Inverse problem of finding surface roughness parameters in rarefied gas flow

Abstract

The new algorithm is proposed to determine the real values of the roughness parameter σ1 from aerodynamic measurements solving the inverse problem. Roughness parameters are measured usually in the experiment from the profile diagram. However, the main parameter defining surface roughness according to usual standard procedures is not σ1, but the square mean deviation σ of the height of the surface. The roughness parameter in rarefied gas σ1 is not measured in the experiments. In addition, even if the parameter σ1 is measured, the main input into the influence of surface roughness on aerodynamic values takes the roughness of smaller scale, usually negligible on the profile diagram. Therefore σ1 must be determined from the solution of the inverse problem. The solution of the inverse problem is based on the simulation of surface roughness on micro-level by Gaussian or poly-Gaussian random field and on the representation of the scattering function on rough surface. The 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 diffuse-specular model of the local scattering function of reflected gas atoms, but also Cercignani–Lampis scattering kernel or phenomenological models of scattering function. From the results we can see that the value of σ1 obtained from the solution of inverse problem is substantially higher than the value of σ1 from the profile diagram measurements.