This paper presents results of unsteady viscous flow calculations and corresponding cold flow experiments of a three-stage low-pressure turbine. The investigation emphasizes the study of unsteady flow interaction. A time-accurate Reynolds-averaged Navier–Stokes solver is applied for the computations. Turbulence is modeled using the Spalart–Allmaras one-equation turbulence model and the influence of modern transition models on the unsteady flow predictions is investigated. The integration of the governing equations in time is performed with a four-stage Runge–Kutta scheme, which is accelerated by a two-grid method in the viscous boundary layer around the blades. At the inlet and outlet, nonreflecting boundary conditions are used. The quasi-three-dimensional calculations are conducted on a stream surface around midspan, allowing a varying stream tube thickness. In order to study the unsteady flow interaction, a three-stage low-pressure turbine rig of a modern commercial jet engine is built up. In addition to the design point, the Reynolds number, the wheel speed, and the pressure ratio are also varied in the tests. The numerical method is able to capture important unsteady effects found in the experiments, i.e., unsteady transition as well as the blade row interaction. In particular, the flow field with respect to time-averaged and unsteady quantities such as surface pressure, entropy, and skin friction is compared with the experiments conducted in the cold air flow test rig. [S0889-504X(00)02004-3]

1.
Halstead
,
D. E.
,
Wisler
,
D. C.
,
Okiishi
,
T. H.
,
Walker
,
G. J.
,
Hodson
,
H. P.
, and
Shin
,
H.-W.
,
1997
, “
Boundary Layer Development in Axial Compressors and Turbines: Part 1-4
,”
ASME J. Turbomach.
,
119
, pp.
114
127
;
2.
119
, pp.
225
237
;
3.
119
, pp.
426
444
;
4.
119
, pp.
128
139
.
1.
Hodson, H. P., 1998, “Blade Row Interference Effects in Axial Turbomachinery Stages: Blade Row Interactions in Low Pressure Turbines,” VKI Lecture, Brussels, Feb.
2.
Fan
,
S.
, and
Lakshminarayana
,
B.
,
1996
, “
Computation and Simulation of Wake-Generated Unsteady Pressure and Boundary Layers in Cascades, Parts 1 & 2
,”
ASME J. Turbomach.
,
118
, pp.
96
121
.
3.
Sharma, O., 1998, “Blade Row Interference Effects in Axial Turbomachinery Stages,” VKI Lecture, Brussels, Feb.
4.
Eulitz, F., and Engel, K., 1998, “Numerical Investigation of Wake Interaction in a Low Pressure Turbine,” ASME Paper No. 98-GT-563.
5.
Abu-Ghannam
,
B.
, and
Shaw
,
R.
,
1980
, “
Natural Transition of Boundary Layers: The Effects of Turbulence, Pressure Gradient and Flow History
,”
J. Mech. Eng. Sci.
,
22
, pp.
213
228
.
6.
Coupland, J., 1995, “Transition Modelling for Turbomachinery Flows,” ERCOFTAC Bulletin, 24, pp. 5–8.
7.
Drela, M., 1995, “MISES Implementation of Modified Abu-Ghannam/Shaw Transition Criterion,” MIT Aero-Astro, Feb.
8.
Eulitz, F., Engel, K., Nu¨rnberger, D., Schmidt, S., and Yamamoto, K., 1998, “On Recent Advances of a Massively-Parallel Time-Accurate Navier–Stokes Solver for Unsteady Turbomachinery Flow,” Proc. ECCOMAS. Athens.
9.
Narasimha, R., 1990, “Modelling the Transitional Boundary Layer,” NASA CR-187487; ICASE Report No. 90-90.
10.
Savill, A. M., 1994, “Transition Modelling for Turbomachinery,” Proc. ERCOFTAC Turbomachinery Special Interest Group Seminar and Workshop on 3D Turbomachinery Flow Prediction, Part 2.
11.
Ekaterinaris
,
J. A.
,
1995
, “
Numerical Investigation of Dynamic Stall of an Oscillating Wing
,”
AIAA J.
,
33
, No.
10
, pp.
1803
1808
.
12.
Spalart, P., and Allmaras, S., 1992, “A One-Equation Turbulence Model for Aerodynamic Flows,” AIAA Paper No. 92-0439.
