A pdf description of momentum fluctuation correlations of a rarefied free shear layer

The mixing properties of various orders of fluctuation correlations are investigated in the present paper for a rarefied gas free shear layer at hypersonic speed. The molecular kinetic theory and the direct simulation Monte Carlo (DSMC) method are employed for the present calculations. The Reynolds average process is assumed in obtaining the correlation functions. The results show that flow field structure was very similar to that of continuum flow ones at high Reynolds numbers. The probability density functions (pdf) in velocity space/(u'), f(v'), and f(u', v') are also calculated to counter explain the distributions of the correlation functions in the mixing layer. From the calculated distributions of the fluctuation correlation functions, 〈u'v'〉, 〈u'〈sup〉2〈/sup〉v'〉, and 〈v'〈sup〉2〈/sup〉u'〉, one can find that the distributions behave similar to the turbulent transport phenomena in that of a continuum flow one. The distributions of the fluctuation correlation functions, 〈u'v'〉, is described via the joint probability density function, f(u' v'). The behavior of the higher-order fluctuation correlation functions, 〈u'〈sup〉2〈/sup〉v'〉, 〈u'〈sup〉3〈 /sup〉〉 and 〈u'〈sup〉4〈/sup〉〉, are also explained via the probability density function.