Experiments are described in which the vortex shedding from a bluff body and the base pressure coefficient have been measured in a shear flow. It is shown that the shedding breaks down into a number of spanwise cells in each of which the frequency is constant. The division between the cells is thought to be marked by a longitudinal vortex in the stream direction and this is supported by evidence from experiments where a longitudinal vortex was generated in an otherwise uniform flow.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112073000236

Vortex shedding from bluff bodies in a shear flow

A numerical analysis of forced-convection heat transfer from a horizontal stationary circular cylinder dissipating a uniform heat flux in a crossflow of air is conducted by solving the full two-dimensional steady-state Navier-Stokes and energy equations in the range of the Reynolds numbers from 100 to 500 (based on diameter). A numerical study by this author for Reynolds numbers less than 100 was previously conducted and therefore is not repeated here. Dependence on the Reynolds number of the flow and thermal fields, vorticity and pressure distributions, separation angle, drag coefficient, and local and average Nusselt number around the cylinder are shown. Correlations for the separation angle and drag coefficient as functions of Reynolds number are suggested. Quantities such as vorticity, pressure, and Nusselt number at the forward and rear (base) stagnation points are also calculated and correlated as functions of Reynolds number. The local and average values of the Nusselt numbers are shown to be in go...

Steady-State Numerical Solution of the Navier-Stokes and Energy Equations around a Horizontal Cylinder at Moderate Reynolds Numbers from 100 to 500

European Mechanics Colloquium number 17 was held at Cambridge from 1 to 3 July 1970, when the subject of bluff bodies and vortex shedding was discussed. The following report summarizes some of the papers presented. No formal proceedings of the meeting will be published.

Bluff bodies and vortex shedding – a report on Euromech 17

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 factor R on 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, R at 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 of R and Cpb, 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 in R and Cpb, 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 in R with Cpb confirm 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 Karman 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.

Energy separation in a vortex street

Two-dimensional vortex shedding behind an inclined flat plate in uniform shear flow is numerically investigated by means of an inviscid discrete-vortex approximation. The points of appearance of the vortices are fixed in the plane of the plate at a short distance downstream of the edges of the plate. The strengths of the vortices are determined from the Kutta condition. On the assumption that the steadily periodic flow patterns are independent of initial conditions, the numerical calculations are performed for an inclined flat plate immersed in an incompressible fluid which is set in motion impulsively from rest with the velocity profile of uniform shear flow. The results of analysis show that the Strouhal number of vortex shedding and the time-averaged values of other hydrodynamic characteristics of the flow such as the outer-edge velocity of the separated shear layers, the convective velocity of the shear layers and the drag force exerted on the plate vary closely linearly with the shear parameter of the approaching shear flow. A linear relation between the Strouhal number and the shear parameter is confirmed by an air-tunnel experiment. The effects of the shear parameter on the calculated vortex patterns in the wake are also presented.

Bruce J. Mangione

Papers

Vortex shedding from circular cylinders in sheared flow.