Turbulent Prandtl number

Ravenn · April 2, 2013, 20:45

Hello,

I'm trying to run a given case and it is said that the turbulent Prandtl number is set to 0.9 (no more information).
I've searched in Fluent and the definition of the turbulent Prandtl number is unclear to me, there are at least 5 different turbulent Prandtl numbers (with SST):
- TKE inner
- TKE outer
- SDR inner
- SDR outer
- Energy
- Wall

I don't think the first four are related to the given turbulent Prandtl number in my paper. But the Energy and Wall turbulent Prandtl number have the same value, close to 0.9. Should I change both of them?
Do you have any information about turbulent Prandtl number?
I've looked at the definition of turbulent Prandtl number (wiki, cfd-online) and at the definition in Fluent Manual, but I can't really figure out which one is concerned here.

The case is about hypersonic interactions and heat transfer.

Thanks for your help,
Ravenn

oj.bulmer · April 3, 2013, 11:57

Can you give more information about the paper you are referring to?

OJ

pete · April 3, 2013, 12:21

The turbulent Prandtl number is used to relate turbulent heat flux with turbulent momentum flux. The definition is given in for example this CFD-Wiki page:

http://www.cfd-online.com/Wiki/Favre...okes_equations

By setting a constant turbulent Prandtl number you can compute the turbulent heat flux based on the turbulent eddy-viscosity that a turbulence model predicts.

Changing the turbulent Prandtl number is a way to tune heat transfer results. So always be skeptical about papers where it is not stated what turbulent Prandtl number has been used.

Ravenn · April 3, 2013, 12:24

I only have hard copies of different papers:
- AIAA paper 93-0779: numerical simulation of crossing shock/turbulent boundary layer interaction at Mach 8.3
"The baldwin-Lomax and the Rodi k-epsilon turbulence models are employed, the molecular viscosity was specified by Sutherland's law. The molecular Prandtl number is 0.73 (air) and the turbulent Prandtl number is 0.9."

- AIAA Journal Vol 39 No 6 June 2001 p: 985-995: Insights in Turbulence Modeling for Crossing-Shock-Wave/Boundary-Layer Interactions
"The Sutherland's law is used to calculate the laminar viscosity,and a constant laminar Prandtl number of 0.72 is assumed. Central differencing is used to evaluate the viscous terms.The steady solution is obtained by applying a time-marching method based on the hybrid approximate actorization/relaxation algorithm. The first solutions presented here are computed with the k–x turbulence model by Wilcox and a constant turbulent Prandtl number of 0.9."

Ravenn

Edit:
That's exactly the problem, I've seen in many papers "constant turbulent Prandtl number of 0.9" without more information, I suppose it is linked to the hypersonic characteristic of the flow, but it dos not seem like a "cheat" or something to obtain better results. Or someone proposed in the 50's to use this value for this case and ever since everybody uses it.

Edit 2:
In the cfd-online wiki page, it is said after equation 26 that:
"Where Prt is a turbulent Prandtl number. Often a constant Prt = 0.9 is used."
In that case, which one of the fluent turbulent Prandtl number is concerned?

Is it possible that turbulent Prendtl numbers in fluent are not this turbulent Prandtl number Prt defined here, hence the Prt would be a results of the calculation and not a property defined before the calculation?

pete · April 3, 2013, 12:50

In laminar flow the viscosity is used to compute the heat-flux using Fourier's law and a laminar, well defined, Prandtl number $Pr \equiv \frac{C_p \mu}{\lambda}$ as:

$q_j = -\lambda \frac{\partial T}{\partial x_j} \equiv -C_p \frac{\mu}{Pr} \frac{\partial T}{\partial x_j}$

Most turbulence models just give a turbulent eddy viscosity $\mu_t$ . By setting a turbulent Prandtl number the turbulent heat flux can be estimated in the same way by just using the turbulent eddy viscosity that the turbulence mode predicts:

$q_j^{turb} \equiv C_p \overline{\rho u''_j T} \approx - C_p \frac{\mu_t}{Pr_t} \frac{\partial \widetilde{T}}{\partial x_j}$

Using a constant turbulent Prandtl number is a simplification and it is not fully correct. Experimentally a value of something close to 0.9 has been measured. You can find more information and further references here:

http://en.wikipedia.org/wiki/Turbulent_Prandtl_number

Ravenn · April 3, 2013, 18:18

So, I've post-processed 2 different calculations, one with the default values for energy and wall Prandtl number, and the other with energy and wall Prandtl number set to 0.9.

I've read carefully fluent user manual and here is what I understood:
- $k_{eff} = k + k_T$
- $\mu_{eff} = \mu + \mu_T$
- $Pr_{eff} = C_p \frac{\mu_{eff}}{k_{eff}}$

In Fluent, it is possible to obtain $k_{eff}$ ,

and $\mu_T$ . With these values on a line normal to a surface, I've calculated $k_{T} = k_{eff}-k$ and then $Pr_{T} = Cp \frac{\mu_T}{k_T}$ .

