A study of pseudopotential lattice Boltzmann method with applications to thermal bubble nucleation

The nature of the work dealt with in this thesis is mathematical modelling of multiphase flows. The main objective of this doctoral work was to study multiphase lattice Boltzmann models (LBM) and to develop an advanced pseudopotential model. Specifically, advanced thermal lattice Boltzmann models were applied to study bubble nucleation in nucleate pool boiling at subatmospheric pressures. The numerical investigations carried out as part of this work follow the format well-established in the literature and allow further studies in more complex geometries. The work carried out contributes to current discussions in the literature and fulfils the recommendations of a number of authors. Fluid-fluid interactions in the Yuan-Schaefer, multipseudopotential interaction and piecewise linear equation of state methods were investigated. Multipseudopotential interaction was established as a practicable method of multiphase simulations by combination with the multiple relaxation time collision operator, surface tension modification methods and with modified temperature double distribution function and hybrid (4th order Runge-Kutta) thermal LBM models. Thermal LBM simulations were found to agree well with experimental findings on the influence of subatmospheric pressure on bubble nucleation. It was found that as pressure is lowered in LBM simulations the size of bubbles nucleated increases, according to bubble diameter ~ pressure-1 , with results falling in between experimental data for brass and stainless steel tubes

Development of a lattice Boltzmann model to investigate the interaction mechanism of surface acoustic wave on a sessile droplet

This study focuses on the development of a three dimensional numerical model, based on the lattice Boltzmann method (LBM), for two-phase fluid flow dynamics employing a multiple-relaxation-time (MRT) pseudopotential scheme. The numerical model is applied in the investigation of acoustic interactions with microscale sessile droplets (1- 10 µl), under surface acoustic wave (SAW) excitation, through the introduction of additonal forcing terms in the LBM scheme. In the study, a range of resonant frequencies (61.7 - 250.1 MHz) are studied and quantatively compared to existing studies and experimental findings to verify the proposed model. The modelling predictions on the roles of forces (SAW, interfacial tension, inertia and viscosity) on the dynamics of mixing, pumping and jetting of a droplet are in good agreement with observations and experimental data. Further examination of the model, through parameter study, identified that the relaxation parameters considered free to tune in the MRT, play an important role in model stability, providing large reductions in spurious velocities, in both the liquid and gas phases, when the values are specified correctly. It has also been discovered that employing a dynamic contact angle hysteresis model increased the adhesion between the liquid droplet and the substrate, improving the agreement with experimental findings by up to 20%. Lastly, an investigation of various equation of state implementations revealed some fascinating differences in droplet dynamics and behaviours, owing primarily to the physical underpinning of which each is based upon. The developed model is successfully applied in the examination of various scenarios including SAW-droplet interactions on an inclined slope, droplet impact on flat (horizontal) and inclined surfaces with and without SAW interactions, and dual SAW interactions on a droplet at several configurations. The findings indicate the importance of applied SAW power, especially in inclined slope scenarios, to overcome the inertia and gravitational forces which act to counteract the droplet motion initiated by the acoustic wave direction of travel. Furthermore, a new multi-component multi-phase multi-pseudopotential (MCMP MPI) LB model is proposed. The study details initial model development and verification for classical benchmark cases, comparing to both the single-component (SCMP MPI) and publicised data. Similar to its SCMP MPI counterpart, the model displays excellent stability, even at high density ratios, and thermodynamic consistency. Comparison to the SCMP MPI model reveals lower spurious velocities are generated in the proposed MCMP model, approximately one order of magnitude lower. Close inspection of the interaction force implementation shows they are analogous whilst similar surface tension values are presented for both models. The proposed scheme signifies a new class of MPI model capable of simulating realistic fluid compositions for use in applications of scientific and engineering interest