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Rajeev Kumar Singh October 24, 2005 01:16

Interesting Question on Boundary Condition
Hi everybody!

I have an interesting question. Suppose we are modelling 3D flow in a cubic cavity. Since the order of differential is 2 in the NS equation so we need 6 boundary condition. which we give in terms of the wall properties on the 6 faces of the cube.

Now consider the case of a cylindrical cavity in which we solve flow. Here again in cylindrical polar co-ordinates the order of differential are 2 (r, theta, z) so we need 6 boundary condition. But we supply only three (2 flat end faces and 1 cylindrical curved face). Where are the other three, how does Fluent describes them

If anyone knows the answer please explain

Regards Rajeev

Vinod Dhiman October 24, 2005 14:01

Re: Interesting Question on Boundary Condition
Hi Rajeev

Its really interesting, however, you statement is contradictory, or should I say, you have asked question without studying it deeply.

You provide two boundary conditions at end faces, z-equation satisfied.

For radius, you provide one condition at outer circumfrential surface. In this case, as you know, the value of velocity has to be maximum at the center, or if it is a solid cylinder and you are considering energy equation temperature has to have some finite value at center, that means the derivative at center is zero for the dependent variable. Fluent, takes it into account automatically, it takes derivate of velocity with respect to radius equal to zero at center.

For theta, you are not considering that equation at all when you say you are not providing any boundary condition for it, since in that case all the derivatives with respect to theta become zero, and that equation is gone. So, the system is effectively 2-D, and that's why we use Cylindrical system, else we can use cartesian system, too, however that will compel us to use all the three equations. Now, if you want to use theta equation, that means that you have variation of velocities along theta. So, you have to account for that variation by taking into account theta equation. However, theta is continuous, so it depends upon the variation or the limits of variation, eg., you may have velocity variation of one kind from 0 degree to 180 degree, and variation of other kind from 180 to 360 degree; for energy equation you may have constant temperature in one half and constant heat flux in second half. There could be any kind of combination.

One more thing, you may have an equation that may give a continuous variation of a particular velocity in terms of theta. In this case, you know the variation of that velocity with theta, so you do not need to solve the equation. You have the solution.

Vinod Dhiman

Rajeev Kumar Singh October 24, 2005 14:14

Re: Interesting Question on Boundary Condition
Thanks for going through my question. But it seems I have not been able to make it clear.

Consider these two cases Case A: Cubic cavity: 1m x 1m x 1m Top face : Moving wall - Translational x-vel = 1m/s Side faces : All wall - Stationary- No slip Bottom face: Stationary wall - No slip

Cylindrical cavity : height 1m , diameter - 1m Top face: Moving wall - Translational x-vel = 1m/s Cynlindrical face : Stationary - No slip Bottom face: Stationary face - No slip.

You can imagine both the domain as a cubic cavity or a cylindrical cavity filled with water where a belt is drawn along the top face at 1m/s in x-direction.

Now I think I have made the picture more clear

Vinod Dhiman October 25, 2005 07:49

Re: Interesting Question on Boundary Condition

This is well explored lid-driven cavity problem. Its 3-D in both the cases, as the velocity changes with height, radius, and along the circumfrence, i.e., along theta. However, I have never studied lid-driven cavity problem. You can look for that. Possibly they may neglect variation along theta.

Vinod Dhiman

Rajeev Kumar Singh October 25, 2005 08:53

Re: Interesting Question on Boundary Condition
That's what I am looking for. Since we supply only three boundary condition. How does Fluent supply the other three if the problem is cylindrical domain


Vinod Dhiman October 26, 2005 05:23

Re: Interesting Question on Boundary Condition

It seems there has never been a computational analysis of 3-D problem like this. All you find, at least on net, are 2-D. For 3-D all are experimental. However, we can think of this problem. It will not be too complicated. I hope you have got my ID. I'll think over this but in the next month.

I have got some information regarding 3-D analysis, its getting being downloaded. I'll check it and talk to you regarding this in next month. Furthermore, I have never used Fluent. I use FORTRAN Code. My labmate uses it.

Vinod Dhiman

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