Hi dear all,

How should I set periodic B.C. for fully developed flow between two parallel plates?

Thanks

M

Depends which software you are using, most have a facility for this.

But, starting from basics, for flow between two fixed flat plates and laminar flow, use the Poiseuille flow equations found in most fluid textbooks.

You can first calculate the variables according to your periodic rules then substitute into the above equation to get the fully developed flow profile.

A simple Fortran program should be employed.

Regards

Hi Jas,

I am not using a code. I just want to learn how i can set this periodic boundary condition.

You mean I have to give plane Pois. flow profile at the inlet plane for the laminar flow computations?

I was thinking just to set:

u_inlet= u_exit,

v_inlet=v_exit,

T_inlet=T_exit

and set a value for the exit pressure - as it is subsonic outflow.

But from what you said, i understnad that the velocity at inlet plane is specified as plane Pois. profile. If so, how should I specify the pressure gradient value in the plane Pois. formula?

Thanks

M

Hi,

If you set the inlet velocity to be constant between your plates, you will not have fully developed flow at your inlet. The fluid will have to travel an 'entry length' in order for the flow to develop. When you mention periodic, what variable is periodic?

Poiseulle formula is for a streamline and P varies only in the x-direction. The solution is the fully developed flow in a channel due to a pressure gradient.

You can choose any pressure gradient and calculate the outlet conditions from your inlet boundary conditions.

Jas

Hi jas,

I think we are talking about two different things:

1) What i understand from your saying:

I just verify that P.P.F (Plane Pois. Flow) is a valid soultion of the code? How do I do that: I give the P.P.F as the initial guess to the code and see if the code converges to the same solution.

2) What I say: I just give uniform inflow, then I determine the exit plane velocity profile. Then force

u_inlet = u_exit

I think this has to work, but I have convergence problem??!!

Which one of the above- approaches you think is good and right?

Thanks

m

(1). Fully-developed flow between two parallel plate, by definition, is 1-D. This is because, the streamwise derivatives are all zero, and also by the continuity equation, the normal velocity v is also zero. (2). As a result, the convection terms are all zero, and the governing equation is reduced to the balance between the pressure gradient term and the diffusion terms. In real life, the pressure gradient is unknown, thus the problem can not be solved without knowing the flow rate throught the channel. (3). In real life, normally the flow rate is specified and the problem is solved, with the pressure gradient and the fully-developed profile as the solution. (4). But there is another way to solve this problem. That is, you can use the pressure gradient as the input parameter, and then solve the flow field. Once the flow field is known, you can calculate the mass flow rate through the channel. If this flow rate is not the target flow rate, you can change the pressure gradient parameter and adjust the flow field until the final flow rate is equal to the target flow rate. (5). The 1-D nature of the problem is in the normal to the parallel plate direction, so, there is no streamwise B.C. required. This is applicable to both the laminar and the turbulent flows. (That is , there is no place to apply the periodic B.C. in this 1-D fully-developed channel flow problem.)

hi,

jhon is right, there is no question of periodic boundary condition in flow between parallel plates, there are no periodic boundaries. If u think otherwise please re-state the problem clearly. If u have taken sufficient duct length then zero gradient at exit for u,v,t will give u convergence. If u have'nt taken sufficient lenght (40-50 *dia of duct) u may have to use asymptotic boundary condition at exit. hope this helps

abhijit

Ok,

For periodic, i thought you were trying to apply a time varying inlet condition and calculate the outlet. If you mean cyclic, i agree with John and Abhijit.

Cyclic boundaries are for pairs of boundaries that repeat themselves. It is mainly used to reduce computational domains in cyclic problems and pressures are identical at corresponding points.

What you are trying to do is to apply an inlet, calculate an outlet, set the inlet to the outlet, calculate the new outlet, set the inlet to the outlet, calculate the new outlet..............and so on forever. I am not surprised it does not converge. Cyclic (or periodic) boundaries are not suitable for flat plate analysis. Anything round along the symmetry axis maybe.

Jas

I tried to solve steady,incompressible, laminar flow through circular pipe to get fully developed velocity and temperature profile without taking a long pipe using a commercial software package PHOENICS. The procedure i have followed: (1) first i set uniform velocity at inlet and constant pressure at exit (2) for the 2nd sweep i set the velocity profile and nondimensional temperature profile at the exit to the inlet(as velocity and nondimensional temperature don't vary in streamwise direction in case of fully developed flow)

I have found the converged solution and also the correct velocity and temperature profile.

Thanks Dilip

Wouldn't it be a good idea if we could draw a diagram on this Post response form. It would save a lot of confusion. Maybe Jonas can oblige.

Shall we start from the beginning again? Can you state the initial problem clearly and explain what you mean by periodic, what you are attempting and what you aim to gain.

Jas

Hi dear all, from John, jas, to ...

1st, thanks for your comments.

2nd the problem i am trying to solve:

I want to obtain fully developed flow between two parallel plates. I have two scenarios to do that:

1) To take a very long channel, as someone had indicated before say about length of the comutational box= 30 to 40 dimater. I was thinking if i can bypass this idea, because in the F.D.R. (fully developed region) the velocity profile does not change along the duct, so I said i can set a periodic B.C. along the channel. How do i do that? I thought the answer is:

2) Rather than taking the duct so long, I just assume the length of the computational box= say 10 X diameter and I give a uniform velocity profile at inlet plane, then compute the exit plane velocity. for the next iteration I force

u_inlet= u_exit Eqn *

I repeat Eqn * for several times until I see not a big change in velocity profile form inlet plane to the exit plane.

Being the Fully Dev. flow One-D, I know in F.D.R., flow velocity does not change along the duct and streamwise velocity component just varies with say y (or r), but i am trying to simulate the problem with a two-D code.

I wonder if no one has seen such a thing before?

Looking forward to hearing.

----------------------------------------------

Part B: One more intersting question,

Why the fully developed length in Laminar flow is Longer than that of turbulent flow? I.e.

(X/D)_entry for laminar flow > (X/D)_entry for turbulent flow

Basically I am asking: say we have a duct with diamter D_1 and a flow with density Rho_1 and viscosity mu_1. If we take the velocity of flow u_1 giving us say Reynolds number equal to 1000 ( which is laminar ). Now with same duct and same flow property if we take flow velocity of u_2=100*u_1 we get Reynolds number 100,000 wich is turbulent. When velocity is u_2, don't you expect the boundary layer from the top and bottom walls reach each other in a furthur distance? which is basically the location that F.D.R. starts.

Sorry for my long posting.