Accurate implementation of forcing terms for two-phase flows into SIMPLE algorithm

作者：Montazeri Hanif^*; Bussmann Markus; Mostaghimi Javad

来源：International Journal of Multiphase Flow, 2012, 45: 40-52.

DOI：10.1016/j.ijmultiphaseflow.2012.05.003

• Pressure-based algorithm
• Level-set method
• Two-phase flow
• Surface tension
• Gravity force
• Ferrofluids
• Piezometric pressure

A consistent numerical method for two-phase flows has been devised, that properly includes generic body forces in the framework of a collocated variable arrangement. We first discuss the accurate implementation of body forces, and then apply this to interfacial forces. Having shown the problems associated with applying forcing terms in a collocated framework, we introduce piezometric pressure into the governing equations for two-phase flow. As a result, the Navier-Stokes equations written for variable property flow, developed by Hong and Walker, are revised to be consistent with the numerical implementation of the level-set function. Consequently, the interfacial forces consist of both surface tension and gravity. We develop appropriate numerical methods to incorporate a generic body force, including the interfacial forces, within the framework of pressure-based algorithms (e.g. SIMPLE algorithm). A suitable pressure-velocity coupling scheme is then proposed for this type of flow solver and compared with other schemes. To validate the formulation, the results of several test cases including the Rayleigh-Taylor instability, a magnetized ferrofluid, and a falling water droplet are presented and compared with the results obtained by a conventional implementation of body forces. The advantages of confining the effect of gravity to the vicinity of an interface are explained, and we demonstrate how this approach enhances numerical solutions.

• 出版日期2012-10