Vortex Frequency and Flow Pattern in the Wake of Two Parallel Cylinders at Varied Spacing Normal to an Air Stream

Abstract

The frequency of vortex formations in the flow about a pair of parallel cylinders, at various separations, is investigated with the hot wire anemometer. A resume of the literature on vortex frequencies is given with a view to relate the studies of obstacles of diverse shapes to the present case. The law of dynamical similitude is developed for individual solids, for the efflux through a rectangular orifice, for secondary eddies, and for the two-cylinder system. When two cylinders are separated by a gap just smaller than the diameter, instability occurs. At larger gaps the cylinders behave like independent bodies. As the gap is decreased, the main sequence of frequencies (probably generated on the outer sides of the cylinders) changes from a value corresponding to a single cylinder, of diameter d, to a value associated with a solid body of breadth equal 2d (at zero gap). A minimum frequency is reached at G/d =* 1 /n , where G is the gap distance. For gaps smaller than the critical, a formula is given to represent the main sequence: fd/U = 0.09 + ! l(G/d) y5]/[(£/<*) + 2 ] p where / is the frequency and U is the velocity. The picture is complicated by vortexes generated within the gap. At spacings less than one-half diameter, a low gap frequency is found. Between one-half and one diameter a high gap frequency is present, decreasing to the independent cylinder value at the critical spacing G/d = 1. In addition, doubled frequencies of the main sequence are also found, generally on the centerline of the wake, attributed to overlapping vortexes from the external sides of the cylinders. For all values of the gap, the dimensionless parameter fd/U is shown to be independent of Reynolds numbers greater than 15,000. Below this value, fd/U rises a t first and then drops sharply, the maximum apparently depending on the gap. The velocity distribution in the wake was obtained by traversing with a pitot static.tube. In a plane four diameters downstream from the center of the system, it was found that the wakes of both cylinders are mixed for gaps below the critical and separate for larger gaps. At G/d less than about one-half, the central pressure drop is great enough to cause the flow to reverse.