Research Papers

Dual-Solution and Choked Flow Treatment in a Streamline Curvature Throughflow Solver

[+] Author and Article Information
Prashant Tiwari

GE Global Research Center,
Niskayuna, NY 12309
e-mail: prashant.tiwari@ge.com

Alex Stein

GE Energy,
Greenville, SC 29615

Yu-Liang Lin

GE Aviation,
Cincinnati, OH 45215

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received December 21, 2011; final manuscript received January 24, 2012; published online June 3, 2013. Assoc. Editor: David Wisler.

J. Turbomach 135(4), 041004 (Jun 03, 2013) (8 pages) Paper No: TURBO-11-1262; doi: 10.1115/1.4007444 History: Received December 21, 2011; Revised January 24, 2012

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.

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Fig. 1

Schematic representation of a throughflow computational grid

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Fig. 2

Streamlines and quasi-orthogonals (S2) representation for the throughflow method

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Fig. 3

Variation of bladerow exit flow angle (β) with average turning (rCu) or total pressure (Pt)

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Fig. 4

Streamline curvature gradient singularity shown at Mm = 1 (plot reproduced from Smith [2])

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Fig. 5

Variation of mass flow with exit pressure. Plot also shows choked flow condition.

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Fig. 6

Sample meanline bladerow turning distribution for two rotors

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Fig. 7

Plot showing the radial distribution of turning (rCu) for throat station under localized streamtube choking (red: after correction, blue: before correction) (see color in the online version)

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Fig. 8

Meridional velocity distribution at TE of eighth stage rotor of the subsonic compressor test case. Results are showing solver consistency for a subsonic test case.

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Fig. 10

Three-dimensional CFD and 2D throughflow comparison for a transonic three-stage turbine test case

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Fig. 9

Predicted meridional Mach number shown for a three-stage transonic turbine test case. Solution obtained using the numerical improvements presented in this paper.



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