[rakadit]

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]

Hi,
the compact form is:

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

[rakadit]

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]

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

[rakadit]

Dear Sir,

Thank you very much.


Rakesh

[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?

[Amir]

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,

[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!

[Amir]

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]

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]

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