# strain rate magnitude

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 July 21, 2011, 05:58 strain rate magnitude #1 Member   Rakesh Join Date: May 2011 Posts: 33 Rep Power: 12 Dear All! what is the correct definition for finding strain rate magnitude? in Fluent. in Flunent ,STRAIN-RATE-MAG(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 21, 2011, 15:42 #2 Senior Member     Amir Join Date: May 2009 Location: Montreal, QC Posts: 735 Blog Entries: 1 Rep Power: 20 Hi, the compact form is: which is: ; i,j=1,2,3 (two inner products) D : strain rate tensor sadjad.s likes this. Last edited by Amir; July 23, 2011 at 04:30.

 July 23, 2011, 03:18 starin rate #3 Member   Rakesh Join Date: May 2011 Posts: 33 Rep Power: 12 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     Amir Join Date: May 2009 Location: Montreal, QC Posts: 735 Blog Entries: 1 Rep Power: 20 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 sadjad.s, Nucleophobe, prasa and 3 others like this. Last edited by Amir; July 23, 2011 at 08:31.

 July 26, 2011, 11:05 #5 Member   Rakesh Join Date: May 2011 Posts: 33 Rep Power: 12 Dear Sir, Thank you very much. Rakesh

 September 20, 2012, 05:00 #6 Unneoetech Guest   Posts: n/a The term you mention is usually defined as the shear rate. Is in Fluent the shear rate and the strain rate equal for Non-Newtonian flow?

September 20, 2012, 10:26
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Quote:
 Originally Posted by Unneoetech The term you mention is usually defined as the shear rate. Is in Fluent the shear rate and the strain rate equal for Non-Newtonian flow?
Dear friend,

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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 September 20, 2012, 10:37 #8 Unneoetech Guest   Posts: n/a 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 8.4-17), the strain rate is related to the second invariant of the rate-of-deformation tensor . Its unit quantity is time-inverse. In 3D Cartesian coordinates, the strain rate,, is defined as Eq. (30.4-30) Thanks for your fast answer!

September 20, 2012, 10:44
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Quote:
 Originally Posted by Unneoetech 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 8.4-17), the strain rate is related to the second invariant of the rate-of-deformation tensor . Its unit quantity is time-inverse. In 3D Cartesian coordinates, the strain rate,, is defined as Eq. (30.4-30) Thanks for your fast answer!
Yes I've seen that.
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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September 25, 2012, 04:52
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Quote:
 Originally Posted by Unneoetech 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 8.4-17), the strain rate is related to the second invariant of the rate-of-deformation tensor . Its unit quantity is time-inverse. In 3D Cartesian coordinates, the strain rate,, is defined as Eq. (30.4-30) Thanks for your fast answer!
Hi,

So is that means in the Fluent, the strain rate equal to shear rate?

Thank you.

Regards,
Naimah

 January 10, 2013, 07:43 mean shear rate #11 New Member   Michael Rembe Join Date: Oct 2009 Location: Germany Posts: 4 Rep Power: 14 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 SMAGORINSKY-model. Thank you very much Michael

August 17, 2014, 17:37
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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?
Quote:
 Originally Posted by Amir 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

August 18, 2014, 08:33
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 Originally Posted by Kanarya 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!
Hi,

No, this is quite straight-forward! 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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August 19, 2014, 09:01
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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:
real puixj[ND_ND][ND_ND];
puixj[0][0]= C_DUDX(c,t);
puixj[1][0]= C_DVDX(c,t);
puixj[0][1]= C_DUDY(c,t);
puixj[1][1]= C_DVDY(c,t);

for(
j=0;j<ND_ND;j++)
{
for(
i=0;i<ND_ND;i++)
{
Og[i][j]=0.5*(puixj[i][j]-puixj[j][i]); //Og is the rotation tensor
}

when I am putting random number to i or j it gives some results which is wrong!For example;even Og[25][20] is giving some result ....
do you know what is the problem here?
Quote:
 Originally Posted by Amir Hi, No, this is quite straight-forward! 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,

August 19, 2014, 10:40
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Quote:
 Originally Posted by Kanarya when I am putting random number to i or j it gives some results which is wrong!For example;even Og[25][20] is giving some result .... do you know what is the problem here? thanks in advance!
I guess, proper definition of the Og tensor as Og[ND_ND][ND_ND] and an initialization of this tensor may fixed this issue! However, I wonder how your UDF may lead to such error during the calculation!
Actually, forcing wrong indices to a matrix may result in previously saved and irrelative data in the memory.

