DNS of Turbulent Channel Flow Obstructed by Rectangular Ribs

Abstract

A low Reynolds number flow in a channel obstructed by rows of ribs is of practical importance with respect to heat transfer enhancement. In order to obtain a high outlet gas temperature in a limited channel length, a flow rate should be low, whilst the flow should be turbulent to ensure an efficient heat transfer. Our preliminary study has indicated that the turbulence can be retained even at a low Reynolds number through the disturbance by the rows of the ribs in the channel. The ribs induce three-dimensional complex flow in their vicinity. The purpose of our research is to examine the influence of the ribs upon the flow and the temperature fields. Direct numerical simulation (DNS) of turbulent heat transfer in a fully developed channel flow has been performed at a friction Reynolds number of Reτ = 80 and a Prandtl number of Pr = 0.71, where Reτ is based on the friction velocity uτ0 , the channel half width δ and the kinematic viscosity ν. The friction velocity uτ0 is defined by the streamwise mean pressure gradient which drives the flow. The non-slip condition is adapted to the top and bottom walls. The periodic boundary condition is imposed in the horizontal directions. The rectangular rib is placed at the center of the computational domain (Fig. 1) and connected directly to both of the top and bottom walls. The rib is treated by the immersed boundary method. The constant wall temperature difference is applied for the temperature field. The flow rate decreases owing to the pressure drag of the rib, and the bulk Reynolds number Rem ( = um·2δ/ν ) drops down to 1120, where um is the bulk mean velocity. In the case of the plane channel without the rib, our additional calculation at this Rem has revealed that the flow becomes laminar. In the present case, the flow remains turbulent since the turbulent kinetic energy is produced in the vicinity of the rib. The instantaneous flow field is shown in Fig.1. Upstream of the rib, a horseshoe vortex is formed near the wall. The flow separates at the forward-edge of the rib. Downstream of the rib, a three-dimensional wake is formed, which contains a lot of vortices. Figure 2 shows the time-averaged local Nusselt number on the bottom wall. The heat transfer is significantly enhanced in front of the rib and the wake region. Upstream of the rib, the local Nusselt number is remarkably large. It indicates that the low temperature fluid in the central region is transported towards the bottom wall by the flow impingement induced by the rib. This region corresponds to that of the horseshoe vortex. In addition, Nu is large in the wake region as a consequence of effective mixing.