Unstable rarefied gas flow conditions in a channel

Abstract

Nonlinear dynamic system corresponding to rarefied gas flow in a channel is investigated. Under certain conditions corresponding iterative equations may have unstable solutions in some regions of the values of gas-surface interaction parameters [1]. Numerical calculations have demonstrated that a negligible change of one of the parameters of scattering function (less than 1%) near the bifurcation points causes the substantial difference in gas flow in a channel. As well non-random solutions as random solutions can be observed on bifurcation diagrams. Some of obtained solutions have a physical meaning of locking the channel, i.e. its conductivity reduces significantly. The scattering function is supposed to be close to ray-diffuse model, where the ray model, as well as the specular model, determines only one velocity of reflected gas atoms by given incident velocity. The ray-diffuse model has better experimental confirmation in comparison with the specular-diffuse model widely applied in practical DSMC calculations. However, the problem of the empirical confirmation of the obtained numerically effect is still difficult, because the scattering conditions of this type are hardly reproducible experimentally. To verify the bifurcations of simulated type experimentally all considered physical values in the flows are to be set exactly to the same values as detected in our calculations. Adding the extra parameter of scattering function allows us extending the region where considered dynamic system (related to rarefied gas flow) is unstable in the parametric space. Simulated unstable states of the system are close to physical situations observed in experiments. Obtained connection between the parameters of nonlinear dynamic system and momentum exchange coefficients (or accommodation coefficients) makes it possible to express analytic evaluations in terms of aerodynamic characteristics including Knudsen and Mach numbers, temperature factor etc.