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![The spanwise-averaged void fraction of an incipient cavity at 10° σ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma _0}$$\end{document} = 2.7 (σ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma _0}$$\end{document}/2α = 7.7, U0 = 8 m/s). The average void fraction is 0.18](publication/331811934/figure/fig16/AS:960083726974989@1605913206401/The-spanwise-averaged-void-fraction-of-an-incipient-cavity-at-10.png)
The spanwise-averaged void fraction of an incipient cavity at 10° σ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma _0}$$\end{document} = 2.7 (σ0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\sigma _0}$$\end{document}/2α = 7.7, U0 = 8 m/s). The average void fraction is 0.18
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The shedding dynamics of partial cavitation forming on a NACA0015 hydrofoil is known from the previous studies to be multimodal, exhibiting abrupt changes in Strouhal number as the cavitation number is reduced (Arndt et al. in Instability of partial cavitation: a numerical/experimental approach. National Academies Press, Washington, D.C., Retrieved...
Citations
... One such study by Mäkiharju et al. [29] investigated the impact of dissolved and injected non-condensable gas on the cavity shedding dynamics along the same wedge. Jahangir et al. [30] and Wu et al. [31] further observed the inner characteristics of two distinct cavity-shedding mechanisms. However, these studies used different boundary conditions to investigate the re-entrant jet and shock wave mechanisms. ...
... The dominant peaks keep switching between the two dynamics with a narrow band at a higher frequency due to the re-entrant jet mechanism and a wider band at a lower frequency due to the shock wave mechanism. Wu et al. [31] studied the partial cavitation shedding dynamics experimentally with a NACA0015 hydrofoil (with chord C = 50 mm). They found different values of the Strouhal number with the transition from the re-entrant jet to the shock wave. ...
... This makes such mixtures compressible and susceptible to shock under certain flow conditions. When the average Mach number of the cavity flow exceeds that required for the generation of strong shocks, the front shock propagates upstream with high pressure, causing the residual sheet cavity to turn into the bubbly region and then collapse immediately [33,34]. The Mach number is defined as M FL = U FL /C 1s [32], where C 1s represents the sound speed of the cavitating flow upstream of the observed shocks. ...
The objective of this paper is to investigate the influence of fluid-structure interaction on the cavity dynamics and the vibrations around a flexible hydrofoil by comparing the experimental results of a rigid hydrofoil. Cavitation behavior, vibrations, and lifts are obtained by a synchronized measured system utilizing a high-speed camera, lift measurement, and a portable laser vibrometer. The nose-up twisting deformation results in an increase in the effective angle of attack, which leads to an increase in cavity length and a reduction of cloud cavity shedding frequency. It also accelerates the transition of the cavitation regimes and shedding mechanism of cloud cavities with the decrease in cavitation number, together with the amplification of vibration velocity, and the suppression of higher-frequency oscillations.
... In the investigation of the cavitation cloud by X-rays, the void fraction of cloud cavitation around the Venturi [48][49][50] and hydrofoil [51][52][53][54][55][56] were evaluated. Vapor bubbles in the Venturi tube profile were detected at 3,000 frames per second using synchrotron radiation at the XOR 32-ID beamline of the Advanced Photon Source (APS), Argonne National Laboratory (ANL) [57]. ...
Hydrodynamic cavitation is useful in many processing applications, for example, in chemical reactors, water treatment and biochemical engineering. An important type of hydrodynamic cavitation that occurs in a Venturi tube is vortex cavitation known to cause luminescence whose intensity is closely related to the size and number of cavitation events. However, the mechanistic origins of bubbles constituting vortex cavitation remains unclear, although it has been concluded that the pressure fields generated by the cavitation collapse strongly depends on the bubble geometry. The common view is that vortex cavitation consists of numerous small spherical bubbles. In the present paper, aspects of vortex cavitation arising in a Venturi tube were visualized using high-speed X-ray imaging at SPring-8 and European XFEL. It was discovered that vortex cavitation in a Venturi tube consisted of angulated rather than spherical bubbles. The tangential velocity of the surface of vortex cavitation was assessed considering the Rankine vortex model.
... The vacuum pump (Heraeus, Hanau, Germany) generates absolute pressures down to 10.3 kPa. A NACA0015 hydrofoil was chosen which has been reported in a large number of both experimental and numerical cavitation studies [23,24], oscillating as well as with fixed angles of attack (AoA). The hydrofoil with a chord length c of 200 mm is mounted vertically between the upper and lower walls of the testing section as shown in Figure 2, allowing only a minimum gap to ensure the unhampered oscillation movement around the axis at 0.25 c. ...
