Explicit Navier-Stokes computation of cascade flows using the k-epsilon turbulence model

A fully explicit two-dimensional flow solver, based on a four-stage Runge-Kutta scheme, has been developed and used to predict two-dimensional viscous flow through turbomachinery cascades for which experimental data are available. The formulation is applied to the density-weighted time-averaged Navier-Stokes equations. Several features of the technique improve the ability of the code to predict high Reynolds number flows on highly stretched grids. These include a low Reynolds number compressible form of the A-e turbulence model, anisotropic scaling of artificial dissipation terms, and locally varying timestep evaluation based on hyperbolic and parabolic stability considerations. Comparisons between computation and experiment are presented for both a supersonic and a low-subsonic compressor cascade. These results indicate that the code is capable of predicting steady two-dimensional viscous cascade flows over a wide range of Mach numbers in reasonable computation times.

[1]  Roger L. Davis,et al.  Cascade viscous flow analysis using the Navier-Stokes equations , 1986 .

[2]  A. Jameson,et al.  Numerical solution of the Euler equations by finite volume methods using Runge Kutta time stepping schemes , 1981 .

[3]  Thomas H. Pulliam,et al.  Artificial Dissipation Models for the Euler Equations , 1985 .

[4]  Eli Turkel,et al.  Artificial dissipation and central difference schemes for the Euler and Navier-Stokes equations , 1987 .

[5]  Effects of numerical dissipation on finite-volume solutions of compressible flow problems , 1988 .

[6]  G. M. Johnson,et al.  Efficient solution of the Euler and Navier-Stokes equations with a vectorized multiple-grid algorithm , 1983 .

[7]  Budugur Lakshminarayana,et al.  Stability of explicit navier-stokes procedures using k-ε and k - ε/algebraic reynolds stress turbulence models , 1992 .

[8]  W. Jones.  Models for turbulent flows with variable density and combustion , 1979 .

[9]  W. C. Zierke,et al.  The Measurement of Boundary Layers on a Compressor Blade in Cascade: Part 4—Flow Fields for Incidence Angles of −1.5 and −8.5 Degrees , 1990 .

[10]  Charles G. Speziale.  Discussion of turbulence modelling: Past and future , 1989 .

[11]  T. J. Coakley,et al.  Turbulence modeling methods for the compressible Navier-Stokes equations , 1983 .

[12]  H. Lomax,et al.  Thin-layer approximation and algebraic model for separated turbulent flows , 1978 .

[13]  K. Chien,et al.  Predictions of Channel and Boundary-Layer Flows with a Low-Reynolds-Number Turbulence Model , 1982 .

[14]  K. Kirtley,et al.  Computation of internal incompressible separated flows using a space-marching technique , 1985 .

[15]  R. Radespiel,et al.  An investigation of cell centered and cell vertex multigrid schemes for the Navier-Stokes equations , 1989 .

[16]  Implicit Navier-Stokes Calculations of Transonic Shock/Turbulent Boundary-Layer Interactions , 1986 .