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The transport mechanism of concentration over an array of cylinders is investigated numerically for a transient low-Reynolds-number flow (Re = 1). This study is motivated by the olfactory sensing of antennules and their bio-inspired applications to chemical sensors. Two types of arrays, a single column of three cylinders and a square array of three by three cylinders, are used as simplified models for collecting concentration, and geometrical parameters such as gap size between the cylinders and initial distance between a concentration patch and the cylinder array are considered to evaluate how they change the concentration flux into the cylinders. The cumulative concentration flux of the array and the spatial distribution of concentration on the surface of the cylinder are compared between low and high Peclet numbers, Pe = 1 and 1000. For the low Peclet number, the flux efficiency is negatively affected by small gaps between the cylinders because the incoming concentration patch detours around the array due to hydrodynamic blockage in the gaps. By contrast, for the high Peclet number, the concentration flux benefits from entrapment of the patch over an extended period inside the array with narrow gaps, and thus, the flux efficiency can be superior to that of a single isolated cylinder. The flux efficiency of the array is in the inverse relationship with the initial distance of the patch from the cylinder array, and the high Peclet number exhibits a more notable drop in the flux efficiency with an increase in initial distance.

We perform two-dimensional simulations of unsteady flow separation around a NACA0015 airfoil. We consider five different angles of attack, 10°, 12.5°, 15°, 17.5°, and 20°, with the Reynolds number varying from 100 to 1300. The central aim is to study the wake dynamics under the low-Reynolds-number condition, when the flow is most likely experiencing transitions between different states. For the low angles of attack of α = 10° and α = 12.5°, we find different branches on the Strouhal-Reynolds number relationship curves. Specifically, for α = 10°, we identify four distinct branches, marked with L1 to L4, in which the second discontinuity between L3 and L4 is proved to be hysteretic, characterized by the wake deflection. The branches L1 and L2 differ from the other two in the near-body flow topology, with the “trailing-edge vortex” mode for the first two, while the “separation vortex” mode for the last two. For the high angles of attack, α = 15°, 17.5°, and 20°, we cannot find marked discontinuity on the Strouhal-Reynolds number relationship curve. We further demonstrate that the flow transits to a chaotic state by a sequence of successive period-doubling bifurcations at α = 20°. Our results suggest that the operation of micro unmanned air vehicles in very low Reynolds numbers should be treated with caution because the flow is very sensitive to the Reynolds number, as well as the angle of attack.We perform two-dimensional simulations of unsteady flow separation around a NACA0015 airfoil. We consider five different angles of attack, 10°, 12.5°, 15°, 17.5°, and 20°, with the Reynolds number varying from 100 to 1300. The central aim is to study the wake dynamics under the low-Reynolds-number condition, when the flow is most likely experiencing transitions between different states. For the low angles of attack of α = 10° and α = 12.5°, we find different branches on the Strouhal-Reynolds number relationship curves. Specifically, for α = 10°, we identify four distinct branches, marked with L1 to L4, in which the second discontinuity between L3 and L4 is proved to be hysteretic, characterized by the wake deflection. The branches L1 and L2 differ from the other two in the near-body flow topology, with the “trailing-edge vortex” mode for the first two, while the “separation vortex” mode for the last two. For the high angles of attack, α = 15°, 17.5°, and 20°, we cannot find marked discontinuity on the Str...

Low Reynolds number flow over rectangular cavities is analyzed. The problem is posed to simulate towing tank experiments of Taneda [J. Phys. Soc. Jpn. 46, 1935 (1979)]. A very good agreement exists between numerical and experimental results. The dividing streamline separates from the cavity side wall below the upper corner. The separation point moves toward this corner when the aspect ratio decreases. Flow structure inside the cavity changes considerably with the aspect ratio. Only corner vortices exist in a cavity of aspect ratio W/h=4.0. A decrease of the aspect ratio leads to the enlargement and eventual merger of these vortices. The merger begins with the formation of a stagnation point separating two vortex centers inside the cavity. These vortex centers become progressively weaker and merge to form a single central vortex in a cavity of aspect ratio W/h=2.0. Further decrease of the aspect ratio results in the enlargement of the new corner vortices and their eventual merger. This process begins in a cavity of aspect ratio between 0.6 and 0.575 and is finished in a cavity of aspect ratio 0.5, where two central vortices have been identified. The further decrease of the aspect ratio leads to the sequential repetition of this process and creation of additional central vortices.

The low Reynolds number flow of a gas past an infinite heated circular cylinder is studied for the case of variable property flow when the temperature difference between the cylinder and free stream is small. The perturbation to the corresponding incompressible velocity field is calculated by the method of matched asymptotic expansions developed by Kaplun, and Proudman and Pearson. When the temperature difference between the cylinder and free stream is appreciable, a solution for the velocity field is found on the assumption that the viscosity and thermal conductivity of the gas are invariant. This solution possesses the interesting property that the zero‐order solution for the velocity field near the cylinder is a uniformly valid solution of the problem.

The Stokes region (where diffusion dominates) is shown to contain two subregions of distinct character—an inner region near the cylinder where the variable transport properties of the gas are of secondary importance and an intermediate region (remainder of Stokes region) where they are of primary importance.