The objective of this research is to study the fluid flow control allowing the reduction of aerodynamic drag around a square cylinder using two parallel partitions placed downstream of the cylinder using the lattice Boltzmann method with multiple relaxation times (MRT-LBM). In contrast to several existing investigations in the literature that study either the effect of position or the effect of length of a single horizontal or vertical plate, this work presents a numerical study on the effect of Reynolds number (Re), horizontal position (g), vertical position (a), and length (Lp) of the two control partitions. Therefore, this work will be considered as an assembly of several results presented in a single work. Indeed, the Reynolds numbers are selected from 20 to 300, the gap spacing (0 ≤ g ≤ 13), the vertical positions (0 ≤ a ≤ 0.8d), and the lengths of partitions (1d ≤ Lp ≤ 5d). To identify the different changes appearing in the flow and forces, we have conducted in this study a detailed analysis of velocity contours, lift and drag coefficients, and the root-mean-square value of the lift coefficient. The obtained results revealed three different flow regimes as the gap spacing was varied. Namely, the extended body regime for 0 ≤ g ≤ 3.9, the attachment flow regime for 4 ≤ g ≤ 5.5, and the completely developed flow regime for 6 ≤ g ≤ 13. A maximal percentage reduction in drag coefficient equal to 12.5%, is given at the critical gap spacing (gcr = 3.9). Also, at the length of the critical partition (Lpcr = 3d), a Cd reduction percentage of 12.95% was found in comparison with the case without control. Moreover, the position of the optimal partition was found to be equal to 0.8d i.e. one is placed on the top edge of the square cylinder and the second one is placed on the bottom edge. The maximum value of the lift coefficient is reached for a plate length Lp = 2d when the plates are placed at a distance g = 4. On the other hand, this coefficient has almost the same mean value for all spacings between the two plates. Similarly, the root means the square value of the lift coefficient (Clrms) admits zero values for low Reynolds numbers and then increases slightly until it reaches its maximum for Re = 300.

A two-dimensional natural convection heat transfer in a square cavity having a hot square obstacle located centrally is investigated numerically by the lattice Boltzmann method. In this paper, the variables of interest like flow velocity and the temperature are treated using the MRT-D2Q9 model and the MRT-D2Q5 model, respectively. The left and right vertical walls are kept at the same cold temperature while the horizontal walls are assumed to be adiabatic. Concerning the bottom square block, a hot temperature is imposed. In the present research the Prandtl number is taken to be 0.71 corresponding to the air. The effects of Rayleigh number ( 10 ³ ≤ Ra ≤ 10 ⁶ ), dimension ( 0.2 ≤ W ≤ 0.8) and location ( 0.1 ≤ D ≤ 0.4) of the active block upon dynamic and thermal fields of fluid are examined. Detailed analysis of results reported in form of the distributions of streamlines, isotherms and local Nusselt are discussed. In general way, the modification of geometrical dimensions of the square block and its horizontal position disrupt the fluid flow and heat transfer structures. The increased block dimensions has enhanced the heat transfer due to increasing the surface area of the bottom block.

Numerical study of various physical phenomena in three dimensions has become a necessity to better understand the physical process than in two dimensions. Thus, in this paper, the code is elaborated to be adapted to the simulation of heat transfer in three dimensions. The numerical simulations are performed using a hybrid method. This method is based on the lattice Boltzmann approach for the computation of velocities, and on the finite difference technique for the calculation of temperature. The used numerical code is validated by examining the free convection in a cubic enclosure filled with air. Then, the analysis of the heat exchange between two cold vertical walls and a heated block located at the center of a cubic cavity is considered. The performed simulations showed that for a small value of the Rayleigh number (Ra=10³ for example), the fluid exchanges its heat almost equally with all hot surfaces of the obstacle. However, for large values of Ra (Ra≥10⁴), the numerical results found showed that the heat exchange rate is greater on the bottom face compared to the other faces of the obstacle.