It appears that for the first calculation, $Pr_{T}=0.85$ outside the laminar part of boundary layer, which is the value of energy and wall Prandtl numbers.
For the second calculation where I changed the value of energy and wall Prandtl numbers to 0.9, $Pr_{T}=0.9$ outside the laminar part of boundary layer.

In the laminar part of boundary layer, $k_{T}=0$ , hence $Pr_{T}$ is undefined, or very high.

I'm wondering now what is the value of $Pr_{T}$ in the laminar part of boundary layer for the papers where $Pr_{T}$ is said to be fixed to 0.9.
In my opinion it depends on which parameter is used to calculate the other:
- $Pr_{T}$ , fixed to 0.9, and $\mu_{T}$ are used to calculate $k_{T}$ (papers)
- $\mu_{T}$ and $k_{T}$ are calculated by the turbulence model, and $Pr_{T}$ can be deduced with the same procedure I used. (Fluent)

Shamoon Jamshed · May 23, 2016, 14:06

Dear Ravenn

I was facing the same issue. I used two turbulence models, kepsilon and k-omega SST. I was getting incorrect Nu from the komega. So I decreased very much the Prt and got my result close to experiment. But since I used very low value (0.35) I am still doubtful. Are you still working on that too? yuor post seems 3 years old

Ravenn · May 24, 2016, 16:57

Hello Shamoon,

I'm sorry but it's been a while since I last worked on this subject (almost 3 years as you see) and I don't really remember everything, I've rediscovered the subject with your question. It appears I still receive the alerts for this post^^

Good luck for your research!

nishidd · July 18, 2016, 23:25

Quote:

Originally Posted by Shamoon Jamshed

Dear Ravenn

I was facing the same issue. I used two turbulence models, kepsilon and k-omega SST. I was getting incorrect Nu from the komega. So I decreased very much the Prt and got my result close to experiment. But since I used very low value (0.35) I am still doubtful. Are you still working on that too? yuor post seems 3 years old

would you mind telling me how to change the Prt with k-e，I do really need it THX

Shamoon Jamshed · July 19, 2016, 12:36

In the model--> viscous select k-epsilon then select realziable
On the right side there is a list of constants among which Energy and Wall Prandtal numbers are there

Shamoon Jamshed · July 19, 2016, 12:38

Quote:

Originally Posted by pete

In laminar flow the viscosity is used to compute the heat-flux using Fourier's law and a laminar, well defined, Prandtl number $Pr \equiv \frac{C_p \mu}{\lambda}$ as:

$q_j = -\lambda \frac{\partial T}{\partial x_j} \equiv -C_p \frac{\mu}{Pr} \frac{\partial T}{\partial x_j}$

Most turbulence models just give a turbulent eddy viscosity $\mu_t$ . By setting a turbulent Prandtl number the turbulent heat flux can be estimated in the same way by just using the turbulent eddy viscosity that the turbulence mode predicts:

$q_j^{turb} \equiv C_p \overline{\rho u''_j T} \approx - C_p \frac{\mu_t}{Pr_t} \frac{\partial \widetilde{T}}{\partial x_j}$

Using a constant turbulent Prandtl number is a simplification and it is not fully correct. Experimentally a value of something close to 0.9 has been measured. You can find more information and further references here:

http://en.wikipedia.org/wiki/Turbulent_Prandtl_number

Dear Ravenn

I was facing the same issue. I used two turbulence models, kepsilon and k-omega SST. I was getting incorrect Nu from the komega. So I decreased very much the Prt and got my result close to experiment. But since I used very low value (0.35) I am still doubtful.

Mazze[ITA] · January 31, 2017, 05:00

Be careful, you are just tuning your turbulent fluxes to match the experimental data. The constant Prt is usually a wrong assumption, as it varies within the domain.

Quote:

Originally Posted by Shamoon Jamshed

Dear Ravenn

I was facing the same issue. I used two turbulence models, kepsilon and k-omega SST. I was getting incorrect Nu from the komega. So I decreased very much the Prt and got my result close to experiment. But since I used very low value (0.35) I am still doubtful.

Shamoon Jamshed · January 31, 2017, 06:55

Quote:

Originally Posted by Mazze[ITA]

Be careful, you are just tuning your turbulent fluxes to match the experimental data. The constant Prt is usually a wrong assumption, as it varies within the domain.

