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The cavitation phenomenon can induce non-uniformity in the fluid, impacting fluid dynamic performance. This paper focuses on the cavitation shedding of the Delft Twist 11 hydrofoil. First, the reliability of numerical simulations is verified by computational fluid dynamics results. Utilizing the variational mode decomposition method, the cavitation signals on two cavitation paths are decomposed. Finally, the cavitation pulsation tracking network method is proposed to extensively investigate the spatial propagation patterns of cavitation signals at various sections above the twisted hydrofoil. The results reveal that typical frequencies at different monitoring planes are 30, 58, and 88 Hz. The corresponding amplitude analysis at these frequencies provides insight into the spatial propagation and attenuation process of cavitation vortices shedding. This study offers a novel perspective for a deeper understanding of cavitation mechanisms. Simultaneously, this provides references for enhancing the performance of mechanical engineering systems, reducing energy consumption, and improving structural reliability. [ABSTRACT FROM AUTHOR]

Lock-in is of great importance in many engineering applications due to its practical implications for structural safety. The influence of composite bend-twist coupling on the wake dynamics and vortex-induced vibration around a carbon fiber composite hydrofoil is investigated and compared to a similar stainless-steel hydrofoil. Experiments are conducted by varying linearly and slowly the upstream velocity back and forth between 5 and 15 m/s, which allows reaching lock-in conditions for both hydrofoils. Due to the blunt truncation of the trailing edge, both hydrofoils produce strong and alternate vortices in their wake, whose effect is visible on vibration spectrograms. The steel hydrofoil produces a classical lock-in onto its first torsion mode, while the composite hydrofoil exhibits two lock-in phenomena onto both torsion and second bending modes. Interestingly, for the second bending mode, the vibration spectrogram reveals the existence of two frequencies: (i) the resonance frequency, which remains almost constant during the lock-in phase, and (ii) the Strouhal frequency, which increases linearly with the upstream velocity. Using flow visualization, we found that this peculiar behavior is the result of the twist-bending coupling, which leads to the co-existence of two different vortex-shedding mechanisms. Close to the hydrofoil tip, the large vibration amplitude dictates the shedding frequency while the shedding follows the Strouhal law elsewhere. This partial lock-in gradually fades away as the velocity is increased. This result provides guidance for the safe design of composite structures. [ABSTRACT FROM AUTHOR]

Cryogenic cavitation exhibits complexities primarily represented by the coupled interactions of thermodynamic effects, vortices, and cavities during the cavitation process. To further investigate this coupling mechanism, this study employed the DDES turbulence model and Sauer–Schnerr cavitation model to perform unsteady numerical simulations of liquid nitrogen cavitation flow around the NACA0015 Hydrofoil. Numerical validation of the model utilized a symmetrical Hord hydrofoil. The results reveal that the upstream development of the recirculation flow under inverse pressure gradients is the fundamental cause of the detachment in the primary cavitation region. At a cavitation number of 0.616, thermodynamic effects noticeably suppress the formation of cavities and alter the range of adverse pressure gradients, consequently influencing the detachment behavior in the primary cavitation region. [ABSTRACT FROM AUTHOR]

The phenomenon of water–jet pump stall can be ascribed to the development of blade boundary layer separation with the transition process playing a significant role in this separation. The hydrofoil is usually used as a simplified model of the water–jet pump impeller blade, and its flow field characteristics have important reference values for analyzing the impeller flow. Based on the transition model and the dynamic mode decomposition method, this article presents the results of a study that was carried out on the stall characteristics of the NACA0009 blunt trailing edge hydrofoil. The transition characteristics of hydrofoil surfaces at different angles of attack (AoA)and Chord-based Reynolds numbers (ReL) are obtained. The hydrofoil boundary layer transition is dominated by natural transition as the AoA is less than 4°, while the transition is dominated by leading-edge separation-induced transition as the AoA is greater than 4°. The investigation yields the dynamic properties of the LSB (Laminar Separation Bubble) as the AoA is varied. The phenomenon known as the deep stall is distinguished by the movement of the stall vortex toward the upstream direction near the trailing-edge region, where it merges with the LSB in the leading-edge region. This phenomenon leads to oscillations in the lift and drag coefficients. The relationship between the LSB and the trailing-edge stall vortex is established using DMD (Dynamic Mode Decomposition) methods. As the phenomenon of the deep stall occurs, it can be observed that the modal energy of the leading-edge LSB is comparatively higher than the modal energy of the trailing-edge stall vortex, inducing the dominant role of the LSB and the movement toward the trailing-edge region and, consequently, the phenomenon of trailing-edge vortex shedding in the hydrofoil. The findings of this study could be guidance for the design of fluid machinery blades. [ABSTRACT FROM AUTHOR]

