Simulation of free surface flows with non-hydrostatic pressure distribution (original) (raw)

Numerical study of flows with multiple free surfaces

International Journal for Numerical Methods in Fluids, 2001

This paper demonstrates that a numerical method based on the generalized simplified marker and cell (GENSMAC) flow solver and Youngs' volume of fluid (Y-VOF) surface-tracking technique is an effective tool for studying the basic mechanics of hydraulic engineering problems with multiple free surfaces and non-hydrostatic pressure distributions. Two-dimensional flow equations in a vertical plane are solved numerically for this purpose. The numerical results are compared with experimental data and earlier numerical results based on a higher-order depth-averaged flow model available in the literature. Two classical problems, (i) flow in a free overfall and (ii) flow past a floor slot, are considered. The numerical results correspond very well with the experimental data for both sub-critical and supercritical flows.

A Novel Algorithm of Advection Procedure in Volume of Fluid Method to Model Free Surface Flows

In this study, the developed procedure of advection in volume of fluid (VOF) method is presented for free surface modeling. The fluid is assumed to be incompressible and viscous and therefore, Navier-Stokes and continuity are considered as governing equations. Applying Youngs’ algorithm in staggered grids, it is assumed that fluid particles in the cell have the same velocity of the cell faces. Therefore, fluxes to neighboring cells are estimated based on cell face velocities. However, these particles can show different velocities between two adjacent cell faces. In developed model, the velocity in mass center of fluid cell is evaluated to calculate fluxes from cell faces. The performance of the model is evaluated using some alternative schemes such as translation, rotation, shear test, and dam break test. These tests showed that the developed procedure improves the results when using coarse grids. Therefore, the Modified Youngs-VOF (MYV) method is suggested as a new VOF algorithm wh...

Numerical simulation of free surface flows

Journal of Computational Physics, 1999

A numerical model is presented for the simulation of complex fluid flows with free surfaces. The unknowns are the velocity and pressure fields in the liquid region, together with a function defining the volume fraction of liquid. Although the mathematical formulation of the model is similar ...

IMPLICIT NUMERICAL SIMULATION OF TWO- AND THREE-DIMENSIONAL FREE-SURFACE FLOW PROBLEMS

The present study proposes a finite-volume implicit numerical scheme for the simulation of two-and three-dimensional free-surface flow problems. The implicit form of the scheme guarantees fast convergence allowing the use of large time steps. The introduction of a non-orthogonal boundary-fitted coordinate system (local coordinates) makes it possible for the model to handle various types of boundary conditions with accuracy. In the case of two-dimensional flow problems, the conservative form of the equations of fluid dynamics is used while the Navier-Stokes equations in combination with the innovative technique of pseudocompressibility are used to describe mathematically the three-dimensional free-surface flow problems. The resulting flow equations are transformed into the local coordinate system and then are solved numerically. The three dimensional scheme is used to analyze the free-surface flow over a double-arc spillway which was mounted in a laboratory flume. Bottom pressures and water levels were measured at various points along the centerline. Successful comparisons between measurements and computed results ensure the credibility of the proposed scheme.

Numerical Modeling and Experimental Validation of Free Surface Flow Problems

In this paper we present a summary of numerical methods for solving free surface and two fluid flow problems. We will focus the attention on level set formulations extensively used in the context of the finite element method. In particular, numerical developments to achieve accurate solutions are described. Specific topics of the algorithms, like mass preservation and interface redefinition, are evaluated. To illustrate these aspects, numerical strategies previously developed are applied to the solution of a sloshing and a water column collapse problems. To assess the capabilities of these techniques, the numerical results are compared against each other and with experimental data. Considering these aspects, the present work is aimed to outline some well reported aspects of level set-like formulations.

Transient Analysis of Two-Dimensional Free Surface Flow Through Hydraulic Structure

sindh univ. Res. Jour. (sci. Ser.), 2015

Computation of fluid flow in contraction and expansion channel located at upstream of channel is presented in this paper. A two–dimensional model is reported for computing incompressible flow of Newtonian fluid adopting Navier–Stokes equations. A semi– implicit Taylor–Galerkin finite element algorithm. The flow is expected at downstream of expansion section is gradually/rapidly varied flow and generating vortices. This approach allows to explore very complex hydrodynamics phenomena like computation and analysis of unsteady/transient free–surface flows present hydraulic structures. The different Reynolds number (Re) values are used for computing of streamline flow pattern, velocity and pressure values. It is observed that, with increasing Reynolds number, the wake on the downstream of expansion of channel increase. The stability and capability of the numerical algorithm can be ascertained from the predicted results that the proposed model can be used efficiently for computing through solving of complex geometrical hydrodynamic problems.

WATER ENTRY AND EXIT OF HORIZONTAL CYLINDER IN FREE SURFACE FLOW

ICHMT DIGITAL …, 2009

This paper describes two-dimensional numerical simulations of the water entry and exit of horizontal circular cylinder at constant velocity. The deformation of free surface is described by Navier-Stokes (NS) equations of incompressible and viscous fluid with additional transport equation of the volume-of-fluid (VOF). The motion of the cylinder is modeled by the associated momentum source term implemented in the PHOENICS (Parabolic Hyperbolic Or Elliptic Numerical Integration Code Series) code. The domain is discretized by a fixed Cartesian grid using a finite volume method and the cylinder is represented and cut cell method. The simulated results are compared with the numerical results of Lin . This comparison shows good agreement in terms of free surface evolution for water exit and sinking. However, for water entry, the jet flow simulated by Lin is not reproduced. The free surface deformation around the cylinder in downward direction is accurately predicted.

Numerical simulation of two-phase free surface flows

Archives of Computational Methods in Engineering, 2005

Free surface flows are of most interest in many engineering or mathematical problems and many methods have been developed for their numerical resolution in various fields of the physics or the engineering. In this work, the volume-of-fluid method is used for the numerical simulation of two-phase free surface flows involving an incompressible liquid and a compressible gas and taking into account the surface tension effects. The incompressible Navier-Stokes equations are assumed to hold in the liquid domain, while the dynamical effects in the ideal gas are disregarded. A time splitting scheme is used together with a two-grids method for the space discretization. An original algorithm is introduced to track the bubbles of gas trapped in the liquid. Numerical results are presented in the frame of mold filling and bubbles and droplets flows. Some theoretical results concerning free boundary problems are also summarized.

Simulations of Dam-Break Flows Using Free Surface Capturing Method

Journal of Mechanics, 2008

A model adopting the surface capturing method is developed for the simulation of dam-break flows by solving the Navier-Stokes equations of weakly compressible and variable density flows in open channels. Due to the characteristics of weakly compressible flow equations, a compressibility parameter describing the compressibility of fluid is determined to obtain the time-accurate flow fields in both liquid and gas regions simultaneously. Accordingly, the location of free surface can be captured as a discontinuity of the density field for dam-break flow simulations. The numerical algorithm in the proposed method is based on the framework of the finite volume method for discretization in space. To deal with the discontinuity property of fluid density near the free surface, the TVD-MUSCL scheme is adopted to overcome numerical oscillations and dissipation. For discretization in time, the explicit 4-stage Runge-Kutta scheme is employed in the model. Finally, several typical dam-break flow ...