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July 21, 2011, 05:58 
strain rate magnitude

#1 
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Rakesh
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Dear All!
what is the correct definition for finding strain rate magnitude? in Fluent. in Flunent ,STRAINRATEMAG(c,t) is defined as: strain_rate_mag(c,t) = sqrt[[C_DUDX(c,t)*(C_DUDX(c,t)+C_DUDX(c,t))+C_DUDY(c,t)* (C_DUDY(c,t)+C_DVDX(c,t))+C_DUDZ(c,t)*(C_DUDZ(c,t) +C_DWDX(c,t))]+ [C_DVDX(c,t)*(C_DVDX(c,t)+C_DUDY(c,t))+C_DVDY(c,t)* (C_DVDY(c,t)+C_DVDY(c,t))+C_DVDZ(c,t)*(C_DVDZ(c,t) +C_DWDY(c,t))]+ [C_DWDX(c,t)*(C_DWDX(c,t)+C_DUDZ(c,t))+C_DWDY(c,t)* (C_DWDY(c,t)+C_DVDZ(c,t))+C_DWDZ(c,t)*(C_DWDZ(c,t) +C_DWDZ(c,t))]]; is the above definition correct .please elaborate on this? Thanks , Rakesh 

July 23, 2011, 03:18 
starin rate

#3 
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Rakesh
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Dear Sir,
Thanks for your quick response. it would be great help If you elaborate a liitle more. is sqrt(Dij Dij) =sqrt(e11^2+e12^2+e13^2+e21^2+......and so on). here e11 etc.means 9 strain rate components. but then how is it equivalent to the relation given in Fluent manual as S^2=delu/delx*(e11)+delu/dely*e12)+delu/delz*(e13)+................and so on. Thanks , Rakesh 

July 23, 2011, 04:43 

#4 
Senior Member

Dear Rakesh,
In Mathematics, the magnitude of a second order tensor is defined as , but here, as you said, we have a convention for shear strain magnitude in which an extra constant coefficient is multiplied, so: strain rate magnitude= = Note that it is equivalent with FLUENT manual interpretation: (after some manipulations) Amir Last edited by Amir; July 23, 2011 at 08:31. 

July 26, 2011, 11:05 

#5 
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Rakesh
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Dear Sir,
Thank you very much. Rakesh 

September 20, 2012, 05:00 

#6 
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Nick
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The term you mention is usually defined as the shear rate. Is in Fluent the shear rate and the strain rate equal for NonNewtonian flow?


September 20, 2012, 10:26 

#7  
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Quote:
These are two different concepts. Strain rate contains both shear and normal rates; you can consider strain rate as rate of deformation where the shear rate is just one part of that. The strain rate tensor is extracted from gradient of velocity field while the fluid type just affects the constitutive relation (relation between stress and rate of strain) so these definitions can be used for each type. Bests,
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Amir 

September 20, 2012, 10:37 

#8 
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Nick
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Hi Amir,
That is just what I found out a couple of seconds ago It is also described in the Fluent manual in Section 30.4 http://hpce.iitm.ac.in/website/Manua...219.htm#217910 Quote: Strain Rate (in the Derivatives... category) relates shear stress to the viscosity. Also called the shear rate ( in Equation 8.417), the strain rate is related to the second invariant of the rateofdeformation tensor . Its unit quantity is timeinverse. In 3D Cartesian coordinates, the strain rate,, is defined as Eq. (30.430) Thanks for your fast answer! 

September 20, 2012, 10:44 

#9  
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Quote:
What I said was the definition in continuum mechanics but in FLUENT some definitions have changed! e.g., wall shear stress is wall traction! Bests,
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Amir 

September 25, 2012, 04:52 

#10  
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Naimah
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Quote:
So is that means in the Fluent, the strain rate equal to shear rate? Thank you. Regards, Naimah 

January 10, 2013, 08:43 
mean shear rate

#11 
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Michael Rembe
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Hi,
I'm not a expert in fluid mechanics. Can you tell me the difference between the strain rate magnitude: and the mean strain rate: Sij=1/2*(dUi/Dxj+dUj/dxi) I need th correct formulation in the SMAGORINSKYmodel. Thank you very much Michael 

August 17, 2014, 17:37 

#12 
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rkhr
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Dear Amir,
I would like to calculate in UDF daviatoric part of strain rate tensor so definition of it as following: S_prime_ij=S_ij  S_mm*kronecker_delta_ij/3, so the part of kronecker_delta_ij is confused me…I must again calculate the magnitude if the S_prime as you explained in this thread or it is different? thanks in advance! Quote:


August 18, 2014, 08:33 

#13  
Senior Member

Quote:
No, this is quite straightforward! Just substitute the S_mm term with sum of the diagonal components. i.e., S_mm=S11+S22+S33 kronecker_delta_ij=0, where i/=j kronecker_delta_ij=1, where i==j Bests,
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Amir 

August 19, 2014, 09:01 

#14 
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rkhr
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thanks Amir!
I am trying to define tensor in UDF but sth is wrong with the code or udf... PHP Code:
do you know what is the problem here? thanks in advance! 

August 19, 2014, 10:40 

#15  
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Quote:
Actually, forcing wrong indices to a matrix may result in previously saved and irrelative data in the memory. Bests,
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Amir 

August 21, 2014, 06:52 

#16  
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rkhr
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Hi Amir,
thanks for the answer! But I am still getting weird values ... For example I trying to define kronecker delta like: PHP Code:
Do you have any idea what is wrong with it? thanks in advance! Quote:


August 21, 2014, 07:48 

#17  
Senior Member

Quote:
You need to put the Message command inside your loop, not out of that! Moreover, this is "\n" not "/n". Bests,
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Amir 

August 21, 2014, 08:48 

#18 
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rkhr
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August 25, 2014, 14:28 

#19 
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rkhr
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Hi Amir,
I have problem with convergence now. It seems residuals are fine but the simulation is stopped. PHP Code:
thanks in advance! 

August 29, 2014, 17:53 

#20  
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rkhr
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Hi,
do you think the problem is coming form the tensor which I have posted in thread 14? may opposite indices are giving the same result? thanks in advance! thanks in advance! Quote:


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