Numerical study of shock wave entry and propagation in a microchannel

The entry of a shock wave with the Mach number M_is = 2.03 into a microchannel and its further propagation is numerically studied with the use of kinetic and continuum approaches. Numerical simulations on the basis of the Navier ?? Stokes equations and the Direct Simulation Monte Carlo method are performed for different Knudsen numbers Kn = 8·10^?3 and 8·10^?2 based on the microchannel half-height. At the Knudsen number Kn = 8·10^?3, amplification of the shock wave after its entry into the microchannel is observed. Further downstream, the shock wave is attenuated, which is in qualitative agreement with experimental data. It is demonstrated that results predicted by a quasi-one-dimensional model (which ignores viscosity and heat conduction) of shock wave propagation over a channel with an abrupt change in the area agrees with results of numerical simulations on the basis of the Euler equations. In both cases, shock wave acceleration (amplification) after its entry into the microchannel is observed. At the Knudsen number Kn = 8·10^?2, the influence of the entrance shape on shock wave propagation over the microchannel is examined. Intense attenuation of the shock wave is observed in three cases: channel with sudden contraction, junction of two channels with an additional thin separating plate, and rounded junction in the form of a sector with an angle of 90° (quarter of a circumference). It is shown that the microchannel entrance shape can affect further propagation of the shock wave. The wave has the highest velocity in the case with a rounded entrance.