I have an open topped cylindrical container partially filled with a molten metal in a vacuum. I want to pour the liquid over the top edge of the container, following (approximately, say plus or minus 20 percent)a pre-defined pour rate profile. I need to know at what rate I should tilt the container, how far horizontally the pour stream will have travelled from the lip of the vessel and the diameter of the stream as it passes through a plane at a known distance below the vessel (where the top of a mold is located). Is this something that's calculatable in a reasonable time (hours or days, not months or years...)with currently available cfd codes by someone in industry on, say, a high end PC? On a workstation? On a Cray? On anything? Any informed advice will be appreciated!

Actually, this seems like a problem which you can solve analytically.... without using computers and cfd codes. Ofcourse , you can always use cfd for this problem if you want to, but you might be able to work out the solution in a few minutes. Since you need only +- 20% accuracy, a uniform, unoscillating free surface model will do. You need to know the viscosity of the liquid, the density, other parameters. You just have to plug these quantities in the Navier stokes equation and you will get a solution.

Actually, this seems like a problem which you can solve analytically.... without using computers and cfd codes. Ofcourse , you can always use cfd for this problem if you want to, but you might be able to work out the solution in a few minutes. Since you need only +- 20% accuracy, a uniform, unoscillating free surface model will do. You need to know the viscosity of the liquid, the density, other parameters. You just have to plug these quantities in the Navier stokes equation and you will get a solution.

Oops... I didn't read the your message properly. I thought that you just wanted to pour the liquid at a fixed rate and you wanted to know how to tilt the container to achieve the fixed rate flow. But the flow is really complex once it leaves the container and getting the diameter of the free flow doesn't look all that easy.... Sorry for the stupid mistake I made.

The problem still looks solvable, though not analytically but definetly with a computer in some few hours.

Hi Ray,

What you are dealing with is a "free-surface" calculation which can be handled by some of the specialized cfd codes but not YET by the gerneral codes like cfx4, cfx-TASCflow, etc. So, you will have to contact one of the sepecialized companies. There is a really cool picture of a wine bottle into a wine glass on the site:

http://www.iccm.de/

this is the sort of code that you are looking for!

As for computer and time requirements, here is how I look at it:

First, we must decide how many of the physical processes we wish to resolve. This determines the number of equations and the terms involved.

Second, you must look at the dimensions which you choose to solve. The full problem is 3 in space and 1 time = 4 but we do not always have to solve everything.

Third, we look at the scale of physical process that we wish to resolve in each of these dimensions, and whether or not we have any symmetry we can use.

Fourth, we look at the overall accuracy which we require and the accuracy-discretization characteristics of the numerical method which we use.

A sample analysis for your problem, as described goes as follows:

1. If we assume that the transfer of momentum, mass and heat between the molten stream and the surroundings is negligible then we only need to solve the momentum equations and continuity for the molten metal. This gives us 3 momentum eqns, 1-continuity, 1-energy (all differential equations), and one algebraic equation of state and variables {u,v,w,p,rho,T}

Otherwise, we would have to solve the momentum and energy equations for the surroundings (air or low vacuum) and an energy equation for heat transfer to the crucible and the mold, etc.

2. Say we want the full 3-d details in time.

3. If we say that we want spacial resolution on the order of the pour stream and not small scale processes like surface waves on the stream and similar time scale resolution: then we have to build a grid in time and space which capture these, say a stream of width 0.1[m] and a pour time of 10[s] You must determine if these are reasonable process scales.

4. We then choose a method for discretization and accuracy.

you stated +/- 20% and say we then have a first order method which will give this accuracy by discretizing scales of dX, dY, dZ. dT = x/10, y/10, z/10, T/10 then we need to solve (10 x 10 x 10) equations at 10 time steps: 1000 eqns @ 10 time steps this can easily be solved on a PC in times of hours.

The problem/computer requirements go up fast if we wish to have higher accuracy. Same first order method, asy we want 1/2 the error (+/- 10%) then for each differential equation in (1) above, we need: (20 x 20 x 20) equations = 8000 at 20 time steps.

- 1/4 error (+/- 5%) then (40 x 40 x 40) equations = 64,000 at 40 time steps.

- 1/8 error (+/- 2.5%) then (80 x 80 x 80) equations = 516,000 at 80 time steps.

now, we are up to a workstation and running for 10's of hours.

etc.

This, is of course, why first order methods are uneconomical for most high accuracy requirement 3-d problems!

And remember, we have 5 differential equations to solve here. Say we wanted to determine 20 species equations in the melt as well and a full Differential Reynolds Stress model (7 or more differential equations)= 32 +

So, the requirements start to grow pretty fast!

It is essential to determine which parts of the problem we wish/need to solve!

Good luck.........................................Duane

Dear Ray:

CFD-ACE+ from CFD Research Corp. has a very nicely working Volume of Fluid (VOF) method which has been successfully used in many instances to simulate droplet formation and pouring of liquids in gas surroundings incl. liquid surface tension.(e.g. ink-jet printer, drain gate)

Please check out the dripping coffee machine on our web-site (www.cfdrc.com).I am happy to send you more info if you are interested.

Regards,

Cornel Mueller

Dear Ray,

As Cornel pointed out, the Volume of Fluid (VOF) method for simulating free surface flows is well-suited for this type of problem. Given a rate of tilt for the container, the VOF method will tell you the pour rate, the trajectory of the stream and the shape/diameter of the stream. However, it sounds like you want to solve the inverse problem: i.e., you give the pour rate, and the CFD program gives you the tilt angle versus time. I don't think the inverse problem is solve-able with commercial software at this time. Rather, you will have to investigate the effect of different tilt rates on the resulting flow.

By the way, Fluent Inc. offers the VOF model in both its finite volume solver, FLUENT, and its finite element solver, FIDAP. I'd be happy to discuss this problem further with you off-line, if you'd like.

Regards,

Eric Grald