The subject of this paper is a numerical method for the calculation of the transonic flow field of multistage turbines, taking high coolant flow into account. To reduce the processing time, a throughflow method based on the principels of Wu is used for the hub-to-tip calculation. The flow field is obtained by an iterative solution between a three-dimensional inviscid hyperbolic time-dependent algorithm with an implicit finite volume method for the blade-to-blade calculations using C-meshes and a single representative meridional S2m-streamsurface. Along the S2m-plane with respect to nonorthogonal curvilinear coordinates, the stream function equation governing fluid flow is established. The cooling air inflow inside the blade passage forbids the assumption of a constant mass flow along the main stream direction. To consider the change of the aerodynamic and thermodynamic behavior, a cooling air model was developed and implemented in the algorithm, which allows the mixing of radially arbitrarily distributed cooling air in the trailing edge section of each blade row. The viscous effects and the influence of cooling air mixing are considered by the use of selected loss correlations for profile, tip leakage, secondary flow and mixing losses in the S2m-plane in terms of entropy. The method is applied to the four-stage high-temperature gas turbine Siemens KWU V84.3. The numerical results obtained are in good agreement with the experimental data.

Issue Section:
Research Papers
Topics:
Coolants, Flow (Dynamics), Turbines, Blades, Cooling, Algorithms, Entropy, Finite volume methods, Fluid dynamics, Gas turbines, High temperature, Inflow, Leakage, Numerical analysis, Transonic flow
1.
Adamczyk
J. J.
,
Celestina
M. L.
, and
Beach
T. A.
,
1990
, “
Simulation of Viscous Flow Within a Multistage Turbine
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
112
, pp.
370
–
376
.
2.
Arnone, A., and Benvenuti, E., 1994, “Three-Dimensional Navier–Stokes Analysis of a Two-Stage Gas Turbine,” ASME Paper No. 94-GT-88.
3.
Arnone
A.
, and
Pacciani
R.
,
1996
, “
Rotor-Stator Interaction Analysis Using the Navier–Stokes Equations and a Multigrid Method
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
118
, pp.
679
–
689
.
4.
Benetschik, H., Lohman, A., Lu¨cke, J. R., and Gallus, H. E., 1996, “Inviscid and Viscous Analysis of Three-Dimensional Turbomachinery Flows Using an Implicit Upwind Algorithm,” AIAA Paper No. 96-2556.
5.
Bohn, D. E., Becker, V. J., Behnke, K. D., and Bonhoff, B. F., 1995, “Experimental and Numerical Investigations of the Aerodynamic Effects of Coolant Injection Through the Trailing Edge of a Guide Vane,” ASME Paper No. 95-GT-26.
6.
Chima, R., 1991, “Viscous Three-Dimensional Calculations of Transonic Fan Performance,” Proc. 77th Symposium of the Propulsion and Energetics Panel, AGARD.
7.
Craig, H. R. M., and Cox, H. J. A., 1970, “Performance Estimation of Axial Flow Turbines,” Proc. Institutions of Mechanical Engineers, Vol. 185, 1970/1991.
8.
Dawes
W. N.
,
1992
, “
Toward Improved Throughflow Capability: The Use of Three-Dimensional Viscous Flow Solvers in a Multistage Environment
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
8
–
17
.
9.
Denton
J. D.
,
1992
, “
The Calculation of Three-Dimensional Viscous Flow Through Multistage Turbines
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
114
, pp.
18
–
26
.
10.
Fan
S.
, and
Lakshminarayana
B.
,
1996
, “
Time Accurate Euler Simulation of Interaction of Nozzle Wake and Secondary Flow With Rotor Blade in an Axial Turbine Stage Using Nonreflecting Boundary Conditions
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
118
, pp.
663
–
678
.
11.
Gallus
H. E.
,
Zeschky
J.
, and
Hah
C.
,
1995
, “
Endwall and Unsteady Flow Phenomena in an Axial Turbine Stage
,”
ASME JOURNAL OF TURBOMACHINERY
, Vol.
117
, pp.
562
–
570
.
12.
Hafez, M., and Lovell, D., 1981, “Numerical Solution of Transonic Stream Function Equation,” AIAA Journal, Vol. 21, No. 3.
13.
Hafez, M., South, J., Murmann, E., 1978, “Artificial Compressibility Methods for Numerical Solutions of Transonic Full Potential Equation,” AIAA Journal, Vol. 17, No. 8.
14.
Harten, A., 1983, “High Resolution Schemes for Hyperbolic Systems of Conservation Laws,” J. Comp. Physics, Vol. 49.
15.
Michelassi, V., Martelli, F., and Amecke, J., 1994, “Aerodynamic Performance of a Transonic Turbine Guide Vane With Trailing Edge Coolant Ejection, Part II: Numerical Approach,” ASME Paper No. 94-GT-248.
16.
Mildner, F., and Gallus, H. E., 1993, “Calculation of Viscous Flow in Turbine Cascades With a Partially-Parabolic Algorithm and Linkage With a Quasi-Three-Dimensional Throughflow Method,” AG TURBO Report No. 1.1.2.7.
17.
Ni, R. H., and Bogoian, J. C., 1989, “Prediction of 3D Multi-Stage Turbine Flow Field Using a Multi-Grid Euler Solver,” AIAA Paper No. 89-0203.
18.
Roe
P. L.
,
1981
, “
Approximate Riemann Solvers, Parameter Vectors and Difference Schemes
,”
J. Comp. Phys.
, Vol.
34
, pp.
357
–
372
.
19.
van Leer
B.
,
1979
, “
Towards the Ultimate Conservative Difference Scheme V. A Second-Order Sequel to Godunov’s Method
,”
J. Comp. Phys.
, Vol.
32
, pp.
101
–
136
.
20.
Wu, Chung-Hua, 1951, “A General Through-Flow-Theory of Fluid Flow With Subsonic or Supersonic Velocity in Turbomachines of Arbitrary Hub and Casing Shapes,” NACA TN 2302.
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