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adding viscous dissipation to openfoam solver 

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January 19, 2018, 09:31 
adding viscous dissipation to openfoam solver

#1 
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A. Min
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Hi
I want to add viscous dissipation to energy eqn. but my fluid is not Newtonian and has a special stress tensor. So the work of stress tensor field is "tau && grad(U)" 1 is it a correct relation for work of stress tensor field? or I should write: tau && [grad(U) + transpose of (grad(U))] 2 is it correct to write: solve ( fvm::div(phi, T)  fvm::laplacian(alphaEff, T)  tau && grad(U) ); thank you 

January 22, 2018, 18:01 

#2 
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Tobias Holzmann
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Hi,
I would expect to have the shear heating given as: However, I am not sure about NonNewtonian fluids. The only change should be in the viscosity (which does not follow a linear profile). The stress tensor itself should be similar to those of Newtonian fluids. I might be wrong in that case and have to proof it somewhere in literature. The equation of the shearheating is correct.
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January 23, 2018, 02:34 

#3 
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Quote:
tau && [grad(U) + transpose of (grad(U))] this relation is valid for viscoelastic fluid, just we should use viscoelastic stress tensor. 

January 23, 2018, 10:48 

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Hi,
this is incorrect. If Tau is Cauchy stress tensor then (does not matter what kind, i.e., viscoelastic fluid etc.) but note that by "additing" transpose of gradient of the velocity to the formula, you really gives less information in the formula as is symmetric part of the gradient of the velocity. This is indeed used in many proofs. Best Ondra 

January 23, 2018, 13:00 

#6 
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Tobias Holzmann
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I don't get your point. Who is wrong and what is correct now?
In general the Cauchy stress tensor is defined as while the shear tensor is such as: while is the deviatoric part of the Cauchy stress tensor and the negative pressure represents the hydrostatic part such as: Based on Bird et al. the viscose heating is related to: but it is mentioned that you have to have an symmetric shear tensor (). Thus, your relation is only valid for symmetric ones; if this was the thing you wanted to point out, I just clearyfied the things. If there is some mistake, please don't hesitate to correct me. only valid for symmetric shear rate tensor while is given as:
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January 23, 2018, 13:24 

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Quote:
Sorry, I forget to cite alimea post. My post was reaction mainly to pointout that it does not matter if the Newtonian fluid is under consideration. I defined Cauchy stress as Tau not Sigma, but it really does not matter in our discussion. Cauchy stress is always symmetric and the D is defined as symmetric part of the gradient of the velocity. So the formula holds always within classical mechanics of continuum. 

January 23, 2018, 14:55 

#8 
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Tobias Holzmann
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I agree, the nomenclature does not play a big deal here. However, do you have any example in which the Cauchy stress tensor, or the general formulation  given in Gurtin et al.  The Mechanics and Thermodynamics of Continua  is not symmetric?
PS: Did you comment in the quotes? I did not mean the gradient. What did you mean there?
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January 23, 2018, 15:09 

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No, as long as conservation of angular momentum holds the Cauchy stress tensor is symmetric.


March 22, 2019, 00:54 

#10 
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Hojatollah Gholami
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Dear alimea
Do you add viscous dissipation to energy equation? I have the same problem, if favor me, I pleasure. thanks 

March 22, 2019, 13:48 

#11 
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March 22, 2019, 14:17 

#12 
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Hojatollah Gholami
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Dear alimea
I want to add a viscous heating term to energy equation as below 

March 23, 2019, 17:21 

#13 
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March 24, 2019, 00:05 

#14  
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Hojatollah Gholami
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I want to add last term to energy equation, So I uses
Quote:


March 24, 2019, 01:09 

#15 
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March 24, 2019, 01:19 

#16 
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Hojatollah Gholami
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