Application of four-equation closure for turbulent heat flux in prediction of convective heat transfer to hydrocarbon fuels at supercritical pressures

Abstract

Accurate modelling of the turbulent thermal fields is of great importance for simulations of convective heat transfer to fluids at supercritical pressures. The widely adopted Reynolds analogy between turbulent momentum transfer and turbulent heat transfer may fail for variable property flows under certain conditions, especially as the fluid approaches the pseudo-critical temperature (Tpc). In order to accurately predict the flow and heat transfer behaviors, the two-equation turbulence model for the thermal field by Hattori, Nagano, and Tagawa (HNT kt−εt) in association with the low-Reynolds number model for the velocity field by Myong and Kasagi (MK k−ε) were incorporated in an in-house code developed within the framework of OpenFOAM. Numerical simulations of convective heat transfer to supercritical pressure hydrocarbon fuels (RP-3 aviation kerosene and n-decane) in vertical heated tubes were performed using the MK-HNT model, MK k−ε model with Prt set as 1.0, and SST k−ω model with Prt set as 1.0. The validity of the models was examined through comparisons with the available experimental data under a variety of operating conditions. All three models performed reasonably well for the cases of normal heat transfer regime. Meanwhile, improvements in the prediction of inner wall temperature could be obtained by the use of the MK-HNT model for cases of heat transfer in the thermal entrance region, heat transfer enhancement (HTE) under forced convection conditions, and heat transfer deterioration (HTD) under mixed convection conditions. Moreover, the different heat transfer mechanisms were investigated by analyzing the predicted turbulent flow and thermal fields. The results indicated that the development of the thermal boundary layer in the entrance region and the drastic variation of specific heat and density in the trans-pseudo-critical region would have considerable effects on the distributions of the Reynolds stress and turbulent heat flux. In addition, it was found that the computational cost was not severely increased by solving two additional turbulence equations.