Oscillating Pressure Gradient at the inlet

hdixit · March 2, 2014, 10:26

Hello all,

I have a uniform inlet flow which is oscillating as $U=U_{\infty} + A \sin(\omega t)$ . If I use the continuity and the momentum equation, I get $\partial u/\partial x=0$ . My x-momentum equation reduces to $\partial p/\partial x = -\partial u/\partial t$ .

This gives me $\partial p/\partial x = -A \omega \cos(\omega t)$ . How do I put in such an oscillating pressure gradient at the inlet? I am looking for something along the lines of OscillatingFixedValue for inputting Dirchelet boundary conditions.

Please note that I have ignored (the constant) density in the above discussion since this can be absorbed in the case of incompressible Newtonian flow.

Thanks,
Harish

razi.me05 · October 10, 2014, 20:07

Hi Harish,

Did you get any solution to your problem? I'm facing exactly the same kind of problem.

steezorigineez · November 12, 2014, 18:14

Hi Guys,

I am currently simulating a pulsatile channel flow using a modified pimpleFoam solver. I am simulating a 2D periodic channel with a cosinusoidal pressure gradient. Using LaunderSharma KE turb model and the mesh is 256 in the wall normal direction and 8 in the axial direction. The inlet and outlet are set as cyclic BCs.

The way I have it set up now is I created a new solver by copying the pimpleFoam solver and adding a pressure gradient with a cosine term to the momentum equation in Ueqn.C. I believe this is the correct way to setup a flow with an oscillating pressure gradient.

I am having trouble in terms of convergence of the phases over each period at the moment.

Let me know if you have any thoughts or questions.

steezorigineez · November 16, 2014, 20:25

Just wanted to update you and let you know that I was able to successfully get a pulsating channel running and the convergence issue is fixed. Let me know if you want the code.

-Ian

canopus · May 26, 2015, 06:02

Hi Ian
Can you please share the code?
I have sent you a pm.
Regards
SM

steezorigineez · May 26, 2015, 11:35

Here is the git link to the code that I have used to successfully simulate a pulsating channel flow with an oscillating pressure gradient. It also includes the transport of scalar temperature. Let me know if you have any questions or comments.

https://github.com/ianbpond/pimpleFoamPulsTemp

canopus · May 27, 2015, 18:24

Hi Ian
I checked out the code and could run it on the test case provided along with.
Sorry for stupid questions as this is my first brush with OF application development

1. I guess you are solving for $U=U_{\infty} + A \sin(\omega t)$ where $U_{\infty} = 0$ ?

2. what does fvOptions(U) do in UEqn.h?

Code:

 fvm::ddt(U) + fvm::div(phi, U) + turbulence->divDevReff(U)
 ==    fvOptions(U) + dpdx*cos(Freq*runTime.time().value())

3.

Code:

dpdx*cos(Freq*runTime.time().value())

is added as a source to momentum equation in UEqn.h and implies pressure gradient is set as $1/\rho( \partial p/\partial x) = -A \omega \cos(\omega t)$ ?

4. Is $-A/\rho \omega$ lumped together in dpdx which is set to 1 in constant/transportProperties? (dpdx sounds bit confusing)

5. constant/transportProperties:alphaPuls is not used ?

Thanks
SM

steezorigineez · May 27, 2015, 19:29

Hi canopus,

1. I designed this code to match a DNS simulation which solves the Navier Stokes eqn in the following form.

$\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j} = -\cos(\omega t) +\frac{1}{Re}\frac{\partial^2 u_i}{\partial x_j^2}$

where $\nu = 1/Re$

2. The fvOptions(U) doesn't do anything as far as I know, I just left it in there. It could be removed I believe.

3. Yes that is the added source term which represents the $-\cos(\omega t)$ in the above equation.

4. For our simulation $\rho = 1$ , so the dpdx term is just an amplitude of the pressure, equal to 1 for our case, I don't have the extra $\omega$ term as you do.

