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<p style="margin-top:0;margin-bottom:0">For a geometry with periodic boundary conditions in the flow direction (e.g., pipe flow with periodic bcs), p54 and p55 control the mass flow rate through the domain.</p>
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<p style="margin-top:0;margin-bottom:0">p54 determines the flow direction to be controlled (which, right now, can only be x, y, or z; but this restriction is readily lifted if there was an application requiring such).</p>
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<p style="margin-top:0;margin-bottom:0">So if |p54| = 1, 2, or 3, the flow rate will be fixed in the x, y, or z direction.</p>
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<p style="margin-top:0;margin-bottom:0">If p54 < 0, then it means that p55 will be the mean velocity in the given direction.</p>
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<p style="margin-top:0;margin-bottom:0">If p54 > 0, then it means that p55 will be the volumetric flow rate: Q= \int u dA.</p>
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<p style="margin-top:0;margin-bottom:0">The flow rate is fixed according to the following algorithm.</p>
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<p style="margin-top:0;margin-bottom:0">The Navier-Stokes equations are advanced in a semi-implicit way, using the following form:</p>
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<p style="margin-top:0;margin-bottom:0"> S(U,p) = NL(u) + f</p>
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<p style="margin-top:0;margin-bottom:0">where NL includes all data that should be on the rhs of the equations and S is a linear Stokes problem to ensure div.U=0, and f is the forcing that corresponds to the mean pressure gradient.</p>
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<p style="margin-top:0;margin-bottom:0">Because it is linear, the Stokes problem can be split into two parts:</p>
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<p style="margin-top:0;margin-bottom:0"> S(U',p') = NL(u)</p>
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<p style="margin-top:0;margin-bottom:0"> S(U0,p0) = 1</p>
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<p style="margin-top:0;margin-bottom:0">Then at every step, set</p>
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<p style="margin-top:0;margin-bottom:0"> U=U' + alpha U0 p=p' + alpha p0</p>
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<p style="margin-top:0;margin-bottom:0">such that \int U.nhat dA = desired flow rate, where nhat is the unit vector</p>
<p style="margin-top:0;margin-bottom:0">in the x,y, or z direction.</p>
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<p style="margin-top:0;margin-bottom:0">hth,</p>
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<p style="margin-top:0;margin-bottom:0">Paul</p>
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Nek5000-users <nek5000-users-bounces@lists.mcs.anl.gov> on behalf of nek5000-users@lists.mcs.anl.gov <nek5000-users@lists.mcs.anl.gov><br>
<b>Sent:</b> Sunday, February 25, 2018 12:48:25 PM<br>
<b>To:</b> nek5000-users@lists.mcs.anl.gov<br>
<b>Subject:</b> Re: [Nek5000-users] Further to the issue of ffx, ffy and ffz</font>
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<div class="BodyFragment"><font size="2"><span style="font-size:11pt;">
<div class="PlainText">Hi,<br>
<br>
The documentation says:<br>
P054: fixed flow rate dir: |p54|=1,2,3=x,y,z<br>
P055: vol.flow rate (p54>0) or Ubar (p54<0)<br>
<br>
So for instance if you want to run a pipe with bulk flow of unity, you set:<br>
p54: -3 (z)<br>
p55: 1<br>
<br>
How this is done in the latest versions I do not know, as we do not use <br>
those for pipe production runs.<br>
<br>
Philipp<br>
<br>
On 2018-02-25 16:06, nek5000-users@lists.mcs.anl.gov wrote:<br>
> Hi,<br>
> <br>
> May I push the following question further? Is there anyone know what are <br>
> the exact meaning for para(54) and (55) in rea file? Such as, what's the <br>
> difference between: 0,0 and -3 1 for (54) and (55) respectively? what's <br>
> meaning for sign (+) or (-)?<br>
> <br>
> Kind regards,<br>
> <br>
> Zhai<br>
> <br>
> <br>
> Hi Philipp,<br>
> <br>
> Yes, they are shear velocity and bulk velocity. Can I say if the ffx, ffy<br>
> or ffz equal to (u_t/u_b)^2, the flow is specified as a fixed pressure<br>
> gradient in the channel, and parameter(54) and para(55) in rea file are<br>
> fixed as 0. Otherwise, if the all ffx, ffy and ffz are 0, the flow is fixed<br>
> at flow rate rather than pressure gradient?<br>
> <br>
> Cheers,<br>
> <br>
> Zhai<br>
> <br>
> <br>
> <br>
> <br>
> _______________________________________________<br>
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