The study based on kinetic theory for rarefied gas flows
Date Issued
2006
Date
2006
Author(s)
Hung, Jeng-Jye
DOI
zh-TW
Abstract
When the degree of rarefaction of gases increases, the description of continuum model in macroscopic level become invalid and the use of microscopic or molecular model to describe the gas flow is necessary. The mathematic model at the microscopic level is Boltzmann equation. It governs the behavior and evolution of the gas distribution function. In this study, a particle simulation method was chosen to solve the problems of rarefied gas flow, namely, the Direct Simulation Monte Carlo method (DSMC) pioneered by Bird. The key of DSMC method to solve the Boltzmann equation is that the coupled behavior between molecular translation and collision can be decoupled when the time step is small enough, and a process of probability is employed to deal with intermolecular collisions.
In this study, a common used DSMC simulation program has been adopted and developed for studying general two- and three-dimensional rarefied gas flows. First, the problem of flow past a two-dimension cylinder with various degree of rarefaction (Kn=0.001、0.01、0.1、1) has been simulated. By observing the structures of various flow fields and the value of drag coefficient, the DSMC results are found in good agreement with the results of Navier-Stokes calculation and available experiments. Second, the problems of flow past a two-dimensional NACA0012 airfoil covering several Mach numbers and Knudsen numbers have been simulated. Compare with both the results of BGK model equation and experiment, good agreement in every case is obtained. These two cases validate the present DSMC code.
Finally, the developed simulation program in this study is extended to simulate the three-dimension flow field and the problems of gas flow past a delta wing at various degrees of rarefaction were studied here. A delta wing is a triangular airfoil of high sweepback angle, and it can offer aircrafts higher lift. The effects of rarefaction to flow field of flow past a delta wing were investigated through the results of the various macroscopic variables contours, the distribution of pressure coefficient on wing surface at different sections, and the value of lift and drag coefficients. Both high resolution Navier-Stokes solutions and DSMC solution are given and compared. It is found that the vortex which appears at leeside of delta wing at high Reynolds number from using continuum model and can offer an additional nonlinear lift may not appear when the degree of rarefaction increases to certain extent.
Subjects
稀薄流
直接模擬蒙地卡羅法
三角翼
Rarefied Gas Flow
DSMC
Delta Wing
Type
thesis