Computational model for turbulent heat transfer in buoyancy-influenced flows at supercritical pressures in circular tubes

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Turbulent heat transfer at supercritical pressures in fluids flowing upward in heated circular tubes is very likely to be affected by buoyancy and, when this buoyancy is stronger than a certain value, mixed convection occurs. The turbulent mixed convection heat transfer is very complex, and none of the existing turbulence models can adequately simulates the experimental or DNS data including mixed convection. A hybrid turbulence model that blended two turbulence models, which used the Kolmogorov velocity scale and wall shear stress, respectively, has shown a good performance in predicting experiments or DNS. However, even the blended model has not been satisfactory for large buoyancy parameter (Bu). It is judged that the inadequacy is due to the treatment of the coefficient of the production term in the dissipation rate equation as a constant. The semi-local scaling concept has been found to be inadequate. As a remedy, the coefficient associated with the production term in the dissipation rate equation is treated as a function of turbulent boundary layer deformation and Bu, and an integrated density concept instead of local density is used in calculating friction velocity. The computational model improved from the previous blended turbulence model by introducing the two concepts satisfactorily predicts the DNS data.