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The overall aim intended of the present work is to simulate an incompressible laminar flow and thermal transfer in a constricted channel. A double multiple relaxation time (DMRT) thermal lattice Boltzmann method is carried out on this problem. The application of this method will be performed using a multiple relaxation time D2Q9 and D2Q5 model to simulate numerically the flow field and the thermal field, respectively. This paper deals with various interesting features of the flow and temperature fields in the constricted channel to describe the fluid behavior. Furthermore, the effects of several parameters (Reynolds number, height of constricted part...) were studied and discussed in detail in order to find some improvements about the heat transfer mechanism in the presence of the constricted part.

A numerical study of a two-dimensional laminar flow and heat transfer characteristics in a horizontal channel containing two in-line obstacles of different shapes, namely an upstream triangular cylinder and a downstream square cylinder, was carried out. It is based on a coupling between the Lattice Boltzmann Method (LBM) and the Finite Difference Method (FDM). The airflow (Pr = 0.71) is assumed to be laminar and incompressible. All physical properties of the fluid, expect its density, are supposed to be constant. The two cylinders are kept at a constant hot temperature, while the incoming flow is at a cold temperature. The Reynolds number and the horizontal separation distance between the cylinders are varied to investigate their influences on fluid flow and heat transfer.

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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.