A preconditioned method for rotating flows at arbitrary mach number

An improved preconditioning is proposed for viscous flow computations in rotating and nonrotating frames at arbitrary Mach numbers. The key to the current method is the use of both free stream Mach number and rotating Mach number to construct a preconditioning matrix, which is applied to the compressible governing equations written in terms of primitive variables. A Fourier analysis is conducted that reveals the efficacy of the modified preconditioning. Numerical approximations for the convective and diffusive fluxes are detailed based on the preconditioned system of equations. A set of boundary conditions using characteristic variables are described for internal and external flow computations. Numerical validations are performed on four realistic viscous flows in both fixed and rotating frames. The results indicated that the modified preconditioning has a superior performance compared to the original method to predict flows from extremely low to supersonic Mach numbers.

[1]  Wayne A. Smith,et al.  Preconditioning Applied to Variable and Constant Density Flows , 1995 .

[2]  Chunhua Sheng,et al.  Numerical Study of Preconditioned Algorithm for Rotational Flows , 2005 .

[3]  Kidambi Sreenivas,et al.  Comparison of computations using Navier-Stokes equations in rotating and fixed coordinates for flow through turbomachinery , 1997 .

[4]  W. Coirier.  An Adaptively-Refined, Cartesian, Cell-Based Scheme for the Euler and Navier-Stokes Equations. Ph.D. Thesis - Michigan Univ. , 1994 .

[5]  Eli Turkel,et al.  Review of preconditioning methods for fluid dynamics , 1993 .

[6]  Christopher J. Chesnakas,et al.  Cavitation and 3-D LDV Tip-Flowfield Measurements of Propeller 5168 , 1998 .

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

[8]  Philip L. Roe,et al.  Characteristic time-stepping or local preconditioning of the Euler equations , 1991 .

[9]  Robert F Roddy.  Investigation of the Stability and Control Characteristics of Several Configurations of the DARPA Suboff Model (DTRC Model 5470) from Captive-Model Experiments , 1990 .

[10]  C. Merkle,et al.  Application of time-iterative schemes to incompressible flow , 1985 .

[11]  W. K. Anderson,et al.  Implicit/Multigrid Algorithms for Incompressible Turbulent Flows on Unstructured Grids , 1995 .

[12]  A. Chorin.  A Numerical Method for Solving Incompressible Viscous Flow Problems , 1997 .

[13]  P. Spalart.  A One-Equation Turbulence Model for Aerodynamic Flows , 1992 .

[14]  Chunhua Sheng,et al.  Characteristic Variable Boundary Conditions for Arbitrary Mach Number Algorithm in Rotating Frame , 2003 .

[15]  John T. Batina,et al.  Implicit flux-split Euler schemes for unsteady aerodynamic analysis involving unstructured dynamic meshes , 1990 .

[16]  E. Turkel,et al.  Preconditioned methods for solving the incompressible low speed compressible equations , 1987 .

[17]  Wayne A. Smith,et al.  Implicit Solution of Preconditioned Navier- Stokes Equations Using Algebraic Multigrid , 1999 .

[18]  J. Bowles,et al.  Fourier Analysis of Numerical Approximations of Hyperbolic Equations , 1987 .

[19]  Lafayette K. Taylor,et al.  High-resolution viscous flow simulations at arbitrary Mach number , 2003 .

[20]  P. Spalart,et al.  On the sensitization of turbulence models to rotation and curvature , 1997 .

[21]  H. L. Liu,et al.  MEASUREMENTS OF FLOWS OVER AN AXISYMMETRIC BODY WITH VARIOUS APPENDAGES IN A WIND TUNNEL: THE DARPA SUBOFF EXPERIMENTAL PROGRAM , 1994 .

[22]  D. Choi,et al.  Computations of 3D viscous flows in rotating turbomachinery blades , 1989 .

[23]  H. Mcdonald,et al.  A low mach number Euler formulation and application to time-iterative LBI schemes , 1983 .

[24]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[25]  F. X. Caradonna,et al.  Experimental and Analytical Studies of a Model Helicopter Rotor in Hover , 1980 .

[26]  Nancy C Groves,et al.  Geometric Characteristics of DARPA (Defense Advanced Research Projects Agency) SUBOFF Models (DTRC Model Numbers 5470 and 5471) , 1989 .

[27]  C. L. Merkle,et al.  The application of preconditioning in viscous flows , 1993 .

[28]  W. K. Anderson,et al.  A grid generation and flow solution method for the Euler equations on unstructured grids , 1994 .