Boundary Condition

C.C · October 3, 2011, 04:50

Hi,

I need to simulate the water flow in a circular pipe. I have some doubts about the outlet boundary condition.
I have five options: velocity; pressure, no viscous stress; pressure; no viscous stress and normal stress. Someone can explain me the difference between the various options and what is the best option for my problem.
There are also the option boundary stress instead of outlet boundary, with this boundary condition I can choose "normal stress, normal flow". What is the difference between boundary stress and outlet boundary?
For the inlet boundary I can give the normal inflow velocity or the velocity field. I have same doubts about the choice of the inlet boundary, I think that I have to choose the velocity field, is that a good choise?
Someone can help me? Where can I find information on these subjects?
Thank you...

Graham81 · October 4, 2011, 04:07

Dear CC,

Using CFD you will solve Navier-Stokes for this problem. How would you define the boundary conditions if you were to solve a set of differential equations describing your problem? How would you estimate whether viscous forces are important to your model equations? (hint: http://en.wikipedia.org/wiki/Reynolds_number )
Without trying to discourage you, I think you should consider reading a general book on fluid dynamics.

I dont know what software package you are using for your simulation, but surely there will be tutorials or a manual available for this type of problem.

Best of luck!

Graham

Rami · October 6, 2011, 10:16

Hello C.C,

Rather than discouraging you, let me try to briefly explain how the BC are arrived at, and what to choose in your specific case. I will use tensor notation.

The momentum eq. reads
$\rho \frac{Du_{i}}{Dt} = \sigma _{ik,k} - \rho G_{i}$
where $\rho$ is the density, $u_{i}$ and $G_{i}$ are the velocity and body force vectors and D/Dt is the material derivative. For simplicity, let us assume the problem is steady.

Now, using the usual FVM practice, integrate over the volume and use the Gauss divergence theorem, resulting in
$0 = \sum_{f}^{ } \left [ \left ( \rho u_{i}\right )_{f} \left ( u_{n} \right )_{f} A_{f}\right ] - \sum_{f}^{ }\left [ A_{f} \left ( \sigma_n \right )_f \right ] - \sum_{P}^{ } \left ( \rho G_{i} V \right ) _ {P}$
with P and f subscripts used for the cell P and its faces, A and V - its face areas and volume, $u_n\doteq u _k n_k$ and $\sigma_n\doteq \sigma _{ik} n_k$ - the normal velocity and traction.

In your case, at the inlet prescribe the density and the velocity vector, so that the first term is determined on all the inlet cell faces. At the outlet - prescribe the normal traction, thus specifying the second term on all the outlet cell faces.

Now, you can read all this and with clearer and more detailed explanations in textbooks (eg., Patankar, Peric etc).

Good luck and happy CFDing!
Rami

October 3, 2011, 04:50	Boundary Condition	#1
C.C Member CC Join Date: Jun 2011 Posts: 73 Rep Power: 14	Hi, I need to simulate the water flow in a circular pipe. I have some doubts about the outlet boundary condition. I have five options: velocity; pressure, no viscous stress; pressure; no viscous stress and normal stress. Someone can explain me the difference between the various options and what is the best option for my problem. There are also the option boundary stress instead of outlet boundary, with this boundary condition I can choose "normal stress, normal flow". What is the difference between boundary stress and outlet boundary? For the inlet boundary I can give the normal inflow velocity or the velocity field. I have same doubts about the choice of the inlet boundary, I think that I have to choose the velocity field, is that a good choise? Someone can help me? Where can I find information on these subjects? Thank you...

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October 4, 2011, 04:07		#2
Graham81 Member Join Date: Dec 2009 Posts: 57 Rep Power: 16	Dear CC, Using CFD you will solve Navier-Stokes for this problem. How would you define the boundary conditions if you were to solve a set of differential equations describing your problem? How would you estimate whether viscous forces are important to your model equations? (hint: http://en.wikipedia.org/wiki/Reynolds_number ) Without trying to discourage you, I think you should consider reading a general book on fluid dynamics. I dont know what software package you are using for your simulation, but surely there will be tutorials or a manual available for this type of problem. Best of luck! Graham

October 6, 2011, 10:16		#3
Rami Senior Member Rami Ben-Zvi Join Date: Mar 2009 Posts: 155 Rep Power: 17	Hello C.C, Rather than discouraging you, let me try to briefly explain how the BC are arrived at, and what to choose in your specific case. I will use tensor notation. The momentum eq. reads $\rho \frac{Du_{i}}{Dt} = \sigma _{ik,k} - \rho G_{i}$ where $\rho$ is the density, $u_{i}$ and $G_{i}$ are the velocity and body force vectors and D/Dt is the material derivative. For simplicity, let us assume the problem is steady. Now, using the usual FVM practice, integrate over the volume and use the Gauss divergence theorem, resulting in $0 = \sum_{f}^{ } \left [ \left ( \rho u_{i}\right )_{f} \left ( u_{n} \right )_{f} A_{f}\right ] - \sum_{f}^{ }\left [ A_{f} \left ( \sigma_n \right )_f \right ] - \sum_{P}^{ } \left ( \rho G_{i} V \right ) _ {P}$ with P and f subscripts used for the cell P and its faces, A and V - its face areas and volume, $u_n\doteq u _k n_k$ and $\sigma_n\doteq \sigma _{ik} n_k$ - the normal velocity and traction. In your case, at the inlet prescribe the density and the velocity vector, so that the first term is determined on all the inlet cell faces. At the outlet - prescribe the normal traction, thus specifying the second term on all the outlet cell faces. Now, you can read all this and with clearer and more detailed explanations in textbooks (eg., Patankar, Peric etc). Good luck and happy CFDing! Rami