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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.

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References

Figures

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Fig. 1

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

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Fig. 2

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

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Fig. 3

Variations of RX and 1/RX with λ

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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

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Fig. 5

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

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Fig. 8

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

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Fig. 9

Velocity diagram of an axial flow turbines under a subcritical condition

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Fig. 7

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

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Fig. 6

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

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