Energy separation in a vortex street

Abstract

When a bluff body is placed in a crossflow, the total temperature in its wake can become substantially less than the incoming one, as manifested by the fact that the recovery factorRon its rearmost surface takes negative values at high subsonic flow: this is the phenomenon referred to here as the Eckert-Weise effect. Although a vortex street has been a suspected cause, the issue of whether this is so, and what the mechanism is, has remained unsettled. In this experimental and theoretical investigation, we first examine the cause of the Eckert-Weise effect by enhancing the vortex shedding through acoustic synchronization: resonance between the vortex shedding and transversely standing acoustic waves in a wind tunnel. At the lowest synchronization, where a ringing sound emanates from the wind tunnel,Rat the rearmost section of the cylinder is found to become negative even at a Mach number of 0.2; the base pressure (Cpb) takes dips correspondingly, indicative of the intensification of the vortex street. At this lowest acoustic resonance, the decrease ofRandCpb, uniform along the span, agrees with the expectation based on the spanwise uniformity of the lowest standing wave. At the next acoustic resonance where the standing wave now varies along the span, the corresponding dips inRandCpb, non-uniform along the span, reveals an interesting ‘strip-theory’-like behaviour of the vortex intensities in the vortex street. These results correlating the change inRwithCpbconfirm that the Eckert-Weise effect is indeed caused by the vortex shedding, the mechanism of which is examined theoretically in the latter half of the paper.A simple theoretical argument, bolstered by a full numerical simulation, shows that the time-varying static pressure field due to the vortex movement separates the instantaneous total temperature into hot and cold spots located around vortices; once time-averaged, however, the total temperature distribution conceals the presence of hot spots and takes the guise of a colder wake, the Eckert-Weise effect. Therefore the correct explanation of the Eckert-Weise effect, a time-averaged phenomenon, emerges only out of, and only as a superposition of, instantaneous total temperature separation around vortices. Such a separation is not confined to the outside of vortex cores; every vortex in its entirety becomes thermally separated. Nor is it limited to the far downstream equilibrium configuration of the Kármán vortex street but applies to the important near-wake vortices, and to any three-dimensional vortical structure as well. For low subsonic flows in particular, this dynamical explanation also leads to a similar separation of total pressure; these features may thus be potentially exploited as a general marker to identify and quantify vortices.