Direct Numerical Simulations of Turbulent Mixed Convection in Enclosures with Heated Obstacles

To simulate turbulent forced and mixed convection flows in complicated three-dimensional domains, a fast finite-volume high-order method based on the Chorin ansatz is developed. The Poisson solver, which is applied to compute the pressure, uses the separation of variables together with capacitance matrix technique as suggested in [Shishkina, Shishkin & Wagner, J. Comput. & Appl. Maths 2009 226, 336–344]. The developed numerical method generally allows to use hexahedral computational meshes, which are non-equidistant in all three directions and non-regular in any two directions. By means of Direct Numerical Simulations (DNS) we investigate instantaneous and statistical characteristics of turbulent forced and mixed convection flows which develop in parallelepiped convective cells with heated parallelepiped obstacles inside. Cold fluid comes into the cell through thin slits close to the top. The outlet slits are located close to the bottom. The working fluid is air with Prandtl number ℘r=0.714. The considered Grashof number $\mathcal{G}r=4.22\times10^{8}$ and Reynolds number based on the velocity of the inlet flow ℛe=2.37×104 and 1.18×104. It is shown that in the cases of forced and mixed convection principally different large-scale circulations of air are developed inside the domain, although the same geometry and the same Reynolds numbers are considered. In particular, for ℛe=2.37×104 a downward flow is developed in the case of forced convection, while mixed convection leads to an upward flow in the central part of the domain. Distribution of the mean heat fluxes at the surfaces of the obstacles is shown to be very irregular and strongly dependent on the positions of the surfaces (vertical or horizontal) as well as on their locations inside the domain.