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

A low Reynolds number turbulence stress and heat flux equation model has been developed to enhance its predictive efficiency and accuracy. Conventional low Reynolds number models need very fine mesh width adjacent to a wall in order to maintain the accuracy of calculations. This need mainly arises from the boundary condition for dissipation rate of turbulent kinetic energy, ε. To improve the capability upon application of a coarse mesh for practical model use, a new method for providing the boundary condition for ε is proposed in this study, based on a DNS data base. The presented method is validated through comparisons of calculated to DNS result for a turbulent plane channel flow, and correlations for constant property gas flow and liquid sodium flow in a circular pipe. The pipe flows are accompanied by turbulent-laminar transition. Therefore the predicted critical Reynolds number is also examined. The calculated results using the present model are in close agreement with DNS, analytic and empirical correlations for pipe flows. We also show that a mesh width about 10 times larger than that used in existing models is applicable by using the present boundary condition. (author)