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The confirmation of the α–β model and the maximum entropy formulation in a thermal wake
Author(s) -
Wang YouQin,
Derksen R. W.
Publication year - 1998
Publication title -
environmetrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.68
H-Index - 58
eISSN - 1099-095X
pISSN - 1180-4009
DOI - 10.1002/(sici)1099-095x(199805/06)9:3<269::aid-env303>3.0.co;2-n
Subject(s) - kurtosis , wake , probability density function , turbulence , skewness , mechanics , reynolds number , root mean square , mathematics , cylinder , thermal , statistical physics , physics , thermodynamics , statistics , geometry , quantum mechanics
We have confirmed the validity of Chatwin and Sullivan's α–β model using our experimental results in a thermal wake. Using the same data set, we have also examined and validated Derksen and Sullivan's maximum entropy formulation to approximate the probability density function of a turbulent contaminant fluctuation when only the fourth and the lower order moments are known. In addition, the paper provides evidence to suggest the kurtosis is quadratically dependent on skewness. The measurements were made in a thermal wake created by a heated cylinder in a fully developed turbulent pipe flow, at 7 stations from 16·7 to 58·3 cylinder diameters downstream of the source. The Reynolds number is 180,000 based on the centreline mean velocity and the pipe diameter (or 11,000 based on the cylinder diameter). The results presented in this paper include the cross‐stream distributions of the mean and root mean square velocity and temperature as well as the probability density functions of the temperature fluctuations. © 1998 John Wiley & Sons, Ltd.