
[Sponsors] 
June 30, 2000, 21:10 
gravitational force for free surface flow

#1 
Guest
Posts: n/a

As a beginner to the free surface flows, I would like to ask your ideas. Currently I am studying twolayered natural convection. The materals are heavy metalic melts such as ferrite and allumina. The density ratio is more than two, so they separate by the gravitational force. As you can imagine, it is a kind of free surface flows. There are some codes to solve free surface flows like solavof and Ripple. Some say light material is neglected if density ratio is very high between two materials such as water and air. But it is possible to solve two materials at the same time no matter hwo the density ratio is.
In my case I should solve two materials for heat and momenta, but the interface between the two materials is assumed not changed. I am using my unstructuredmesh solver which is based on SIMPLE, Colocated(nonstaggered), RhieChow interpolation. The problem is how to treat gravitational body force. The book written by Peric said hydrostatic head is added to pressure therm. And it makes the computation more stable. I agree on that. But if there are two different materials, I think it is impossible. At first I used the gravitational source term as rho*g = rho_ref*[1 beta*(TT_ref)]*g (1) ,where hydrostatic head is not subtracted. When the eq (1) is used, I modified the boundary pressure extrapolation like p_b = p_o + rho*g*( x_b  x_o ). Except the problem with garvitational force boundary face pressure is same as boundary cell pressure.(Zero order extrapolation) I didn't use free surface capturing schem, in other words I didn't solve VOF equation. I just fixed the interface. When the density ratio is near one I could get the solution to the twolayered natural convection. The materials are naturally stratified. But with the density ratio very larger than 1 it failed. So I simplified the problem by not solving energy equation. This is just hydrostatic problem, and exact solution is stationary flow with hydrostatic pressure field( p = rho*g*h ). The cells adjacent to interface have infinitesimal source of the difference between dp/dy and rho*g_y. This discrepancy is amplified and the code is diverged. Oh. I am sorry, it is too long to explain my trouble. I would like to simplify my questions. 1) How to treat the gravitational body force and pressure gradient terms. 2) Is there a special way to integrate pressure gradient term in momentum equations(In case of nonstaggered algorithm) 3) If you know some papers related twolayered free surface problem with nonstaggered method, could you tell me them? 4) What is the initial pressure field for that? Some solved air, water and bubble interactions. I think it is very difficult to initialize the hydrostatic pressure field. Currently I am studying the basics of the numerical methods for free surface. If you give me your idea, I can reduce the time to dig the problem. In advence I want to thank you for your forever kindness. 

July 2, 2000, 12:57 
Re: gravitational force for free surface flow

#2 
Guest
Posts: n/a

(1). You have a natural convection problem, where the density of the liquid is not uniform. (2). If you ignore the shape of the free surface and the interface between two liquids, then you basically have two problems in two domains. (3). The interaction between the two problem is through the fixed interface surface. (4). What I would suggest is, solve it as coupled problem, each with uniform density (material). that is, a natural convection problemA with heavy material on the bottom, and a given interface condition. And another natural convection problem with a light material on the top. (5). With this approach, the material will be uniform (not the density), and the boundary conditions are specified on the fixed given locations for each problem and domain. (6). You can used zero interface velocity boundary condition to simulate a real wall, or you can relax it to simulate the real interface condition.


Thread Tools  Search this Thread 
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Calculating forces on a nonclosed surface  ScottN  FLUENT  0  March 1, 2011 18:18 
Lift force coefficient for 2phase flow  Summer  FLUENT  0  April 29, 2008 18:58 
mass flow rate on the Isoclip surface & interior  Sunil Gupta  FLUENT  0  April 22, 2008 10:29 
drag force in two phase flow  Ken  CFX  5  November 21, 2005 16:28 
Inviscid Drag at subsonic, subcritical Mach #  Axel Rohde  Main CFD Forum  1  November 19, 2001 13:19 