The influence of sweep angles on cavitation characteristics and mechanisms of a wedge-section hydrofoil is investigated experimentally and numerically. Four hydrofoils with sweep angles of 0° (straight), 30°, 45°, and 60° are considered across a range of cavitation numbers from 2.00 to 0.48 and angle of attack (AOA) of 0°, 5°, 10°, and 15°. Two high-speed cameras are used to visualize the cavitation flow in a high-speed cavitation tunnel. The numerical simulation is conducted using unsteady Reynolds-averaged Navier–Stokes equations through OpenFOAM. At an AOA of 0° and 5°, vortex cavitation first appears in the wake region of all models at a cavitation number of 0.98. However, at higher AOA values of 10° and 15°, tip-vortex cavitation (TVC) begins first for the straight foil, and this is followed by sheet and wake cavitation. In contrast, the swept foil does not succumb to TVC. Instead, as the sweep angle increases, sheet cavitation develops into root leading-edge vortex cavitation (LEVC). The inclination angle of the LEVC from the leading edge is observed to be between 6° and 15°, depending on the sweep angle, and it is independent of the cavitation number and AOA. The wake vortex changes from eddy vortex shedding at the wake region of the straight hydrofoil into two root trailing-edge vortices as the sweep angle increases. The swept hydrofoil reduces the average cavity volume by more than 45% compared with the straight foil. The lift coefficient of the straight hydrofoil increases as sheet cavitation is generated and reaches a maximum value of 0.6 when cavitation covers the suction side of the hydrofoil before dropping sharply when it extends to the wake region. However, there is only minor deterioration in the lift coefficient of the 60° swept-angle foil when the cavitation occurs. The drag coefficient reduces when cavitation forms for both foils. However, the drag coefficient of the swept hydrofoil is lower than that of the straight foil. These findings offer valuable insight into the design and optimization of foils for various applications where cavitation affects their performance and stability. [ABSTRACT FROM AUTHOR]

The objective of this paper is to understand the effects of waves and vaporous cavitation upon the hydrodynamic and hydroelastic responses of a flexible surface-piercing hydrofoil, adding to the subcavitating results presented in Part 1. In general, the presence of a sufficiently large vaporous cavitation bubble facilitated the formation of a ventilated cavity, substantially reducing the angle of attack or speed required to induce fully ventilated flow, relative to subcavitating conditions. A new co-analysis procedure was used to isolate synchronous hydrodynamic modes and structural operating deflection shapes. Significant dynamic load amplification occurred when the resonant frequencies of the first twisting and second bending modes coalesced in both fully wetted and partially cavitating flows. The presence of waves did not diminish the effect of frequency coalescence, but did encourage intermittent lock-in with both leading edge cavity shedding and trailing edge vortex shedding at certain speeds. Partial cavity shedding typically had a negligible impact on the power spectral densities of structural motions because of incoherent cavity shedding. However, lock-in between the cavity shedding frequency and modal coalescence frequency led to shifting of the primary frequency peak, as well as amplified harmonics and interactions between the cavity shedding frequency and vortex shedding frequency. The transition from partially cavitating to fully ventilated flow caused sudden and large drops in the mean hydrodynamic loads and deformations, as well as substantial reductions in the intensity of the fluctuations. [ABSTRACT FROM AUTHOR]

A Karman vortex is a phenomenon of fluid flow that can cause fluctuation and vibration. As a result, it leads to fatigue damage to structures and induces safety accidents. Therefore, the analysis of the shedding law and strength of the Karman vortex is significant. To further understand the laws of turbulent Karman vortex shedding and strength, this study conducts a numerical vorticity simulation of a Karman vortex at the trailing edge of a hydrofoil based on the two-dimensional simplified model of the NACA0009 hydrofoil under different Reynolds numbers. Combined with image segmentation technology, the fractal characteristics of a turbulent Karman vortex at the trailing edge of a hydrofoil are extracted, the number and total area of vortex cores are calculated, and the fractal dimension of the vortex is obtained. The results show that the fractal dimension can characterize the change in vortex shape and strength under different Reynolds numbers, and that the fractal analysis method is feasible and effective for the shedding analysis of a turbulent Karman vortex. [ABSTRACT FROM AUTHOR]

