|From:||Ulf D Schiller|
|Subject:||Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??|
|Date:||Tue, 15 Mar 2016 13:07:48 +0000|
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.
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-------- 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.
So I still don’t get the deviation to the theoretical value…
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...
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?
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