Large eddy simulation of turbulent flow and heat transfer in a square duct with unstable natural convection on the cross section

In this paper, large eddy simulations with the dynamic Smagorinsky eddy viscosity model are performed for a fully developed turbulent flow and heat transfer in a square duct with unstable natural convection on the cross section at a turbulent Reynolds number of 400, a Prandtl number of 0.7 and different Grashof numbers from 10⁵ to 5 × 10⁷. The MPI parallel programming language is implemented to speed up the calculations. The influences of the buoyancy force on the mean flow and heat transfer, turbulent intensity and Reynolds stresses are analyzed. The results show that the mean velocity decreases while the subgrid viscosity, turbulent intensity and heat transfer increase obviously with the increase of Grashof number. The turbulent intensity in the streamwise direction decreases considerably in the near-wall region while the turbulent intensity in the spanwise direction increases clearly in almost whole regions with an increase in Grashof number. The spatial distribution of Reynolds stresses are mainly influenced by the thermal buoyancy force. The turbulence production rate and the buoyancy force production term of Reynolds stress component 〈v'v'〉 increase with the increase of Grashof number.