Burnett Simulation Of Micro-and Nanoscale Gas Flow And Heat Transfer

The deviation of rarefied gas from the equilibrium state of continuum is characterized by Knudsen number, Kn, which is defined as the ratio of mean free path to system's characteristic length. In micro- and nanoscale gas flows, the flow falls into the transition flow regime. There are not enough molecule collisions in the flow, so the gas deviates from the equilibrium. The Navier-Stokes (N-S) equations, which is based on linear constitutive relation between the stress and strain, fails to describe the gas flow in this regime. On the other hand, the direct simulation Monte Carlo (DSMC) method, which is molecule based, converges slowly and requires lots of computational time, especially for the low velocity flow. As a result, the Burnett equations are used in the present thesis to study the flow and heat transfer characteristics in micro- and nanoscale gas flow. The Burnett equations are an approximate solution of the Boltzmann equation when considering the first three terms in Chapman-Enskog Expansion, which represents a second-order departure from the thermal equilibrium.The stability of one-dimensional conventional Burnett, augmented Burnett, BGK Burnett and Woods equations were studied systematically for the first time using linear perturbation method. The results show that the exact forms of these four equations are all unstable against small perturbations. The critical Kn of these unstable equations were obtained. For these four original equations, the critical Kn are 0.105, 0.105, 0.158 and 0.074, respectively. The material derivatives in these equations can be approximated by the Euler or N-S equations. When Euler equations were used, the augmented Burnett and BGK Burnett equations are stable against any small perturbations. But the conventional Burnett and Woods equations are unstable when Kn is larger than some critical value. The critical Kn for conventional Burnett and Woods equations are 0.499 and 0.184, respectively. When N-S equations were used to approximate the material derivatives, all these four equations are stable.The augmented Burnett equations were then used to simulate the micro- and nanoscale gas flow and heat transfer in Couette flow. A second order velocity-slip and temperature-jump condition and a relaxation method on the boundary value were adopted in the present study. Convergent solutions to the Burnett equations were obtained on arbitrary fine grids for all Kn up to the limit of the equations' validity. The results of Burnett equations agree very well with those of DSMC and Information Preservation methods. When Kn is small, the results of N-S and Burnett equations agree well with each other. But the N-S equations fails to model the gas flow when Kn is large, while the results of Burnett equations can still agree well with those of DSMC method. The flow and heat transfer characters in Couette flow at different Kn and Mach numbers were also studied in the present thesis.The Burnett equations with high order slip boundary conditions were used to simulate the compressible gas flow and heat transfer in micro Poiseuille flow in the slip and transition regime. A relaxation method on Burnett terms was proposed in the present study and convergent solutions to the Burnett equations can be obtained even when Kn≤0.4. Excellent agreement can be achieved when the results of Burnett equations are compared with those of analytical, experimental and DSMC results. The results of Burnett and N-S equations agree well with each other when Kn is small but only Burnett equation can be used in transition flow regime. The gas flow and heat transfer characteristics in Poiseuille flow were then studied.The present paper systematically studied the usage of the Burnett equations in micro- and nanoscale gas flows for the first time. The stability of the Burnett equations was improved and the flow and heat transfer in Couette and Poiseuille flows were studied. The continuum based models can be extended to the transition flow regime.