations of flow around a NACA 4412 airfoil using unstructured grids , 1995 .

[15]  Y. Kallinderis,et al.  Adaptive refinement-coarsening scheme for three-dimensional unstructured meshes , 1993 .

[16]  H. Paillere,et al.  Upwind residual distribution methods for compressible flow: An alternative to finite volume and finite element methods , 1997 .

[17]  B. Lakshminarayana,et al.  An Assessment of Computational Fluid Dynamic Techniques in the Analysis and Design of Turbomachinery—The 1990 Freeman Scholar Lecture , 1991 .

[18]  Budugur Lakshminarayana,et al.  Turbulence modeling for complex shear flows , 1985 .

[19]  Joel H. Ferziger,et al.  Effect of rotation on isotropic turbulence: computation and modelling , 1985, Journal of Fluid Mechanics.

[20]  D. Eckardt,et al.  Detailed Flow Investigations Within a High-Speed Centrifugal Compressor Impeller , 1976 .

[21]  Ugo Piomelli,et al.  Large-eddy simulation of rotating channel flows using a localized dynamic model , 1995 .

[22]  C. Fureby,et al.  On subgrid scale modeling in large eddy simulations of compressible fluid flow , 1996 .

[23]  Y. Kallinderis,et al.  New multigrid approach for three-dimensional unstructured, adaptive grids , 1994 .

[24]  F. Bastin,et al.  Jet Noise Using Large Eddy Simulation , 1996 .

[25]  R. Kristoffersen,et al.  Direct simulations of low-Reynolds-number turbulent flow in a rotating channel , 1993, Journal of Fluid Mechanics.

[26]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[27]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .