A new efficient implicit scheme, based on the second-order time and spatial difference algorithm for solving steady flow by using time-marching Navier–Stokes equations, was developed for predicting turbine cascade flows and heat transfer. The difference scheme comprises an explicit part in the intermediate time-step and an implicit part in the local time-step. The viscous flux vectors are decomposed to simplify the flow calculation in the explicit step. The time difference terms are expressed in terms of the viscous dependent terms that appear in the diffusion terms in the form by adding eigenvalues of viscous flux matrices into the time derivation term. In the presently proposed scheme, the two-sweep procedure is used in the implicit step instead of employing a traditional matrix operation to save the computational time. This method has been used to calculate the flow around C3X and VKI cascades. The computed results were compared with experimental data as well as with other published computations. The comparisons for both surface pressure and heat transfer coefficient showed good agreement with the experiments. [S0889-504X(00)01702-5]

Issue Section:
Technical Papers
Keywords:
Navier-Stokes equations, flow simulation, finite difference methods, viscosity, heat transfer, computational fluid dynamics
Topics:
Cascades (Fluid dynamics), Computation, Flow (Dynamics), Heat transfer, Turbines, Eigenvalues, Pressure, Algorithms, Navier-Stokes equations, Mach number, Blades
1.
Denton
,
J. D.
,
1983
, “
An Improved Time Marching Method for Turbomachinery Flow Calculation
,”
ASME J. Eng. Gas Turbines Power
,
105
, pp.
514
–
521
.
2.
Weinberg
,
B. C.
,
Yang
,
R.-J.
,
McDonald
,
H.
, and
Shamroth
,
S. J.
,
1986
, “
Calculations of Two and Three Dimensional Transonic Cascade Flow Fields Using the Navier–Stokes Equations
,”
ASME J. Eng. Gas Turbines Power
,
108
, pp.
93
–
102
.
3.
Kwon
,
O. K.
,
1988
, “
Navier–Stokes Solution for Steady Two-Dimensional Transonic Cascade Flows
,”
ASME J. Turbomach.
,
110
, pp.
339
–
346
.
4.
Liu
,
F.
, and
Jameson
,
A.
,
1993
, “
Cascade Flow Calculations by a Multigrid Euler Method
,”
J. Propul. Power
,
9
, pp.
90
–
97
.
5.
Turkel
,
E.
, and
Vatsa
,
V. N.
,
1994
, “
Effect of Artificial Viscosity on Three-Dimensional Flow Solutions
,”
AIAA J.
,
32
, pp.
39
–
45
.
6.
Douglass
,
J.
, and
Gunn
,
J. E.
,
1964
, “
A General Formulation of Alternating Direction Method
,”
Numer. Math.
,
6
, pp.
428
–
453
.
7.
Briley, W. R., and McDonald, H., 1975, “Solution of the Three-Dimensional Compressible Navier–Stokes Equations by an Implicit Technique,” Proc. 4th Int. Conf. on Numerical Methods in Fluid Dynamics, 35, pp. 105–110.
8.
Briley
,
W. R.
, and
McDonald
,
H.
,
1977
, “
Solution of the Multidimensional Compressible Navier–Stokes Equations by a Generalized Implicit Method
,”
J. Comput. Phys.
,
24
, pp.
372
–
397
.
9.
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
.
10.
Ames, W. F., 1977, Numerical Method for Partial Differential Equations, 2nd ed., Academic, New York.
11.
Lee
,
J.
,
1992
, “
Simplification of Beam and Warming’s Implicit Scheme for Two-Dimensional Compressible Flow
,”
AIAA J.
,
30
, pp.
266
–
268
.
12.
Chakravarthy, S. R., Anderson, D. A., and Salas, M. D., 1980, “The Split Coefficient Matrix Method for Hyperbolic Systems of Gasdynamics Equations,” AIAA Paper No. 80–0268.
13.
Sieverding, C., ed., 1982, “Test Case 1: 2-D Transonic Turbine Nozzle Blade,” Von Karman Inst. for Fluid Dynamics Lecture Series, 1982-05, Rhode-Saint-Genese, Belgium.
14.
Younis
,
M. E.
, and
Camarero
,
R.
,
1981
, “
Finite Volume Method for Blade to Blade Flow Using a Body Fitted Mesh
,”
AIAA J.
,
19
, No.
11
, pp.
1500
–
1502
.
15.
Maruszewski
,
J. P.
, and
Amano
,
R. S.
,
1992
, “
Grid Generation and Its Application to Separated Flows
,”
Numer. Heat Transfer, Part B
,
21
, pp.
183
–
197
.
16.
Hylton, L. D., Mihelc, M. S., Turner, E. R., Nealy, D. A., and York, R. E., 1983, “Analytical and Experimental Evaluation of Heat Transfer Distribution Over the Surfaces of Turbine Vanes,” NASA-CR-168015.
17.
Kiss
,
T.
,
Schetz
,
J. A.
, and
Moses
,
H. L.
,
1996
, “
Experimental and Numerical Study of Transonic Turbine Cascade Flow
,”
AIAA J.
,
34
, pp.
104
–
109
.
18.
Baldwin, B. S., and Lomax, H., 1978, “
Thin Layer Approximation and Algebraic Model for Separated Turbulent Flows,” AIAA Paper No. 78-257
.
Copyright © 2000
 by ASME
You do not currently have access to this content.