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近似积分原理在叶片机械的试验与计算中的一些应用——一组新的比切比雪夫公式更适用的积分公式

张春霖   

  1. 703研究所
  • 出版日期:1981-02-20 发布日期:1981-02-20

张春霖. 近似积分原理在叶片机械的试验与计算中的一些应用——一组新的比切比雪夫公式更适用的积分公式[J]. 数值计算与计算机应用, 1981, 2(2): 82-93.

APPLICATION OF APPROXIMATE INTEGRATION THEORY TO TURBOMACHINERY TESTING AND CALCULATION

  1. Zhang Chun-lin 703 Institute
  • Online:1981-02-20 Published:1981-02-20
一、问题的提出 测量速度和压力等参数的平均值,用所推荐的公式比原来常用的方法有很大改进.但不难发现,用于测点布置切比雪夫公式有时还不够理想,因为,测点布置的指导思想应该是,用较少的测点尽量获得较高的精度.而切比雪夫公式因其插值点的位置已确定,有时分布很不均匀(如n=6和n=7时较为突出),而且“外插区”比较大.对气动测
This paper is a refinement of a previous [1]. A set of new integral formulas ia pro-posed concerning the distribution of probe points of turbomachinery tests. The distinc-tive features of the said formulas consist in the fact that the weights of various test pointsare arranged in two groups and the distribution of interpolation points is adjusted bychanging the proportion factors of weights of the two groups, so that a moreaccurate approximation of the integrand can be attained. With this method, a greater,accuracy then can be achieved by Chebichev formula. In addition, it is more practicaland easier to use than the Gauss formula. To ensure the relatively high measurementaccuracy in cases when the results of certain probe points are unreliable, this papersuggests that the integraton by "weighting method" be used after discarding certainprobe point whose measurements are thought to be untrustworthy. Formulas for weight-ed means are given for instances of discarding a probe point in commonly used probepoint distribution arrangements.
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[1] 张春霖,近似积分公式在叶片机测试和计算中的应用,舰船透平锅炉,第一期(1976) .
[2] 中国科学院计算技术研究所,计算方法讲义,1958年.
[3] А.Н克雷洛夫著,吕茂烈,吕季美译,近似计算讲义.
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