Generalized pressure-correction for viscous potential flow simulations of multiphase flows using boundary element method

Abstract

A new formulation for correcting the pressure field in Viscous Potential Theory (VPT) is developed, generalizing previous Viscous Pressure Correction (VPC) methods to simulate multi-phase flows based on VPT. The latter theory is now applicable to a wider range of flow problems. Without limiting the general applicability of the formulation, the present work focuses on the dynamics of two-dimensional liquid blobs and liquid films in a void. The governing equations of the method are solved using the traditional Boundary Element Method together with fourth-order Runge-Kutta time-integration, thereby reducing the spatial dimension of the problem by one and increasing the computational efficiency dramatically as compared to general purpose solvers for interfacial flows. Verification and Validation of the new method and algorithm are carried out through comparison of the simulation results with those obtained from (semi-)analytical models, a general-purpose OpenFOAM solver with Volume-of-Fluid interface treatment, and a Smoothed-Particle Hydrodynamics solver. Several benchmark cases and a wide range of viscosities are considered. Significantly improved accuracy of the newly proposed method as compared to the original Viscous Pressure Correction of Viscous Potential Flow (VCVPF) approach is demonstrated for the case of a retracting free liquid film or ligament. In order to demonstrate the capacity of the present method and algorithm in handling complex multiphase flow problems and in providing physical insight into such phenomena, the disintegration mechanism of a strongly modulated discharging liquid sheet under the influence of gravity is analyzed.