A three-dimensional Navier–Stokes procedure has been used to compute the three-dimensional viscous flow through the turbine nozzle passage of a single-stage turbine. A low-Reynolds-number k–ε model and a zonal k-ε/ARSM (algebraic Reynolds stress model) are utilized for turbulence closure. The algebraic Reynolds stress model is used only in the endwall region to represent the anisotropy of turbulence. A four-stage Runge–Kutta scheme is used for time integration of both the mean-flow and the turbulence transport equations. For the turbine nozzle flow, comprehensive comparisons between the predictions and the experimental data obtained at Penn State show that most features of the vortex-dominated endwall flow, as well as nozzle wake structure, have been captured well by the numerical procedure. An assessment of the performance of the turbulence models has been carried out. The two models are found to provide similar predictions for the mean flow parameters, although slight improvement in the prediction of some secondary flow quantities has been obtained by the ARSM model.

1.
Arnone
A.
,
Liou
M.-S.
, and
Povinelli
L. A.
,
1993
, “
Multigrid Calculation of Three-Dimensional Viscous Cascade Flows
,”
Journal of Propulsion and Power
, Vol.
9
, No.
4
, pp.
605
614
.
2.
Beach, T. A., 1990, “An Interactive Grid Generation Procedure for Axial and Radial Flow Turbomachinery,” AIAA Paper No. 90-0344.
3.
Chien, K. Y., 1982, “Prediction of Channel and Boundary-Layer Flows With a Low-Reynolds-Number Turbulence Model,” AIAA Journal, Vol. 20, No. 1.
4.
Choi, D., and Knight, C. J., 1991, “Aerodynamic and Heat Transfer Analysis for a Low Aspect Ratio Turbine Using a 3D Navier–Stokes Code,” AIAA Paper No. 91-2240.
5.
Cleak
J. G. E.
, and
Gregory-Smith
D. G.
,
1992
, “
Turbulence Modeling for Secondary Flow Prediction in a Turbine Cascade
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
590
598
.
6.
Demuren
A. O.
, and
Rodi
W.
,
1984
, “
Calculation of Turbulence-Driven Secondary Motion in Non-circular Ducts
,”
J. Fluid Mech.
, Vol.
140
, pp.
189
222
.
7.
Dorney
D. J.
, and
Davis
R. L.
,
1992
, “
Navier–Stokes Analysis of Turbine Blade Heat Transfer and Performance
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
479
485
.
8.
Dring, R. P., Joslyn, H. D., and Blair, M. F., 1987, “The Effects of Inlet Turbulence and Rotor/Stator Interactions on the Aerodynamics and Heat Transfer of a Large-Scale Rotating Turbine Model,” NASA-CR-179469, Vol. 4.
9.
Goldman, L. J., and Seasholtz, R. G., 1992, “Laser Anemometer Measurements and Computations in an Annular Cascade of High Turning Core Turbine Vanes,” NASA TP 3252.
10.
Gregory-Smith
D. G.
, and
Cleak
J. G. E.
,
1992
, “
Secondary Flow Measurements in a Turbine Cascade With High Inlet Turbulence
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
173
183
.
11.
Hah, C., 1989, “Numerical Study of Three-Dimensional Flow and Heat Transfer Near the Endwall of a Turbine Blade Row,” AIAA Paper No. 89-1689.
12.
Ho
Y.-H.
, and
Lakshminarayana
B.
,
1996
, “
Computational Modeling of Three-Dimensional Endwall Flow Through a Turbine Rotor Cascade With Strong Secondary Flows
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
118
, pp.
250
261
.
13.
Jameson, A., Schmidt, W., and Turkel, E., 1981, “Numerical Solutions of Euler Equations by Finite Volume Methods Using Runge–Kutta Time-Stepping Schemes,” AIAA Paper No. 81-1259.
14.
Kunz, R. F., 1991, “Explicit Navier–Stokes Computation of Turbomachinery Flows,” Ph.D. thesis, Penn State University.
15.
Kunz
R. F.
, and
Lakshminarayana
B.
,
1992
, “
Three-Dimensional Navier–Stokes Computation of Turbomachinery Flows Using an Explicit Numerical Procudure and a Coupled k–ε Turbulence Model
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, p.
627
627
.
16.
Lakshminarayana
B.
,
1991
, “
An Assessment of Computational Fluid Dynamic Techniques in the Analysis and Design of Turbomachinery—The 1990 Freeman Scholar Lecture
,”
ASME Journal of Fluids Engineering
, Vol.
113
, p.
315
315
.
17.
Langston
L. S.
,
Nice
M. L.
, and
Hooper
R. M.
,
1977
, “
Three-Dimensional Flow Within a Turbine Cascade Passage
,”
ASME Journal of Engineering for Power
, Vol.
99
, No.
1
, pp.
21
28
.
18.
Launder
B. E.
,
1989
, “
Second Moment Closure: Present … and Future?
International Journal of Heat and Fluid Flow
, Vol.
10
, No.
4
, pp.
282
299
.
19.
Launder
B. E.
,
Reece
G. J.
, and
Rodi
W.
,
1975
, “
Progress in the Development of a Reynolds-Stress Turbulence Closure
,”
J. Fluid Mech.
, Vol.
68
, p.
537
537
.
20.
Monson, D. J., Seegmiller, H. L., McConnaughey, P. K., and Chen, Y. S., 1990, “Comparison of Experiment With Calculations Using Curvature-Corrected Zero and Two Equation Turbulence Models for a Two-Dimensional U-Duct,” AIAA Paper No. 90-1484.
21.
Moore
J.
,
Shaffer
D. M.
, and
Moore
J. G.
,
1987
, “
Reynolds Stresses and Dissipation Mechanisms Downstream of a Turbine Cascade
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
109
, pp.
258
267
.
22.
Rodi
W.
,
1976
, “
A New Algebraic Relation for Calculating Reynolds Stress
,”
ZAMM
, Vol.
56
, p.
219
219
.
23.
Raj
R.
, and
Lakshminarayana
B.
,
1973
, “
Characteristics of the Wake Behind a Cascade of Airfoils
,”
J. Fluid Mech.
, Vol.
61
, pp.
707
730
.
24.
Sieverding
C. H.
,
1985
, “
Recent Progress in the Understanding of Basic Aspects of Secondary Flows in Turbine Blade Passages
,”
ASME Journal of Engineering for Gas Turbines and Power
, Vol.
107
, pp.
248
257
.
25.
Zaccaria
M.
,
Ristic
D.
, and
Lakshminarayana
B.
,
1996
, “
Three-Dimensional Flow Field in a Turbine Nozzle Passage
,”
J. of Propulsion and Power
, Vol.
12
, pp.
974
983
.
26.
Zaccaria
M.
, and
Lakshminarayana
B.
,
1995
, “
Investigation of Three-Dimensional Turbine Flow Field at the Exit of the Nozzle
,”
J. of Propulsion and Power
, Vol.
11
, No.
1
, p.
55
55
.
This content is only available via PDF.
You do not currently have access to this content.