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The dynamics of cloud cavitation about a three-dimensional hydrofoil are investigated experimentally in a cavitation tunnel with depleted, sparse and abundant free-stream nuclei populations. A rectangular planform, NACA 0015 hydrofoil was tested at a Reynolds number of $1.4\\times 10^{6}$, an incidence of $6^{\\circ }$ and a range of cavitation numbers from single-phase flow to supercavitation. High-speed photographs of cavitation shedding phenomena were acquired simultaneously with unsteady force measurement to enable identification of cavity shedding modes corresponding to force spectral peaks. The shedding modes were analysed through spectral decomposition of the high-speed movies, revealing different shedding instabilities according to the nuclei content. With no active nuclei, the fundamental shedding mode occurs at a Strouhal number of 0.28 and is defined by large-scale re-entrant jet formation during the growth phase, but shockwave propagation for the collapse phase of the cycle. Harmonic and subharmonic modes also occur due to local tip shedding. For the abundant case, the fundamental shedding is again large-scale but with a much slower growth phase resulting in a frequency of $St=0.15$. A harmonic mode forms in this case due to the propagation of two shockwaves; an initial slow propagating wave followed by a second faster wave. The passage of the first wave causes partial condensation leading to lower void fraction and consequent increase in the speed of the second wave along with larger-scale condensation. For a sparsely seeded flow, coherent fluctuations are reduced due to intermittent, disperse nuclei activation and cavity breakup resulting in an optimal condition with maximum reduction in unsteady lift.

The influence of nucleation on cavitation about a sphere from inception through to supercavitation at a transcritical Reynolds number of $1.5\\times 10^{6}$ is investigated experimentally. Two extreme free-stream nuclei populations, deplete and abundant, were investigated. Unsteady surface pressures from two sensors on opposing sides of the sphere were acquired simultaneous with high-resolution high-speed photography at cavitation numbers between 1.0 and 0.3. High-resolution spectrograms derived from these measurements reveal principally bi-modal shedding in attached and detached regimes. Correlations between unsteady pressure measurements show the high modes to be axisymmetric and low modes asymmetric. Modal topology is also discerned from the high-speed imaging. The bi-modal shedding for lower cavitation numbers is driven by coupled re-entrant jet formation and upstream shockwave propagation. The attached regime is shown to have two sub-regimes. For the abundant case, the continuous supply of activated nuclei around the sphere periphery in the first bi-modal regime has the effect of driving the high symmetric mode preferentially over the asymmetric low mode compared with the deplete case. For the first bi-modal regime, frequencies were unaffected by nucleation changes although peak responses were centred at a cavitation number of about 0.8 for the deplete and 0.825 for the abundant. For the second attached regime, where cavity lengths are of the order of the sphere size, changes in nucleation altered frequencies and amplitudes of peak unsteady pressures. For the abundant case, the continuous nuclei supply significantly reduced coherence with modal peak amplitudes reduced by an order compared with the deplete case. Continuous nuclei activation increased the probability of the high mode over the low compared with the deplete case but to a lesser extent than the first regime. Nuclei activations also significantly reduced inter-cavity and cavity durations, but not growth and collapse phases, which increased modal frequencies compared with the deplete case. The second regime asymmetric low mode topology, for both nucleation cases, is shown to be alternate shedding of oblique vortices from diametrically opposing sides of the sphere similar to low Reynolds number shedding about spheres and other axisymmetric bluff bodies in single-phase flows.

