On the Free Shear Layer Downstream of a Backstep in Supersonic Flow

Abstract

The free shear layer downstream of a backstep immersed in a supersonic stream is analyzed. The effects of the initial boundary layer and the expansion at the step corner are taken into account. The shear layer is divided into two distinct regions, an outer rotational nondissipative region and an inner dissipative locally similar mixing region which spreads both into the rotational outer region and the wake. The dynamic characteristics of the shear layer including the rate of spread of the inner mixing layer and the location of the jet boundary streamline are determined by an integral technique. Comparison of predicted velocity profiles with experimental data shows reasonable agreement.

Closure to “Discussion of ‘Design and Construction of a Wind Tunnel for Mass Transfer Studies in Incompressible Boundary Layers’” (1975, ASME J. Fluids Eng., 97, p. 275)

“…Amplitude and frequency bounds for the cable lock-in with the vortex shedding coincided remarkably well with bounds for a rigid circular cylinder [4]. The longitudinal vortex spacing and convection speed, up to 8 diameters downstream from the cable antinode, were also found to be related to the frequency in the same way as had been previously obtained for a rigid cylinder [2]. This infers that the longitudinal spacing will be uniform across the wake behind the cable.…”

“…As Professor Bearman correctly points out, the vortex strength varies along the span of the cable. The local vortex strength and fluid forces can be found from rigid cylinder results [2] and compare favorably with similar results for a cable [3], but only for those portions of the cable over which the vortex and vibration frequencies are locked together. To further support this observation, measurements were made of velocity crosscorrelations in the vortex wake of a cable [1].…”

“…The major reason for Mr. Kneidel's work [l], 3 which is briefly described in the note under discussion, was to consider suggested improvements to the model of Gerhart and Korst [2]. The most serious shortcomings of the Gerhart-Korst model are the oversimplification of the steam tube expansion model, as discussed by Small and Page [3] and the discontinuous nature of the shear layer velocity profile which results from the assumption of a linear velocity profile in the inner region.…”

“…J -co PaUa data presented in [2]. Complete comparisons with both sets of data is made in Mr. Kneidel's thesis [1].…”

“…The values of Re given in the paper appear to us to be reasonable; if, as a rough guide, one accepts Re =^ 360 as a laminar-turbulent and turbulent-laminar transition criterion, 3 then the reported values (see Table 1 WILLIAM J. COOK. 2 This technical brief considers three refinements to the model developed in reference [1] of the paper for the free shear layer that forms downstream of a backstep in supersonic flow. These refinements deal with the initial expansion of the upstream turbulent boundary layer over the corner, the velocity profile assumed for the mixing layer, and the viscosity formulation employed in evaluating the turbulent shear stress along the jet boundary streamline.…”