I did not get the meaning of assumption and also its variation within the domain, I read that it was fixed based on the experiment. Usually it does not need to be changed.
So I rechecked my simulation and correct my tube length adn now its ok

Mazze[ITA] · January 31, 2017, 10:11

Quote:

Originally Posted by Shamoon Jamshed

I did not get the meaning of assumption and also its variation within the domain, I read that it was fixed based on the experiment. Usually it does not need to be changed.
So I rechecked my simulation and correct my tube length adn now its ok

Eddy viscosity models usually understimate mixing, therefore it is common practice to lower the values of Prt and Sct to increase the turbulent fluxes.

That is however not representative of the reality. There are several publications in which turbulent fluxes are calculated with LES to produce the equivalent Prt/Sct distributions.

In literature there are also several attempts to modify classical turbulence modeles to account for variable Prt/Sct number (see for example works by Goldberg et al. or Keistler).

vcvedant · June 20, 2017, 12:13

Turbulent Prandtl number affects the heat transfer calculations as it is used to calculate turbulent heat flux.
A experiment based variable turbulent Pr number correlation can be used as given by Kays & Crawford. It can be added to Fluent using UDF:

DEFINE_PRANDTL_T(Prt, c, t)
{
Prt = [some expression];
return Prt;
}

It can be added by compiling/interpreting this UDF and adding the new Prandtl number from Models->Viscous->k-e (or any other) -> drop down menu for Temperature Prandtl number

April 2, 2013, 20:45	Turbulent Prandtl number	#1
Ravenn New Member Join Date: Jan 2013 Posts: 11 Rep Power: 13	Hello, I'm trying to run a given case and it is said that the turbulent Prandtl number is set to 0.9 (no more information). I've searched in Fluent and the definition of the turbulent Prandtl number is unclear to me, there are at least 5 different turbulent Prandtl numbers (with SST): - TKE inner - TKE outer - SDR inner - SDR outer - Energy - Wall I don't think the first four are related to the given turbulent Prandtl number in my paper. But the Energy and Wall turbulent Prandtl number have the same value, close to 0.9. Should I change both of them? Do you have any information about turbulent Prandtl number? I've looked at the definition of turbulent Prandtl number (wiki, cfd-online) and at the definition in Fluent Manual, but I can't really figure out which one is concerned here. The case is about hypersonic interactions and heat transfer. Thanks for your help, Ravenn

April 3, 2013, 12:21		#3
pete Administrator Peter Jones Join Date: Jan 2009 Posts: 682 Rep Power: 10	The turbulent Prandtl number is used to relate turbulent heat flux with turbulent momentum flux. The definition is given in for example this CFD-Wiki page: http://www.cfd-online.com/Wiki/Favre...okes_equations By setting a constant turbulent Prandtl number you can compute the turbulent heat flux based on the turbulent eddy-viscosity that a turbulence model predicts. Changing the turbulent Prandtl number is a way to tune heat transfer results. So always be skeptical about papers where it is not stated what turbulent Prandtl number has been used. stingph, happideepi, kooki_13 and 1 others like this.

April 3, 2013, 12:24		#4
Ravenn New Member Join Date: Jan 2013 Posts: 11 Rep Power: 13	I only have hard copies of different papers: - AIAA paper 93-0779: numerical simulation of crossing shock/turbulent boundary layer interaction at Mach 8.3 "The baldwin-Lomax and the Rodi k-epsilon turbulence models are employed, the molecular viscosity was specified by Sutherland's law. The molecular Prandtl number is 0.73 (air) and the turbulent Prandtl number is 0.9." - AIAA Journal Vol 39 No 6 June 2001 p: 985-995: Insights in Turbulence Modeling for Crossing-Shock-Wave/Boundary-Layer Interactions "The Sutherland's law is used to calculate the laminar viscosity,and a constant laminar Prandtl number of 0.72 is assumed. Central differencing is used to evaluate the viscous terms.The steady solution is obtained by applying a time-marching method based on the hybrid approximate actorization/relaxation algorithm. The first solutions presented here are computed with the k–x turbulence model by Wilcox and a constant turbulent Prandtl number of 0.9." Ravenn Edit: That's exactly the problem, I've seen in many papers "constant turbulent Prandtl number of 0.9" without more information, I suppose it is linked to the hypersonic characteristic of the flow, but it dos not seem like a "cheat" or something to obtain better results. Or someone proposed in the 50's to use this value for this case and ever since everybody uses it. Edit 2: In the cfd-online wiki page, it is said after equation 26 that: "Where Prt is a turbulent Prandtl number. Often a constant Prt = 0.9 is used." In that case, which one of the fluent turbulent Prandtl number is concerned? Is it possible that turbulent Prendtl numbers in fluent are not this turbulent Prandtl number Prt defined here, hence the Prt would be a results of the calculation and not a property defined before the calculation? Last edited by Ravenn; April 3, 2013 at 12:40.