5. You are correct, alphaPuls is not used

Let me know if you still have questions.

canopus · May 29, 2015, 11:32

Thank you!
Could you please point to the DNS and your own work
in case they are available in public domain?

steezorigineez · June 8, 2015, 10:45

Hi Canopus,

At the moment, the DNS data are not available in the pulbic domain. However, I will update when they do become available.

steezorigineez · June 26, 2015, 11:34

I believe I may have an error in my referenced equation that is being solved. Sorry for any confusion. I will reply with the corrected equation soon.

steezorigineez · June 26, 2015, 13:50

Please take note of an error in my original equation. It should be as follows.

$\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j} = -\frac{dP}{dx} +\frac{1}{Re}\frac{\partial^2 u_i}{\partial x_j^2}$

where,

$-\frac{dP}{dx} = A \cos(\omega t)$

with A = 1.

I apologize for any confusion.

Linse · June 26, 2015, 19:47

Concerning the fvOptions-part: If I am not mistaken, this is part of one of the latest flexibility additions in OpenFOAM. This entry looks for runTime-Code in the case structure. This way it is possible to add entries/source terms to the different equations without fully recompiling the code.

Please do not ask me further questions about this capability! I am right at the beginning of looking into it...

March 2, 2014, 10:26	Oscillating Pressure Gradient at the inlet	#1
hdixit New Member Harish Dixit Join Date: Feb 2014 Posts: 2 Rep Power: 0	Hello all, I have a uniform inlet flow which is oscillating as $U=U_{\infty} + A \sin(\omega t)$ . If I use the continuity and the momentum equation, I get $\partial u/\partial x=0$ . My x-momentum equation reduces to $\partial p/\partial x = -\partial u/\partial t$ . This gives me $\partial p/\partial x = -A \omega \cos(\omega t)$ . How do I put in such an oscillating pressure gradient at the inlet? I am looking for something along the lines of OscillatingFixedValue for inputting Dirchelet boundary conditions. Please note that I have ignored (the constant) density in the above discussion since this can be absorbed in the case of incompressible Newtonian flow. Thanks, Harish

May 26, 2015, 06:02	need code	#5
canopus Member SM Join Date: Dec 2010 Posts: 97 Rep Power: 15	Hi Ian Can you please share the code? I have sent you a pm. Regards SM

May 26, 2015, 11:35		#6
steezorigineez New Member Ian Pond Join Date: Jan 2013 Posts: 11 Rep Power: 13	Here is the git link to the code that I have used to successfully simulate a pulsating channel flow with an oscillating pressure gradient. It also includes the transport of scalar temperature. Let me know if you have any questions or comments. https://github.com/ianbpond/pimpleFoamPulsTemp canopus likes this.

May 27, 2015, 18:24	questions	#7
canopus Member SM Join Date: Dec 2010 Posts: 97 Rep Power: 15	Hi Ian I checked out the code and could run it on the test case provided along with. Sorry for stupid questions as this is my first brush with OF application development 1. I guess you are solving for $U=U_{\infty} + A \sin(\omega t)$ where $U_{\infty} = 0$ ? 2. what does fvOptions(U) do in UEqn.h? Code: fvm::ddt(U) + fvm::div(phi, U) + turbulence->divDevReff(U) == fvOptions(U) + dpdxcos(FreqrunTime.time().value()) 3. Code: dpdxcos(FreqrunTime.time().value()) is added as a source to momentum equation in UEqn.h and implies pressure gradient is set as $1/\rho( \partial p/\partial x) = -A \omega \cos(\omega t)$ ? 4. Is $-A/\rho \omega$ lumped together in dpdx which is set to 1 in constant/transportProperties? (dpdx sounds bit confusing) 5. constant/transportProperties:alphaPuls is not used ? Thanks SM

June 26, 2015, 11:34		#11
steezorigineez New Member Ian Pond Join Date: Jan 2013 Posts: 11 Rep Power: 13	I believe I may have an error in my referenced equation that is being solved. Sorry for any confusion. I will reply with the corrected equation soon. Last edited by steezorigineez; June 26, 2015 at 11:39. Reason: Need to rewrite equation

October 10, 2014, 20:07		#2
razi.me05 Member Nevada Join Date: Apr 2014 Posts: 32 Rep Power: 12	Hi Harish, Did you get any solution to your problem? I'm facing exactly the same kind of problem.

