"This dissertation is devoted to the computational investigation of supersonic gas flows in rectangular nanochannels with scales between 100 nm and 1000 nm, using an unstructured three-dimensional Direct Simulation Monte Carlo (U3DSMC) methodology. This dissertation also contributes to the computational mathematics background of the U3DSMC method with validations and verifications at the micronscale and nanoscale, as well as with the investigation of the statistical fluctuations and errors associated with U3DSMC simulations at the nanoscale. The U3DSMC code is validated by comparisons with previous two dimensional DSMC simulations of flows in micron-scale rectangular channels. The simulation involves the supersonic flow of nitrogen into a microchannel with height of 1.2 m and width of 6 m. The free stream conditions correspond to a pressure of 72,450 Pa, Mach number , Knudsen number and mean free path nm. The U3DSMC centerline temperature, heat flux to the wall, and mean velocity as a function of the transverse direction are in very good agreement with previous 2D results. Statistical fluctuations and errors in U3DSMC have added significance in nanoscale domains because the number of real particles can be very small inside a computational cell. The effect of the number of samples, the number of computational particles in a Delaunay cell, and the Mach number on the fractional errors of density, velocity and temperature are investigated for uniform and pressure-driven nanoscale flows. The uniform nanoflow is implemented by applying a and free stream boundary condition with m-3, K, nm in a domain that requires resolution of a characteristic length scale nm. The pressure-driven flows consider a nanochannel of 500 nm height, 100 nm width and 4 m length. Subsonic boundary conditions are applied with inlet pressure 101,325 Pa and outlet pressure of 10132.5 Pa. The analysis shows that U3DSMC simulations at nanoscales featuring 10-30 particles per Delaunay cell result in statistical errors that are consistent with theoretical estimates. The rarefied flow of nitrogen with speed ratio of 2, 5, and 10, pressure of 10.132 kPa into rectangular nanochannels with height of 100, 500 and 1000 nm is investigated using U3DSMC. The investigation considers rarefaction effects with =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 analysis is based on the phase space distributions as well as macroscopic flow variables sampled in cells along the centerline. 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. The 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 and 100 nanochannels the gas reaches near equilibrium with the wall temperature. The heat transfer rate is largest near the inlet region where non-equilibrium effects are dominant. For =0.481, 0.962, 4.81, vacuum back pressure, and AR=1, the nanoflow is supersonic throughout the nanochannel, while for AR=10 and 100, the nanoflow is subsonic at the inlet and becomes sonic at the outlet. For =0.962, AR=1, and imposed back pressure of 120 kPa and 200 kPa, the nanoflow becomes subsonic at the outlet. For =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 qualitative characteristics found in microchannels ad well as continuum compressible flows in channels with friction and heat loss. The rarefied flow of nitrogen with speed ratio of 2, 5, 10, at an atmospheric pressure of 101.32 kPa into rectangular nanochannels with height of 100 and 500 nm is investigated using U3DSMC. The investigation considers rarefaction effects with =0.0962 and 4.81, geometric effects with nanochannel aspect ratios of (L/H) of AR=1 and 10 and vacuum back-pressure. Phase plots and sample-averaged macroscopic parameters are used in the analysis. Under vacuum back pressure the centerline velocity decreases in the buffer region from its free stream value. For 0.481, 0.0962 and AR=1 the Mach number is supersonic at the inlet and remains supersonic throughout the nanochannel. For 0.481, 0.0962 and AR=10, the flow becomes subsonic at the inlet and shows a sharp increase in pressure. The Mach number, subsequently, increases and reaches the sonic point at the outlet. For 0.481, 0.0962 and AR=1 the translational temperature reaches a maximum near the inlet and decreases monotonically up to the outlet. For 0.481, 0.0962 and AR=10, the translational temperature reaches a maximum near the inlet and then decreases to come in near equilibration with the wall temperature of 273 K. "


Worcester Polytechnic Institute

Degree Name



Mechanical Engineering

Project Type


Date Accepted





Micro/Nano flows, DSMC, Nanochannel