Investigation of rarefied supersonic flows into rectangular nanochannels using a three-dimensional direct simulation Monte Carlo method

Abstract

The rarefied flow of nitrogen with speed ratio (mean speed over most probable speed) of S=2,5,10, pressure of 10.132 kPa into rectangular nanochannels with height of 100, 500, and 1000 nm is investigated using a three-dimensional, unstructured, direct simulation Monte Carlo method. The parametric computational investigation considers rarefaction effects with Knudsen number Kn=0.481,0.962,4.81, geometric effects with nanochannel aspect ratios of (L/H) from AR=1,10,100, and back-pressure effects with imposed pressures from 0 to 200 kPa. The computational domain features a buffer region upstream of the inlet and the nanochannel walls are assumed to be diffusively reflecting at the free stream temperature of 273 K. The flow analysis is based on the phase space distributions while macroscopic flow variables sampled in cells along the centerline are used to corroborate the microscopic analysis. The phase-space distributions show the formation of a disturbance region ahead of the inlet due to slow particles backstreaming through the inlet and the formation of a density enhancement with its maximum inside the nanochannel. Velocity phase-space distributions show a low-speed particle population generated inside the nanochannel due to wall collisions which is superimposed with the free stream high-speed population. The mean velocity decreases, while the number density increases in the buffer region. The translational temperature increases in the buffer region and reaches its maximum near the inlet. For AR=10,100 nanochannels the gas reaches near equilibrium with the wall temperature. The heat transfer rate is largest near the inlet region where nonequilibrium effects are dominant. For Kn=0.481,0.962,4.81, vacuum back pressure, and AR=1, the nanoflow is supersonic throughout the nanochannel, while for AR=10,100, the nanoflow is subsonic at the inlet and becomes sonic at the outlet. For Kn=0.962, AR=1, and imposed back pressure of 120 and 200 kPa, the nanoflow becomes subsonic at the outlet. For Kn=0.962 and AR=10, the outlet pressure nearly matches the imposed back pressure with the nanoflow becoming sonic at 40 kPa and subsonic at 100 kPa. Heat transfer rates at the inlet and mass flow rates at the outlet are in good agreement with those obtained from theoretical free-molecular models. The flows in these nanochannels share qualitatively characteristics found in microflows and continuum compressible flows in channels with friction and heat loss.