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Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??
From: |
Ulf Schiller |
Subject: |
Re: [ESPResSo-users] No conservation of momentum/mass in LBM ?? |
Date: |
Fri, 18 Mar 2016 08:22:29 -0400 |
User-agent: |
Mozilla/5.0 (X11; Linux i686; rv:38.0) Gecko/20100101 Thunderbird/38.1.0 |
On 03/18/2016 04:11 AM, Wink, Markus wrote:
> Hello everybody,
>
>
>
> the mass flux is constant in the system. Makes sense ... Thanks a lot!
>
>
>
> The only question that is left for me now is, why the entry and outlet
> are not symmetric. Actually I am not sure anymore, if they should be
> symmetric. The system does not exhibit a mirror symmetry, so my
> assumption of having symmetric in- and outlet effects might not be valid
> (but I am not sure about it).
>
>
>
> Any ideas about it? Notice, that although the graph implies the in- and
> outlet have different velocities, I set the velocities of the rhomboids
> at both sides to same velocities.
In the plot it looks like the velocity decays to zero at the outlet,
which I find a bit weird. How does the *momentum profile* look along the
channel? What happens when you change the sign of the velocity of the
rhomboids?
Just diggin'
Cheers,
Ulf
> *Von:*Joost de Graaf [mailto:address@hidden
> *Gesendet:* Donnerstag, 17. März 2016 16:58
> *An:* Georg Rempfer
> *Cc:* Wink, Markus; address@hidden; Ulf Schiller
> *Betreff:* Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??
>
>
>
> Georg is right. Done that once for a sphere, it worked out perfectly
> back then.
>
>
>
> On 17 March 2016 at 15:55, Georg Rempfer <address@hidden
> <mailto:address@hidden>> wrote:
>
> If the density goes up along the channel, the velocity has to go down to
> fulfill mass conservation.
>
>
>
> Since there are density variations in the system, you should check the
> actual mass flux instead of the averaged velocity. That means you should
> integrate density*velocity over every slice and look at the component
> normal to the slice.
>
>
>
> On Thu, Mar 17, 2016 at 10:33 AM, Wink, Markus
> <address@hidden <mailto:address@hidden>>
> wrote:
>
> Hello everybody,
>
> I checked the mass flux. It is constant over the length of the channel
> (some oscillations at the outlet, but I am not concerned about it). I
> revised the script and now I get the maximum velocity right (less than
> 1% deviation to the theoretical one). But I am still puzzling with some
> aspects. First of all I checked whether the density is constant. Within
> one plane perpendicular to the direction of flow, that is the case.
> Along the direction of transport, I notice a drop of the density. This
> makes sense to me, since the density is proportional to the pressure and
> I expect a linear pressure profile along the channel.
>
> Nevertheless, there are some questions left.
>
> 1) I have noticed, that in both cases, whether if I apply a body force
> to the fluid or an constant velocity inlet boundary condition, the
> maximum velocity of the profile is a bit lower than the expected one
> (although it is quite good with less than 1% deviation). I am just
> wondering, since I checked two "methods", whether this deviation lies in
> the nature of the LBM algorithm?
> 3) With a constant velocity inlet and constant velocity outlet I have
> inlet and outlet effects of cause a certain length (until the profile
> develops). I was expecting that the two lengths should be equal, since I
> have equivalent boundary conditions. In the appendix you will see, that
> this is not the case (it shows the velocity as a function of the
> x-position, while y- and z- are set to half the channel width/height).
> The entry effect seems to be much more pronounced, but I am not sure
> why. Does anyone have an idea?
> 4) As an outlet condition it would be neat to have a constant pressure
> boundary condition (with that, one would eliminate the outlet effect). I
> was thinking to put the outlet-nodes to a constant pressure via lbnode
> set. Is there a command for setting the pressure of a node to a given
> value (investigating the source code it seems, that there is only
> "lbnode x y z print pi" but not set).
> 5) What is the proper way to get the mean velocity out of the mass flux?
> If I sum up the velocities and divide by the cross section, I get a
> slight increase of v_mean along the channel (I have no idea why).
> 6) Have anyone ever checked the second order accuracy of the LBM in
> ESPResSo?
>
> Greetings and thanks a lot for your help!
>
> Markus
>
>
>
>
> -----Ursprüngliche Nachricht-----
> Von: address@hidden
> <mailto:address@hidden>
> [mailto:espressomd-users-bounces+markus.wink
> <mailto:espressomd-users-bounces%2Bmarkus.wink>address@hidden
> <mailto:address@hidden>] Im Auftrag von Ulf Schiller
> Gesendet: Mittwoch, 16. März 2016 13:49
> An: address@hidden <mailto:address@hidden>
> Betreff: Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??
>
>
> Hi Markus,
>
> sorry for the confusion. In my earlier email I should have said mass
> flux of course, i.e., the Q in the formulas Kai provided. You can
> calculate that from the simulated velocity profile for each plane along
> the channel, and it should be constant.
