A filtering approach for applying the two-fluid model to gas-liquid flows on high resolution grids

The two-fluid model is usually combined with closure forces designed for applications on coarse grids, i.e. bubbles (or particles) are typically assumed to be smaller than a grid cell. Practical applications however include situations where the mesh is comparatively fine, e.g. when meshing the wall boundary layer or in cases with growing bubbles. This may lead to non-convergent behaviour in mesh studies or to void fraction oscillations. To tackle this problem, a filtering approach is proposed, based on an additional diffusion term in the continuity equation. This approach increases the robustness of the results in regions of high spatial resolution, significantly reducing mesh-dependency of the simulation results. The implementation is straightforward, without a need to solve any additional system of equations. It is analysed in four different bubbly flow cases with varying characteristics: 2D/3D, wedge, square, and cuboid computational domains, with resolutions up to 32 cells per bubble diameter, laminar and turbulent flows, and several ways of gas injection. The additional computational effort varies, but is moderate. The proposed approach is applicable in multi-field two-fluid models for which a stable Euler-Euler behaviour on fine meshes is required, for example to prepare the transfer to an interface-resolving volume-of-fluid representation in morphology-adaptive approaches.