Sloshing and Free-Surface Flow Simulations | Institute for Fluid Dynamics and Ship Theory

Free-Surface Flow Computations using FreSCo+

Similar to other methods, FreSCo uses a volume-of-fluid (VOF) approach to simulate two-phase flows. The challenge refers to the simulation immiscible fluids, e.g. air and water, which feature a discontinous transition between the two phases. Accordingly, the maintenance of a sharp interface is often difficult to realise.

Background

Although dedicated, downwind-biased interpolation schemes are used in VOF-based two-phase flow simulations, the predicted free surface often tends to become blurred. Particularly when the free surface is oriented perpendicular to the face normals, the predicitve accuracy might be disappointing on coarse mehses. The effect is more or less pronounced, depending on the choice of the interpolation scheme, the orientation of the grid and the application.

Methodology

Next to a number of downwind-biased interpolation schemes (HRIC, CICSAM, SHIP etc.) FreSCo offers an explicit interface sharpening approach (eis) which can be coupled to any interpolation practice. The latter works as a fully-conservative supplement at negligible computational expenses and is driven by flow physics rather than maths. The approach facillitates interfaces of the utmost sharpness (i.e. transition within one cell) but still resolves liquid splashes in line with the grid resolution. The above given figure comparing experiments and computation for a blunt bare-hull flow at Fn=0.7 and Re=3.4 Mio. illustrates the attainable predictive accuracy for steady wave-field simulations.

Examplary Application - Long Term Behaviour of a Sloshing Tank

An important maritime application pertains to sloshing flows, where the slope of the free-surface significantly varies over space and time on a fixed mesh. Therefore, an sharpening approach is an essential add-on feature. The impact of the sharpening approach is illustrated by the below given sloshing example which refers to an experiment performed at NMRI. The geometry is a simple rectangular at 20% filling tank featuring a width of b = 1.2m, height h = b/2. The translational excitation of the tank refers to a period length T = 1.94s and an amplitude of a=b/20.

Animated results pertain to two laminar flow simulations, using an identical computational model with a time step of dt = 0.002. The top simulation refers to the simulation based on the explicit interface sharpening approach (eis), the bottom simulation employs a standard high-resolution interface-capturing scheme. As indicated by the animation, an unsharpend solution gets blurred and provides inaccurate pressure predictions by means of both phase and amplitude.

The free-surface treatment is supplemented by an efficient dynamic mesh-refinement and -coarsening technique, which helps to capture massively transient physics at modest computational effort.