Numerical study of forced turbulent heat convection in a straight square duct

This paper presents the coarse-grid direct numerical simulation (c-DNS) of forced turbulent heat convection in a straight square duct (SSD) at a bulk Reynolds number of 104. The temperature was considered as a passive scalar due to the neglect of the buoyancy effect. This c-DNS based on the recent nonstandard analysis of turbulence was carried out in a staggered grid system with a projection method on the basis of finite difference. To reduce numerical errors due to the staggered grid arrangement and enhance the finite difference accuracy, the grid-dependent interpolation remainders were derived in the calculation of cross-convection velocities by using Taylor expansion. These remainders were used to design an improved fourth-order upwind scheme for the finite difference of convection terms. The c-DNS results show that the novel numerical scheme can give satisfactory solutions of the turbulent SSD flow with passive scalar transport under an isoflux condition. The predicted mean Nusselt number is excellently consistent with the value based on the published correlations. The effect of the mean secondary flow can significantly increase the ratio between the temperature and velocity dissipation time scales in the corner region between the mean secondary counter-rotating vortices.