Coherence Measurements in an Axisymmetric Wake

DIES of the structure of the wake behind axisymmetric lurit-based bodies extend over a period of many years. Much of the early work concentrated on low Reynolds number flow (e.g., see Ref. 1) and was mainly confined to flow visualization studies. A notable exception is the work of Winny2 who examined concurrent signals from two hot wires in an attempt to detect the wake structure behind a sphere, at high Reynolds numbers. More recently a number of experimental studies of axisymmetric wake flows at high Reynolds numbers have been published3"9 and various aerospace problems which have arisen in the last few years have stimulated renewed interest in this aspect of bluff-body aerodynamics.9 Previous studies have established, by spectral analysis of single hot wire signals, that a definite periodicity exists in axisymmetric wake flows behind blunt-based bodies but the actual wake structure, for Reynolds numbers above a few hundred, is still unknown. It has been suggested by Calvert 7 and others5 that the analysis of concurrent signals from two hot wires, and in particular the cross-spectral analysis of such signals, is likely to yield considerable information on the wake structure. The purpose of this Note is to report the results of a series of such measurements. This approach is, of course, in the spirit of Winny's early work but advantage can now be taken of developments which have occurred in hot wire instrumentation and in the statistical analysis of random signals. Winny's work was restricted to a visual examination of concurrent hot wire signals and this enabled only very rough estimates of phase relationships to be made. In contrast, in the present work, the very powerful techniques of digital spectral and cross-spectral analysis are employed to yield precise quantitative information on the frequency dependence of the correlation and phase relationships between hot wire signals. 2. Experimental Equipment The experimental measurements were performed in a closed circuit wind tunnel having a test section measuring 3 ft square by 14.5 ft long. The background turbulence intensity was less than 0.5% throughout the test section. A 3-in.-diam stainless steel disk, with a sharp edged upstream face, was mounted on wires, normal to the flow, at a position 6 ft downstream of the inlet to the test section, and in the center of the tunnel. By observing the reflection of a pair of crossed wires in the highly polished upstream face of the disk, with a telescope, this face was accurately aligned to be normal to the centerline of the tunnel test section.