Stereoscopic particle image velocimetry (PIV) measurements are made in streamwisespanwise and inclined cross-stream planes (inclined at 45 • and 135 • to the principal flow direction) of a turbulent boundary layer at moderate Reynolds number (Re τ ∼ 1100). Two-point spatial velocity correlations computed using the PIV data reveal results that are consistent with an earlier study in which packets of hairpin vortices were identified by a feature-detection algorithm in the log region, but not in the outer wake region. Both streamwise-streamwise (R uu) and streamwise-wall-normal (R uw) correlations are significant for streamwise displacements of more than 1500 wall units. Zero crossing data for the streamwise fluctuating component u reveal that streamwise strips between zero crossings of 1500 wall units or longer occur more frequently for negative u than positive u, suggesting that long streamwise correlations in R uu are dominated by slower streamwise structures. Additional analysis of R ww correlations suggests that the long streamwise slow-moving regions contain discrete zones of strong upwash over extended streamwise distances, as might occur within packets of angled hairpin vortices. At a wall-normal location outside of the log region (z/δ = 0.5), the correlations are shorter in the streamwise direction and broader in the spanwise direction. Correlations in the inclined cross-stream plane data reveal good agreement with the streamwise-spanwise plane. R uu in the 45 • plane is more elongated along the in-plane wall-normal direction than in the 135 • plane, which is consistent with the presence of hairpin packets with a low-speed region lifting away from the wall.
This work can be viewed as a reprise of Head & Bandyopadhyay's (J. Fluid Mech. vol. 107, 1981, p. 297) original boundary-layer visualization study although in this instance we make use of stereo particle image velocimetry (PIV), techniques to obtain a quantitative view of the turbulent structure. By arranging the laser light-sheet and image plane of a stereo PIV system in inclined spanwise/wall-normal planes (inclined at both 45 • and 135 • to the streamwise axis) a unique quantitative view of the turbulent boundary layer is obtained. Experiments are repeated across a range of Reynolds numbers, Re τ ≈ 690-2800. Despite numerous experimental challenges (due to the large out-of-plane velocity components), mean flow and Reynolds stress profiles indicate that the salient features of the turbulent flow have been well resolved. The data are analysed with specific attention to a proposed hairpin eddy model. In-plane two-dimensional swirl is used to identify vortical eddy structures piercing the inclined planes. The vast majority of this activity occurs in the 135 • plane, indicating an inclined eddy structure, and Biot-Savart law calculations are carried out to aid in the discussion. Conditional averaging and linear stochastic estimation results also support the presence of inclined eddies, arranged about low-speed regions. In the 135 • plane, instantaneous swirl patterns exhibit a predisposition for counter-rotating vortex pairs (arranged with an ejection at their confluence). Such arrangements are consistent with the hairpin packet model. Correlation and scaling results show outer-scaling to be the correct way to quantify the characteristic spanwise length scale across the log and wake regions of the boundary layers (for the range of Reynolds numbers tested). A closer investigation of two-point velocity correlation contours indicates the occurrence of a distinct two-regime behaviour, in which contours (and hence streamwise velocity fluctuations) either appear to be 'attached' to the buffer region, or 'detaching' from it. The demarcation between these two regimes is found to scale well with outer variables. The results are consistent with a coherent structure that becomes increasingly uncoupled (or decorrelated) from the wall as it grows beyond the logarithmic region, providing additional support for a wall-wake description of turbulent boundary layers.
Stereoscopic particle image velocimetry (PIV) measurements were taken simultaneously in streamwise-spanwise and streamwise-wall-normal planes in a zeropressure-gradient turbulent boundary layer over a flat plate. Polarization techniques were employed to allow PIV to be taken in both planes simultaneously. Image preprocessing techniques were used to improve the quality of data near the line of intersection of the planes. Linear stochastic estimation was performed on these data, revealing the streamwise, spanwise, and wall-normal extent of swirl events primarily near the top of the log region of the boundary layer. Swirl events with rotation consistent with the mean vorticity are found to have a large footprint in the lower limit of the log region whereas swirls with opposite-signed vorticity are found to have little influence lower in the boundary layer. These long-time-averaged statistics contain features that are consistent with the hairpin packet model (or its kinematic equivalent). This model also seems to provide a reasonable description of many instantaneous events involving large-scale coherence, where long regions of streamwise momentum deficit are surrounded by vortex cores.
An experimental study of air supply to bottom cavities stabilized within a recess under a horizontal surface has been carried out in a specially designed water tunnel. The air supply necessary for creating and maintaining an air cavity in steady and gust flows has been determined over a wide range of speed. Flux-free ventilated cavitation at low flow speeds has been observed. Stable multiwave cavity forms at subcritical values of Froude number were also observed. It was found that the cross-sectional area of the air supply ducting has a substantial effect on the air demand. Air supply scaling laws were deduced and verified with the experimental data obtained.
Although cavitation inception in jets has been studied extensively, little is known about the more complex problem of a jet flow interacting with an outer flow behind a moving body. This problem is studied experimentally by considering inception behind an axisymmetric body driven by a waterjet. Tests were carried out for various water tunnel velocities and jet speeds such that jet velocity ratio UJ/U could be varied in the range of 0–2. Distinctly different cavitation patterns were observed at zero jet velocity (when cavitation appeared in spiral vortices in such flows) and at various jet velocity ratios (when cavitation appeared around the jet in such flows). A simple superposition analysis, utilizing particle imaging velocimetry (PIV) measurements, is able to qualitatively predict the experimental result. On the basis of these observations, a numerical prediction of cavitation inception number based on viscous-inviscid interaction concept is suggested.
Cavitation inception behind an axissymmetric body driven by a waterjet has been studied experimentally and numerically. Water tunnel tests have been performed with the body mounted on a force balance. The transom of the body contained a nozzle located along the centerline. Tests were carried out for various water tunnel speeds such that jet velocity ratio, VJ/U, could be varied in the range 0 to 2. Distinctly different cavitation patterns were observed at zero jet velocity (when cavitation appeared in spiral vortices in such flows) and at a various jet velocity ratios (when cavitation appeared between counter-rotating vortices around the jet in such flows). Cavitation inception/disappearance has been determined visually. The body drag was also measured. An analytical method for determination of cavitation inception index has been developed on the basis of a viscous-inviscid interaction concept, with employment of special semiempirical approximations for vortices and consideration of surface tension. These approximations have been preliminarily validated for nozzle jet cavitation (for nozzle discharge in co-flow). It was assumed that visualization allows detection of cavities (bubbles) of 0.4mm-0.5mm diameter or larger. The cavitation inception index is defined as the cavitation index for cavities of such minimum diameter when these cavities are located between counter-rotating vortices. The initial comparison of predicted and measured values of the cavitation inception index shows good agreement.
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