A Navier-Stokes time-accurate solver has been extended to the analysis of unsteady rotor-stator interaction. In the proposed method, a fully-implicit time discretization is used to remove stability limitations. 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. Those accelerating strategies include local time stepping, residual smoothing, and multigrid. Direct interpolation of the conservative variables is used to handle the interfaces between blade rows. Two-dimensional viscous calculations of unsteady rotor-stator interaction in a modern gas turbine stage are presented to check for the capability of the procedure.
Issue Section:
Research Papers
1.
Adamczyk
J. J.
Celestina
M. L.
Beach
T. A.
Barnett
M.
1990
, “Simulation of Three-Dimensional Viscous Flow Within a Multistage Turbine
,” ASME Journal of Turbomachinery
, Vol. 112
, July, pp. 370
–376
.2.
Arnone
A.
Swanson
R. C.
1993
, “A Navier-Stokes Solver for Turbomachinery Applications
,” ASME Journal of Turbomachinery
, Vol. 115
, Apr., pp. 305
–313
.3.
Arnone
A.
Liou
M.-S.
Povinelli
L. A.
1992
, “Navier-Stokes Solution of Transonic Cascade Flow Using Non-Periodic C-Type Grids
,” Journal of Propulsion and Power
, Vol. 8
, No. 2
, Mar.-Apr., pp. 410
–417
.4.
Arnone
A.
Liou
M.-S.
Povinelli
L. A.
1993
, “Multigrid Calculation of Three-Dimensional Viscous Cascade Flows
,” Journal of Propulsion and Power
, Vol. 9
, No. 4
, July-Aug., pp. 605
–614
.5.
Arnone, A., 1993, “Viscous Analysis of Three-Dimensional Rotor Flows Using a Multigrid Method,” ASME Paper 93-GT-19.
6.
Arnone, A., Liou, M.-S., and Povinelli, L. A., 1993, “Multigrid Time-Accurate Integration of Navier-Stokes Equations,” AIAA Paper 93-3361-CP.
7.
Baldwin, B. S., and Lomax, H., 1978, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA paper 78-257.
8.
Brandt, A., 1979, “Multi-Level Adaptive Computations in Fluid Dynamics,” AIAA paper 79-1455.
9.
Chima, R. V., and Yokota, J. W., 1988, “Numerical Analysis of Three-Dimensional Viscous Internal Flows,” NASA TM 100878.
10.
Choi
D.
Knight
C. J.
1988
, “Computation of Three-Dimensional Viscous Linear Cascade Flows
,” AIAA Journal
, Vol. 26
, No. 12
, Dec., pp. 1477
–1482
.11.
Davis
R. L.
Hobbs
D. E.
Weingold
H. D.
1988
, “Prediction of Compressor Cascade Performance Using a Naveir-Stokes Technique
,” ASME Journal of Turbomachinery
, Vol. 110
, pp. 520
–531
.12.
Dawes, N. W., 1990, “Towards Improved Throughflow Capability: The Use of 3D Viscous Flow Solvers in a Multistage Environment,” ASME Paper 90-GT-18.
13.
Dawes, N. W., 1991, “The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology,” ASME Paper 91-GT-124.
14.
Hah, C., 1989, “Numerical Study of Three-Dimensional Flow and Heat Transfer Near the Endwall of a Turbine Blade Row,” AIAA paper 89-1689.
15.
Jameson, A., 1983, “Transonic Flow Calculations,” MAE Report 1651, MAE Department, Princeton University, July 1983.
16.
Jameson, A., 1991, “Time Dependent Calculations Using Multigrid with Applications to Unsteady Flows Past Airfoils and Wings,” AIAA Paper 91-1596.
17.
Jameson, A., Schmidt, W., and Turkel, E., 1981, “Numerical Solutions of the Euler Equations by Finite Volume Methods Using Runge-Kutta Time-Stepping Schemes,” AIAA paper 81-1259.
18.
Jennions, I. K., and Turner, M. G., 1992, “Three-Dimensional Navier-Stokes Computations of Transonic Fan Flow Using an Explicit Flow Solver and an Implicit k-ε Solver,” ASME Paper 92-GT-309.
19.
Jorgenson, P. C. E., and Chima, R., 1988, “An Explicit Runge-Kutta Method for Unsteady Rotor/Stator Interaction,” AIAA Paper 88-0049.
20.
Martinelli, L., and Jameson, A., 1988, “Validation of a Multigrid Method for the Reynolds Averaged Equations,” AIAA paper 88-0414.
21.
Nakahashi
K.
Nozaki
O.
Kikuchi
K.
Tamura
A.
1989
, “Navier-Stokes Computations of Two- and Three-Dimensional Cascade Flowfields
,” Journal of Propulsion and Power
, Vol. 5
, No. 3
, May, pp. 320
–326
.22.
Pulliam
T. H.
1986
, “Artificial Dissipation Models for the Euler Equations
,” AIAA Journal
, Vol. 24
, No. 12
, Dec., pp. 1931
–1940
.23.
Radespiel
R.
Rossow
C.
Swanson
R. C.
1990
, “Efficient Cell-Vertex Multigrid Scheme for the Three-Dimensional Navier-Stokes Equations
,” AIAA Journal
, Vol. 28
, No. 8
, Aug., pp. 1464
–1472
.24.
Rai, M. M., 1987, “Unsteady Three-Dimensional Navier-Stokes Simulations of Turbine Rotor Stator Interactions,” AIAA paper 87-2058.
25.
Rao, K. V., and Delaney, R. A., 1992, “Investigation of Unsteady Flow Through a Transonic Turbine Stage, Part I, Analysis,” AIAA paper 90-2408.
26.
Subramanian, S. V., and Bozzola, R., 1987, “Numerical Simulation of Three-Dimensional Flow Fields in Turbomachinery Blade Rows Using the Compressible Navier-Stokes Equations,” AIAA paper 87-1314.
27.
Swanson, R. C., and Turkel, E., 1987, “Artificial Dissipation and Central Difference Schemes for the Euler and Navier-Stokes Equations,” AIAA paper 87-1107.
28.
Weber, K. F., and Delaney, R. A., 1991, “Viscous Analysis of Three-Dimensional Turbomachinery Flows on Body Conforming Grids Using an Implicit Solver,” ASME paper 91-GT-205.
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