Simulation of flows with violent free surface motion and moving objects using unstructured grids

This is the peer reviewed version of the following article: [Löhner, R. , Yang, C. and Oñate, E. (2007), Simulation of flows with violent free surface motion and moving objects using unstructured grids. Int. J. Numer. Meth. Fluids, 53: 1315-1338. doi:10.1002/fld.1244], which has been published in final form at https://doi.org/10.1002/fld.1244. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A volume of fluid (VOF) technique has been developed and coupled with an incompressible Euler/Navier–Stokes solver operating on adaptive, unstructured grids to simulate the interactions of extreme waves and three-dimensional structures. The present implementation follows the classic VOF implementation for the liquid–gas system, considering only the liquid phase. Extrapolation algorithms are used to obtain velocities and pressure in the gas region near the free surface. The VOF technique is validated against the classic dam-break problem, as well as series of 2D sloshing experiments and results from SPH calculations. These and a series of other examples demonstrate that the ability of the present approach to simulate violent free surface flows with strong nonlinear behaviour.Peer ReviewedPostprint (author's final draft

Coarse-grained description of thermo-capillary flow

A mesoscopic or coarse-grained approach is presented to study thermo-capillary induced flows. An order parameter representation of a two-phase binary fluid is used in which the interfacial region separating the phases naturally occupies a transition zone of small width. The order parameter satisfies the Cahn-Hilliard equation with advective transport. A modified Navier-Stokes equation that incorporates an explicit coupling to the order parameter field governs fluid flow. It reduces, in the limit of an infinitely thin interface, to the Navier-Stokes equation within the bulk phases and to two interfacial forces: a normal capillary force proportional to the surface tension and the mean curvature of the surface, and a tangential force proportional to the tangential derivative of the surface tension. The method is illustrated in two cases: thermo-capillary migration of drops and phase separation via spinodal decomposition, both in an externally imposed temperature gradient.Comment: To appear in Phys. Fluids. Also at http://www.scri.fsu.edu/~vinals/dj1.p

A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects

In this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component while maintaining thermodynamic consistency. The governing equations of the model including the Navier-Stokes equations with additional stress term, Cahn-Hilliard equations and energy balance equation are derived within a thermodynamic framework based on entropy generation, which guarantees thermodynamic consistency. A sharp-interface limit analysis is carried out to show that the interfacial conditions of the classical sharp-interface models can be recovered from our phase-field model. Moreover, some numerical examples including thermocapillary convections in a two-layer fluid system and thermocapillary migration of a drop are computed using a continuous finite element method. The results are compared to the corresponding analytical solutions and the existing numerical results as validations for our model

Numerical simulation of liquid sloshing in LNG tanks using a compressible two-fluid flow model

In this investigation the Reynolds-Averaged Navier-Stokes (RANS) equations are modified to account for variable density and viscosity of the two-fluids flow (i.e. water-air), assuming both fluids compressible. By introducing a preconditioner, the governing equations in terms of primitive variables are solved for both fluids in a unified manner. The non-conservative implicit Split Coefficient Matrix Method (SCMM) is modified to approximate convective flux vectors in the dual time formulation. The free surface waves inside the tank, due to sloshing, are implicitly captured by using a level set approach. The method is illustrated through applications to rectangular and chamfered tanks subject to sway or roll motions at different filling levels and excitation conditions (i.e. amplitude and frequency of oscillation). Comparisons are made between calculated and experimental pressures, where available

Large-eddy simulation and wall modelling of turbulent channel flow

We report large-eddy simulation (LES) of turbulent channel flow. This LES neither resolves nor partially resolves the near-wall region. Instead, we develop a special near-wall subgrid-scale (SGS) model based on wall-parallel filtering and wall-normal averaging of the streamwise momentum equation, with an assumption of local inner scaling used to reduce the unsteady term. This gives an ordinary differential equation (ODE) for the wall shear stress at every wall location that is coupled with the LES. An extended form of the stretched-vortex SGS model, which incorporates the production of near-wall Reynolds shear stress due to the winding of streamwise momentum by near-wall attached SGS vortices, then provides a log relation for the streamwise velocity at the top boundary of the near-wall averaged domain. This allows calculation of an instantaneous slip velocity that is then used as a ‘virtual-wall’ boundary condition for the LES. A Kármán-like constant is calculated dynamically as part of the LES. With this closure we perform LES of turbulent channel flow for Reynolds numbers Re_τ based on the friction velocity u_τ and the channel half-width δ in the range 2 × 10^3 to 2 × 10^7. Results, including SGS-extended longitudinal spectra, compare favourably with the direct numerical simulation (DNS) data of Hoyas & Jiménez (2006) at Re_τ = 2003 and maintain an O(1) grid dependence on Re_τ