Development of a low Reynolds number turbulence stress and heat flux equation model; A New type wall boundary condition for dissipation rate of turbulent kinetic energy aided by DNS data base

Nishimura, Motohiko

To predict thermal-hydraulic phenomena in actual plant under various conditions acculately, adequate simulation of laminar-turbulent flow transition is of importance. A low Reynolds number turbulence model is commonly used for a numerical simulation of the laminar-turbulent transition. The existing low Reynolds number turbulence models generally demands very thin mesh width between a wall and a first computational node from the wall, to keep accuracy and stability of numerical analyses. There is a criterion for the distance between the wall and the first computational node in which non-dimensional distance y must be less than 0.5. Due to this criterion the suitable distance depends on Reynolds number. A liquid metal sodium is used for a coolant in first reactors therefore, Reynolds number is usually one or two order higher than that of the usual plants in which air and water are used for the work fluid. This makes the load of thermal-hydraulic numerical simulation of the liquid sodium relatively heavier. From above context, a new method is proposed for providing wall boundary condition of turbulent kinetic energy dissipation rate . The present method enables the wall-first node distance 10 times larger compared to the existing models. A function of the wall boundary condition has been constructed aided by a direct numerical simulation (DNS) data base. The method was validated through calculations of a turbulent Couette flow and a fully developed pipe flow and its laminar-turbulent transition. The predicted critical Reynolds number lay between 2300 and 2500, where commonly known value 2,320 was included. The error of the calculated Nusselt number and friction factor were comparable to uncertainties of empirical correlations. Thus the present method and modeling are capable of predicting the laminar-turbulent transition with less mesh numbers i.e. lighter computational loads.