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| 1 | +# Conjugate Heat Transfer (CHT) Capability |
| 2 | + |
| 3 | +This summarizes the design and details of the conjugate heat transfer capabilities |
| 4 | +with the linear finite volume system through the [SIMPLE.md] executioner. |
| 5 | + |
| 6 | +This capability is activated by specifying a boundary on the [!param](/Executioner/SIMPLE/cht_interfaces) |
| 7 | +parameter. Other cht-related parameters can control the iteration between the solid and fluid |
| 8 | +energy equations. Once the capability is activated it will check if the |
| 9 | +used boundary conditions are compatible or not. In general, we introduced CHT versions of |
| 10 | +common boundary conditions such as [LinearFVRobinCHTBC.md] and [LinearFVDirichletCHTBC.md] |
| 11 | +that are dedicated for CHT applications. |
| 12 | + |
| 13 | +For coupling purposes several new functors are created under the hood: |
| 14 | + |
| 15 | +- +heat_flux_to_solid_*+ (where * is the interface boundary name), |
| 16 | +- +heat_flux_to_fluid_*+ (where * is the interface boundary name), |
| 17 | +- +interface_temperature_solid_*+ (where * is the interface boundary name), |
| 18 | +- +interface_temperature_fluid_*+ (where * is the interface boundary name), |
| 19 | + |
| 20 | +where the first two describe the heat flux from one domain to the other, while the |
| 21 | +other express the interface temperatures from both sides. |
| 22 | + |
| 23 | +## Energy Conservation Equations |
| 24 | + |
| 25 | +The energy conservation equations for fluid and solid domains are: |
| 26 | + |
| 27 | +\begin{equation} |
| 28 | + \frac{\partial \rho h_f}{\partial t} + \nabla \cdot \left(\rho \mathbf{u} h_f \right) = \nabla \cdot \left(k_f \nabla T_f\right) + Q_f\,, |
| 29 | +\end{equation} |
| 30 | +\begin{equation} |
| 31 | + \frac{\partial \rho h_s}{\partial t} = \nabla \cdot \left(k_s \nabla T_s\right) + Q_s\,, |
| 32 | +\end{equation} |
| 33 | + |
| 34 | +Where $h_f = f(T_f)$ and $h_s = f(T_s)$ are the fluid and solid specific enthalpies, $k_f$ and $k_s$ are the thermal conductivities, and $Q_f$ and $Q_s$ are the external heat sources. |
| 35 | + |
| 36 | +## Boundary Conditions |
| 37 | + |
| 38 | +The coupling of the solid and fluid domains is done through boundary conditions that ensure: |
| 39 | + |
| 40 | +1. **Continuity of Interface Temperature** |
| 41 | + \begin{equation} |
| 42 | + T_\mathrm{f,wall} = T_\mathrm{s,wall} |
| 43 | + \end{equation} |
| 44 | + |
| 45 | +2. **Continuity of Conductive Flux at the Interface** |
| 46 | + \begin{equation} |
| 47 | + q_\mathrm{f,wall} = -q_\mathrm{s,wall} |
| 48 | + \end{equation} |
| 49 | + |
| 50 | +## Coupling Methods |
| 51 | + |
| 52 | +The methods currently recommended for CHT utilize [LinearFVDirichletCHTBC.md] and |
| 53 | +[LinearFVRobinCHTBC.md] in the two different ways listed below. The Robin BC can also |
| 54 | +emulate a Neumann BC by setting the [!param](/LinearFVBCs/LinearFVRobinCHTBC/h) parameter to 0. |
| 55 | + |
| 56 | +- +Neumann-Dirichlet Coupling+ |
| 57 | + |
| 58 | +!algorithm |
| 59 | +[!function!begin name=NeumannDirichletCoupling] |
| 60 | +[!state text=Initialize $T_\mathrm{fluid,wall}^0$, $q_\mathrm{solid,wall}^0$] |
| 61 | +[!while!begin condition=Convergence criteria not met] |
| 62 | +[!state text=1. Solve fluid equation] |
| 63 | +[!state text=2. Update heat flux from fluid to solid $q_\mathrm{s,wall}^n$] |
| 64 | +[!state text=3. Solve solid equation] |
| 65 | +[!state text=4. Update boundary temperature $T_\mathrm{f,wall}^n$] |
| 66 | +[!while!end] |
| 67 | +[!function!end] |
| 68 | + |
| 69 | +- +Robin-Robin Coupling+ |
| 70 | + |
| 71 | +!algorithm |
| 72 | +[!function!begin name=RobinRobinCoupling] |
| 73 | +[!state text=Initialize $T_\mathrm{fluid,wall}^0$, $q_\mathrm{s\rightarrow f}^0 = 0$] |
| 74 | +[!while!begin condition=Convergence criteria not met] |
| 75 | +[!state text=1. Solve fluid equation with Robin boundary condition using $T_\mathrm{s,wall}^{n-1}$ and $q_\mathrm{s\rightarrow f}^{n-1}$] |
| 76 | +[!state text=2. Update wall temperature $T_\mathrm{f,wall}^n$] |
| 77 | +[!state text=3. Update heat flux $q_\mathrm{f\rightarrow s}^n$] |
| 78 | +[!state text=4. Solve solid equation with Robin boundary condition using $T_\mathrm{f,wall}^{n}$ and $q_\mathrm{f\rightarrow s}^{n}$] |
| 79 | +[!state text=5. Update wall temperature $T_\mathrm{s,wall}^n$] |
| 80 | +[!state text=6. Update heat flux $q_\mathrm{s\rightarrow f}^n$] |
| 81 | +[!while!end] |
| 82 | +[!function!end] |
| 83 | + |
| 84 | + |
| 85 | +The Robin-Robin method introduces virtual heat transfer coefficients $h_f$ and $h_s$ to enhance stability and convergence. |
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