Two-dimensional incompressible fluid flow around a rectangular shape placed over a larger rectangular shape is analyzed numerically. The vortex shedding is investigated at different arrangements of the two shapes. The calculations are carried out for several values of Reynolds numbers from low values up to 52. At low Reynolds number, the flow remains steady. The flow characteristics are analyzed for each configuration. The analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a bifurcation. It is observed that the transition to unsteady regime is performed by a Hopf bifurcation. The critical Reynolds number beyond which the flow becomes unsteady is determined for each configuration.

The fluid flow over three staggered square cylinders at two symmetrical arrangements has been numerically investigated in this study. The numerical calculations are carried out for several values of the Reynolds number (Re) ranging from 1 to 180. The results are presented in the form of vorticity contours and temporal histories of drag and lift coefficients. Furthermore, the physical parameters, namely, the average drag and lift coefficients and Strouhal number are presented as a function of Re. Two different states of flow are found in this work by systematically varying Re: steady and unsteady states. The transition to unsteady state regime is exhibited via Hopf bifurcation first in the second configuration followed consequently by the first one with critical Reynolds number of Re[Formula: see text] and Re[Formula: see text], respectively. It is observed that the bifurcation point of the steady regime to the unsteady one is very much influenced by the change in the geometry of the obstacle. The unsteady periodic wake is characterized by the Strouhal number, which varies with the Reynolds number and the obstacle geometry. Hence, the values of vortex shedding frequencies are estimated for both the considered configurations. Computations obtained also reveal that the spacing in the wake leads to reducing the pressure and enhancing the fluid flow velocity for both arrangements by monotonically strengthening the Reynolds number value. Furthermore, the drag and lift coefficients are determined, which allowed determining; the best configuration in terms of both lift and drag. It is observed that the drag force is dependent on the obstacle geometry and strengthens while lowering the Reynolds number. On the other hand, an opposite trend of the lift drag evolutions is observed for both configurations and considerably affected by the arrangements shape.

Purpose Two-dimensional incompressible fluid flows around a rectangular shape placed over a larger rectangular shape at low Reynolds numbers (Re) have been numerically analyzed in the present work. The vortex shedding is investigated at different arrangements of the two shapes allowing the investigation of three possible configurations. The calculations are carried out for several values of Re ranging from 1 to 200. The effect of the obstacle geometry on the vortex shedding is analyzed for crawling, steady and unsteady regimes. The analysis of the flow evolution shows that with increasing Re beyond a certain critical value, the flow becomes unstable and undergoes a bifurcation. This paper aims to observe that the transition of the unsteady regime is performed by a Hopf bifurcation. The critical Re beyond which the flow becomes unsteady is determined for each configuration. A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed determining; the best configuration in terms of both drag and lift. The unsteady periodic wake is characterized by the Strouhal number, which varies with the Re and the obstacle geometry. Hence, the values of vortex shedding frequencies are calculated in this work. Design/methodology/approach The dimensionless Navier–Stokes equations were numerically solved using the following numerical technique based on the finite volume method. The temporal discretization of the time derivative is performed by an Euler backward second-order implicit scheme. Non-linear terms are evaluated explicitly; while, viscous terms are treated implicitly. The strong velocity–pressure coupling present in the continuity and the momentum equations are handled by implementing the projection method. Findings The present paper aims to numerically study the effect of the obstacle geometry on the vortex shedding and on the drag and lift forces to analyze the flow structure around three configurations at crawling, steady and unsteady regimes. Originality/value A special attention is paid to compute the drag and lift forces acting on the rectangular shapes, which allowed determining; the best shapes configuration in terms of both drag and lift.

Two-dimensional, incompressible fluid flow past a circular cylinder, having a variable diameter, is analyzed numerically at low Reynolds numbers (Re). The Reynolds number is based on the cylinder diameter and free-stream velocity. Numerical outcomes demonstrate that at low Reynolds number, the flow remains steady. Analysis of the flow evolution also shows that with enhancing Re beyond a certain critical value, the flow becomes unstable and undergoes a Hop bifurcation. The critical Reynolds number beyond which the flow becomes unsteady is determined for each configuration by an extrapolation procedure. A nonuniform variation of the critical Reynolds number (Rec) with the diameter is observed. On the other hand, it is observed that elongating the diameter of the cylinder leads to increasing the critical Reynolds number. It was also noted that the variation of the diameter value has a significant influence on the different regimes criteria as well as on the vortex detachment. Besides, it is seen that the diameter variation may lead to the birth of vortices with different oscillating frequencies due to the increase of the cylinder diameter that modifies considerably the Strouhal number.