Presenting a novel higher-order bounded convection scheme for simulation of multiphase flows and convection heat transfer

Abstract

The primary aim of the current study is to enhance the stability and accuracy of the Volume-Of-Fluid (VOF) method for modeling free-surface flows with large topological changes and high density ratio. For accurate capturing of fluid interfaces, a novel higher-order bounded convection scheme is first constructed based on the total variation diminishing (TVD) concept and is then employed for the discretization of convection terms in Navier-Stokes, energy and transport equations. In the second step, the classical PISO algorithm is modified according to the two-step projection method (Chorin's model) and the combined model (PISOC) is then applied for the treatment of the pressure-velocity coupling. Moreover, the second-order accurate piecewise-linear interface reconstruction technique (PLIC-ELVIRA) is used for determining the normal direction and curvature of the interface. The robustness and accuracy of the proposed models in handling multiphase flows with interface rupture and coalescence are verified against several experimental and numerical benchmark solutions such as: dam break, Rayleigh-Taylor instability, bubble rising, rotation of a slotted disk (Zalesak's problem), deformation of a 2D disk and pure convection of a step profile. The results show that, the proposed third-order TVD flux-limiter scheme can considerably reduce the false-diffusion errors and ensure the boundedness of the volume fraction while retaining the sharpness and shape of the interface. Furthermore, it is found that the proposed PISOC algorithm has strong stability and convergence characteristics in strongly coupled multiphase problems and is less susceptible to divergence when larger pressure under-relaxation factor is used. The performance and effectiveness of the proposed modifications are further demonstrated by analyzing transient entropy generation due to conjugate natural convection heat transfer in two different canonical test cases (i.e. Differentially Heated Cavity and Rayleigh-Bénard Convection) and good agreements are found with previously published works.