The strong increase in anthropogenic underwater noise has caused a growing intention to design quieter ships given that ship propellers are one of the dominating noise sources along the worldwide shipping routes. This creates an imminent demand for deeper knowledge on the noise generation mechanisms of propeller cavitation. A cavitating, oscillating two-dimensional NACA0015 hydrofoil is analyzed with hydrophone and high-speed video recording as a simplified and manipulatable representative of a propeller blade in a ship’s wake field for the identification of major influencing parameters on the radiated noise. A pneumatic drive allows the application of asymmetrical temporal courses of the angle of attack, a novel amendment to the widely reported sinusoidal setups. Three different courses are tested with various cavitation numbers. The combination of a moderate angle increase and a rapid decrease is found to generate significantly higher pressure peaks compared to symmetrical angular courses. Considering that the rapid change of the angle of attack caused by the inhomogeneous wake field behind the hull is the core of the cavitation occurrence, the understanding of its influence may contribute to the design of quieter ships in the future while still allowing for the necessary high propeller efficiency.
... However, such a method cannot be easily extended into the developed cavity, e.g., sheet/cloud cavitation, where the vapor/gas void fraction is much higher. Studies have been conducted to study the temporal features and the correlation with transient cavity behaviors of the wall-pressure fluctuations induced by cavitation on the surface of a solid body [25][26][27][28]. Specifically, Le et al. [29] experimentally measured distributions of the pressure pulse height spectrum (PPHS) by mounting pressure transducers on a foil surface. ...
... Their measurement successfully captured the pressure rise caused by the bubbly shockwave. Wu et al. [27] employed unsteady pressure transducers to study the wall-pressure fluctuations on a NACA0015 hydrofoil. In a study of the physical process of different cavity breakup and shedding mechanisms, namely, the reentrant jet mechanism and shockwave mechanism, Wang et al. [33] observed that under the reentrant jet mechanism, relatively lower pressure fluctuations were captured at the head of the reentrant jet, and under the shockwave mechanism, a large pressure pulse was captured at the shockwave front during its propagation. ...
... This large-scale cavity cloud shedding process is supposed to be caused by the reentrant jet dynamics beneath the cavity, which is called cloud cavitation with reentrant jet dominant cloud shedding (RJ). Due to its destructive features, cloud cavitation has attracted much interest and has been widely documented [9,27,[36][37][38][39]. Abundant vortex structures are generated around the cavity cloud, as indicated by the white circle in Fig. 7(c), indicating the complex cavitation-vortex interaction in the cloud shedding process. ...
The objective of this work is to examine the wall pressure fluctuations associated with attached turbulent cavitating flows, especially the statistical features. Wall pressure fluctuations are experimentally measured using four flush-mounted unsteady pressure transducers beneath attached cavities. Cavitating flows are generated behind a backward-facing wedge model, and a simultaneous sampling technique is adopted to synchronize the transient cavity behaviors and wall pressure fluctuations. The results show that with decreasing cavitation number, cavity length oscillations increase and cavity regimes change from a stable inception cavity and an intermittent sheet cavity to an unsteady quasiperiodic cloud cavity. However, the time-averaged cavity shape under different cavity regimes shows self-similarity. Inspired by this geometrical self-similarity, several statistical features of wall-pressure fluctuations both inside and outside the attached cavitation are analyzed. Specifically, the root mean square (RMS) value of wall pressure fluctuations approaches its maximum near the cavity closure, and its amplitude is independent of the cavitation number. The probability density function (PDF) shape presents non-Gaussian and asymmetric behaviors. Generally, the PDF shape is positively skewed at the cavity leading edge, approaching Gaussian behaviors near cavity closure and slightly negatively skewed outside the cavity. Spectral analysis indicates that the scaling regions obtained by fast Fourier transform are usually classified as (1) low-frequency range; (2) mid-frequency range, spectra typically show the f-2 behavior; (3) universal range, with an f-7/3 relation; and (4) high-frequency range, with an f-3.2 relation. Remarkably, the Reynolds number effects significantly enhance the non-Gaussian and asymmetric behaviors of wall pressure fluctuation PDFs. Our study can help to improve both cavitation modeling and hydraulic designs.
