Lattice Boltzmann Method For Thermoacoustics Simulation And PIV Study On Thermoacoustic Resonator

Thermoacoustic heat engine is novel energy-utilization equipment with wide application prospects. Research on thermoacoustic is an intersectional fundamental study related to several fields, such as acoustics, thermodynamics, heat transfer, fluid mechanics and so on, and is of great science interest and engineering value. There are a number of complicated scientific issues in thermoacoustic systems, for example, low Mach compressible fluid flow and heat transfer, nonlinear effects and multiscale effects in both space and time. At the present, our understandings and studies on these issues are far from being enough. This is because it is quite difficult to study with conventional theoretical analysis, field simulation and experimental investigation. Thus, some novel ideas of research should be developed.Considering the characters of the lattice Boltzmann method, which is a mesoscopic method, this dissertation implements numerical simulation for the thermoacoustic engine based on the lattice Boltzmann method, and in conjunction with visualization through PIV investigates the scientific issues involved in depth.This dissertation consists of three parts: extensions of the basic theory of the lattice Boltzmann method, numerical studies and experimental measurements. On the lattice Boltzmann method theoretical aspect, an implicit-explicit finite-difference lattice Boltzmann method, and a polynomial kernel function based lattice Boltzmann model for viscous compressible flows are proposed to overcome the shortcomings of the previous lattice Boltzmann method. On the numerical aspect, several issues such as oscillating flow and heat transfer, Rayleigh-Bénard convection, sound wave attenuation, thermoacoustic resonator and nonlinear onset are numerical studied with the lattice Boltzmann method. On the experimental aspect, a visual test rig with PIV technology is designed and established, and gas oscillating in a thermoacoustic resonator is experimental measured. Major contents of this dissertation are as follows.Extensions of the theory of the lattice Boltzmann method: (1) A novel algorithm, named implicit-explicit finite-difference lattice Boltzmann method, is proposed to improve the computational efficiency of the lattice Boltzmann method, so that a macroscopic study on thermoacoustic engine can be conducted. Owing to the characteristic of the collision invariants, the implicitness in the implicit-explicit scheme can be completely eliminated, thus no extra iteration is needed in practice, and the advantages of both explicit and implicit are remained in the algorithm at the same time. Numerical examples demonstrate that this scheme can significantly improve computational efficiency with guaranteed stability. In addition, for the proposed algorithm, non-uniform meshes can be implemented with ease, schemes for space and time discretization can be chosen flexibly and the numerical stability can be guaranteed via the Courant-Friedricks-Lewey condition. The standard lattice Boltzmann method does not possess these features.(2) A polynomial kernel function based lattice Boltzmann model is developed for the simulation of viscous compressible flows. The coupled double distribution function approach is adopted in such a model. A polynomial kernel function satisfying all statistical constrains is specified firstly with the method of indeterminate coefficients. A discrete equilibrium density distribution function and a discrete equilibrium total energy distribution function are obtained from the discretization of the given polynomial kernel function with Lagrangian interpolation. The equilibrium distribution functions are then coupled via the equation of state. Numerical tests indicate that this model can be used within a wide range of Ma numbers, for example, in the tests, the minimal Ma number is 0.0845, whereas maximal one 10. Such model can work with flexible Ma number, viscosity, specific-heat ratio and Pr number.Numerical studies:(3) Incompressible oscillating flow in a two-dimensional channel is numerical studied using the standard lattice Boltzmann method. The dependence of the fluid flow and heat transfer characteristics on various oscillating frequencies, amplitudes of the pressure gradient and locations are analyzed. From this study, the feasibility of applying the lattice Boltzmann method for simulating complicated physical process, such as oscillating flow is demonstrated.(4) Attenuation of plane sound waves both in one- and two-dimensional channels are numerical studied using the standard lattice Boltzmann method. The results show that the waves attenuate along the propagating direction due to the internal viscous dissipation of the propagation medium, and the friction of the walls (for the two-dimensional case only), and the amplitudes of the velocity oscillation and density oscillation become smaller and smaller. With the increase of the wavelength or the decrease of the medium viscosity, the attenuation of sound waves becomes slower. The attenuation of the sound waves leads to a negative exponent pressure gradient, and with the increase in wave length the decease in the pressure gradient becomes smaller. (5) Two-dimensional Rayleigh-Bénard convection is numerical studied using the interpolation-supplemented lattice Boltzmann method. The evolvement process of the convection is observed. The steady-state streamlines and isotherms are given for different Ra numbers. The dependence of the fluid flow and heat transfer characteristics on various Ra numbers and locations are presented. The obtained Nu numbers as a function of Ra numbers are consistent with those from previous references. Moreover, numerical results also indicate that although the interpolation-supplemented lattice Boltzmann method can be used to increase the size of the computational domain with finite meshes, computation will overflow when the ratio of interpolation is larger than 20. As a result, the interpolation-supplemented lattice Boltzmann method is not suitable for simulating the thermoacoustic issues.(6) Gas oscillation in a two-dimensional closed resonator is numerical studied using the standard lattice Boltzmann method and the implicit-explicit finite-difference lattice Boltzmann method, respectively. The dependences of the density, velocity and pressure of the gas on various oscillating frequencies, time and locations are obtained. Shock wave propagation is clearly captured. Therein, the oscillating pressure wave obtained with the implicit-explicit finite-difference lattice Boltzmann method agree quantitatively with experimental data available in the literatures.(7) Thermoacoustic nonlinear self-excited onset of the Rijke is numerical studied using the implicit-explicit finite-difference lattice Boltzmann method and the polynomial kernel function based compressible model. Onset of the Rijke tube is simulated successfully with a parallel code developed in OpenMP. The obtained oscillating frequency of the gas is 171.2Hz, and agrees with theoretical prediction. Gas flow and heat transfer characteristics beyond the limit cycle are also investigated. Experiment investigations:(8) A visual test rig with PIV technology is designed and established, and gas oscillating in a thermoacoustic resonator is experimentally measured. Two resonators with lengths of 1020.5mm and 517mm are adopted in experiment. The obtained resonance frequencies are 78.8Hz and 134.7Hz, respectively. Some representative velocity fields within fundamental resonant frequency are obtained. The dependence of the in-tube pressure and velocity on various frequencies, powers and locations and the lengths of tube are also investigated.