Bests,
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August 21, 2014, 06:52
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Hi Amir,
But I am still getting weird values ...
For example I trying to define kronecker delta like:
PHP Code:
for(jj=0;jj<ND_ND;jj++)
{
for(
ii=0;ii<ND_ND;ii++)
{
if (
ii==jj)

delta[ii][jj]=1;
else

delta[ii][jj]=0;
}
}
and print
it out with:
Message("delta: %g/n",delta[ii][jj]);
the result is always "0"
Do you have any idea what is wrong with it?
Quote:
 Originally Posted by Amir I guess, proper definition of the Og tensor as Og[ND_ND][ND_ND] and an initialization of this tensor may fixed this issue! However, I wonder how your UDF may lead to such error during the calculation! Actually, forcing wrong indices to a matrix may result in previously saved and irrelative data in the memory. Bests,

August 21, 2014, 07:48
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Quote:
 Originally Posted by Kanarya Hi Amir, thanks for the answer! But I am still getting weird values ... For example I trying to define kronecker delta like: PHP Code: for(jj=0;jj
Hi,
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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August 21, 2014, 08:48
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thanks Amir,
it seems it is fine now
Best!
Quote:
 Originally Posted by Amir Hi, You need to put the Message command inside your loop, not out of that! Moreover, this is "\n" not "/n". Bests,

August 25, 2014, 14:28
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Hi Amir,
I have problem with convergence now.
It seems residuals are fine but the simulation is stopped.
PHP Code:
Updating solution at time levels N and N-1.
done
.

iter  continuity       u-gas     u-solid       v-gas     v-solid       uds-0       uds-1    vf-solid     time/iter
9481 solution is converged
9481  7.9111e-04  1.2569e-06  8.8861e-08  6.0119e-07  7.8996e-09  2.7750e-07  2.6720e-07  3.6096e-07  0
:00:02  100
Re
0
reyp
0
9482  2.0487e-03  1.0965e-05  1.4955e-05  3.5806e-06  3.8082e-06  2.1239e-04  2.2740e-04  1.4775e-05  0
:00:02   99
Re
0
reyp
0
9483  1.8130e-03  4.3936e-06  4.6505e-06  1.4881e-06  1.1923e-06  7.8683e-06  6.0966e-06  7.5522e-06  0
:00:02   98
Re
0
reyp
0
# Divergence detected in AMG solver: uds-1 -> Increasing relaxation sweeps!

Divergence detected in AMG solveruds-1
Divergence detected in AMG solver
uds-1
Divergence detected in AMG solver
uds-1
Divergence detected in AMG solver
uds-1
Divergence detected in AMG solver
uds-1
Divergence detected in AMG solver
uds-1
Divergence detected in AMG solver
uds-1
Divergence detected in AMG solver
uds-1
Warning
An error or interrupt occurred while reading the journal file.
Some commands may not have been completed.

Halting due to end of file on input
Do you have any idea about it?
Quote:
 Originally Posted by Amir Hi, You need to put the Message command inside your loop, not out of that! Moreover, this is "\n" not "/n". Bests,

August 29, 2014, 17:53
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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?
Quote:
 Originally Posted by Kanarya Hi Amir, I have problem with convergence now. It seems residuals are fine but the simulation is stopped. PHP Code: Updating solution at time levels N and N-1.  done.   iter  continuity       u-gas     u-solid       v-gas     v-solid       uds-0       uds-1    vf-solid     time/iter ! 9481 solution is converged   9481  7.9111e-04  1.2569e-06  8.8861e-08  6.0119e-07  7.8996e-09  2.7750e-07  2.6720e-07  3.6096e-07  0:00:02  100 Re: 0 reyp: 0   9482  2.0487e-03  1.0965e-05  1.4955e-05  3.5806e-06  3.8082e-06  2.1239e-04  2.2740e-04  1.4775e-05  0:00:02   99 Re: 0 reyp: 0   9483  1.8130e-03  4.3936e-06  4.6505e-06  1.4881e-06  1.1923e-06  7.8683e-06  6.0966e-06  7.5522e-06  0:00:02   98 Re: 0 reyp: 0 # Divergence detected in AMG solver: uds-1 -> Increasing relaxation sweeps! Divergence detected in AMG solver: uds-1 Divergence detected in AMG solver: uds-1 Divergence detected in AMG solver: uds-1 Divergence detected in AMG solver: uds-1 Divergence detected in AMG solver: uds-1 Divergence detected in AMG solver: uds-1 Divergence detected in AMG solver: uds-1 Divergence detected in AMG solver: uds-1 Warning: An error or interrupt occurred while reading the journal file. Some commands may not have been completed. > Halting due to end of file on input.  Do you have any idea about it? thanks in advance!