Unstable rarefied gas flow conditions in a channel

Rough Surface Aerodynamic Computation in Rarefied Gas Flow Applying the Solution of Inverse Problem

“…Applying the expression of scattering function (1) to compute aerodynamic characteristic of rarefied gas flow near rough surface, we have trouble computing the conditional probability Π (1) by given z, z x , z y Π (1) (θ, σ 1 ; z, z x , z y ) = P {z(0, y) ≤ z + y cot θ|z(0, 0) = z, z x (0, 0) = z x , z y (0, 0) = z y },…”

“…because Π (1) is the probability that the trajectory of the gas atom has no crossings with random field z(x, y), and the calculation of such probabilities is known complex promlem in the theory of random fields [1], [5], [6].…”

“…The factor Π (1) in ( 1) is important, because it takes into consideration significant effect: incident or reflected rarefied gas atoms could not reach substantial part of the area on a rough surface being blocked by emerging peaks of rough relief. Hence, these parts of the area are not to be accounted in rarefied gas-surface interaction.…”

“…x ) 1/2 = (M z 2 y ) 1/2 determined not by surface height z, but by its partial derivatives z x = ∂z/∂x and z x = ∂z/∂y in directions x and y of the mean level of a random field [1]- [6]. But the technical standard of surface quality does not contain the value σ 1 .…”

“…But the technical standard of surface quality does not contain the value σ 1 . Conquently, to find the parameter σ 1 in the papers becomes a complicated problem, and the measurements of σ 1 on the profile diagrams are extremely inaccurate [1]. Thus, retrieveing the roughness parameter σ 1 from aerodynamic experiments solving the inverse problem remains the only exact algorithm to determine its real values.…”