Flow About a Pair of Adjacent, Parallel Cylinders Normal to Stream. Theoretical Analysis

摘要

To account for the behavior of a pair of adjacent parallel cylinders normal to a stream, a photographic study of the wake was undertaken. Three types of wake were found, only one of which could cause the cylinders of the pair to vibrate transversely with a phase difference of 180 degrees. By investigating theoretically a necessary condition for the stability of four rows of vortices, criteria were found from which the type of wake can be predicted. In the case of laminar flow in the boundary layer of the cylinders, there is only a small range of the spacing-diameter ratio of the cylinders, about 1.5, in which the proper wake for the cylinders to vibrate 180 degrees out of phase is obtained. When the boundary-layer flow is turbulent, however, the proper wake can be obtained for all space-diameter ratios that are, roughly, less than unity. These conclusions are in complete agreement with both the photographic study of the wake and the observed behavior of adjacent parallel cylinders. The speed and spacing of the vortices in the wake of two parallel cylinders were measured from the photographs and the Strouhal numbers and drag coefficients were calculated. The Strouhal numbers are about 1/3 larger than those for a single cylinder. The variation of the drag coefficient with spacing is in good agreement with directly determined experimental values. (Author)