Vortex-corner interactions in a cavity shear layer elucidated by time-resolved measurements of the pressure field

Abstract

The flow structure and turbulence in an open cavity shear layer has been investigated experimentally at a Reynolds number of $4. 0\times 1{0}^{4} $, with an emphasis on interactions of the unsteady pressure field with the cavity corners. A large database of time-resolved two-dimensional PIV measurements has been used to obtain the velocity distributions and calculate the pressure by spatially integrating the material acceleration at a series of sample areas covering the entire shear layer and the flow surrounding the corners. Conditional sampling, low-pass filtering and time correlations among variables enable us to elucidate several processes, which have distinctly different frequency ranges, that dominate the shear layer interactions with the corners. Kelvin–Helmholtz shear layer eddies have the expected Strouhal number range of 0.5–3.2. Their interactions with the trailing corner introduce two sources of vorticity fluctuations above the corner. The first is caused by the expected advection of remnants of the shear layer eddies. The second source involves fluctuations in local viscous vorticity flux away from the wall caused by periodic variations in the streamwise pressure gradients. This local production peaks when the shear layer vortices are located away from the corner, creating a lingering region with peak vorticity just above the corner. The associated periodic pressure minima there are lower than any other point in the entire flow field, making the region above the corner most prone to cavitation inception. Flapping of the shear layer and boundary layer upstream of the leading corner occurs at very low Strouhal numbers of ∼0.05, affecting all the flow and turbulence quantities around both corners. Time-dependent correlations of the shear layer elevation show that the flapping starts in the boundary layer upstream of the leading corner and propagates downstream at the free stream speed. Near the trailing corner, when the shear layer elevation is low, the stagnation pressure in front of the wall, the downward jetting flow along this wall, the fraction of shear layer vorticity entrained back into the cavity, and the magnitude of the pressure minimum above the corner are higher than those measured when the shear layer is high. However, the variations in downward jetting decay rapidly with increasing distance from the trailing corner, indicating that it does not play a direct role in a feedback mechanism that sustains the flapping. There is also low correlation between the boundary/shear layer elevation and the returning flow along the upstream vertical wall, providing little evidence that this returning flow affects the flapping directly. However, the characteristic period of flapping, ∼0.6 s, is consistent with recirculation time of the fluid within the cavity away from boundaries. The high negative correlations of shear/boundary layer elevation with the streamwise pressure gradient above the leading corner introduce a plausible mechanism that sustains the flapping: when the shear layer is low, the boundary layer is subjected to high adverse streamwise pressure gradients that force it to widen, and when the shear layer is high, the pressure gradients decrease, allowing the boundary layer to thin down. Flow mechanisms that would cause the flapping-induced pressure changes, and their relations to the flow within the cavity are discussed.

Field and Numerical Investigation of Transport Mechanisms in a Surface Storage Zone

“…This TKE distribution also differs from experimental results for idealized geometries with similar aspect ratios (Jackson et al, ; Liu & Katz, ), where the presence of a sharp edge at the end of the cavity produces an impingement point with a strong adverse pressure gradient and unsteady transport of vorticity. These features, associated with a constant water depth, produces an increase of the TKE along the mixing layer in idealized cases.…”

“…In nondimensional terms, these frequencies correspond to Strouhal numbers ( St = fL / U b ) of 0.155 and 0.388, respectively. The first low‐frequency mode is in the range reported by Liu and Katz () for the slow flapping of the mixing layer, in a similar aspect ratio cavity. For the second leading frequency, the Strouhal number is consistent with the vortex shedding frequencies obtained by Jackson et al (), for several study cases in semicircular, backward conic, and forward conic cavities for similar aspect ratio and Reynolds numbers.…”

Comparative assessment of pressure field reconstructions from particle image velocimetry measurements and Lagrangian particle tracking

“…The ZDES simulation data are first interpolated to the same grid points as used for the pressure results. Spectra are obtained by applying the FFT algorithm after using the symmetric straight line approach as outlined in Foucaut et al (2004) and without any windowing function, similarly to the approach used in Liu and Katz (2013). The wavelength is scaled by the interrogation window size used in the PIV correlation analysis, which is equal to four times the grid spacing.…”

A posteriori uncertainty quantification of PIV-based pressure data

“…Industrial tests typically require pressure information, for the evaluation of forces. Pressure fluctuations are important when dealing with fatigue studies and aeroacoustic source measurements (Haigermoser 2009;Liu and Katz 2013;Pröbsting et al 2013).…”