A wavelet based numerical simulation technique for two-phase flows using the phase field method

Abstract

In multiphase flow phenomena, bubbles and droplets are advected, deformed, break up into smaller ones, and coalesce with each other. A primary challenge of classical computational fluid dynamics (CFD) methods for such flows is to effectively describe a transition zone between phases across which physical properties vary steeply but continuously. Based on the van der Walls theory, Allen-Cahn phase field method describes the face-to-face existence of two fluids with a free-energy functional of mass density or molar concentration, without imposing topological constraints on interface as phase boundary. In this article, a CFD simulation methodology is described by solving the Allen-Cahn-Navier-Stokes equations using a wavelet collocation method. The second order temporal accuracy is verified by simulating a moving sharp interface. The average terminal velocity of a rising gas bubble in a liquid that is computed by the present method has agreed with that computed by a laboratory experiment. The calculation of the surface tension force by the present method also shows an excellent agreement with what was obtained by an experiment. The up-welling and down-welling disturbances in a Rayleigh-Taylor instability are computed and compared with that from a reference numerical simulation. These results show that the wavelet based phase-field method is an efficient CFD simulation technique for gas-liquid or liquid-liquid flows.

Advances of Phase-Field Model in the Numerical Simulation of Multiphase Flows: A Review

“…Numerical cases illustrate the proposed scheme is unconditionally energy stable and can converge in time with the second-order accuracy. Ahammad et al [49] and Alam [50] presented a wavelet-based approach for the phase-field modeling of two-phase flows, in which the interfacial dynamics are described by the AC-NS equation and are solved by a weighted residual collocation method based on Deslauriers-Dubuc interpolating wavelets.…”

“…Other effective numerical methods have also been developed by considering the specific characteristics of the investigated problems. For example, Ahammad et al [49] and Alam [50] solved two-phase flows described by the AC-NS equation through the wavelet transform method.…”

Oil/water flow in a horizontal pipe—dispersed flow regime

“…In addition to the experimental studies, flow simulations have also been extensively developed. Numerical simulations have been performed using methods based on the solution of the transport equations for the fluids through the direct simulation of local and instantaneous equations, such as level-set method [16][17][18], phase-field method [19,20] or volume of fluids method [20,21], or through the solution of the average equations. In the latter case, the systems can be modelled using a homogeneous model, where the phases are treated as pseudofluids with average properties, and in this approach, the flow pattern is treated in a less detailed way [22], through a Lagrangian-Eulerian approach, where one of the phases is treated from an Eulerian perspective (as in the single phase flow) and the other phase receives a Lagrangian treatment [23,24], or using an Eulerian-Eulerian approach, where each phase is treated continuously and the coupling between the phases occurs through interfacial terms [25][26][27].…”

Chebyshev wavelets collocation method for simulating a two-phase flow of immiscible fluids in a reservoir with different capillary effects

“…The models describing flow of fluids in a reservoir are mostly nonlinear or coupled partial differential equations with its solution providing insight into the dynamics of the flow process. The simultaneous flow of fluids in a reservoir and many other porous media is a highly complex phenomena (Alam 2017;Szymkiewicz 2007). Numerical simulation of two-phase flow through a reservoir remains very challenging (Ahammad and Alam 2017; de la Cruz and Monsivais 2013).…”