The physics associated with various cavitation regimes about a hydrofoil is investigated in a variable-pressure water tunnel using high-speed photography and synchronised force measurements. Experiments were conducted on a relatively stiff stainless steel hydrofoil at a chord-based Reynolds number,$Re=0.8\\times 10^{6}$for cavitation numbers,$\\unicode[STIX]{x1D70E}$, ranging from 0.2 to 1.2, with the hydrofoil experiencing sheet, cloud and supercavitation regimes. The NACA0009 model of tapered planform was vertically mounted in a cantilevered configuration to a six-component force balance at an incidence,$\\unicode[STIX]{x1D6FC}$, of$6^{\\circ }$to the oncoming flow. Tip deformations and cavitation behaviour were recorded with synchronised force measurements utilising two high-speed cameras mounted underneath and to the side of the test section. Break-up and shedding of an attached cavity was found to be due to either interfacial instabilities, re-entrant jet formation, shockwave propagation or a complex coupled mechanism, depending on$\\unicode[STIX]{x1D70E}$. Three primary shedding modes are identified. The Type IIa and IIb re-entrant jet-driven oscillations exhibit a non-linear dependence on$\\unicode[STIX]{x1D70E}$, decreasing in frequency with decreasing$\\unicode[STIX]{x1D70E}$due to growth in the cavity length, and occur at higher$\\unicode[STIX]{x1D70E}$values (Type IIa: 0.4–1.0; Type IIb: 0.7–0.9). Shockwave-driven Type I shedding occurs for lower$\\unicode[STIX]{x1D70E}$values (0.3–0.6) with the oscillation frequency being practically independent of$\\unicode[STIX]{x1D70E}$. The Type IIa oscillations locked in to the first sub-harmonic of the hydrofoil’s first bending mode in water which has been modulated due to the reduced added mass of the vapour cavity. Supplementary movies are available with the online version of the paper.

The influence of fluid–structure interaction on cloud cavitation about a hydrofoil is investigated by comparing results from a relatively stiff reference hydrofoil, presented in Part 1, with those obtained on a geometrically identical flexible hydrofoil. Measurements were conducted with a chord-based Reynolds number $Re=0.8\\times 10^{6}$ for cavitation numbers, $\\unicode[STIX]{x1D70E}$, ranging from 0.2 to 1.2 while the hydrofoil was mounted at an incidence, $\\unicode[STIX]{x1D6FC}$, of $6^{\\circ }$ to the oncoming flow. Tip deformations and cavitation behaviour were recorded with synchronised force measurements utilising two high-speed cameras. The flexible composite hydrofoil was manufactured as a carbon/glass-epoxy hybrid structure with a lay-up sequence selected principally to consider spanwise bending deformations with no material-induced bend–twist coupling. Hydrodynamic bend–twist coupling is seen to result in nose-up twist deformations causing frequency modulation from the increase in cavity length. The lock-in phenomenon driven by re-entrant jet shedding observed on the stiff hydrofoil is also evident on the flexible hydrofoil at $0.70\\leqslant \\unicode[STIX]{x1D70E}\\leqslant 0.75$, but occurs between different modes. Flexibility is observed to accelerate cavitation regime transition with reducing $\\unicode[STIX]{x1D70E}$. This is seen with the rapid growth and influence the shockwave instability has on the forces, deflections and cavitation behaviour on the flexible hydrofoil, suggesting structural behaviour plays a significant role in modifying cavity physics. The reduced stiffness causes secondary lock-in of the flexible hydrofoil’s one-quarter sub-harmonic, $f_{n}/4$, at $\\unicode[STIX]{x1D70E}$ = 0.4. This leads to the most severe deflections observed in the conditions tested along with a shift in phase between normal force and tip deflection.

The topology and unsteady behaviour of ventilated and natural cavity flows over a two-dimensional (2-D) wall-mounted fence are investigated for fixed length cavities with varying free-stream velocity using high-speed and still imaging, X-ray densitometry and dynamic surface pressure measurement in two experimental facilities. Cavities in both ventilated and natural flows were found to have a re-entrant jet closure, but not to exhibit large-scale oscillations, yet the irregular small-scale shedding at the cavity closure. Small-scale cavity break-up was associated with a high-frequency broadband peak in the wall pressure spectra, found to be governed by the overlying turbulent boundary layer characteristics, similar to observations from single-phase flow over a forward-facing step. A low-frequency peak reflecting the oscillations in size of the re-entrant jet region, analogous to ‘flapping’ motion in single-phase flow, was found to be modulated by gravity effects (i.e. a Froude number dependence). Likewise, a significant change in cavity behaviour was observed as the flow underwent transition analogous to the transition from sub- to super-critical regime in open-channel flow. Differences in wake topology were examined using shadowgraphy and proper orthogonal decomposition, from which it was found that the size and number of shed structures increased with an increase in free-stream velocity for the ventilated case, while remaining nominally constant in naturally cavitating flow due to condensation of vaporous structures.

