Search

(1986). Low Reynolds Number Flow Heat Exchangers. Nuclear Technology: Vol. 73, No. 1, pp. 129-130.

Jeffery's solution in bi-polar co-ordinates of the two-dimensional Stokes equations cannot be applied to the low-Reynolds-number flow past two parallel circular cylinders because of severe mathematical difficulties. These difficulties can be overcome by considering the flow field far from the cylinders and then modifying the solution near the cylinders so that it becomes the inner expansion for an application of the method of matched asymptotic expansions. After the calculation of the drag, lift and moment coefficients of two adjacent equal circular cylinders to O(1) in the Reynolds number R, the analysis is extended to incorporate partially the effects of fluid inertia of order R. The results show fairly good agreement with Taneda's experimental data.

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.