13.
Niehuis R., 1997, “Luftfahrtforschung und -technologie Engine 3E 2010 Programm fu¨r zivile MTU-Antriebsprojekte, Turbinen fu¨r Triebwerke der unteren Schubklasse Phase A,” Daimler-Benz Aerospace MTU Mu¨nchen.
14.
Dorney, D. J., Sondak, D. L., Ciszmas, P. G. A., Saren, V. E., and Savin, N. M., 1999, “Full-Annulus Simulations of Airfoil Clocking in a 1 1/2 Stage Axial Compressor,” ASME Paper No. 98-GT-23.
15.
Huber
,
F. W.
,
Johnson
,
P. D.
,
Sharma
,
O. P.
,
Staubach
,
J. B.
, and
Gaddis
,
S. W.
,
1996
, “
Performance Improvement Through Indexing of Turbine Airfoils: Part 1—Experimental Investigation
,”
ASME J. Turbomach.
,
118
, pp.
630
635
.
16.
Sondak
,
D.
, and
Dorney
,
D. J.
,
1999
, “
Simulation of Vortex Shedding in a Turbine Stage
,”
ASME J. Turbomach.
,
121
, pp.
428
435
.
17.
Valkov
,
T. V.
, and
Tan
,
C. S.
,
1999
, “
Effect of Upstream Rotor Vortical Disturbances on the Time-Average Performance of Axial Compressor Stators: Part 1—Framework of Technical Approach and Wake-Stator Blade Interactions; Part 2—Rotor Tip Vortex/Streamwise Vortex-Stator Blade Interactions
,”
ASME J. Turbomach.
,
121
, pp.
377
397
.
18.
Platzer, M. F., and Tuncer, I. H., 1995, “Analysis of Unsteady Airfoil Interference Effects Using a Zonal Navier–Stokes Solver,” AIAA-95-0307.
19.
Heisler, L., 1999, “E3E, NDT-Rig 448 Bau 03 vorla¨ufige Versuchsergebnisse,” 27.09.99, MTU, Mu¨nchen.
20.
Roe
,
P.
,
1981
, “
Approximative Riemann Solvers, Parameter Vector and Differences Schemes
,”
J. Comput. Phys.
,
43
, pp.
357
372
.
21.
van Leer
,
B.
,
1979
, “
Towards the Ultimate Conservation Difference Scheme, A Second Order Sequel to Godunov’s Method
,”
J. Comput. Phys.
,
32
, pp.
101
136
.
22.
He
,
L.
,
1993
, “
New Two-Grid Acceleration Method for Unsteady Navier–Stokes Calculations
,”
AIAA J. Propul. Power
,
9
, p.
272
272
.
23.
Saxer
,
A. P.
, and
Giles
,
M.
,
1993
, “
Quasi Three Dimensional Nonreflecting Boundary Conditions for Euler Equations Calculations
,”
AIAA J. Propul. Power
,
9
, No.
2
, pp.
263
271
.
24.
Acton, E., and Cargill, M., 1988, “Non-Reflecting Boundary Conditions for Computations of Unsteady Turbomachinery Flow,” Proc. 4th Int. Symp. Unsteady Aerodynamics and Aeroelasticity of Turbomachines and Propellers, pp. 211–228.
25.
Giles, M., 1991, “UNSFLO: A Numerical Method for the Calculation of Unsteady Flow in Turbomachinery,” GTL-Report 205, MIT-GTL.
26.
Engel, K., Eulitz, F., Pokorny, S., and Faden, M., 1996, “Validation of Different TVD-Schemes for the Calculation of the Unsteady Turbomachinery Flow,” 14. ICNMFD, Bangalore, India.
27.
Boussinesq, T. V., 1877, Mem. Pres, Acad. Sci., 3rd ed. Paris XXIII, p. 46.
28.
Hodson
,
H. P.
,
Huntsmann
,
L.
, and
Steele
,
A. B.
,
1994
, “
An Investigation of Boundary Layer Development in a Mutlistage LP Turbine
,”
ASME J. Turbomach.
,
116
, pp.
375
383
.
You do not currently have access to this content.