Prediction of noise generation by using modeled Boltzmann Equation (BE)

Pao Yue-kong Library Electronic Theses Database

Prediction of noise generation by using modeled Boltzmann Equation (BE)

 

Author: Kam, Wing-sze 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: One-step CAA methods aim at resolving the flow and the acoustic fields simultaneously. A set of unsteady compressible Navier-Stokes (NS) Equations are solved in order to capture both the sound generated mechanism and the fluid-sound 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 non-reflecting 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 One-Step Computational Aeroacoustics (CAA) method has been studied and analyzed with respect to the above aspects. First of all, an appropriate non-reflecting boundary condition is crucial for CAA studies, since the rebound waves from boundaries would contaminate the computational domain and drive the solutions to a non-physical one. In this thesis, different types of non-reflecting 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 Chapman-Enskog 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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