Time Resolved Measurements of the Pressure Field Generated by Vortex-Corner Interactions in a Cavity Shear Layer

Abstract

A 2D open cavity shear layer flow, especially its interaction with the trailing corner of the cavity, is investigated experimentally in a water tunnel, at a Reynolds number of 4.0×104, based on cavity length. Time-resolved PIV, at an image sampling rate of 4500 fps is used to simultaneously measure the instantaneous velocity, material acceleration and pressure distribution. The pressure is obtained by spatially integrating the material acceleration (Liu and Katz [19]). A large database of instantaneous realizations enables detailed visualization of the dynamic changes to the shear layer vortices, including convection, deformation and breakup as they impinge on the cavity trailing corner, as well as their interactions with the freshly generated boundary layer around the corner walls. The vorticity on top of the corner is originated from advected shear layer vortices and locally generated vorticity associated with the local pressure gradients. The resulting periodic recirculating flow above the corner generates the lowest mean pressure in the entire flow field. Two mechanisms with distinct characteristic frequencies affect the periodic variations in vorticity and pressure around the corner. The first is caused by streamwise transport of the large shear layer vortices. For example, when these vortices are located just upstream of the corner, they induce a downwash, which periodically eliminates the recirculating flow there. This recirculation and the associated low pressure reappear after the vortex climbs over the corner. The second mechanism involves low frequency undulations of the entire shear layer, which affect its interaction with the corner, and causes substantial variations in the pressure maximum along the vertical wall of the corner, and pressure minimum above it. These undulations are self sustained since the corner pressure fluctuations alter the recirculation speed in the cavity, which in turn change the shear layer elevation during initial rollup, and even modify the boundary layer upstream of the cavity. The time resolved pressure distribution can also be used for estimating the dipole noise radiated from the corner. The characteristic frequencies of the hydraulic and acoustic fields can be traced back to specific flow phenomena. Analysis shows that the unsteady surface pressure along the vertical wall of the trailing corner is a major dominant source of low frequency noise.

Error propagation from the PIV-based pressure gradient to the integrated pressure by the omnidirectional integration method

“…Plugging equation (25) into equation ( 24), we have (26) where ε lA , by following the definition in equation ( 13), is…”

“…A mathematical model for the error propagation from the pressure gradient to the pressure reconstructed using omnidirectional integration is introduced in section 3. As indicated in equation (26), the error for the pressure at each inner node point is the average of the pressure error term ε lA as defined in equation ( 27), the truncation error ε t(l,ijk) along the paths linking boundary point s l to inner nodal point s ijk , and the line integration of the error embedded in the pressure gradient ε ∇p along paths from s l to s ijk . Since ε lA is only an average of the truncation terms ε t (m,l) and ε t (m,r) and the line integration of the pressure gradient error term ε ∇p as defined in equation (27), overall ε ijk is only a function of the truncation error terms and the pressure gradient error terms.…”

“…More recently, an improved Poisson equation approach is proposed by Auteri et al [23]. Following the advent of time-resolved PIV, the pressure reconstruction has also been adapted for measuring the temporal derivatives of surface pressure distribution, which is further used for estimating the acoustic pressure radiated from a surface [24][25][26][27].…”

PIV-based pressure measurement

“…The (iterative) procedure starts by establishing the pressure on the image boundary and then computing the pressure in the interior by means of a weighted omnidirectional path integration procedure along lines generated from the grid points on a virtual boundary encompassing the image domain. In later implementations, a circular shape of the virtual boundary has been adopted (Haigermoser 2009, Liu andKatz 2011).…”

“…For the larger aspect ratio the acoustic pressure spectrum is also broader, which is attributed to the effect of the downstream circulation zone on the shear-layer instabilities, by destroying their regular pattern. Also the study reported by Liu and Katz (2011) considers the analysis of the acoustic behaviour of a 2D cavity flow in a water channel, with interest in the pressure field generated by vortex-corner interactions of the shear layer. Time-resolved PIV at an image sampling rate of 4500 fps provided the basis of instantaneous pressure determination, allowing to elucidate the relation between flow phenomena and noise production.…”