Rotor-Stator Interaction Analysis Using the Navier–Stokes Equations and a Multigrid Method

A recently developed, time-accurate multigrid viscous solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully implicit discretization is used to remove stability limitations. By means of a dual time-stepping approach, a four-stage Runge-Kutta scheme is used in conjunction with several accelerating techniques typical of steady-state solvers, instead of traditional time-expensive factorizations. The accelerating strategies include local time stepping, residual smoothing, and multigrid. Two-dimensional viscous calculations of unsteady rotor-stator interaction in the first stage of a modern gas turbine are presented. The stage analysis is based on the introduction of several blade passages to approximate the stator:rotor count ratio. Particular attention is dedicated to grid dependency in space and time as well as to the influence of the number of blades included in the calculations.

[1]  M. Giles,et al.  UNSFLO : a numerical method for unsteady inviscid flow in turbomachinery , 1988 .

[2]  Andrea Arnone,et al.  A Navier-Stokes solver for turbomachinery applications , 1993 .

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

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

[5]  Man Mohan Rai,et al.  Unsteady three-dimensional Navier-Stokes simulations of turbine rotor-stator interaction , 1987 .

[6]  Antony Jameson,et al.  Validation of a multigrid method for the Reynolds averaged equations , 1988 .

[7]  Andrea Arnone.  Viscous Analysis of Three-Dimensional Rotor Flow Using a Multigrid Method , 1994 .

[8]  R. A. Delaney,et al.  Numerical prediction of turbine vane-blade aerodynamic interaction , 1987 .

[9]  Philip C. E. Jorgenson,et al.  Explicit Runge-Kutta method for unsteady rotor/stator interaction , 1988 .

[10]  Alessandra Sestini,et al.  Multigrid computations of unsteady rotor-stator interaction using the Navier-Stokes equations , 1995 .

[11]  R. Delaney,et al.  Investigation of unsteady flow through transonic turbine stage. I - Analysis , 1990 .

[12]  Andrea Arnone,et al.  Rotor-Stator Interaction Analysis Using the Navier-Stokes Equations and a Multigrid Method , 1995 .

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

[14]  J. Erdos,et al.  Numerical Solution of Periodic Transonic Flow through a Fan Stage , 1977 .

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

[16]  Achi Brandt,et al.  Multilevel Adaptive Computations in Fluid Dynamics , 1980 .

[17]  John D. Denton,et al.  Three-dimensional time-marching inviscid and viscous solutions for unsteady flows around vibrating blades , 1993 .

[18]  Meng-Sing Liou,et al.  Multigrid Time-Accurate Integrations of Navier-Stokes Equations , 1993 .

[19]  M. Liou,et al.  Navier-Stokes solution of transonic cascade flows using nonperiodic C-type grids , 1992 .