[Tobi]

Hi all,

actually I don´t have a question but it would be nice to have someone who proofs my statement. Right now I am doing a rhoSimpleFoam calculation in an exhaust gas system. During the calculation, we solve for p, U, h. By knowing the fluxes, I am moving on with an own solver. There, I am solving the temperature equation as:

    cp
  *(
        ddt(rho, T)
     + div(phi, T)) 
    )
== 
    laplacian(lambdaEff, T);

The question arises about the effective thermal conductivity. While just using the laminar conductivity, everything is fine but as I do have a high turbulent flow, the heat transfer should be totally underpredicted. It is clear that the effective conductivity is:



The laminar one was calculated using the VDI Wärmeatlas. So actually it is dry air with 10 % of water and is implemented as a polynomial function of temperature. However, the turbulent thermal conductivity is not known out of the box. In the thermodynamic libraries of FOAM, I saw that kappaEff (which is the effective termal conductivity) is calculated as:

kappaEff = kappa + cp*alphat

During my rhoSimpleFoam calculation, the field alphat is calculated. Based on the fact that I do have the heat capacity field of my fluid, I would simply calculate the effective heat conductivity by:

• calculate the laminar thermal conductivity (kappa or lambda - my nomenclature is lambda; FOAM´s is kappa)
• calculate the turbulent thermal conductivity (cp * alphat)
• Summing both
• Done

Additionally, I made a test where I compared the chtMultiRegionFoam (with frozen flow - energy equation is solved) to my own solver (temperature equation is solved). In both equations the effective field in the laplacian term was used. At the end, both gave the same results (with some small errors).

However, doing so, the effective conductivity of the air is between 1e-3 W/m/K to 200 W/m/K which is very high and I have no experience if this value is a physical range.

Note, my fluid flow is high turbulent. I have around 50 m/s inside the pipes.


My Question
Can anyone confirm that I did the calculation of the turbulent thermal conductivity correct?

[Tobi]

Hi all,

I just confirm that the steps I did are correct.

[Santiago]

are you doing LES or RANS?

[Tobi]

I am doing RANS but it does not matter as the only difference is related to the mut calculation. Thus, alphaEff will change and that´s it.

[Santiago]

Originally Posted by Tobi

I am doing RANS but it does not matter as the only difference is related to the mut calculation. Thus, alphaEff will change and that´s it.

Well, those differences you're seeing are quite important. Are you using the Reynolds analogy for turbulent fluxes of vT?

[cryabroad]

Originally Posted by Tobi

Hi all,

I just confirm that the steps I did are correct.

Tobi,

I'm interested in this topic, when you mentioned confirming your steps, are you comparing your results to an experimental or a numerical case? I'm kind of surprised that no Prandtl number appears in your implementation, or maybe it's already included in the calculation of alphat by OpenFOAM? Sometimes I see people use both a laminar Prandtl number and a turbulent Prandtl number for the laminar part and turbulent part of the heat diffusion coefficients, respectively.

Thanks,

Ruiyan

[boundary93]

Do you use any wallfunction for alphat? I just noticed that my turbulent Prandtl number is always 1 if I dont use any. Because of that I implemented a function for the turbulent Prandlt number.



So do you keep the turbulent Prandtl number constant?