Turbulence Prandtl Number Prt

Techies · July 4, 2021, 10:41

Hi everyone,
I'm simulating heat transfer and i have some questions.
What is Turbulence Prandtl Number and how to specify it ?
What is different between using Prt and no using Prt?
Thanks all

LuckyTran · July 4, 2021, 18:00

When you do Reynolds Averaging, turbulence stresses appear that need to be modeled with closure models. For the momentum equations, it ends up being a model for the turbulent viscosity. For the energy equation, you also need a model for the turbulent conductivity (or turbulent thermal diffusivity).

Usually, we calculate the turbulent conductivity from the turbulent viscosity by the turbulent Prandtl number the same way you can calculate conductivity from molecular viscosity if you prescribe a Prandtl number.
$Pr_t=\frac{\nu_t}{\alpha_t}$

If you are doing RANS and simulating heat transfer, you'll almost always have a turbulent Prandtl number unless have your own special turbulent heat flux model.

The value of the turbulent Prandtl number is flow dependent but it typically is in the range of 0.8-0.9 (but not always and it is not universal). In general, it needs its own model.

Tian Hongkang · November 20, 2021, 07:51

Quote:

Originally Posted by LuckyTran

When you do Reynolds Averaging, turbulence stresses appear that need to be modeled with closure models. For the momentum equations, it ends up being a model for the turbulent viscosity. For the energy equation, you also need a model for the turbulent conductivity (or turbulent thermal diffusivity).

Usually, we calculate the turbulent conductivity from the turbulent viscosity by the turbulent Prandtl number the same way you can calculate conductivity from molecular viscosity if you prescribe a Prandtl number.
$Pr_t=\frac{\nu_t}{\alpha_t}$

If you are doing RANS and simulating heat transfer, you'll almost always have a turbulent Prandtl number unless have your own special turbulent heat flux model.

The value of the turbulent Prandtl number is flow dependent but it typically is in the range of 0.8-0.9 (but not always and it is not universal). In general, it needs its own model.

Thanks for your answer, do you know where I can change the constant Prt to my own models in OpenFOAM?

LuckyTran · November 20, 2021, 14:45

Answered already in your query in the Fluent forum.

cramr5 · April 5, 2023, 07:33

Quote:

Originally Posted by LuckyTran

The value of the turbulent Prandtl number is flow dependent but it typically is in the range of 0.8-0.9 (but not always and it is not universal). In general, it needs its own model.

Is that for Air only? what about for Fluids like Water or similar?

thanks

LuckyTran · April 5, 2023, 09:29

What this means? Give an example?

Turbulent Prandtl number is a property of the flow, not a fluid property. It's like asking whether velocity depends if it is air or water. Well yes it does, but also, what is even the question?

July 4, 2021, 10:41	Turbulence Prandtl Number Prt	#1
Techies Member Mercurial Join Date: Mar 2021 Posts: 72 Rep Power: 5	Hi everyone, I'm simulating heat transfer and i have some questions. What is Turbulence Prandtl Number and how to specify it ? What is different between using Prt and no using Prt? Thanks all

July 4, 2021, 18:00		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,677 Rep Power: 66	When you do Reynolds Averaging, turbulence stresses appear that need to be modeled with closure models. For the momentum equations, it ends up being a model for the turbulent viscosity. For the energy equation, you also need a model for the turbulent conductivity (or turbulent thermal diffusivity). Usually, we calculate the turbulent conductivity from the turbulent viscosity by the turbulent Prandtl number the same way you can calculate conductivity from molecular viscosity if you prescribe a Prandtl number. $Pr_t=\frac{\nu_t}{\alpha_t}$ If you are doing RANS and simulating heat transfer, you'll almost always have a turbulent Prandtl number unless have your own special turbulent heat flux model. The value of the turbulent Prandtl number is flow dependent but it typically is in the range of 0.8-0.9 (but not always and it is not universal). In general, it needs its own model. Techies likes this.

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LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,677 Rep Power: 66	What this means? Give an example? Turbulent Prandtl number is a property of the flow, not a fluid property. It's like asking whether velocity depends if it is air or water. Well yes it does, but also, what is even the question?