In most turbomachinery design systems, streamline curvature based throughflow calculations make the backbone of aero design process. The fast, reliable, and easy to understand solution is especially useful in performing several multistage design iterations in a short period of time. Although the streamline curvature based technique enjoys many benefits for subsonic applications, there are some challenges for transonic and supersonic flow applications, which is the focus of this paper. In this work, it is concluded that three key improvements are required to handle transonic flows in a streamline curvature throughflow solver. These are (1) the ability to overcome dual sub and supersonic solutions and guide the solver towards a supersonic flow solution where applicable; (2) a suitable technique to calculate the streamline curvature gradient term, which can avoid singularity at sonic meridional Mach number and high gradient values in transonic flows; and (3) a suitable technique to handle choked flow in the turbomachinery flowpath. Solution procedures for “dual-solution” and choked flow treatment are new and developed as part of this work. However, a procedure for calculating streamline curvature gradient is leveraged from earlier work done by Denton (1978, “Throughflow Calculations for Transonic Axial Flow Turbines,” Trans. ASME, 100, pp. 212–218) and Came (1995, “Streamline Curvature Throughflow Analysis,” VDI-Ber., 1185, p. 291). Implementation of these improvements is performed in a streamline curvature based throughflow solver. Numerical improvements presented here have been tested for a range of compressor and turbine cases (both subsonic and supersonic). It is shown that the numerical improvements presented in this paper resulted in an enhanced version of the streamline curvature throughflow solver. The new code produces consistent solutions for subsonic applications with no sacrifice in the accuracy of the solver. However, considerable robustness improvements are achieved for transonic turbine cases.

References

References
1.
Wu
,
C. H.
,
1952
, “
A General Theory of Three-Dimensional Flow in Subsonic, and Supersonic Turbomachines of Axial, Radial and Mixed-Flow Types
,”
Trans. ASME
, pp.
1363
1380
, available at http://naca.central.cranfield.ac.uk/reports/1952/naca-tn-2604.pdf
2.
Smith
,
L. H.
, Jr.
,
1966
, “
The Radial-Equilibrium Equation of Turbomachinery
,”
ASME J. Eng. Power
,
88
, pp.
1
22
.10.1115/1.3678471
3.
Marsh
,
H.
,
1968
, “
A Digital Computer Program for the Throughflow Fluid Mechanics in an Arbitrary Turbo Machine Using a Matrix Method
,” Aeronautical Research Council, Report No. 3509.
4.
Marsh
,
H.
,
1971
, “
The Uniqueness of Turbomachinery Flow Calculations Using the Streamline Curvature and Matrix Through-Flow Methods
,”
J. Mech. Eng. Sci.
,
12
(
6
), pp.
376
379
.10.1243/JMES_JOUR_1971_013_058_02
5.
Novak
,
R. A.
,
1967
, “
Streamline Curvature Computing Procedures for Fluid-Flow Problems
,”
ASME J. Eng. for Industry
,
89
(
3
), pp.
478
490
.10.1115/1.3610089
6.
Bindon
,
J. P.
,
1973
, “
Stability and Convergence of Streamline Curvature Flow Analysis Procedure
,”
Int. J. Numer. Methods Eng.
,
7
(
1
), pp.
69
83
.10.1002/nme.1620070106
7.
Wilkinson
,
D. H.
,
1970
, “
Stability, Convergence, and Accuracy of Two-Dimensional Streamline Curvature Methods Using Quasi-Orthogonals
,”
Proc. Inst. Mech. Eng.
,
184
, pp.
108
124
.10.1243/PIME_CONF_1969_184_168_02
8.
Stow
,
P.
,
1972
, “
The Solution of Isentropic Flow
,”
J. Inst. Math. Appl.
,
9
, pp.
35
46
.10.1093/imamat/9.1.35
9.
Hafez
,
M.
,
South
,
J.
, and
Murman
,
E.
,
1978
, “
Artificial Compressibility Methods for Numerical Solutions of Transonic Full Potential Equation
,”
AIAA J.
,
17
(
8
), pp.
838
844
.10.2514/3.61235
10.
Murman
,
E. M.
, and
Cole
,
J. D.
,
1971
, “
Calculation of Plane Steady Transonic Flows
,”
AIAA J.
,
9
(
1
), pp.
114
121
.10.2514/3.6131
11.
Denton
,
J. D.
,
1978
, “
Throughflow Calculations for Transonic Axial Flow Turbines
,”
ASME J. Eng. Power
,
100
(
2
), pp.
212
218
.10.1115/1.3446336
12.
Came
,
P. M.
,
1995
, “
Streamline Curvature Throughflow Analysis
,”
VDI-Ber.
,
1185
, p.
291
.
13.
Casey
,
M.
, and
Robinson
,
C.
,
2008
, “
A New Streamline Curvature Throughflow Method for Radial Turbomachinery
,”
Proceedings of the ASME Turbo Expo 2008
,
ASME
Paper No. GT2008-50187.10.1115/GT2008-50187
14.
Sayari
,
N.
, and
Bölcs
,
A.
,
1995
, “
A New Throughflow Approach for Transonic Axial Compressor Stage Analysis
,” ASME Paper No. 95-GT-195.
15.
Denton
,
J. D.
,
1993
, “
Loss Mechanism in Turbomachines
,”
ASME J. Turbomach.
,
115
, pp.
621
656
.10.1115/1.2929299
16.
Koch
,
C. C.
, and
Smith
,
L. H.
, Jr
.
,
1976
, “
Loss Sources and Magnitudes in Axial-Flow Compressors
,”
ASME J. Eng. Power
,
98
, pp.
411
424
.10.1115/1.3446202
17.
Adkins
,
G. G.
, and
Smith
,
L. H.
, Jr.
,
1982
, “
Spanwise Mixing in Axial Flow Turbomachines
,”
ASME, J. Eng. Power
,
104
, pp.
97
110
.10.1115/1.3227271
18.
Genrup
,
M.
,
2003
, “
Theory of Turbomachinery Degradation and Monitoring Tools
,”
Ph.D. thesis
,
Lund University
,
Lund, Sweden
.
19.
Pachidis
,
V.
,
Templalexis
,
I.
, and
Pilidis
,
P.
,
2009
, “
A Dynamic Convergence Control Algorithm for the Solution of Two-Dimensional Streamline Curvature Methods
,”
Proceedings of the ASME Turbo Expo 2009
,
ASME
Paper No. GT2009-59758.10.1115/GT2009-59758
20.
Aungier
,
R. H.
,
2006
,
Turbine Aerodynamics—Axial-Flow and Radial-Flow Turbine Design and Analysis
,
ASME Press
,
New York
.
21.
Anderson
,
J. D.
, Jr.
,
1991
,
Fundamentals of Aeromechanics
,
2nd ed.
,
McGraw-Hill
,
New York
.
22.
Craig
,
H. R. M.
, and
Cox
,
H. J. A.
,
1970
, “
Performance Estimation of Axial Flow Turbines
,”
Proc. Inst. Mech. Eng.
,
185
, pp.
407
424
.10.1243/PIME_PROC_1970_185_048_02
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