November 12, 2014, 18:14		#3
steezorigineez New Member Ian Pond Join Date: Jan 2013 Posts: 11 Rep Power: 13	Hi Guys, I am currently simulating a pulsatile channel flow using a modified pimpleFoam solver. I am simulating a 2D periodic channel with a cosinusoidal pressure gradient. Using LaunderSharma KE turb model and the mesh is 256 in the wall normal direction and 8 in the axial direction. The inlet and outlet are set as cyclic BCs. The way I have it set up now is I created a new solver by copying the pimpleFoam solver and adding a pressure gradient with a cosine term to the momentum equation in Ueqn.C. I believe this is the correct way to setup a flow with an oscillating pressure gradient. I am having trouble in terms of convergence of the phases over each period at the moment. Let me know if you have any thoughts or questions.

November 16, 2014, 20:25		#4
steezorigineez New Member Ian Pond Join Date: Jan 2013 Posts: 11 Rep Power: 13	Just wanted to update you and let you know that I was able to successfully get a pulsating channel running and the convergence issue is fixed. Let me know if you want the code. -Ian

May 27, 2015, 19:29		#8
steezorigineez New Member Ian Pond Join Date: Jan 2013 Posts: 11 Rep Power: 13	Hi canopus, 1. I designed this code to match a DNS simulation which solves the Navier Stokes eqn in the following form. $\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j} = -\cos(\omega t) +\frac{1}{Re}\frac{\partial^2 u_i}{\partial x_j^2}$ where $\nu = 1/Re$ 2. The fvOptions(U) doesn't do anything as far as I know, I just left it in there. It could be removed I believe. 3. Yes that is the added source term which represents the $-\cos(\omega t)$ in the above equation. 4. For our simulation $\rho = 1$ , so the dpdx term is just an amplitude of the pressure, equal to 1 for our case, I don't have the extra $\omega$ term as you do. 5. You are correct, alphaPuls is not used Let me know if you still have questions.

May 29, 2015, 11:32		#9
canopus Member SM Join Date: Dec 2010 Posts: 97 Rep Power: 15	Thank you! Could you please point to the DNS and your own work in case they are available in public domain?

June 8, 2015, 10:45		#10
steezorigineez New Member Ian Pond Join Date: Jan 2013 Posts: 11 Rep Power: 13	Hi Canopus, At the moment, the DNS data are not available in the pulbic domain. However, I will update when they do become available.

June 26, 2015, 13:50		#12
steezorigineez New Member Ian Pond Join Date: Jan 2013 Posts: 11 Rep Power: 13	Please take note of an error in my original equation. It should be as follows. $\frac{\partial u_i}{\partial t} + u_j\frac{\partial u_i}{\partial x_j} = -\frac{dP}{dx} +\frac{1}{Re}\frac{\partial^2 u_i}{\partial x_j^2}$ where, $-\frac{dP}{dx} = A \cos(\omega t)$ with A = 1. I apologize for any confusion.

June 26, 2015, 19:47		#13
Linse Senior Member Bernhard Linseisen Join Date: May 2010 Location: Heilbronn Posts: 183 Blog Entries: 1 Rep Power: 15	Concerning the fvOptions-part: If I am not mistaken, this is part of one of the latest flexibility additions in OpenFOAM. This entry looks for runTime-Code in the case structure. This way it is possible to add entries/source terms to the different equations without fully recompiling the code. Please do not ask me further questions about this capability! I am right at the beginning of looking into it...

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