Peculiarities of low-Reynolds-number supersonic flows in long microchannel

Abstract

The characteristics of low-Reynolds-number supersonic flows in a long microchannel having a rectangular cross section are investigated computationally. The channel is composed of a Laval nozzle and a straight duct. The design Mach number of the nozzle is 2.0 and the Reynolds number calculated at the nozzle exit is 3100. The length of the straight duct is changed from 2 to 18 h, where h is the duct height. In the computations, the Navier–Stokes equations are numerically solved. The computational code is validated using the experimental data measured by the laser-induced fluorescence (LIF) technique. The computational results demonstrate that neither a normal shock wave nor a pseudo-shock wave, which corresponds to the starting shock wave in a supersonic wind tunnel, appears in microchannel flows. Namely, a low-Reynolds-number supersonic flow is created in a channel without the starting shock wave passing along the duct, although it has been believed that a supersonic internal flow should have been formed through the starting shock wave. In addition, it is found that the microchannel flow changes gradually its supersonic state with the channel length under an underexpanded condition, although a starting shock wave for high-Reynolds-number flows suddenly appears in a channel just as its length exceeds a certain specific length. Such unexpected phenomena originate from the peculiarity that the low-Reynolds-number flows can expand (accelerate) along a straight duct at supersonic speeds, although the high-Reynolds-number flows cannot.