3D velocity profile for Rectangular inlet
 

Hello every body.

I want to use a 3D parabolic velocity profile in an inlet on ZY plan. the velocity will be normal to this surface (- X).

I find two equation for X velocity which is vary by both Z and Y.

x = -1 + 2*z - 3*z*z

x = -1 + 2*y - 3*y*y

For 2D, it is not difficult, but I don't know how to do it in 3D:
I am appreciate, if anybody can help me.
Thanks.

have i fixed the problem as i am trying the same thing. I have the profile for xy plane and how do i write it for 3d?

i would appreciate your help

You first need one equation for the x-velocity. Not two, as in the opening post, that is wrong.

u_x = f(y,z).

Once you have that, you can implement it in exactly the same way as for the 2d case.

Did you get the right equation for 3d case.
could you please share that equation.

The equation depends on the shape. The easiest is circular, that one you can look up in most CFD books. I think all others shapes are difficult.

Hello!
I have found a solution for my case and it worked well for me.
The shape is not matter, if you can derive the equation in 2D. Let's assume that you want to impose a 3D velocity profile (normal to X direction) to a quadratic door. First you need to know how your velocity will be change in Z and Y direction. finally you will have two equation same as the following:

x = -1 + 2*z - 3*z*z
x = -1 + 2*y - 3*y*y

then simple add these two equation such as the following:
x = (-1 + 2*z - 3*z*z) + (-1 + 2*y - 3*y*y)

finally you need to normalize your equation to got the right velocity at the center of the door.
Hope it useful.

Hi Asal,

What you suggest is not correct.

First of all, your equations are not really parabolic profiles, they are always negative, but let's assume that you chose the wrong coefficients, and write them as:
x = 1-z*z
x = 1-y*y

The first equation is a parabolic profile that is zero at z=-1 and z=1. The second is a parabolic profile which is zero at y=-1 and y=1. So far so good.

But what happens if you add them?

x = 2 - z*z - y*y

This is zero when z*z+y*y=2, in other words a circle with sphere sqrt(2). In the opening that you are simulating, that is only the 4 corners, all other points of this circle are outside your geometry. More specificly: at the boundary of your inlet, the velocity is generally speaking NOT zero.

You can only have such a simple profile when the opening is circular. And then it is the solution that I just showed. When the opening is not circular, you don't have a simple parabolic profile.

Hello!

This is just an approximation, since I found no better solution. I have used this equation and got reasonable result. The profile will be parabolic, and the mismatch at the boundaries may have a negligible affect on the results.
Although, if you have any better solution, we appreciate to hear it!!

The problem is that you asked the wrong question.
Your question:
"I want to use a 3D parabolic velocity profile in an inlet on ZY plane."

You now made a solution that is not parabolic, and yet you are happy. That means that your original question was not the thing that you really want.

I guess that what you want, is have an inlet distribution that is close to the flow that you would have if you would have a very long pipe before the inlet. So that you have inlet entrance effect in your CFD simulation. In that case, your approach could work more or less. A simpler solution would be to use a mass-flow-inlet.

But you don't have a truly parabolic profile. You say that your solution is parabolic, but I can assure you it is not, it is mathematically impossible. The shape might resemble a parabola, but that is not the same. For you, that may not matter. But other people, maybe making a more theoretical model which requires a truly parabolic profile, might read your post and think that you solved their problem, which you didn't.

If you are happy with your solution, then use it and stay happy; my post was not meant for you, but for other people who might find this post by Google and falsely believe that it solves their problem.