... As the basic structural unit of fluid mechanics, the study of shock waves during cavitation collapse of hydrofoil is also crucial. [49][50][51][52][53][54][55][56][57][58] Cavity shedding mechanisms, such as those due to re-entrant jets and condensation shocks, are important but challenging topics in cavitating flows. Luo et al. 59 conducted numerical simulation of the cavity detachment of a twisted hydrofoil and analyzed the pressure wave propagation during cavity evolution. ...
The finite-time Lyapunov exponent (FTLE) method is a mature and practical method for analyzing the characteristics of Lagrangian coherent structures. It can be used for studying the severe impacts of cavitation on the coherent structure of flow. The reduced-order modeling (ROM) method has also significant advantages in extract key features of flow structure. This study analyzed the cloud cavitation flow structure of National Advisory Committee for Aeronautics (NACA)0015 hydrofoil. The backward FTLE and ROM were combined, and a comparison was made between the low-order modes of FTLE structure and the FTLE obtained from the low-order modes. The results indicate that the two methods have effectively captured the main coherent structural features of cloud cavitation flow fields. The main characteristic structures captured by the FTLE obtained from the low-order modes of the flow field are much clearer. The first two coherent structures of the FTLE obtained from the low-order modes of the flow field decompose the FTLE of the velocity field into three distinct parts: the leading-edge structure of the hydrofoil, the reflux structure in the middle of the hydrofoil, and the wake region of the hydrofoil. It is proved that the combination of FTLE and ROM can provide a new perspective and means for the analysis of turbulent structures.
... Historically, two main mechanisms have been proposed for the cavity shedding: re-entrant jets and condensation shocks. 11,22,23 Recently, Zhang et al. 24 proposed the collapse-induced pressure wave caused by the shed cloud as another mechanism for cavity shedding based on the experimental observations. Such pressure wave can disturb the growing cavity and travels faster than the condensation shock in the mixture flow. ...
... 18,25 Condensation fronts in cavitating flows have been observed numerically and experimentally, expressed as a moving front associated with significant condensation phase change. 11,22,25,26 The phenomenon is quite different from shocks produced by the collapse of cavities, reported as a highly compressible process involving high pressure differences. Note that those collapse-induced shocks can trigger the condensation front formation, 25,27 but they are not a necessary condition for the formation of condensation fronts. ...
... Table VII shows the results based on the two post-front points, in all cases close to the speed computed from the x À t diagram in Table V. This analysis confirms that the 1D condensation front velocity can be reasonably estimated by Eq. (22) as was done in the experiments. It is important to note that though the condensation front analyzed at the mixture level (or one fluid level) satisfies the 1D jump condition as a traditional shock does, the mechanism behind them is different. ...
We study the cavitating flow over a backward facing step with an incompressible polydisperse cavitation model. The model can predict experimental observations for this flow reasonably well, including the shedding cloud characterized by the condensation front, cavity length, void fraction, and shedding frequency. All model variations produced shedding cavities, but the turbulence model and grid resolution are essential for better predictions, with delayed detached eddy simulation (DDES) performing better than Reynolds-averaged Navier–Stokes. Quantities, such as pressures at key points, maximum void fraction location, and shedding frequency, are mildly sensitive to those factors. Finer DDES grid resolution, crucial to resolve small vortices where cavitation occurs in their low pressure cores, improves predictions. Since a fully incompressible model produces a condensation front that follows well the experimental trends, it is concluded that compressibility is not a necessary condition for the formation of a condensation front. Consequently, the speed of sound in the mixture does not appear to play an important role in the front formation and evolution. The polydisperse nature of the model allows prediction of the bubble size distribution. Small bubbles concentrate on the downstream section of the cavity, where cavity collapse is strongest and bubble fission is most intense, while larger bubbles reside near the step where the flow is milder. The condensation front is a moving source of vorticity for the liquid phase where the “compressibility,” in the sense of mixture density changes due to void fraction changes, and baroclinic effects are significant, but the buoyancy effect is negligible.
... The magnitudes are of the same order as the other cloud cavitation flows using x-ray visualization. [52][53][54] Next, we emphasize the possible error in obtaining the bubble velocity. Figure 11 is an ideal situation when the probe pierces the bubble through its center. ...
The bubble size distribution (BSD) in hydrodynamic cloud cavitation is poorly understood, in spite of its importance in cavitation erosion and noise. Challenges arise owing to the heterogeneous turbulent flows and high void fraction in the cavitation regime. The use of a fiber optical probe enables us to obtain the BSD in a cavitation cloud. Two distinct power law scalings at the early stage of cloud cavitation are identified. The first generation of bubbles is produced by the fission to the shedding cavitation pocket by large-scale turbulence, whose isotro-pic part leads to the basic scaling À10=3, while the anisotropic part due to the effect of hydrofoil wall contributes to the deviation. The successive fragmentation of bubbles accompanied with turbulent energy cascade results in the fairly uniform scaling À4=3. The results indicate that turbulence plays a dominant role in bubble breakup at the early stage of cloud cavitation. Published under an exclusive license by AIP Publishing. https://doi.
