Author:  Kam, Wingsze Elizabeth 
Title:  Prediction of noise generation by using modeled Boltzmann Equation (BE) 
Degree:  Ph.D. 
Year:  2008 
Subject:  Hong Kong Polytechnic University  Dissertations. Transport theory. Noise generators (Electronics) Aerodynamic noise  Mathematics. 
Department:  Dept. of Mechanical Engineering 
Pages:  210 p. : ill. (some col.) ; 30 cm. 
Language:  English 
InnoPac Record:  http://library.polyu.edu.hk/record=b2232937 
URI:  http://theses.lib.polyu.edu.hk/handle/200/1196 
Abstract:  Onestep CAA methods aim at resolving the flow and the acoustic fields simultaneously. A set of unsteady compressible NavierStokes (NS) Equations are solved in order to capture both the sound generated mechanism and the fluidsound interaction at the near field. The physical challenge of aeroacoustics simulation comes from the disparity of aerodynamic and acoustic scales. Since the smaller acoustic scale has to be taken account for throughout the simulation, it is computational costly to solve the nonlinear NS Equations. As a result, the direct methods, although accurate, are limited to simple cases. Instead of solving a set of nonlinear NS equations, the particle distribution function is being tracked by solving the Modeled BE with BGK model. The desirable macroscopic properties in both the aerodynamic and acoustic scales can be obtained by taking moment of the particle distribution function. The accuracy and robustness of Modeled BE for CAA studies depends on 1. An appropriate nonreflecting boundary conditions for aeroacoustics simulations 2. The ability and extent of the Modeled BE to recover the unsteady compressible NS equations (Recovery of transport coefficients in macroscopic equations) In this thesis, the Modeled Boltzmann Equation (BE) as a OneStep Computational Aeroacoustics (CAA) method has been studied and analyzed with respect to the above aspects. First of all, an appropriate nonreflecting boundary condition is crucial for CAA studies, since the rebound waves from boundaries would contaminate the computational domain and drive the solutions to a nonphysical one. In this thesis, different types of nonreflecting boundary conditions are studied and compared, with respect to two benchmarked aeroacoustics problems. Physically, the particle distribution function in the Boltzmann Equation can be expanded to recover the unsteady compressible NS equations via ChapmanEnskog procedure. However, there exist limitations on application by using different numerical schemes. The corresponding limitations are analyzed in the first aspect. The macroscopic transport coefficients are closely related to the relaxation of particle collision. Therefore, the transport coefficients should be recovered by physical laws via the relaxation of particle collision. The first coefficient of viscosity related to momentum relaxation has been recovered by Sutherland's Law by Li et al. (2006). In this thesis, the coefficient of thermal conductivity is recovered by Eucken's model, with respect to the energy relaxation. Case studies of aeroacoustics problems with thermal effect are presented accordingly. 
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