A parametric study which investigates the influence of viscous effects on the damping behavior of vibrating compressor cascades is presented here. To demonstrate the dependence of unsteady aerodynamic forces on the flow viscosity, a computational study was performed for a transonic compressor cascade of which the blades underwent tuned pitching oscillations while the flow conditions extended from fully subsonic to highly transonic flow. Additionally, the reduced frequency and Reynolds number were varied. In order to check the linear behavior of the aerodynamic forces, all calculations were carried out for three different oscillation amplitudes. Comparisons with inviscid Euler results helped identify the influence of viscous effects. The computations were performed with a Navier-Stokes code, the basic features of which are the use of an AUSM upwind scheme, an implicit time integration, and the implementation of the Baldwin-Lomax turbulence model. In order to demonstrate the possibility of this code to correctly predict the unsteady behavior of strong shock-boundary layer interactions, the experiment of Yamamoto and Tanida on a self-induced shock oscillation due to shock-boundary layer interaction was calculated. A significant improvement in the prediction of the shock amplitude was achieved by a slight modification of the Baldwin Lomax turbulence model. An important result of the presented compressor cascade investigations is that viscous effects may cause a significant change in the aerodynamic damping. This behavior is demonstrated by two cases in which an Euler calculation predicts a damped oscillation whereas a Navier-Stokes computation leads to an excited vibration. It was found that the reason for these contrary results are shock-boundary-layer interactions which dramatically change the aerodynamic damping.

Issue Section:
Technical Papers
Keywords:
gas turbines, compressors, transonic flow, shock waves, viscosity, flow simulation, vibrations, oscillations, Navier-Stokes equations, boundary layers, aerodynamics
Topics:
Blades, Compressors, Damping, Flow (Dynamics), Oscillations, Shock (Mechanics), Vibration, Pressure, Viscosity, Turbulence, Boundary layers, Cascades (Fluid dynamics), Reynolds number
1.
Hall
,
K. C.
, and
Crawley
,
E. F.
,
1989
, “
Calculation of Unsteady Flows in Turbomachinery Using the Linearized Euler Equations
,”
AIAA J.
,
27
, pp.
777
–
787
.
2.
Kahl, G., and Klose, A., 1993, “Computation of the Linearized Transonic Flow in Oscillating Cascades,” ASME Paper No. 93-GT-269.
3.
Montgomery, M. D., and Verdon, J. M., 1997, “A 3D Linearized Unsteady Euler Analysis for Turbomachinery Blade Rows, Part 1: Aerodynamic and Numerical Formulations, Part 2: Unsteady Aerodynamic Response Predictions,” Proceedings of the 8th International Symposium on Unsteady Arodynamics and Aeroelasticity of Turbomachines, Stockholm, Sweden, Sept. 14–18.
4.
Holmes, D. G., Mitchell, B. E., and Lorence, C. A., 1997, “Three Dimensional Linearized Navier-Stokes Calculations for Flutter and Forced Response,” Proceedings of the 8th International Symposium on Unsteady Arodynamics and Aeroelasticity of Turbomachines, Stockholm, Sweden, Sept. 14–18.
5.
Clark, W. S., and Hall, K. C., 1995, “A Numerical Model of the Onset of Stall Flutter in Cascades,” ASME Paper No. 95-GT-377.
6.
Clark, W. S., and Hall, K. C., 1999, “A Time-Linearized Navier-Stokes Analysis of Stall Flutter,” ASME Paper No. 99-GT-383.
7.
Gerolymos
,
G. A.
,
1988
, “
Numerical Integration of the Blade-to-Blade Surface Euler Equations in Vibrating Cascades
,”
AIAA J.
,
26
, pp.
1483
–
1492
.
8.
Gerolymos, G. A., and Vallet, I., 1994, “Validation of 3D Euler Methods for Vibrating Cascade Aerodynamics,” ASME Paper No. 94-GT-294.
9.
He, L., 1989, “An Euler Solution for Unsteady Flows Around Oscillating Blades,” ASME Paper No. 89-GT-279.
10.
Carstens, V., 1991, “Computation of the Unsteady Transonic 2D Cascade Flow by an Euler Algorithm with Interactive Grid Generation,” AGARD CP 507, Transonic Unsteady Aerodynamics and Aeroelasticity, San Diego, USA, October 7–11.
11.
