Investigation on third-order diffusion models for prediction of turbulent thermal dispersion behind a line heat source

Abstract

Second-order Reynolds stress/heat flux closure models are applied to predict the turbulent thermal dispersion behind a line heat source in a uniformly sheared flow and behind a cylinder in a uniform velocity flow : closure models are investigated for $\overline{u_iu_j^θ}$ and $\overline{u_iθ^2}$ which appear in the second moment equations for the Reynolds stress $\overline{u_i u_j}$, scalar flux $\overline{u_iθ}$ and scalar variance $\overline{θ^2}$. The exact governing equations for Reynolds stress, heat flux and other scalar fluctuating quantities are formulated and modeled. The concept of effective buoyancy Reynolds stress ▷수식 삽입◁(원문을 참조하세요) is introduced to incorporate the buoyancy effect in the turbulent thermal diffusion. In addition, buoyancy effect ▷수식 삽입◁(원문을 참조하세요) is considered also in time scale in order to consider the suppression effect in stable area of turbulent flow. The model predictions are compared with the relevant experiments. The simple gradient transport model predictions are also included for comparison. The predictions for the proposed models were compared with the two experiments for the turbulent wake behind a line heat source and a cylinder in a uniformly sheared flow. For the weekly shear flow, the calculated results are acceptable although there is some discrepancy between calculation and measurement for the turbulent shear stress. It was found that the present model proposed in this study yields much better numerical values when applied to predict third-order transport terms in the vertical direction like $\overline{ν^2θ}$, $\overline{νθ^2}$ in comparison with the simple gradient model. For all the variables in a wake flow behind a cylinder experiment, the agreement between prediction and measurement is also very excellent. Therefore, the adopted second-order thermal turbulence model is capable of simulating the thermal dispersion in free wake flows. As compared with the simple gradient model, it was revealed that the present mod...