Research Papers

Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines

[+] Author and Article Information
Ming Wei

Turbo Machinery Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: Wm8748@gmail.com

Yonghong Wang

Turbo Machinery Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: wangyh@sjtu.edu.cn

Huafen Song

Turbo Machinery Institute,
Shanghai Jiao Tong University,
Shanghai 200240, China
e-mail: hfsong@sjtu.edu.cn

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 31, 2013; final manuscript received March 30, 2014; published online May 2, 2014. Assoc. Editor: John Clark.

J. Turbomach 136(9), 091006 (May 02, 2014) (8 pages) Paper No: TURBO-13-1175; doi: 10.1115/1.4027372 History: Received July 31, 2013; Revised March 30, 2014

Sensitivity and numerical stability of an algorithm are two of the most important criteria to evaluate its performance. For all published turbine flow models, except Wang method, can be named the “top-down” method (TDM) in which the performance of turbines is calculated from the first stage to the last stage row by row; only Wang method originally proposed by Yonghong Wang can be named the “bottom-up” method (BUM) in which the performance of turbines is calculated from the last stage to the first stage row by row. To find the reason why the stability of the two methods is of great difference, the Wang flow model is researched. The model readily applies to TDM and BUM. How the stability of the two algorithms affected by input error and rounding error is analyzed, the error propagation and distribution in the two methods are obtained. In order to explain the problem more intuitively, the stability of the two methods is described by geometrical ideas. To compare with the known data, the performance of a particular type of turbine is calculated through a series of procedures based on the two algorithms. The results are as follows. The more the calculating point approaches the critical point, the poorer the stability of TDM is. The poor stability can even cause failure in the calculation of TDM. However, BUM has not only good stability but also high accuracy. The result provides an accurate and reliable method (BUM) for estimating the performance of turbines, and it can apply to all one-dimensional performance calculation method for turbine.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.


Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., and Tarantola, S., 2008, Global Sensitivity Analysis: The Primer, Wiley-Interscience, Chichester, UK.
Grosche, G., 2003, Teubner-Taschenbuch Der Mathematik, BG Teubner Verlag, Wiesbaden, Germany.
Anderson, J. D., 1990, Modern Compressible Flow: With Historical Perspective, McGraw-Hill, New York.
Fang-Yuan, Z., 1987, Gas Turbine Design Basis, China Machine Press, Beijing.
Saravanamuttoo, H. I. H., Rogers, G. F. C., and Cohen, H., 2001, Gas Turbine Theory, Pearson Education, Essex, UK.
Cao, Q., Yong-Hong, W., Hua-Fen, S., and Ming-Hai, H., 2009, “Performance Estimation of Variable Geometry Turbines,” Proc. IMechE, Part A: J. Power Energy, 223(4), pp. 441–449. [CrossRef]
Kotlial, I. V., 1965, The Changed Condition of Gas Turbine, Shanghai Scientific & Technical Publishers, Shanghai.
Cherkasov, B. A., and Yemin, O. H., 1959, “Research of the Process of Gas Turbine in One Stage,” Analytical Calculation of Gas Turbine Characteristic Curve, National Defence Industrial Press, Hong Kong.
Ainley, D. G., and Mathieson, G. C. R., 1951, “A Method of Performance Estimation for Axial-Flow Turbines,” British Aeronautical Research Council, London, Report No. 2974.
Yong-Hong, W., 1990, “A New Method of Predicting the Turbine Flow Characteristics,” Ship Eng., 05, pp. 25–33.
Yong-Hong, W., 1991, “A New Method of Predicting the Performance of Gas Turbine Engines,” ASME J. Eng. Gas Turbines Power, 113(1), pp. 106–111. [CrossRef]
Kacker, S. C., and Okapuu, U., 1982, “A Mean Line Prediction Method for Axial Flow Turbine Efficiency,” ASME J. Eng. Gas Turbines Power, 104(1), pp. 111–119. [CrossRef]


Grahic Jump Location
Fig. 1

Variation of pneumatic function X(λ, γ) with dimensionless velocity λ

Grahic Jump Location
Fig. 2

Variation of pneumatic function Y(λ, θ, γ) with dimensionless velocity λ, θ = 0.8, 0.9, and 1.0

Grahic Jump Location
Fig. 3

Variations of RX and 1/RX with λ

Grahic Jump Location
Fig. 4

Variations of RY and 1/RY with λ, the curves of RY is the range of RY < 1, the curves of 1/RY is the range of RY > 1

Grahic Jump Location
Fig. 5

Sketch for explaining the difference of sensitivity and stability with TDM and BUM

Grahic Jump Location
Fig. 6

The error between the known λcs and λcal,cs calculated with TDM and BUM

Grahic Jump Location
Fig. 7

The error of λcs with TDM, the inputs are λc0 and (1 ± 0.1%) × λc0, λc0 = 0.1349

Grahic Jump Location
Fig. 8

The error of λcs with bum, the inputs are λc2 and (1 ± 0.1%) × λc2, λc2 = 0.4072

Grahic Jump Location
Fig. 9

Velocity diagram of an axial flow turbines under a subcritical condition



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In