Development of Coupled Dual grid Level Set and Lattice Boltzmann based Multi-Phase Flow Solver

Abstract

Lattice Boltzmann Method (LBM) is a Lagrangian approach among different methods present under Computational Fluid Dynamics through which a detail study of fluid flow and heat transfer is possible. In Lattice Boltzmann method a discrete Boltzmann equation is used for simulating a Newtonian fluid flow using a collision model known as Bhatnager-Gross-Krook (BGK). Boltzmann method basically depends on mesoscopic approach which is in between microscopic and macroscopic approaches. In the present study, use of LBM with single-relaxation-time (SRT) collision model and multi-relaxation-time (MRT) model for higher stability and accuracy is demonstrated. The main aim of the present study is to develop a module using Boltzmann method to analyze fluid flow and validate the obtained results of LBM with the published results obtained by solving Navier stokes equation. Based on a single phase flow, Several problems such as Lid-driven cavity, flow through channel, flow over a backward facing step and flow over a square cylinder are simulated and validated with the published numerical Benchmark results. The results obtained are found to be in exact agreement with the published literature. The Lid driven cavity problem is solved at 1000 Reynolds number and the results are validated with the standard numerical Benchmark results of Ghia and Ghia. The flow through channel problem is simulated at 400 Reynolds number. The boundary layer formation was captured and hydrodynamic entrance length is used as a validating parameter. Acceptable results are obtained for the same. The Backward facing step problem is simulated at 800 Reynolds number and the results are validate in terms of Re-attachment length and was found in good agreement with the published literature. The flow over a square cylinder was simulated at two different Reynolds number, 60 and 100. The validation is done in terms of velocity contour, streamline patterns, vortex shedding with the published numerical results obtained using LB method as well as solving Navier Stokes equation. In recent trend, various computational methods are used for solving fluid flow problem at different computational scales. Navier Stoke (NS) solver is considered to be an efficient and easy to implement for solving different fluid flow and heat transfer phenomena. The major disadvantage while solving the NS equation - particularly for multiphase flow - is modeling of the source term arise due to interfacial transport. Further, it also required larger computational effort to accurately capture the complex interfacial transport phenomena in multiphase flow problems. In the present work, an in-house code, based on combine the Lattice Boltzmann (for the conservation equations) and the Level Set method (for interface representation) is developed, named as LBLS. Bhatnagar-Gross-Krook collision model is used for solving the governing equations of LBM with Multiple relaxation time (MRT) scheme for transformation of velocity distribution function to momentum distribution function. Diffused interface Level set scheme is coupled with the lattice Boltzmann method for capturing the interface dynamics pertaining to two immiscible fluids. Finite difference based discretization technique on D2Q9 lattice model is used to incorporate the force terms (coming across the interface) in the governing equations of LB. The proposed LBLS is validate for standard multiphase flow problems: The Young’s Laplace test and the Buoyancy driven bubble problem. Excellent agreement is observed between the proposed methodology and the published numerical/analytical results for above mentioned problems. The validation also suggests that the spurious velocity (across the interface) is always found to be negligible (order of 1e-6), suggesting robustness of the LBLS. Further, the LBLS is used to capture the interface dynamics for a liquid Jet injected upwards into another liquid.