Development of a Lattice Boltzmann based Multiphase flow solver

Abstract

In this work the study for different types of fluid flow problems was carried out based on the history of the research problems. In the beginning a general introduction to the various conventional and also the particle based methods is given in brief and the reason why LBM has been used in this work to simulate the fluid problems. Initially the review of the literature is done for thorough understanding of the LBM and also the basic methodology including the derivation of the famous Lattice Boltzmann equation from the distribution function concept for the same is given in a simple language . It has been found that multiple relaxation scheme is very effective for the simulation of single and multiple phase problems. The types of boundary conditions is explained and how to implement it in the solver is shown as well. As per the standard problems used by many researchers we have identified the common practical problems such as a 2D flow in a channel and lid driven cavity . The open source code for all the cases with the implementation of the LBM with help of the MRT technique have been studied and an attempt to modify and develop the same is done in this work. The 2D flow through a channel problem code is simulated a number of times for the grid size of 1000 x 40 and 125 x 5 by varying the Reynolds number from Re =400 , 1000 , 2000 and the center-line velocity uw = 0.05 , 0.1 and the results for the same have been shown and validated with the published literature. The Lid driven cavity problem is simulated for 100 x 100 grid size and the velocity contours were plotted with streamlines and the same was validated with published work and the vortex were found to be in good agreement and velocity profiles are in good agreement. The validation of these standard problems have been done with the reputed published literature and the results are found to be in good agreement with published literature. Further the work is carried out for the multiphase flow where developing the in house code by modifying the modules of these codes and simulating the typical multiphase flow problems such as Young Laplace Test , 2D Rising bubble and later on Rayleigh Taylor instability was done. The results obtained from the simulation were plotted in accordance with the published literature to study and validate the results of solver proposed with appropriate grid indepedence. In the Young Laplace test, we have used test case for Re=35 and Eo=10 and density ratio=10 and viscosity ratio =10 and the results for spurious velocity vectors and contours are plotted and also the pressure jump contours across the interface is shown alongwith plots of pressure jump for different grid size of 40 x 40 ad 80 x 80. For the 2D Rising bubble problem the no slip BC's on top and bottom and free-slip BC's were implemented for the grid sizes of 40 x 80 , 80 x 160 ,160 x 320 and the results of the Circularity , Bubble velocity and Bubble centroid position were plotted w.r.t. time and the units were non-dimensionalized in macroscale from the mesoscopic scale. The bubble interface was captured for different time steps and the results were validated with published literature and were found to be in agreement with the published work. The Rayleigh Taylor instability solver was used for simulation for the grid sizes of 16 x 128 , 32 x 256 and 64 x 512 and Re= 256 and Re=2048 , Eo=125 and At=0.5 and typically obtained results for the change in shape of the interface betweeen the two fluids ad how the two fluids mix up when given the perturbation. A brief conclusion was made regarding the application of the solver for which cases and typically at what parameters it depends followed with the future scope in the same domain .