Experimental studies of the influence of fluid–structure interaction on cloud cavitation about a stiff stainless steel (SS) and a flexible composite (CF) hydrofoil have been presented in Parts I (Smith et al., J. Fluid Mech., vol. 896, 2020a, p. A1) and II (Smith et al., J. Fluid Mech., vol. 897, 2020b, p. A28). This work further analyses the data and complements the measurements with reduced-order model predictions to explain the complex response. A two degrees-of-freedom steady-state model is used to explain why the tip bending and twisting deformations are much higher for the CF hydrofoil, while the hydrodynamic load coefficients are very similar. A one degree-of-freedom dynamic model, which considers the spanwise bending deflection only, is used to capture the dynamic response of both hydrofoils. Peaks in the frequency response spectrum are observed at the re-entrant jet-driven and shock-wave-driven cavity shedding frequencies, system bending frequency and heterodyne frequencies caused by the mixing of the two cavity shedding frequencies. The predictions capture the increase of the mean system bending frequency and wider bandwidth of frequency modulation with decreasing cavitation number. The results show that, in general, the amplitude of the deformation fluctuation is higher, but the amplitude of the load fluctuation is lower for the CF hydrofoil compared with the SS hydrofoil. Significant dynamic load amplification is observed at subharmonic lock-in when the shock-wave-driven cavity shedding frequency matches with the nearest subharmonic of the system bending frequency of the CF hydrofoil. Both measurements and predictions show an absence of dynamic load amplification at primary lock-in because of the low intensity of cavity load fluctuations with high cavitation number.

Cavitating and bubbly flows involve a host of physical phenomena and processes ranging from nucleation, surface and interfacial effects, mass transfer via diffusion and phase change to macroscopic flow physics involving bubble dynamics, turbulent flow interactions and two-phase compressible effects. The complex physics that result from these phenomena and their interactions make for flows that are difficult to investigate and analyse. From an experimental perspective, evolving sensing technology and data processing provide opportunities for gaining new insight and understanding of these complex flows, and the continuous wavelet transform (CWT) is a powerful tool to aid in their elucidation. Five case studies are presented involving many of these phenomena in which the CWT was key to data analysis and interpretation. A diverse set of experiments are presented involving a range of physical and temporal scales and experimental techniques. Bubble turbulent break-up is investigated using hydroacoustics, bubble dynamics and high-speed imaging; microbubbles are sized using light scattering and ultrasonic sensing, and large-scale coherent shedding driven by various mechanisms are analysed using simultaneous high-speed imaging and physical measurement techniques. The experimental set-up, aspect of cavitation being addressed, how the wavelets were applied, their advantages over other techniques and key findings are presented for each case study. This paper is part of the theme issue 'Redundancy rules: the continuous wavelet transform comes of age'.

Cavitating and bubbly flows involve a host of physical phenomena and processes ranging from nucleation, surface and interfacial effects, mass transfer via diffusion and phase change to macroscopic flow physics involving bubble dynamics, turbulent flow interactions and two-phase compressible effects. The complex physics that result from these phenomena and their interactions make for flows that are difficult to investigate and analyse. From an experimental perspective, evolving sensing technology and data processing provide opportunities for gaining new insight and understanding of these complex flows, and the continuous wavelet transform (CWT) is a powerful tool to aid in their elucidation. Five case studies are presented involving many of these phenomena in which the CWT was key to data analysis and interpretation. A diverse set of experiments are presented involving a range of physical and temporal scales and experimental techniques. Bubble turbulent break-up is investigated using hydroacoustics, bubble dynamics and high-speed imaging; microbubbles are sized using light scattering and ultrasonic sensing, and large-scale coherent shedding driven by various mechanisms are analysed using simultaneous high-speed imaging and physical measurement techniques. The experimental set-up, aspect of cavitation being addressed, how the wavelets were applied, their advantages over other techniques and key findings are presented for each case study. This paper is part of the theme issue ‘Redundancy rules: the continuous wavelet transform comes of age’.