This work describes the effects of waves on the hydroelastic response of a hydrofoil in fully wetted and ventilated flows. In the absence of vaporous cavitation (described in Part 2 of this paper series), shallow long-period non-breaking waves delayed ventilation inception because velocity fluctuations prevent the formation of a stably separated region of flow at the foil's leading edge. Aerated von Kármán vortex shedding occurred from the blunt trailing edge, producing vortex-induced vibration of the hydrofoil at a near-constant Strouhal number. Regular waves led to near sinusoidal oscillations of the load and deformations at the wave encounter frequency, while the mean response and the dynamic response at other frequency peaks corresponding to hydrodynamic and structural modes remained mostly unaffected. Significant dynamic load amplification was observed at a submerged aspect ratio of 2 for cases with low angles of attack because of coalescence between the second and third wetted structural modes; at high angles of attack, the amplitude of the load fluctuations and flow-induced vibrations reduced because energy was diverted away from the coalescence frequencies to the nearby vortex shedding frequency. In both calm water and wave conditions, transition from fully wetted to fully ventilated flow resulted in sudden and significant reduction in the load coefficients, as well as foil deflections. An impulse-like signature was observed in the time-frequency spectra during these transitions. In many of the cases, transition to fully ventilated flow also led to substantially reduced amplitudes in the load and deformation fluctuations. [ABSTRACT FROM AUTHOR]

Large-eddy simulations are reported on a system consisting of a marine propeller and a downstream, semi-infinite hydrofoil, carried out on a cylindrical grid of about 3.8 × 109 points. The results are compared with those of an earlier study, considering a similar hydrofoil of infinite spanwise extent, to shed light on the influence of the end effects on the wake flow. The comparisons show good agreement between the two cases at conditions of no incidence of the hydrofoil. However, as its incidence angle grows, end effects become important. Accounting for the limited spanwise extent of the hydrofoil results in the generation of a couple of streamwise-oriented vortices from the port and starboard edges of its tip, a reduced spanwise elongation of the propeller wake, and lower turbulent stresses on the suction side of the hydrofoil, where the massive separation phenomena characterizing the infinite hydrofoil at large incidence angles are missing. In the wake of the overall system, the peak values of turbulent stresses are produced in the region of shear between the vortex shed from the pressure side edge of the tip of the hydrofoil and the tip vortices from the propeller. The latter vortices roll around the former, resulting in an intense interaction between them. In contrast, downstream of the infinite hydrofoil, the highest turbulent stresses are achieved within its wake, due to its shear with the elongated wake of the propeller. [ABSTRACT FROM AUTHOR]

The vortex structure is a typically coherent structure. The influence of hydrofoil jets with different chordal positions on the vortex structure in the hydrofoil flow field is investigated to improve the suppression mechanism of cavitation by jet hydrofoils. The investigation is based on a vortex identification method and the chordal position with the best suppression effect on the large-scale vortex on the hydrofoil surface is explored. In addition, the dynamics of the vortex structure in different cavitation states are analyzed by means of vortex transport equations based on the optimal chordwise position. The results show that the U-shaped vortex is the main morphology of the hydrofoil surface bubble shedding; the results show that the U-shaped vortex is the main form of cavitation shedding on the hydrofoil surface; compared with the original hydrofoil and other jet positions, the shedding of large-scale vortex structure can be suppressed better when the jet is located at 0.6c; the dominant vorticity transport terms are different in various cavitation stages. In the primary cavitation stage, the vorticity dilatation term is dominant. In contrast, during the development, maturation, and shedding phases, the vortex stretching term dominates, reducing the pressure gradient in the hydrofoil flow field and suppressing the strength of the return jet. [ABSTRACT FROM AUTHOR]

The dynamical response of a 3D hydrofoil in the cavitation flow is investigated. Fluid and Structure Interaction (FSI) simulation was performed using ANSYS Fluent Software. First, the validation of cavitation flow around NACA 0015 hydrofoil was carried out. To predict the essential features of cavitation flow, like the shedding of vortex and cloud cavities, the turbulent viscosity of SST (Shear-Stress Transport) k-ω model was modified by writing a UDF (User-Defined Function) code. To ensure the simulation of two-way Fluid-Structure Interaction (FSI), the results of NACA 66 hydrofoil in the uniform flow at non-cavitation conditions (wetted flow) are compared with experimental results, which indicates a good agreement. The results show that metallic alloys (aluminium and magnesium) have a slight effect on hydrofoil performance in comparison to each other. At the flexible foils, the hydrodynamic loads would cause bending and twisting deformations of the foil and the foil vibration. [ABSTRACT FROM AUTHOR]

