截尾Gauss概率密度函数的性质及待定参数的求解

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

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μ和σ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f与g值下的待定参数μ和σ,并建立了相应的表格.

The clipped Gaussian distribution is a probability density function of instantaneous scalar, which is commonly used in turbulent combustions. However, it is difficult 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 scal^r （9） becomes large, the unknown parameters t~ and 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 # and a are determined rapidly under different values of f and g. A data table is established.