Author(s): Norjan H. Jumaa; David I. Graham

Linked Author(s):

Keywords: Lattice Boltzmann method; Multiphase flows; Rayleigh-Taylor instability; High density ratio; Standing waves

Abstract: We present simulations for some complex flows including 2D single and multiple mode Rayleigh-Taylor Instability and both high and low viscosity standing waves. We used a Lattice Boltzmann Method (LBM) for multiphase flows with high viscosity and density ratios. Following Banari et al. (2014), the motion of the interface between fluids is modelled by solving the Cahn-Hilliard (CH) equation with LBM. Incompressibility of the velocity fields in each phase is imposed by using a pressure correction scheme. We use a unified LBM approach with separate formulations for the phase field, the pressure-less Navier-Stokes (NS) equations and the pressure Poisson equation required for correction of the velocity field. The implementation has been verified for various test cases. The Rayleigh-Taylor instability (RTI) appears when a low-density fluid sits below the more dense fluid. The low-density fluid rises when the denser fluid drops according to the gravitational acceleration g. An initial interface location in the 1 × 4 domain is specified as y(x) = 2 + A cos(2πx) with disturbance amplitude A = 0.1. The g value is chosen to achieve the characteristic velocity Uc = √lxg = 0.04 in lattice units, where lx, ly are the numbers of lattice points in the x, y-directions. Here we present the time evolution of the two fluid interface from a single mode perturbation of RTI with different density ratios. The agreement is good. To indicate the effectiveness of the model at high density ratios, we also illustrate the results with density ratio 100 and viscosity ratio 0.1. In the multiple mode RTI, Uc = 0.08 and the initial interface function is defined as a random combination of frequency modes with amplitudes chosen randomly from a Gaussian distribution. We illustrate the evolution of the two-fluid interfaces for different values of the surface tension coefficient, showing the expected increasing complexity of the interface as surface tension decreases. We also present results for a standing wave with density ratio 2, with initial interface at y(x) = 1/2 + A cos(2πx) in a 1 × 1 domain for both low and high viscosity. The predicted period and decay rate agree well with results from Buick et al. (1998).

DOI: https://doi.org/10.3850/978-981-11-2731-1_099-cd

Year: 2018