>
> Best,
> Ulf
>
> On 03/16/2016 08:21 AM, Georg Rempfer wrote:
>> Assuming the fluid is not compressed (you could check that, but it's
>> likely true), the mass flux is proportional to the velocity. You claim
>> the average velocity in the channel direction is too low half way
>> between inlet and outlet. This implies that mass gets lost between the
>> inlet/outlet and the middle (or that the lb fluid is denser in the
>> middle). Can you check that?
>>
>> On Wed, Mar 16, 2016 at 1:02 PM, Wink, Markus
>> <address@hidden <mailto:address@hidden>
> <mailto:address@hidden
> <mailto:address@hidden>>>
>> wrote:
>>
>> Hello everybody,____
>>
>> __ __
>>
>> thank you for your answers. I did not get it. Which quantity is of
>> interest? Mass flux or momentum flux? I am not sure about it,
>> although to check whether mass conservation is fulfilled, both
>> should work, am I right?____
>>
>> __ __
>>
>> __ __
>>
>> Greetings____
>>
>> __ __
>>
>> Markus____
>>
>> ____
>>
>> __ __
>>
>> __ __
>>
>>
> *Von:address@hidden
> <mailto:address@hidden>
>> <mailto:address@hidden
> <mailto:address@hidden>>
>> [mailto:espressomd-users-bounces+markus.wink
> <mailto:espressomd-users-bounces%2Bmarkus.wink>
>> <mailto:espressomd-users-bounces%2Bmarkus.wink
> <mailto:espressomd-users-bounces%252Bmarkus.wink>>address@hidden
> <mailto:address@hidden>
>> <mailto:address@hidden
> <mailto:address@hidden>>] *Im Auftrag von *Georg Rempfer
>> *Gesendet:* Mittwoch, 16. März 2016 11:26
>> *An:* Kai Szuttor
>> *Cc:* address@hidden
> <mailto:address@hidden> <mailto:address@hidden
> <mailto:address@hidden>>
>> *Betreff:* Re: [ESPResSo-users] No conservation of momentum/mass in
>> LBM ??____
>>
>> __ __
>>
>> I agree with you argument, Markus. Mass conservation dictates that
>> the normal flow through every surface along the channel should be
>> the same (assuming the flow is incompressible). Together with the
>> fixed shape of the fully developed flow profile, this uniquely
>> determines the flow in regions far away from the inlet/outlet. So if
>> this does not come out correctly, mass conservation should be broken
>> somewhere. I don't think this is possible in the LB. Can you
>> calculate this flux through the surfaces along the channel and show
>> us where exactly it differs from the inlet/outlet?____
>>
>> __ __
>>
>> On Tue, Mar 15, 2016 at 5:09 PM, Kai Szuttor
>> <address@hidden <mailto:address@hidden>
> <mailto:address@hidden <mailto:address@hidden>>>
>> wrote:____
>>
>> Now with attachment :)
>>
>> Am 15/03/16 um 14:07 schrieb 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
> <mailto:address@hidden>
>> <mailto:address@hidden
> <mailto:address@hidden>>>
>> > Date: 3/15/2016 8:47 AM (GMT-05:00)
>> > To: 'Ivan Cimrak' <address@hidden <mailto:address@hidden>
> <mailto:address@hidden <mailto:address@hidden>>>,
>> address@hidden <mailto:address@hidden>
> <mailto:address@hidden <mailto: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:address@hidden
> <mailto:address@hidden>
>> <mailto:address@hidden
> <mailto:address@hidden>>
>> > [mailto:espressomd-users-bounces+markus.wink
> <mailto:espressomd-users-bounces%2Bmarkus.wink>
>> <mailto:espressomd-users-bounces%2Bmarkus.wink
> <mailto:espressomd-users-bounces%252Bmarkus.wink>>address@hidden
> <mailto:address@hidden>
>> <mailto:address@hidden
> <mailto:address@hidden>>] *Im Auftrag von *Ivan Cimrak
>> > *Gesendet:* Dienstag, 15. März 2016 13:22
>> > *An:* address@hidden
> <mailto:address@hidden> <mailto:address@hidden
> <mailto: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
>> >
>> >
>> >
>> >
>> >____
>>
>> __ __
>>
>>
>
>
> --
> Dr. Ulf D. Schiller
> Assistant Professor
> Department of Materials Science and Engineering Clemson University
> 161 Sirrine Hall
> Clemson, SC 29634
>
> Office: 299c Sirrine Hall
> Phone: 1-864-656-2669 <tel:1-864-656-2669>
> Fax: 1-864-656-5973 <tel:1-864-656-5973>
>
>
>
>
>
--
Dr. Ulf D. Schiller
Assistant Professor
Department of Materials Science and Engineering
Clemson University
161 Sirrine Hall
Clemson, SC 29634
Office: 299c Sirrine Hall
Phone: 1-864-656-2669
Fax: 1-864-656-5973
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, (continued)
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf Schiller, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf Schiller, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Georg Rempfer, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Joost de Graaf, 2016/03/17
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/18
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Georg Rempfer, 2016/03/18
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Wink, Markus, 2016/03/21
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??, Ulf Schiller, 2016/03/21
- Re: [ESPResSo-users] No conservation of momentum/mass in LBM ??,
Ulf Schiller <=