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The two-dimensional asymmetrical flow in a two-sided lid-driven square cavity is numerically analyzed by the finite volume method (FVM). The top and bottom walls slide in parallel and antiparallel motions with various velocity ratio (UT/Ub=λ) where |λ|=2, 4, 8, and 10. In this study, the Reynolds number Re1 = 200, 400, 800 and 1000 is applied for the upper side and Re2 = 100 constant on the lower side. The numerical results are presented in terms of streamlines, vorticity contours and velocity profiles. These results reveal the effect of varying the velocity ratio and consequently the Reynolds ratio on the flow behaviour and fluid characteristics inside the cavity. Unlike conventional symmetrical driven flows, asymmetrical flow patterns and velocity distributions distinct the bulk of the cavity with the rising Reynolds ratio. For λ>2, in addition to the main vortex, the parallel motion of the walls induces two secondary vortices near the bottom cavity corners. however, the antiparallel motion generates two secondary vortices on the bottom right corner. The parallel flow proves affected considerably compared to the antiparallel flow.

The main purpose of this study is to numerically investigate the Prandtl number effect on mixed convection in a horizontal channel heated from below using the thermal lattice Boltzmann method (TLBM). The double-population model with two different lattices is used, in particular, the D2Q9 for the velocity field and D2Q5 for the thermal field. The developed lattice Boltzmann method code to simulate the fluid flow and heat transfer in the channel was validated with available literature results based on classical numerical methods, especially the finite volume method for Pr = 6.4 and the finite difference method for Pr = 0.667. The results obtained with the TLBM have shown good agreement with the conventional methods cited. The dynamic and thermal characteristics of the fluid flow were examined in the field of low Prandtl number, such that 0.05 ≤ Pr ≤ 0.667, and also compared to Pr = 6.4; for Ra = 2420 and 7400, the Reynolds number was fixed at 1. The results showed that the influence is relatively significant for the dynamic structure of flow convection for Pr ≤ 0.3 and is little influential beyond this value.

In this paper, the case of the steady two-dimensional flow in a two-sided lid-driven square cavity is numerically investigated by the finite volume method (FVM). The flow motion is due to the top and bottom horizontal walls sliding symmetrically in the opposite direction with equal velocities, UT and UB, obtained through three respective Reynolds numbers, Re1,2=10000, 15000, and 20000. Due to the lack of availability of experimental results in this Reynolds number margin for this type of flow, the problem is first examined by considering that the flow is turbulent with the inclusion of four commonly used RANS turbulence models: Omega RSM, SST k-ω, RNG k-ε and Spalart-Allmaras (SA). Next, the regime is considered being laminar in the same range of Reynolds numbers. A systematic evaluation of the flow characteristics is performed in terms of stream-function contour, velocity profiles, and secondary vortices depth. Examination of the calculation results reveals the existence of a great similarity of the predicted flow structures between the Omega RSM model and those from the laminar flow assumption. On the other hand, the computed flow with the SST k-ω model, the RNG k-ε model, and the SA model reveals a remarkable under-prediction which appears clearly in the size and number of secondary vortices in the near-wall regions. Various benchmarking results are presented in this study.

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