Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??

[Ulf D Schiller]

Did you check the flow rates directly, i.e., the momentum flux per plane? Your argument seems correct, so I can only guess that there's some flaw in the calculation of the mean velocity. I think there's an _expression_ for the flux in rectangular channels that one could use.

Best,

Ulf 

Sent from a mobile device.

-------- Original message --------

From: "Wink, Markus" <address@hidden>

Date: 3/15/2016 8:47 AM (GMT-05:00)

To: 'Ivan Cimrak' <address@hidden>, address@hidden

Subject: Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??

Hi Ivan, Hi Florian,

 

> How did you compute the expected maximum velocity? As far as I know, the poisseuille flow has an exact _expression_ for the velocity in the case of channel with circular cross section, and you have a rectangular one.

 

I know the velocity of the rhomboid. Thus I know the mean velocity of the fluid (assuming it is incompressible). I took that for calculating the Reynoldsnumber, pressure gradient and theoretical velocity profile (using the _expression_ in the book  “Viscous Fluid Flow” of Frank M. White).

 

> The boundaries are momentum sinks. (Florian)

> Now I read the comment of Florian - does that mean that amount of fluid is decreasing when no-slip is prescribed?

I still don’t get it. That the boundaries are momentum sinks, I agree. Due to the present of the walls and the “friction” of the fluid there, I achieve the poiseuille profile. But I still hold the opinion, that the mean velocity of the fluid should be the same.
Imagine the following physical experiment: you have a syringe pump set up with a constant flow rate Q0 connected to a rectangular channel having a cross section A=w*h. The fluid in the channel then has a mean velocity of v_mean=Q/A. Assuming an incompressible medium, this means the velocity should be the same at every slice normal the direction of transport.
In my simulation, the mean velocity should be velocity v0 of the rhomboid.

So I still don’t get the deviation to the theoretical value…

Greetings Markus

 

 

 

Von: espressomd-users-bounces+address@hidden [mailto:espressomd-users-bounces+address@hidden Im Auftrag von Ivan Cimrak
Gesendet: Dienstag, 15. März 2016 13:22
An: address@hidden
Betreff: Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??

 

Hi Markus,

 

Hello Everybody,

 

so far, in the LBM scheme only the body force is implemented and no velocity/pressure boundary condition. So I was thinking on a way of mimicking a “velocity boundary” condition without changing the source code. I am aware that one should, as a proper approach, using Zou/He boundary conditions and adjusting the distribution functions according to the boundary conditions.

 

For that I have constructed a channel with rectangular cross section and put the fluid inside. Furthermore, two rhomboids where put inside, one at the inlet of the channel, one at the outlet. The cross section of the two rhomboids is equal to the cross section of the channel, furthermore they have a constant velocity v0.

My idea was, that, since the no-slip boundary condition is implemented, I force the fluid nodes adjacent to the rhomboids to have a constant velocity, thus achieving constant velocity inlet/outlet condition.

 

As a result I achieve a poiseuille profile in the middle of the channel (fully developed flow after inlet/outlet effects). The qualitative pressure gradient looks proper, too.

Nevertheless, the maximum velocity is not the same as I expected (factor 3 to the expected one).

How did you compute the expected maximum velocity? As far as I know, the poisseuille flow has an exact _expression_ for the velocity in the case of channel with circular cross section, and you have a rectangular one.

I have checked the mean velocity. I would expect, that the mean velocity of the fluid should be the velocity v0 of the rhomboid (due to mass/momentum conservation), I get less (10 %).

This is strange. The amount of fluid at the inlet (integral of velocity over the inlet surface, in this case is the velocity constant over the inlet surface) should be the same as integral over the middle cross section, as well as integral over the outlet surface.... Supposing you computed the average velocity as sum of velocities over the LB nodes at middle cross section divided by number of these nodes, you should have obtained the velocity at the inlet...

Now I read the comment of Florian - does that mean that amount of fluid is decreasing when no-slip is prescribed?

Ivan

 

What is wrong with my idea stated here? Obviously, something is not correct, but I have no idea, what the reason for that is. Where does the momentum vanish?

 

Does anybody have an idea?

 

Sincerely,

 

Markus