力学与实践 ›› 2013, Vol. 35 ›› Issue (4): 48-52.DOI: 10.6052/1000-0879-13-072

• 应用研究 • 上一篇    下一篇

截尾Gauss概率密度函数的性质及待定参数的求解

庞杰, 张健   

  1. 清华大学工程力学系, 北京100084
  • 收稿日期:2013-03-05 修回日期:2013-06-09 出版日期:2013-08-08 发布日期:2013-08-26
  • 通讯作者: 张健,E-mail:jianzhang@mail.tsinghua.edu.cn
  • 基金资助:

    国家自然科学基金资助项目(51076082).

PROPERTIES OF THE CLIPPED GAUSSIAN PROBABILITY DENSITY FUNCTION AND THE DETERMINATION OF ITS UNKNOWN PARAMETERS

PANG Jie, ZHANG Jian   

  1. Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
  • Received:2013-03-05 Revised:2013-06-09 Online:2013-08-08 Published:2013-08-26

摘要:

截尾Gauss 分布是湍流燃烧中常用的一种瞬时标量概率密度函数形式,但其中的待定参数较难以计算. 本文对截尾Gauss 分布进行了理论分析,获得了截尾Gauss 分布的若干性质. 表明当标量脉动均方值(g) 较大时,待定参数μσ之间呈线性关系,这使得求解待定参数的方程组退化为包含单一变量的方程. 在一般的g 取值条件下,通过提取标量平均值(f) 的等值线并沿其进行插值,可快速地求解出不同fg 值下的待定参数μσ,并建立了相应的表格.

关键词:

截尾Gauss 分布|概率密度函数|湍流燃烧

Abstract:

The clipped Gaussian distribution is a probability density function of instantaneous scalar, which is commonly used in turbulent combustions. However, it is diffcult to determine its unknown parameters. A theoretical analysis is made for the clipped Gaussian distribution in this paper. Some of its properties are discussed. When the mean square of the fluctuating scalar (g) becomes large, the unknown parameters μ and σ have a linear relationship. Thus the determination of the unknown parameters is reduced to the determination of a single parameter. For general values of g, the contour lines of the averaged scalar (f) are extracted and the interpolation along them is performed. The unknown parameters μ and σ are determined rapidly under different values of f and g. A data table is established.

Key words:

clipped gaussian distribution|probability density function|turbulent combustion

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