Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines
Sensitivity Analysis and Numerical Stability Analysis of the Algorithms for Predicting the Performance of Turbines
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DOI：
10.1115/gt2013-94482
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发表时间：
2013-06
期刊：
影响因子：
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通讯作者：
M. Wei;Yonghong Wang;Huafen Song
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文献类型：
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作者：
M. Wei;Yonghong Wang;Huafen Song
算法的灵敏度和数值稳定性是评估其性能的两个最重要的标准。对于所有已发表的涡轮流动模型，除Wang方法外，都可以称为“自上而下”方法（TDM），其中从第一级到最后一级逐行计算涡轮机的性能；只有王永红最初提出的Wang方法可以称为“自下而上”方法（BUM），其中从最后一级到第一级逐行计算涡轮机的性能。为了找出两种方法稳定性差异较大的原因，对Wang流模型进行了研究。该模型很容易适用于 TDM 和 BUM。分析了两种算法的稳定性如何受输入误差和舍入误差的影响，得到了两种方法中的误差传播和分布。为了更直观地解释问题，用几何思想来描述两种方法的稳定性。为了与已知数据进行比较，基于两种算法通过一系列程序计算特定类型涡轮机的性能。结果如下。工作点越接近临界点，TDM的稳定性越差。稳定性差甚至会导致TDM计算失败。但BUM不仅稳定性好，而且精度高。该结果为估算汽轮机性能提供了一种准确可靠的方法（BUM），适用于汽轮机所有一维性能计算方法。Copyright © 2013 by ASME
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 closer the operating 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 © 2013 by ASME