Application Study On Numerical Algorithm For Solving Boltzmann Model Equation Involving The Effect Of Internal Energy

Boltzmann equation, as the basic equation of gas kinetic theory, is fit for all theflow regimes from continuum to rarefied transition. However, it is very difficult tosolve this equation because of the complex collision term, which is a nonlinearmultiple integral and contains several variables. Thus, it has been suggested that theBoltzmann equation should be solved by using the simple model equationsapproximately instead of the original collision term. A unified algorithm for flowsfrom rarefied transition to continuum using finite-difference, discrete velocityordinate and numerical integration was developed by Li Zhihui.Based on the theory and computing rules of the Gas-Kinetic Unified Algorithm(GKUA) by solving the Boltzmann model equation, this thesis apply and extend theunified algorithm to flows with effect of internal energy. The physical model of thegas molecules is studied to develop the theory of vibrational excitation. Somecomplex flows involving non-equilibrium influence of internal rotational energy arecomputed from the whole of flow regimes, and the flow field characteristic isanalyzed with different Mach numbers. This thesis contains six chapters.The first chapter is an introduction. The researching methods of rarefied gasdynamics are introduced briefly, and then, the developing actuality and direction ofBoltzmann equation and Boltzmann model equation is reviewed and analyzed.Finally, the main work of this thesis is presented.In Chapter2, the physical model of the gas molecules is presented. The internallevels of rotational energy and vibrational energy of the molecules are described byusing semi-classical and semi-quantum mechanics. Besides, the representation formof the molecular velocity distribution function and the energy distribution functionare also given. Finally, it is made clear why the WCU equation considering theinternal energy is difficult to solve. Chapter3presents the two-level simplifiedmodel, and its application to the WCU equation in order to reduce the huge memoryrequirements and computing loads of the equation.An introduction of computational principle for Boltzmann model equationconsidering the non-equilibrium effect of rotational energy is made in Chapter4under the theoretical and computational framework of the GKUA, and the one-andtwo-dimensional flows with different Mach numbers (1.53M s25) and differentKnudsen numbers (0.0001Kn10) are simulated covering various flowregimes. The simulations of the steady normal shock wave structures with high Machnumbers and the two-dimensional flows past a blunt body validate the precision andthe reliability of the unified algorithm involving rotational non-equilibrium effect.The flow characteristic involving rotational non-equilibrium effect is analyzed. Theconsistency applicability of the GKUA covering various flow regimes is displayedby simulating the flows from complete free-molecule to continuum regimes. On thisbasis, the GKUA with rotational excitation is applied to simulate thethree-dimensional flow field around the re-entry double-cone (CUBRC) bodycovering various flow regimes in the fifth chapter. The rotational non-equilibriumeffects in rarefied transitional regime and the interaction of shock wave and viscosityare revealed by simulating the hypersonic flows around the CUBRC.The concluding remarks of this thesis are given in Chapter6. The summary ofthe studying work of this thesis are finished. The shortages and unsolved problemsare also indicated on this thesis, and the researching orientations in the future arealso suggested.