strain rate magnitude

rakadit · July 21, 2011, 06:58

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

Amir · July 21, 2011, 16:42

Hi,
the compact form is:
$\sqrt{2*D:D}$
which is:
$\sqrt{2*DijDij}$ ; i,j=1,2,3 (two inner products)
D : strain rate tensor

rakadit · July 23, 2011, 04:18

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

Amir · July 23, 2011, 05:43

Dear Rakesh,
In Mathematics, the magnitude of a second order tensor is defined as $\sqrt{T:T}$ , 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= $\sqrt{2*D:D}$ = $\sqrt{2*D^{2}_{11}+2*D^{2}_{12}+...}$
Note that it is equivalent with FLUENT manual interpretation: (after some manipulations)
$s=\sqrt{2u^{2}_{x}+2v^{2}_{y}+2w^{2}_{z}+(u_{z}+w_{x})^{2}+(u_{y}+v_{x})^{2}+(w_{y}+v_{z})^{2}}$

Amir

rakadit · July 26, 2011, 12:05

Dear Sir,

Thank you very much.

Rakesh

September 20, 2012, 06:00

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?

Amir · September 20, 2012, 11:26

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,

September 20, 2012, 11:37

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!

Amir · September 20, 2012, 11:44

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,

wanna88 · September 25, 2012, 05:52

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

rembe · January 10, 2013, 08:43

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

Kanarya · August 17, 2014, 18:37

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:

Originally Posted by Amir

Dear Rakesh,
In Mathematics, the magnitude of a second order tensor is defined as $\sqrt{T:T}$ , 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= $\sqrt{2*D:D}$ = $\sqrt{2*D^{2}_{11}+2*D^{2}_{12}+...}$
Note that it is equivalent with FLUENT manual interpretation: (after some manipulations)
$s=\sqrt{2u^{2}_{x}+2v^{2}_{y}+2w^{2}_{z}+(u_{z}+w_{x})^{2}+(u_{y}+v_{x})^{2}+(w_{y}+v_{z})^{2}}$

Amir

Amir · August 18, 2014, 09:33

Quote:

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,

Kanarya · August 19, 2014, 10:01

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?
thanks in advance!

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,

Amir · August 19, 2014, 11:40

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,

Kanarya · August 21, 2014, 07:52

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<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?
thanks in advance!

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,

Amir · August 21, 2014, 08:48

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<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?
thanks in advance!

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

Bests,

Kanarya · August 21, 2014, 09:48

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,

Kanarya · August 25, 2014, 15:28

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!

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,

Kanarya · August 29, 2014, 18:53

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:

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!

July 21, 2011, 06:58	strain rate magnitude	#1
rakadit Member Rakesh Join Date: May 2011 Posts: 33 Rep Power: 15	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 23, 2011, 04:18	starin rate	#3
rakadit Member Rakesh Join Date: May 2011 Posts: 33 Rep Power: 15	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/delye12)+delu/delz*(e13)+................and so on. Thanks , Rakesh

July 23, 2011, 05:43		#4
Amir Senior Member Amir Join Date: May 2009 Location: Montreal, QC Posts: 735 Blog Entries: 1 Rep Power: 23	Dear Rakesh, In Mathematics, the magnitude of a second order tensor is defined as $\sqrt{T:T}$ , 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= $\sqrt{2D:D}$ = $\sqrt{2D^{2}_{11}+2D^{2}_{12}+...}$ Note that it is equivalent with FLUENT manual interpretation: (after some manipulations) $s=\sqrt{2u^{2}_{x}+2v^{2}_{y}+2w^{2}_{z}+(u_{z}+w_{x})^{2}+(u_{y}+v_{x})^{2}+(w_{y}+v_{z})^{2}}$ Amir sadjad.s, Nucleophobe, prasa and 5 others like this. Last edited by Amir; July 23, 2011 at 09:31.*

January 10, 2013, 08:43	mean shear rate	#11
rembe New Member Michael Rembe Join Date: Oct 2009 Location: Germany Posts: 4 Rep Power: 17	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

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July 21, 2011, 16:42		#2
Amir Senior Member Amir Join Date: May 2009 Location: Montreal, QC Posts: 735 Blog Entries: 1 Rep Power: 23	Hi, the compact form is: $\sqrt{2D:D}$ which is: $\sqrt{2DijDij}$ ; i,j=1,2,3 (two inner products) D : strain rate tensor sadjad.s and alainislas like this. Last edited by Amir; July 23, 2011 at 05:30.

July 26, 2011, 12:05		#5
rakadit Member Rakesh Join Date: May 2011 Posts: 33 Rep Power: 15	Dear Sir, Thank you very much. Rakesh

September 20, 2012, 06:00		#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, 11:37		#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!

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