The Characteristic Of Nonlinear Acoustic Resonator And Its Gas-kinetic BGK Scheme Method Simulation

With the development and application of acoustic or thermo-acoustic devices, the high amplitude acoustic resonator becomes a key component for increasing power density and improving thermoacoustic effects. Yet, the high amplitude acoustic oscillations in the resonator will always cause much undesired nonlinear dissipation, which is a dilemma for researchers and engineers to face and necessarily solve in thermoacoustic applications. Therefore, it is significantly of importance for researchers to have a good knowledge of the mechanisms and main factors inducing various nonlinear dissipations, as well as of some methods to suppress or decrease these dissipations in actual thermoacoustic applications. So far, some nonlinear phenomena and problems have not yet been well understood and solved, because of the relatively big challenges in theory analysis, traditional numerical modeling as well as experiment measurements. Thus new approaches are needed to explore, which is the motivation of this dissertation.The research objection of this thesis is to apply and develop an effective numerical algorithm suitable for modeling nonlinear problems in an acoustic or thermoacoustic resonator, to explore the intrinsic mechanisms and main factors inducing various nonlinear dissipation, to search effective measures for suppressing or decreasing these dissipation, as well as to obtain the good characteristic of a high amplitude acoustic resonator for practice applications. For this purpose, taking into account some advantages of the gas-kinetic scheme based on BGK (GKS-BGK), this thesis conducts some numerical simulations through GKS-BGK for acquiring relevant basic information, regular characteristic, mechanism of loss, as well as design theory about high amplitude acoustic resonators. In addition, the mechanism of nonlinear dissipation and relevant effective methods to suppress them are closely studied and analyzed numerically and theoretically.The content of this thesis is composed of three parts, including the extended GKS-BGK model, numerical simulation and theory analysis. The main creative academic contributions are in that the following aspects. Specifically, in establishing of a model, the multi-dimension N-S (Navier-Stokes) equations instead of the one-dimension model are used to describe the flow motions in the resonator. Moreover, a GKS-BGK on the unstructured triangle mesh is constructed to simulate the nonlinear oscillations and two- dimension flow fields in the resonator with variable cross-section, and relevant model is established; Numerically, these characteristics of nonlinear oscillations and the dissipation mechanisms are closely investigated by the developed GKS-BGK for both the constant and the variable cross sectional resonant tube. Moreover a self-owned program code and the simulation software are developed. Theoretically, a one dimensional analytic method is proposed for predicting the characteristics of nonlinear oscillations in a variable cross-section resonator.The following summarizes the main studied work of this thesis.(1) Nonlinear oscillations in a resonator with constant cross-section are simulated by the GKS-BGK based on a two-dimensional rectangle mesh. Simulated results are obtained in consistence with those of previous research from theoretical, numerical and experimental literature. And the model algorithm is thus verified. Additionally, the evolution process of acoustic pressure and transient as well as steady-states flow fields are closely investigated taking seven separate driving frequencies near the resonant frequence into accounts. Also obtained is the detailed information on various nonlinear effects in two-dimensional flow fields at resonance. Of these nonlinear effects, shock waves, high order harmonic waves, acoustic saturation, coupling of harmonic waves, as well as energy cascade process from fundamental wave to harmonic waves are especially analyzed for searching their nonlinear dissipation mechanisms.(2) For finite amplitudes and large amplitudes, the analyses are carried out on the nonlinear dissipation and energy losses in a constant cross section resonator. The characteristics of acoustic fields and flow fields are studied by the previously verified two-dimensional GKS-BGK model for five separate driving displacement amplitudes ranging from linear to high amplitude domain. Nonlinear effects in high amplitude of acoustic oscillations are closely investigated. The effect of the driving displacement amplitude is in detail numerically analyzed on waveforms of pressure and velocity waves, transient steady-state flow fields as well as average mass flow fields. Additionally, the mechanisms of nonlinear energy losses, such as shock wave, higher harmonic, acoustic streaming, vortex, as well as boundary layer effect are also explored. These researches above will provide some basic numerical data for enhancing acoustic amplitude by some measures to decrease or suppress these undesired losses. (3) The propagating mechanism of nonlinear acoustics in a varying cross-section resonator is analyzed theoretically. These frequence relations between resonant modes for several different shaped resonators are independently derived and obtained through the asymptotic expansion method for ideal gas. Especially, the approximate analytic solution is obtained for acoustic variables in an exponential resonator. These theoretically analytic results are significantly helpful for the optimal design of high amplitude acoustic resonators, as well as for a verification and comparison of numerical results.(4) A GKS-BGK model based on the unstructured triangle mesh is constructed for simulating nonlinear effects in the variable cross-section resonator. And, the characteristics of high amplitude acoustic oscillations and acoustic streaming in an exponential resonator are simulated using this self-designed GKS-BGK model. First, the effective function of an exponential resonator is revealed in suppressing the shock wave and higher harmonic, as well as in enhancing acoustic amplitude and pressure ratio. An optimal flare parameter value is obtained for an exponential resonator and is in consistence with the theoretical one. Then, the changes of the acoustic field characteristic and streaming pattern with the driving amplitude are compared between the constant and the varying cross-section resonator. These model algorithms belong to author’s creative work, which will provide a new approach and prompt the advance in the research of varying cross-section resonator.