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strain rate magnitude

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 15:42

Hi,
the compact form is:

which is:
; i,j=1,2,3 (two inner products)
D : strain rate tensor

starin rate

Dear Sir,
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 04:43

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

Dear Sir,

Thank you very much.

Rakesh

 Unneoetech September 20, 2012 05:00

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 10:26

Quote:
 Originally Posted by Unneoetech (Post 382719) 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,

 Unneoetech September 20, 2012 10:37

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)

 Amir September 20, 2012 10:44

Quote:
 Originally Posted by Unneoetech (Post 382791) 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 04:52

Quote:
 Originally Posted by Unneoetech (Post 382791) 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

mean shear rate

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 17:37

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?
Quote:
 Originally Posted by Amir (Post 317181) 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

 Amir August 18, 2014 08:33

Quote:
 Originally Posted by Kanarya (Post 506377) 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 09:01

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?
Quote:
 Originally Posted by Amir (Post 506466) 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 10:40

Quote:
 Originally Posted by Kanarya (Post 506621) 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 06:52

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 (Post 506659) 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 07:48

Quote:
 Originally Posted by Kanarya (Post 507006) 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,

 Kanarya August 21, 2014 08:48

thanks Amir,
it seems it is fine now:)
Best!
Quote:
 Originally Posted by Amir (Post 507013) 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 14:28

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?
Quote:
 Originally Posted by Amir (Post 507013) 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 17:53

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?
 Originally Posted by Kanarya (Post 507732) 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!