April 3, 2013, 12:50		#5
pete Administrator Peter Jones Join Date: Jan 2009 Posts: 682 Rep Power: 10	In laminar flow the viscosity is used to compute the heat-flux using Fourier's law and a laminar, well defined, Prandtl number $Pr \equiv \frac{C_p \mu}{\lambda}$ as: $q_j = -\lambda \frac{\partial T}{\partial x_j} \equiv -C_p \frac{\mu}{Pr} \frac{\partial T}{\partial x_j}$ Most turbulence models just give a turbulent eddy viscosity $\mu_t$ . By setting a turbulent Prandtl number the turbulent heat flux can be estimated in the same way by just using the turbulent eddy viscosity that the turbulence mode predicts: $q_j^{turb} \equiv C_p \overline{\rho u''_j T} \approx - C_p \frac{\mu_t}{Pr_t} \frac{\partial \widetilde{T}}{\partial x_j}$ Using a constant turbulent Prandtl number is a simplification and it is not fully correct. Experimentally a value of something close to 0.9 has been measured. You can find more information and further references here: http://en.wikipedia.org/wiki/Turbulent_Prandtl_number jzc, PJTsai, pavlossemelides and 1 others like this.

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April 3, 2013, 11:57		#2
oj.bulmer Senior Member OJ Join Date: Apr 2012 Location: United Kindom Posts: 473 Rep Power: 20	Can you give more information about the paper you are referring to? OJ

April 3, 2013, 18:18		#6
Ravenn New Member Join Date: Jan 2013 Posts: 11 Rep Power: 13	So, I've post-processed 2 different calculations, one with the default values for energy and wall Prandtl number, and the other with energy and wall Prandtl number set to 0.9. I've read carefully fluent user manual and here is what I understood: - $k_{eff} = k + k_T$ - $\mu_{eff} = \mu + \mu_T$ - $Pr_{eff} = C_p \frac{\mu_{eff}}{k_{eff}}$ In Fluent, it is possible to obtain $k_{eff}$ , and $\mu_T$ . With these values on a line normal to a surface, I've calculated $k_{T} = k_{eff}-k$ and then $Pr_{T} = Cp \frac{\mu_T}{k_T}$ . It appears that for the first calculation, $Pr_{T}=0.85$ outside the laminar part of boundary layer, which is the value of energy and wall Prandtl numbers. For the second calculation where I changed the value of energy and wall Prandtl numbers to 0.9, $Pr_{T}=0.9$ outside the laminar part of boundary layer. In the laminar part of boundary layer, $k_{T}=0$ , hence $Pr_{T}$ is undefined, or very high. I'm wondering now what is the value of $Pr_{T}$ in the laminar part of boundary layer for the papers where $Pr_{T}$ is said to be fixed to 0.9. In my opinion it depends on which parameter is used to calculate the other: - $Pr_{T}$ , fixed to 0.9, and $\mu_{T}$ are used to calculate $k_{T}$ (papers) - $\mu_{T}$ and $k_{T}$ are calculated by the turbulence model, and $Pr_{T}$ can be deduced with the same procedure I used. (Fluent)

May 23, 2016, 14:06		#7
Shamoon Jamshed Senior Member Shamoon Jamshed Join Date: Apr 2009 Location: Karachi Posts: 381 Rep Power: 18	Dear Ravenn I was facing the same issue. I used two turbulence models, kepsilon and k-omega SST. I was getting incorrect Nu from the komega. So I decreased very much the Prt and got my result close to experiment. But since I used very low value (0.35) I am still doubtful. Are you still working on that too? yuor post seems 3 years old

May 24, 2016, 16:57		#8
Ravenn New Member Join Date: Jan 2013 Posts: 11 Rep Power: 13	Hello Shamoon, I'm sorry but it's been a while since I last worked on this subject (almost 3 years as you see) and I don't really remember everything, I've rediscovered the subject with your question. It appears I still receive the alerts for this post^^ Good luck for your research!

July 19, 2016, 12:36		#10
Shamoon Jamshed Senior Member Shamoon Jamshed Join Date: Apr 2009 Location: Karachi Posts: 381 Rep Power: 18	In the model--> viscous select k-epsilon then select realziable On the right side there is a list of constants among which Energy and Wall Prandtal numbers are there

June 20, 2017, 12:13		#15
vcvedant Member Vedamt Chittlangia Join Date: Feb 2016 Posts: 64 Rep Power: 9	Turbulent Prandtl number affects the heat transfer calculations as it is used to calculate turbulent heat flux. A experiment based variable turbulent Pr number correlation can be used as given by Kays & Crawford. It can be added to Fluent using UDF: DEFINE_PRANDTL_T(Prt, c, t) { Prt = [some expression]; return Prt; } It can be added by compiling/interpreting this UDF and adding the new Prandtl number from Models->Viscous->k-e (or any other) -> drop down menu for Temperature Prandtl number