Evaluation of two-phase flow solvers using Level Set and Volume of Fluid methods

Abstract

Two principal methods have been used to simulate the evolution of two-phase immiscible flows of liquid and gas separated by an interface. These are the Level-Set (LS) method and the Volume of Fluid (VoF) method. Both methods attempt to represent the very sharp interface between the phases and to deal with the large jumps in physical properties associated with it. Both methods have their own strengths and weaknesses. For example, the VoF method is known to be prone to excessive numerical diffusion, while the basic LS method has some difficulty in conserving mass. Major progress has been made in remedying these deficiencies, and both methods have now reached a high level of physical accuracy. Nevertheless, there remains an issue, in that each of these methods has been developed by different research groups, using different codes and most importantly the implementations have been fine tuned to tackle different applications. Thus, it remains unclear what are the remaining advantages and drawbacks of each method relative to the other, and what might be the optimal way to unify them. In this paper, we address this gap by performing a direct comparison of two current state-of-the-art variations of these methods (LS: RCLSFoam and VoF: interPore) and implemented in the same code (OpenFoam). We subject both methods to a pair of benchmark test cases while using the same numerical meshes to examine a) the accuracy of curvature representation, b) the effect of tuning parameters, c) the ability to minimise spurious velocities and d) the ability to tackle fluids with very different densities. For each method, one of the test cases is chosen to be fairly benign while the other test case is expected to present a greater challenge. The results indicate that both methods can be made to work well on both test cases, while displaying different sensitivity to the relevant parameters.

A conservative flux‐corrected continuous finite element method for fluid interface dynamics

“…Notwithstanding, an acceptable agreement is extended up to t ≈ 0.3 s, consistent with the symmetry, still clearly identified. We find a good agreement with the results in the work of Bilger et al 31 both in qualitative description (see Figure 7) and in quantitative form (see Figure 8).…”

“…A manifest symmetry is detected in Figures A to C, violated at ensuing times by thin filaments (see Figure D, t =1.2 s). Figure displays the lowest position of the jet s ( t ) by the current numerical method, by a numerical solution in the work of Bilger et al, and by the theoretical solution for inviscid flows without surface tension, where the initial position of the front is denoted as s 0 , and its value is of 0.05 m. Numerical solution has a close agreement with theoretical solution for inviscid flows at early stages of motion, when nonlinearity is weak and perturbation amplitude is much smaller than its wavenumber. Notwithstanding, an acceptable agreement is extended up to t ≈0.3 s, consistent with the symmetry, still clearly identified.…”

“…Rayleigh‐Taylor instability. Amplitude growth, comparison with theoretical results, and with numerical model in the work of Bilger et al…”

“…The linear triangular structured mesh has = √ 2 128 m and Δt = 10 −4 s. The interface has a thickness of 2Δx at t=0 to attain a better definition of perturbation (33). To be consistent with the preceding reports (eg, in the work of Bilger et al 31 ), the slip boundary condition is prescribed on vertical walls and no-slip condition on horizontal walls. Figure 7 illustrates the evolution of the instability.…”

“…A manifest symmetry is detected in Figures 7A to C, violated at ensuing times by thin filaments (see Figure 7D, t=1.2 s). Figure 8 displays the lowest position of the jet s(t) by the current numerical method, by a numerical solution in the work of Bilger et al, 31 and by the theoretical solution for inviscid flows without surface tension, 32 s = s 0 cosh (Ψt) ,…”