... Studies have primarily focused on the cavitation on hydrofoils [9][10][11]. From these studies [10][11][12][13], it is known that partial cavitation is formed on the suction side of the hydrofoil as a vapor-filled pocket is attached at the leading edge. With decreasing cavitation number, the cavity sheet grows along the hydrofoil surface and becomes unsteady after it reaches a certain length. ...
... Generally, cavitation regimes can vary significantly based on factors such as the hydrofoil type, angle of attack, and flow conditions. Previous studies discussed the cavitation dynamics on NACA0015 hydrofoil in detail [12,13,27]. In the current experiment of unheated and heated NACA0015 hydrofoils, five different cavitation regimes were observed, which are defined as follows: ...
An experimental study of cavitating flow on a heated NACA0015 hydrofoil was conducted in a cavitation tunnel to investigate the influence of the hydrofoil surface temperature on the cavitating flow. The cavitation behavior under different heating conditions was examined using highspeed video, and an image processing method was used to obtain the periodic characteristics of the cavitating flow. The results revealed that attached sheet cavitation and supercavitation occurred on both heated and unheated hydrofoils. However, sheet-cloud cavitation was observed only on the unheated hydrofoil, whereas transient cavitation was observed only on the heated hydrofoil. Transient cavitation also exhibited periodic growth/collapse behavior; however, there was no shedding of a large vapor cloud. Moreover, with a further increase in the hydrofoil surface temperature, transient cavitation turned into opentype cavitation. The cavitating flow exhibited a quasisteady cavity length with an open cavity closure. It was considered that the surface temperature promoted vapor generation at the cavity leading edge, which enlarged the vapor-filled fore part of the sheet cavity. This enlarged sheet cavity prevented the reentrant flow from moving upstream and thus turned the cavity closure into an open type. Once the cavity closure turned into an open type, the local disturbance led to a smaller adverse pressure gradient, which was not sufficiently strong to create a reentrant flow. In this case, if the vapor production at the cavity leading edge was sufficiently large to reach a balance with vapor condensation at the open cavity closure, the cavity would be steady.
... The mean partial cavity length and shedding frequency vary as a function of cavitation number for a given angle of attack. Data from the present experiments are also compared with previous results from Arndt et al. (2000) and Wu et al. (2019). Arndt et al. (2000) report visual cavity length data taken at two different facilities (denoted as 'Arndt' and 'Obernach'). ...
... Arndt et al. (2000) report visual cavity length data taken at two different facilities (denoted as 'Arndt' and 'Obernach'). Figure 2 shows the mean cavity length, L C , determined from both high-speed videos and X-ray densitometry based void fraction measurements using the method of Wu et al. (2019). For periodically shedding cavities, the average of the maximum cavity length was designated as L C in the high-speed images shown in figure 2(a). ...
... Figure 3 shows the cavity length, L C , varying with σ 0 /2α, and the shedding cavity regimes summarized in table 1. Also included are data reported by Wu et al. (2019) and Arndt (2012). To compare the changes in L C from different studies, a velocity based blockage correction using the following equation was made: Arndt et al. (2000) reported data from Obernach for α = 8 • at u 0 = 8 m s −1 , green dagger and u 0 = 10 m s −1 , green multiple symbol. ...
Partial cavity flows forming on a NACA0015 hydrofoil are visualized using high-speed cinematography and time-resolved X-ray densitometry. These observations reveal the underlying flow features that lead to the cloud cavity shedding. Previous studies have reported that both near-surface liquid re-entrant flow and bubbly shock waves can serve as the mechanisms causing cavity pinch-off and cloud shedding. We identify both mechanisms in the current study. The cavity shedding frequency was also examined and related to the underlying flow dynamics. The probability of re-entrant flow or bubbly shock-induced shedding processes are quantified, and the likelihood of each mechanism is shown to be a function of both the cavitation number and the Mach number of the bubbly mixture within the separated region of the cavity. When the Mach number of the two-phase mixture in the cavity exceeds unity, shock waves become the dominant mechanism that lead to large-scale cavity shedding and cloud cavitation.
