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How to Implement an Algebraic Turbulent Heat Flux Model in FLUENT

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Old   May 12, 2022, 03:39
Default How to Implement an Algebraic Turbulent Heat Flux Model in FLUENT
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jiangyanming
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Hello everyone, I'm working on an algebraic turbulent heat flux model for low Prandtl number fluids. Currently, some of the literature I've investigated uses OPENFOAM or STAR CCM+, and no one uses FLUENT to implement this model.

In Ansys Fluent, turbulent heat transport is modeled using the concept of Reynolds’ analogy to turbulent momentum transfer. The "modeled" energy equation is therefore given by:
\frac{\partial}{\partial t}(\rho E)+\frac{\partial}{\partial x_{i}}\left[u_{i}(\rho E+p)\right]=\frac{\partial}{\partial x_{j}}\left(k_{e f f} \frac{\partial T}{\partial x_{j}}+u_{i}\left(\tau_{i j}\right)_{e f f}\right)+S_{h}

For the standard and realizable k-e models, the effective thermal conductivity is given by:
k_{e f f}=k+\frac{C_{p} \mu_{t}}{P_{t}}

In the literature I researched, the Reynolds-averaged energy equation can be written as:
\frac{\partial\left(\rho c_{p} T\right)}{\partial t}+\frac{\partial\left(\rho c_{p} T u_{i}\right)}{\partial x_{i}}=\frac{\partial}{\partial x_{i}}\left[\left(k \frac{\partial T}{\partial x_{i}}\right)-\left(\rho c_{p} \overline{\theta u_{i}}\right)\right]

And the temperature flux model is based on an algebraic formulation for the turbulent heat flux and is given as:
\overline{\theta u_{i}}=-C_{t_{0}} \frac{k}{\varepsilon}\left(C_{t_{1}} \overline{u_{i} u_{j}} \frac{\partial T}{\partial x_{j}}+C_{t_{2}} \overline{\theta u_{j}} \frac{\partial U_{i}}{\partial x_{j}}+C_{t_{3}} \beta g_{i} \overline{\theta^{2}}\right)+C_{t_{4}} a_{i j} \overline{\theta u_{j}}

How can I change \overline{\theta u_{i}} in FLUENT to implement an algebraic turbulent heat flux model?

Thank you sincerely.
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