Asymptotic Expansions for Low Reynolds Number Flow past a Cylindrical Body

概要

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An incompressible stationary flow past a two-dimensional cylinder at low Reynolds number is analyzed by an asymptotic approach. In the previous work of the present authors the non-linear integral expressions of the generalized Oseen and Stokes limits were derived, so the main purpose of the present paper is to show that from these expressions we can obtain the same aerodynamic results as earlier ones, examine the overlap hypothesis by applying Kida's extension lemma, and confirm Skinner's theoretical results on the drag force which has been noted in the previous paper. We further show that we can bridge the 1/log Re series expansions of the solution to the next order which is of order Re including 1/log Re series expansion. In the present paper, a simple expression of the drag force of the first approximation is derived and it is available only by determining the Stokes solution. From the results for a circular cylinder, we have the following : the overlap hypothesis is satisfied, the simple expression of the drag force agrees remarkably well with experiments in a wide range of low Reynolds numbers, and there is a missing term in the second-order approximation of Skinner's theoretical result.
一般社団法人日本機械学会の論文
1992-05-15