Analytic Model of the Effect of Poly-Gaussian Roughness on Rarefied Gas Flow near the Surface.

The dependence of the macro-parameters of the flow on surface roughness of the walls and on geometrical shape of the surface is investigated asymptotically and numerically in a rarefied gas molecular flow at high Knudsen numbers. Surface roughness is approximated in statistical simulation by the model of poly-Gaussian (with probability density as the mixture of Gaussian densities [1]) random process. Substantial difference is detected for considered models of the roughness (Gaussian, poly-Gaussian and simple models applied by other researchers), as well in asymptotical expressions [3], as in numerical results. For instance, the influence of surface roughness on momentum and energy exchange coefficients increases noticeably for poly-Gaussian model compared to Gaussian one (although the main properties of poly-Gaussian random processes and fields are similar to corresponding properties of Gaussian processes and fields). Main advantage of the model is based on relative simple relations between the parameters of the model and the basic statistical characteristics of random field. Considered statistical approach permits to apply not only diffusespecular model of the local scattering function V0 of reflected gas atoms, but also Cercignani-Lampis scattering kernel or phenomenological models of scattering function. Thus, the comparison between poly-Gaussian and Gaussian models shows more significant effect of roughness in aerodynamic values for poly-Gaussian model. [ABSTRACT FROM AUTHOR]