Self-sustained low-frequency components in an impinging shear layer

Abstract

Oscillations of a cavity shear layer, involving a downstream-travelling wave and associated vortex formation, its impingement upon the cavity corner, and upstream influence of this vortex-corner interaction are the subject of this experimental investigation.Spectral analysis of the downstream-travelling wave reveals low-frequency components having substantial amplitudes relative to that of the fundamental (instability) frequency component; using bicoherence analysis it is shown that the lowest-frequency component can interact with the fundamental either to reinforce itself or to produce an additional (weaker) low-frequency component. In both cases, all frequency components exhibit an overall phase difference of almost 2kπ(k = 1, 2,…) between separation and impingement. Furthermore, the low-frequency and fundamental components have approximately the same amplitude growth rates and phase speeds; this suggests that the instability wave is amplitude-modulated at the low frequency, as confirmed by the form of instantaneous velocity traces.At the downstream corner of the cavity, successive vortices, arising from the amplified instability wave, undergo organized variations in (transverse) impingement location, producing a low-frequency component(s) of corner pressure. The spectral content and instantaneous trace of this impingement pressure are consistent with those of velocity fluctuations near the (upstream) shear-layer separation edge, giving evidence of the strong upstream influence of the corner region.

On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities

“…Notice that the total phase variation from the shear-layer convection (downstream) and acoustic propagation (upstream) is almost exactly 2πn, where n is the index of the Rossiter mode. This phase criterion is similar to that found in several experiments (Knisely & Rockwell 1982;Rockwell & Schachenmann 1982;Gharib & Roshko 1987), which show that in the low-Mach-number limit, the total phase variation in the shear layer alone is a multiple of 2π. In this limit, the acoustic propagation is of course instantaneous, so for our compressible simulations we must add the phase variation of the finite-speed acoustic propagation.…”

“…The measured growth rates are significantly smaller than those predicted by the linear theory, which is surprising, because several experiments show the amplitude is predicted well, at least for moderate values of x/θ. Knisely & Rockwell (1982) used a constant-thickness mean profile, and found that the amplitude matched the linear theory well, for x/θ 0 6 30; Cattafesta et al (1997) found good agreement for x/θ 0 6 60, also using a constant-thickness mean profile. However, our Reynolds number is much smaller than that in either of these experiments, so presumably a viscous stability calculation would agree better.…”

“…This effect is most likely for longer shear layers (large L/θ 0 ), as in the experiments of Cattafesta et al (1997), which had a very thin upstream boundary layer (L/θ 0 = 328). Knisely & Rockwell (1982) also attributed their saturation to this mechanism, although it is also plausible that the saturation might be explained by mean flow spreading, as the linear stability calculation they compared to had a constant-thickness shear profile.…”

Challenges of Investigating Fluid-Elastic Lock-In of a Shallow Cavity and a Cantilevered Beam at Low Mach Numbers

“…This nonlinear contribution is confirmed in low flow water cavity hydrodynamic experiments (Knisely and Rockwell, 1982;Ziada and Rockwell, 1982).…”

Numerical Analysis of Control of Flow Oscillations in Open Cavity Using Moving Bottom Wall

“…7, the Strouhal number obtained in the present Fig. 7 Comparison of Strouhal number based on momentum thickness at upstream edge of cavity for baseline case with experimental data computation is compared with the previous experimental data obtained by Knisely and Rockwell (8) and Kuo and Huang (3) . Our result closely agrees with the solid curve fitted to the measured data of Knisely and Rockwell.…”