Binary droplet collision simulations by a multiphase cascaded lattice Boltzmann method

Daniel Lycett-Brown,Kai H Luo,Pengmei Lv,Ronghou Liu

doi:10.1063/1.4866146

Abstract

Three-dimensional binary droplet collisions are studied using a multiphase cascaded lattice Boltzmann method (LBM). With this model it is possible to simulate collisions with a Weber number of up to 100 and a Reynolds number of up to 1000, at a liquid to gas density ratio of over 100. This is made possible by improvements to the collision operator of the LBM. The cascaded LBM in three dimensions is introduced, in which additional relaxation rates for higher order moments, defined in a co-moving reference frame, are incorporated into the collision operator. It is shown that these relaxation rates can be tuned to reduce spurious velocities around curved phase boundaries, without compromising the accuracy of the simulation results. The range of attainable Reynolds numbers is therefore increased. Different outcomes from both head-on and off-centre collisions are simulated, for both equal and unequal size droplets, including coalescence, head-on separation, and off-centre separation. For head-on collisions the critical Weber number between coalescence and separation is shown to decrease with decreasing ambient gas pressure. The variation of critical Weber number with droplet size ratio is also studied. Comparisons are made with the theoretical predictions of Tang et al. [“Bouncing, coalescence, and separation in head-on collision of unequal-size droplets,” Phys. Fluids 24, 022101 (2012)], and the effect of ambient gas pressure is again considered. For off-centre collisions, boundaries between different collision outcomes are accurately defined and quantitative comparisons are made with the theoretical predictions of Rabe et al. [“Experimental investigation of water droplet binary collisions and description of outcomes with a symmetric Weber number,” Phys. Fluids 22, 047101 (2010)]. While general agreement between the simulated and theoretical boundaries is presented, deviations due to varying liquid viscosity are observed. Finally, the prediction of the independence of regime boundaries with varying droplet size ratio, when using the symmetric Weber number as defined by Rabe et al., is discussed. Simulation results showing qualitative agreement are presented, although some discrepancies are reported.

Highlights

For off-centre collisions, boundaries between different collision outcomes are accurately defined and quantitative comparisons are made with the theoretical predictions of Rabe et al [“Experimental investigation of water droplet binary collisions and description of outcomes with a symmetric Weber number,” Phys
In the 2D case we have shown that for the specific case of calculating the multiphase force term with the Shan-Chen model[10,11] and incorporating this into the collision operator using the exact difference method (EDM),[12] these improvements are of the same order as those of the more established multiple relaxation time (MRT) method
It has been shown that the cascaded lattice Boltzmann method (LBM) can significantly reduce spurious velocities around curved phase boundaries, and increase the range of attainable Reynolds numbers

Summary

Introduction

Instead of solving the macroscopic Navier-Stokes equations as in traditional CFD, the LBM works on the mesoscopic scales, solving a discretised Boltzmann equation, designed to recover the NavierStokes equations in the macroscopic limit. As the LBM works with particle distribution functions, complex macroscopic fluid behaviours which occur as a result of particle interactions, such as phase separation, can be included. As interfaces between high and low density phases arise naturally, no interface tracking is required, representing a significant advantage over traditional CFD methods for multiphase flows. This method is applied to the modelling of binary droplet collisions

Methods

Results

Conclusion