EFFECT OF MULTIPHASE LATTICE BOLTZMANN COLLISION MODELS WITH SINGLE- AND MULTI-\RELAXATION TIMES FOR SIMULATION OF LIQUID-VAPOR TWO-PHASE FLOWS USING

In this paper, the multiphase lattice Boltzmann collision models are evaluated by a comparative study for the simulation of liquid-vapor two-phase flow problems. Herein, the single-relaxation-time (SRT) scheme based on the Bhatnagar-Gross-Krook (BGK) approximation and the multiple-relaxation-time (MRT) method with two different forcing schemes are considered. The pseudo-potential Shan-Chen (SC) model is used to resolve the inter-particle interactions between the liquid and gas phases. In the standard form of the SC model, the interaction force is imposed in the momentum field which unphysically causes the density ratio to change with the variation of relaxation time. In this study, a modified form of this model is implemented to decouple these two physical parameters. Herein, the interaction force is imposed using the exact difference method (EDM). The efficiency and accuracy of the present numerical scheme based on the lattice Boltzmann method (LBM) with the SRT and MRT schemes are examined for simulation of two-phase flows in different conditions. The equilibrium state of a droplet in the periodic flow domain and on the flat surface with hydrophobic and hydrophilic wetting condition are computed to investigate the robustness and performance of the collision operators applied. The results obtained for these problems are compared with the analytical solutions which shows a good agreement. The collision of a droplet on the liquid film at various flow conditions is investigated and the predicted results are presented at a range of the Weber and Reynolds numbers. The present study demonstrates that the SRT model suffers from the spurious velocity in the interfacial region which causes numerical instabilities at moderate Reynolds and Weber numbers. It is found that the MRT model is stable for all the cases considered in the present work even at high Reynolds and Weber numbers. In terms of the computational efficiency, the SRT scheme is slightly attractive, although the computational cost of this model is not considerably lower than MRT scheme. The present study suggests the lattice Boltzmann method with the MRT collision operator incorporated with the EDM technique is robust, sufficiently accurate and computationally efficient to resolve the practical liquid-vapor two-phase flow structures and properties.