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fix(SU2_CFD, Common): Fix physical correctness, robustness, and MDO compatibility #2669
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Show me the derivation of the CHT boundary condition from first principles.
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In the flamelet model with preferential diffusion enabled, the total diffusive heat flux$\vec{q}$ is not governed solely by Fourier's law ($-\lambda \nabla T$ ). Instead, it includes the contribution of species enthalpy transport due to differential diffusion: $$\vec{q} = -\lambda \nabla T + \sum h_i \rho Y_i \vec{V}_i$$ Substituting Fick’s law with differential diffusion coefficients $D_i$ : $$\vec{q} = -\lambda \nabla T - \sum h_i \rho D_i \nabla Y_i$$
In the Flamelet Generated Manifold (FGM) approach, species mass fractions$Y_i$ are functions of the controlling variables. When these terms are projected onto the enthalpy equation used in SU2, an effective thermal conductivity $\lambda_{eff}$ is defined to maintain consistency with the interior discretisation.
Specifically,$\beta_{enth, thermal}$ is the manifold-derived correction factor such that $\lambda_{eff} = \lambda \cdot \beta_{enth, thermal}$ captures the part of the heat flux aligned with the temperature gradient while accounting for the differential species diffusion.
For the CHT (Conjugate Heat Transfer) boundary condition, first principles require the matching of heat fluxes at the interface:$q_{fluid} = q_{solid}$ . To ensure energy conservation and consistency with the interior Viscous_Residual implementation (see CSpeciesFlameletSolver.cpp:726-729), the fluid-side heat flux $q_{fluid}$ must be calculated using the same $\lambda_{eff}$ . Neglecting this term at the wall would result in a non-conservative flux balance at the interface.