截尾Gauss概率密度函数的性质及待定参数的求解

doi:10.6052/1000-0879-13-072

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

截尾Gauss概率密度函数的性质及待定参数的求解

庞杰, 张健

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

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/Abstract

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.

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

中图分类号:

TK16

庞杰, 张健. 截尾Gauss概率密度函数的性质及待定参数的求解[J]. 力学与实践, 2013, 35(4): 48-52.

PANG Jie, ZHANG Jian. PROPERTIES OF THE CLIPPED GAUSSIAN PROBABILITY DENSITY FUNCTION AND THE DETERMINATION OF ITS UNKNOWN PARAMETERS[J]. Mechanics in Engineering, 2013, 35(4): 48-52.

参考文献

1 Smoot LD, Smith PJ. Coal Combustion and Gasiˉcation. New York: Plenum Press, 1985
2 Pope SB. Turbulen Flows. Cambridge: Cambridge University Press, 2000
3 Peters N. Turbulent Combustion. Cambridge: Cambridge University Press, 2000
4 周力行. 多相湍流反应流体力学. 北京:国防工业出版社,2002
5 Cannon SM, Brewster BS, Smoot LD. PDF modeling of lean premixed combustion using in situ tabulated chemistry. Combustion and Flame, 1999, 119(3): 233-252
6 Cao RR, Pope SB. The influence of chemical mechanisms on PDF calculations of nonpremixed piloted jet flames. Combustion and Flame, 2005, 143(4): 450-470
7 Jones WP, Whitelaw JH. Calculation methods for reacting turbulent flows: A review. Combustion and Flame, 1982,48: 1-26
8 Warnatz J, Maas U, Dibble RW. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation. Berlin: Springer, 1999
9 Liu F, Guo H, Smallwood GJ, et al. A robust and accurate algorithm of the β-PDF integration and its application to turbulent methane-air di.usion combustion in a gas turbine combustor simulator. International Journal of Thermal Sciences, 2002, 41: 763-772
10 Bray, KNC, Champion M, Libby PA, et al. Finite rate chemistry and presumed PDF models for premixed turbulent combustion. Combustion and Flame, 2006, 146: 665-673
11 张洪涛,张健. 截尾Gauss 概率密度函数中待定参数的确定. 力学与实践, 2007, 29(1): 64-68, 57 (Zhang Hongtao, Zhang Jian. Determination of parameters for the clipped Gauss probability density function. Mechanics in Engineering,2007, 29(1): 64-48, 57 (in Chinese))
12 李庆扬,关治,白峰杉. 数值计算原理. 北京: 清华大学出版社,2000
13 王涛,毋河海,刘纪平. 基于区间树索引的等高线提取算法. 武汉大学学报(信息科学版), 2007, 32(2): 131-134 (Wang Tao, Wu Hehai, Liu Jiping. An algorithm for extracting contour lines based on interval tree from grid DEM. Geomatics and Information Science of Wuhan University, 2007,32(2): 131-134 (in Chinese))
14 边淑莉,柳佳佳,王海龙等. 基于规则格网DEM 的等高线提取算法的优化与实现. 测绘科学, 2008, 23(6): 151-153 (Bian Shuli, Liu Jiajia,Wang Hailong, et al. An improvement and realization of contour extraction algorithm based on RGD. Science of Surveying and Mapping, 2008, 23(6): 151-153 (in Chinese))
15 张瑞超,叶海建,王彦. 满足方向一致性的等高线提取算法. 计算机工程与设计, 2010, 31(11): 2602-2605 (Zhang Ruichao, Ye Haijian, Wang Yan. Algorithm for extracting contour lines with consistent direction. Computer Engineering and Design, 2010, 31(11): 2602-2605 (in Chinese))

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

PDF (PC)

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价