Large-eddy simulations on a grid consisting of 3.8 billion points are reported, dealing with a system composed of a propeller and a downstream semi-infinite hydrofoil, mimicking a propeller–rudder system typical of surface ships. The analysis is focused on the tip vortices shed by the hydrofoil across four values of incidence angle. The results of the simulations highlight the generation of two vortices, from the pressure and suction edges of the tip of the hydrofoil, respectively, with the former more intense than the latter. They promote higher turbulence levels and pressure fluctuations at the tip of the suction side of the hydrofoil and especially at its bottom end, while the pressure side is almost unaffected. For large incidence angles, they join in the near wake of the system into a single streamwise-oriented structure. This dominates the wake signature. It is a location of minima of pressure and maxima of turbulence, which affect performance in terms of cavitation and noise. Large levels of turbulent kinetic energy are also achieved in the region of shear of this vortex with the tip vortices shed by the propeller and coming from the pressure side of the hydrofoil, rolling around the vortex from the tip of the hydrofoil. In contrast, at no incidence or for small angles, the wake of the system is dominated by the shear layer shed from the trailing edge of the hydrofoil and by the hub and tip vortices populating the wake of the propeller. [ABSTRACT FROM AUTHOR]

The large eddy simulation model coupled with the modified Schnerr–Sauer cavitation model has been used to numerically simulate the unsteady cavitation and noncavitation flow of the three-dimensional NACA66 (National Advisory Committee for Aeronautics) hydrofoil under different operating conditions. The results show that the magnitude of the cavitation number plays a decisive role in the hydrofoil cavitation quasiperiodic phenomenon. The cavitation number of 1.25 is used as a typical working condition for analysis. Using the Ffowcs Williams–Hawkings acoustic analogy approach accompanied by the vorticity transport equation splitting, the growth and shedding of cavitation also lead to the growth and shedding of the vortex structure. The cavitation–vortex interaction is mainly influenced by the vortex stretching term and vortex dilatation term and amplitude of them are larger than 500. The baroclinic torque term may be responsible for generating vorticity during the cloud cavitation collapse and has a lower amplitude about 200. The cavity volume acceleration is the main influencing factor of the low-frequency pressure fluctuation around the cavitating hydrofoil. Moreover, the NACA66 hydrofoil surface-pressure data are collected for dynamic mode decomposition to locate the hydrofoil surface noise sources. The alternate high and low amplitude regions in the mode results overlap highly with the cavitation transformation regions. The cavity transformation and pressure fluctuations are the main reason for the generation of periodic low-frequency noise source regions on the hydrofoil surface. Moreover, the corresponding frequencies of each order mode are linearly correlated with the cavitation shedding frequency of 5.70 Hz. Combined with the results of the multiple mode comparisons, it can be inferred that the hydrofoil suction surface under the cavitation effect will generate quasiperiodic waves starting from upstream and moving downstream. [ABSTRACT FROM AUTHOR]

Hydrofoils are widely applied in the maritime domain, and their vibrational characteristics significantly influence the genesis and evolution of vortices. Consequently, modulating vortex shedding through the active vibration of hydrofoils may lead to the enhancement of the hydrodynamic performance of bluff bodies. In order to study the influence of structural oscillations on vortex shedding, both Computational Fluid Dynamics (CFD) and wake oscillator models were used to simulate the modulations of vortex shedding caused by an actively oscillating hydrofoil. By altering the vibration frequency and amplitude, the shedding frequency of vortices can be locked onto the structural vibration frequency. Another important discovery is that the dominant frequency of noise at the trailing edge of the actively vibrated hydrofoil has significantly shifted. Alongside the shift, there is a marked reduction in noise amplitude, denoting a dual acoustical modulation stemming from the vibratory intervention. These advancements provide pivotal contributions to the understanding of fluid-structure interactions and their resultant acoustic phenomena. • NACA0009 Hydrodynamic modelling of hydrofoils demonstrates excellent concordance between the predicted vortex shedding frequencies and experimental observations, affirming the accuracy of the simulations. • Numerical simulation evidence robustly supports that active vibration of the hydrofoil effectively alters the vortex shedding frequency. • Successfully delineated the vortex shedding locking boundaries for the NACA0009 active vibrating hydrofoil, providing a pivotal reference for wake oscillator model investigations. • Identified a significant shift in the noise dominant frequency at the trailing edge of the actively vibrating hydrofoil, accompanied by a noticeable attenuation in the corresponding noise amplitude. [ABSTRACT FROM AUTHOR]

