evaluate effective viscosity from U and p already known

Cyp · January 18, 2012, 03:03

Hi!

I would like to evaluate an effective viscosity from pressure and velocity field already computed. I mean that I am looking for a field nuEff that obey to:
$\nabla \cdot (U U) + \nabla p = \nabla \cdot (\nu_{eff} \nabla U)$

In this equation, U and p result from a previous computation.

Does anybody know a method to do such a thing ?

Regards,
Cyp

Bernhard · January 19, 2012, 03:03

If you work out the brackets in the term on the right hand side, can't you just solve it like any other equation in OpenFOAM? So you use fvc instead of fvm on the terms with p and U and solve for nuEff. I can imagine that this will work, but I'll give you now guarantee.

Cyp · January 19, 2012, 03:11

Yes, but in that case, I will have :

T1 = fvc::laplacian(U) which is a vector

T2 = fvc::grad(p)/rho + fvc::div(phi,U) which is a vector as well.

How can I deduce the value of nuEff which should be a scalar (or may be a tensor) ??

Bernhard · January 19, 2012, 05:53

For the right hand side, don't you get something like

fvm::grad(nuEff) & fvc::grad(U) + nuEff * fvc::laplacian(U)

or something like that, which you can solve if you supply boundary conditions?

But you mean this is an overdetermined system or something? Maybe you can work component-wise?

Cyp · January 19, 2012, 07:31

In fact, what I look for is a method to evaluate an effective viscosity that result from a turbulent calculation (RANS, LES).
In case of RANS simulation, I should recover the value of nut and it will be a test case to validate the approach.

I was thinking that the effective viscosity may satisfy :
$\nu_{eff}=(\textbf{U}\textbf{U}+p\textbf{I})\cdot(\nabla U)^{-1}$
but I am not sure about that.

I missed the point with your rewritting of the RHS ? if I am right, fvm::grad() has no sense in OF..

Bernhard · January 19, 2012, 11:22

Why don't you just write nut directly then? Seems like a unnecessary exercise to me...

Cyp · January 20, 2012, 03:13

Because the RANS approach are just a particular approach of what I need. It makes sense when LES is considered for example.

Bernhard · January 20, 2012, 03:41

Why? Then you still have an effective viscosity in the way it is implemented in OpenFOAM.

Cyp · January 20, 2012, 03:44

Yes, but what I look for is the effective viscosity that corresponds to time-average velocity and pressure fields. It is not the case of the nuSgs of the LES..

Bernhard · January 20, 2012, 03:59

Why don't you use the time-averaged value of nuSgs/nut? I don't think this will make a very big difference compared to what you want to do. I still don't get why you want to do it this complex...

Cyp · January 20, 2012, 04:22

Because I do not have it and the simulations are too long to be start one more time...

Cyp · January 23, 2012, 08:42

I keep working on this problem and I identified some issues.

I need to calculate
$Cste*x*\textbf{I}$

where I is the identity tensor and x is the position in the x-direction.

How can I access to the value of x ?

January 18, 2012, 03:03	evaluate effective viscosity from U and p already known	#1
Cyp Senior Member Cyprien Join Date: Feb 2010 Location: Stanford University Posts: 299 Rep Power: 18	Hi! I would like to evaluate an effective viscosity from pressure and velocity field already computed. I mean that I am looking for a field nuEff that obey to: $\nabla \cdot (U U) + \nabla p = \nabla \cdot (\nu_{eff} \nabla U)$ In this equation, U and p result from a previous computation. Does anybody know a method to do such a thing ? Regards, Cyp

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January 19, 2012, 03:03		#2
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	If you work out the brackets in the term on the right hand side, can't you just solve it like any other equation in OpenFOAM? So you use fvc instead of fvm on the terms with p and U and solve for nuEff. I can imagine that this will work, but I'll give you now guarantee.

January 19, 2012, 03:11		#3
Cyp Senior Member Cyprien Join Date: Feb 2010 Location: Stanford University Posts: 299 Rep Power: 18	Yes, but in that case, I will have : T1 = fvc::laplacian(U) which is a vector T2 = fvc::grad(p)/rho + fvc::div(phi,U) which is a vector as well. How can I deduce the value of nuEff which should be a scalar (or may be a tensor) ??

January 19, 2012, 05:53		#4
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	For the right hand side, don't you get something like fvm::grad(nuEff) & fvc::grad(U) + nuEff * fvc::laplacian(U) or something like that, which you can solve if you supply boundary conditions? But you mean this is an overdetermined system or something? Maybe you can work component-wise?

January 19, 2012, 07:31		#5
Cyp Senior Member Cyprien Join Date: Feb 2010 Location: Stanford University Posts: 299 Rep Power: 18	In fact, what I look for is a method to evaluate an effective viscosity that result from a turbulent calculation (RANS, LES). In case of RANS simulation, I should recover the value of nut and it will be a test case to validate the approach. I was thinking that the effective viscosity may satisfy : $\nu_{eff}=(\textbf{U}\textbf{U}+p\textbf{I})\cdot(\nabla U)^{-1}$ but I am not sure about that. I missed the point with your rewritting of the RHS ? if I am right, fvm::grad() has no sense in OF..

January 19, 2012, 11:22		#6
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	Why don't you just write nut directly then? Seems like a unnecessary exercise to me...

January 20, 2012, 03:13		#7
Cyp Senior Member Cyprien Join Date: Feb 2010 Location: Stanford University Posts: 299 Rep Power: 18	Because the RANS approach are just a particular approach of what I need. It makes sense when LES is considered for example.

January 20, 2012, 03:41		#8
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	Why? Then you still have an effective viscosity in the way it is implemented in OpenFOAM.

January 20, 2012, 03:44		#9
Cyp Senior Member Cyprien Join Date: Feb 2010 Location: Stanford University Posts: 299 Rep Power: 18	Yes, but what I look for is the effective viscosity that corresponds to time-average velocity and pressure fields. It is not the case of the nuSgs of the LES..

January 20, 2012, 03:59		#10
Bernhard Senior Member Bernhard Join Date: Sep 2009 Location: Delft Posts: 790 Rep Power: 21	Why don't you use the time-averaged value of nuSgs/nut? I don't think this will make a very big difference compared to what you want to do. I still don't get why you want to do it this complex...

January 20, 2012, 04:22		#11
Cyp Senior Member Cyprien Join Date: Feb 2010 Location: Stanford University Posts: 299 Rep Power: 18	Because I do not have it and the simulations are too long to be start one more time...

January 23, 2012, 08:42		#12
Cyp Senior Member Cyprien Join Date: Feb 2010 Location: Stanford University Posts: 299 Rep Power: 18	I keep working on this problem and I identified some issues. I need to calculate $Cstex\textbf{I}$ where I is the identity tensor and x is the position in the x-direction. How can I access to the value of x ?