The objective of this paper is to investigate the three-dimensional unsteady flow interactions in a turbomachine stage. A three-dimensional time-accurate Euler code has been developed using an explicit four-stage Runge–Kutta scheme. Three-dimensional unsteady nonreflecting boundary conditions are formulated at the inlet and the outlet of the computational domain to remove the spurious numerical reflections. The three-dimensional code is first validated for two-dimensional and three-dimensional cascades with harmonic vortical inlet distortions. The effectiveness of the nonreflecting boundary conditions is demonstrated. The unsteady Euler solver is then used to simulate the propagation of nozzle wake and secondary flow through the rotor and the resulting unsteady pressure field in an axial turbine stage. The three-dimensional and time-dependent propagation of nozzle wakes in the rotor blade row and the effects of nozzle secondary flow on the rotor unsteady surface pressure and passage flow field are studied. It was found that the unsteady flow field in the rotor is highly three dimensional and the nozzle secondary flow has significant contribution to the unsteady pressure on the blade surfaces. Even though the steady flow at the midspan is nearly two dimensional, the unsteady flow is three dimensional and the unsteady pressure distribution cannot be predicted by a two-dimensional analysis.

1.
Beach, T. A., 1990, “An Interactive Grid Generation Procedure for Axial and Radial Flow Turbomachinery,” AIAA Paper No. 90-0344.
2.
Fan, S., 1995, “Computation and Turbulence Modeling of Unsteady Flows Due to Rotor/Stator Interaction in Turbomachines,” Ph.D. Thesis, Department of Aerospace Engineering, The Pennsylvania State University.
3.
Giles
M. B.
,
1990
, “
Non-reflecting Boundary Conditions for Euler Equation Calculations
,”
AIAA Journal
, Vol.
28
, No.
12
, pp.
2050
2058
.
4.
Giles, M. B., 1993, “A Framework for Multi-stage Unsteady Flow Calculations,” in: Unsteady Aerodynamics, Aeroacoustics, and Aeroelasticity of Turbomachines and Propellers, H. M. Atassi, ed., Springer-Verlag, pp. 57–72.
5.
Hodson
H. P.
,
1985
, “
An Inviscid Blade-to-Blade Prediction of a Wake-Generated Unsteady Flow
,”
ASME Journal of Engineering for Gas Turbines and Power
, Vol.
107
, pp.
337
344
.
6.
Korakianitis
T.
,
1992
, “
On the Prediction of Unsteady Forces on Gas Turbine Blades: Part 1—Description of the Approach; Part 2—Analysis of the Results
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
114
131
.
7.
Korakianitis
T.
,
1993
, “
On the Propagation of Viscous Wakes and Potential Flow in Axial-Turbine Cascades
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
115
, pp.
118
127
.
8.
Kunz
R. F.
, and
Lakshminarayana
B.
,
1992
, “
Three-Dimensional Navier–Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procedure and a Coupled k–ε Turbulence Model
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
627
642
.
9.
Lakshminarayana, B., Camci, C., Halliwell, I., and Zaccaria, M., 1992, “Investigation of Three Dimensional Flow Field in a Turbine Including Rotor/Stator Interaction, Part 1: Design, Development and Performance of Turbine Facility,” AIAA Paper No. 92-3325.
10.
Manwaring
S. R.
, and
Wisler
D. C.
,
1993
, “
Unsteady Aerodynamics and Gust Response in Compressors and Turbines
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
115
, pp.
724
740
.
11.
Rai, M., 1989, “Three Dimensional Navier–Stokes Simulation of Turbine-Stator Interaction, Part 1—Methodology, Part 2—Results,” Journal of Propulsion and Power, May-June, pp. 305–311.
12.
Saxer
A. P.
, and
Giles
M. B.
,
1993
, “
Quasi-Three-Dimensional Nonreflecting Boundary Conditions for Euler Equation Calculations
,”
Journal of Propulsion and Power
, Vol.
9
, No.
2
, pp.
263
271
.
13.
Verdon, J. M., Barnett, M., Hall, K. C., and Ayer, T. C., 1991, “Development of Unsteady Aerodynamic Analyses for Turbomachinery Aeroelastic and Aeroacoustic Applications,” NASA CR 4405.
14.
Zaccaria, M., and Lakshminarayana, B., 1992, “Investigation of Three Dimensional Flow Field in a Turbine Including Rotor/Stator Interaction, Part 2: Three-Dimensional Flow Field at the Exit of the Nozzle,” AIAA Paper No. 92-3326.
15.
Zaccaria, M., 1994, “An Experimental Investigation Into the Steady and Unsteady Flow Field in an Axial Flow Turbine,” Ph.D. Thesis, Department of Aerospace Engineering, The Pennsylvania State University.
This content is only available via PDF.
You do not currently have access to this content.