Carstens, V., Bo¨lcs, A., and Ko¨rba¨cher, H., 1993, “Comparison of Experimental and Theoretical Results for Unsteady Transonic Cascade Flow at Design and Off-Design Conditions,” ASME Paper No. 93-GT-100.
12.
Peitsch, D., Gallus, H. E., and Weber, S., 1994, “Computation of Unsteady Transonic 3D-Flow in Turbomachine Bladings,” Proceedings of the 7th International Symposium on Unsteady Arodynamics and Aeroelasticity of Turbomachines, Fukuoka, Japan, Sept. 25–29.
13.
Chuang, H. A., and Verdon, J. M., 1998, “A Nonlinear Numerical Simulator for Three Dimensional Flows through Vibrating Blade Rows,” ASME Paper No. 98-GT-18.
14.
He
,
L.
,
1993
, “
New Two-Grid Acceleration Method for Unsteady Navier-Stokes Calculations
,”
J. Propul. Power
,
9
, No.
2
, March–April, pp.
272
–
280
.
15.
Abhari, R. S., and Giles, M., 1995, “A Navier-Stokes Analysis of Airfoils in Oscillating Transonic Cascades for the Prediction of Aerodynamic Damping,” ASME Paper No. 95-GT-182.
16.
Ayer
,
T. C.
, and
Verdon
,
J. M.
,
1998
, “
Validation of a Nonlinear Unsteady Aerodynamic Simulator for Vibrating Blade Rows
,”
ASME J. Turbomach.
,
120
, No.
1
, pp.
112
–
121
.
17.
Gru¨ber
,
B.
, and
Carstens
,
V.
,
1998
, “
Computation of the Unsteady Transonic Flow in Harmonically Oscillating Turbine Cascades Taking Into Account Viscous Effects
,”
ASME J. Turbomach.
,
120
, No.
1
, pp.
104
–
111
.
18.
Weber, S., Benetschik, H., Peitsch, D., and Gallus, H. E., 1997, “A Numerical Approach to Unstalled and Stalled Flutter Phenomena in Turbomachinery Cascades,” ASME Paper No. 97-GT-102.
19.
Isomura, K., and Giles, M.B., 1997, “A Numerical Study of Flutter in a Transonic Fan,” ASME Paper No. 97-GT-235.
20.
Fransson, T.H., Jo¨cker, M., Bo¨lcs, A., and Ott, P., 1998, “Viscous and Inviscid Linear/Nonlinear Calculations Versus Quasi 3D Experimental Cascade Data for a New Aeroelastic Turbine Standard Configuration,” ASME Paper No. 98-GT-490.
21.
Liou
,
M. S.
, and
Steffen
, Jr.,
C. J.
,
1993
, “
A New Flux Splitting Scheme
,”
J. Comput. Phys.
,
107
, pp.
23
–
39
.
22.
van Leer
,
B.
,
1979
, “
Towards the Ultimate Conservative Difference Scheme, V. A Second Order Sequel to Godunov’s Method
,”
J. Comput. Phys.
,
32
, pp.
101
–
136
.
23.
Beam
,
R. M.
, and
Warming
,
R. F.
,
1976
, “
An Implicit Finite-Difference Algorithm for Hyperbolic Systems in Conservation-Law Form
,”
J. Comput. Phys.
,
22
, pp.
87
–
110
.
24.
Baldwin, B. S., and Lomax, H., 1978, “Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA-78-257.
25.
Chakravarthy, S. R., 1982, “Euler Equations—Implicit Schemes and Boundary Conditions,” AIAA Paper No. 82-0228.
26.
Carstens, V., 1988, “Two-Dimensional Elliptic Grid Generation for Airfoils and Cascades,” DLR-FB, pp. 88–52.
27.
Yamamoto, K., and Tanida, T., 1987, “Self-Exited Oscillation of Shock Waves on an Airfoil in Two-Dimensional Transonic Channel Flow,” Proceeding of Fourth Symposium on Unsteady Aerodynamics and Aeroelasticity of Turbomachines and Propellers, Aachen, pp. 769–783.
28.
Yamamoto, K., and Tanida, T., 1989, “Self-Excited Oscillation of Transonic Flow Around an Airfoil in a Two-Dimensional Channel,” ASME Paper No. 89-GT-58.
Copyright © 2001
 by ASME
You do not currently have access to this content.