Vortex-induced vibration (VIV) of hydrofoils is a pivotal concern in the field of ocean engineering. This study performs a parametric analysis on VIV of an elastic hydrofoil, specifically focusing on the vortex shedding frequency, trailing edge vibration and vortex intensity. The effects induced by vortex shedding are captured through combining the finite volume solid stress method and the Shear Stress Transport (SST) k–ω model. Frequency domain analysis of the hydrodynamic coefficients is conducted using the fast Fourier transform (FFT). Based on extensive convergence study, the effects of oncoming velocity, thickness, and the angle of attack are investigated in detail. The results show that the trailing edge thickness or relative thickness of the hydrofoil can be adjusted to avoid excessive vibration when the lock-in phenomenon occurs. It is also found that the influence of angle of attack on lock-in vibration primarily lies in the shedding of the trailing vortex. It can be attributed to the forward movement of the transition position of the boundary layer on the upper trailing edge of the hydrofoil, leading to an earlier separation of the boundary layer. • This study focuses on the VIV and lock-in phenomenon of hydrofoil with different geometric parameters. • Strouhal number's maximum value is corresponding to the lower bound of the lock-in interval. • By changing the trailing edge thickness and maximum thickness of the hydrofoil, the wake vortex. • Shedding frequency was effectively controlled to inhabit the VIV of hydrofoils. [ABSTRACT FROM AUTHOR]

The influence of cavitation on the wake behind a NACA 0009 hydrofoil with a truncated trailing edge has been numerically investigated using a homogeneous mixture model coupled with a controlled decay SST γ - Re θt turbulence model. Using optimal definitions of the inlet turbulent intensity and the empirical condensation and vaporization coefficients of the cavitation model, simulated results have shown a good agreement with experimental data. Notably, the numerical results exhibit negligible deviations of less than 0.7% in vortex shedding frequencies for different cavitation levels. If the size of the vortex cavitation grows, a substantial increase in both lift and drag coefficients on the hydrofoil is observed. Furthermore, the influence of cavitation on the trajectories of vortex centers and the morphology of the primary shedding vortices has been revealed using a vortex identification method. The findings highlight that the cavitation development enhances the advected velocity of the shedding vortices while decreasing the streamwise inter-vortex spacing. Consequently, both factors are found to contribute to the increase of the vortex-shedding frequency behind the NACA 0009 hydrofoil with the truncated trailing edge when cavitation appears and develops. • Accurate simulation of the cavitating wake behind a truncated NACA hydrofoil. • High-fidelity modelling in terms of boundary layer transition and cavitation. • Cavitation changes the fluid forces and the trajectories of the primary vortices. • Cavitation increases the shedding frequency and the advected velocity. • Cavitation reduces the streamwise inter-vortex spacing. [ABSTRACT FROM AUTHOR]

The acoustic analogy is adopted to reconstruct the sound generated by a system consisting of a hydrofoil and a downstream propeller. The data from high-fidelity large-eddy simulations with the hydrofoil at angles of incidence of 0 ° , 10 ° , and 20 ° were generated using a cylindrical grid consisting of 1.7 × 109 points. The results of the analysis demonstrate the following: (i) the strong influence by the incidence of the hydrofoil on the acoustic signature of the system; (ii) the leading role of the non-linear component of sound at small radial coordinates in the vicinity of the wake, especially moving away from the propeller plane; (iii) the leading role of the linear component of sound from the surface of the propeller moving away along the radial direction; (iv) the importance of the shear between the wakes shed by the hydrofoil and the propeller in accelerating the process of instability of the coherent structures and reinforcing the non-linear sources of sound; and (v) the strong, complex directivity of sound at small radial coordinates, as a consequence of the interaction between the wakes from the hydrofoil and the propeller. [ABSTRACT FROM AUTHOR]

The Karman vortex street is a common flow phenomenon. In hydraulic machinery, it is usually located downstream of the guide vanes and the runner blades, which reduces hydraulic performance and may also cause fatigue damage to the structure. The latest research suggested that the difference in velocity gradient on each side of the blade trailing edge may have a significant impact on the strength of the wake vortex. The current work aims to verify the above conclusion and further explore the influence of asymmetry of flow velocity on the wake vortex. A numerical model with the velocity ratio, α, between the two sides of the hydrofoil as the only variable was designed, and the wake characteristics were solved by a computational fluid dynamics (CFD) method based on the finite volume. The unsteady Reynolds-average Navier–Stokes (URANS) equations were numerically solved by coupling with a transitional shear-stress transport (SST) turbulence model. The results showed that with the increase of α, the vortex shedding frequency decreased first, and then increased after reaching the critical velocity ratio αc1 ≈ 1.4. The vortex intensity first gradually decreased, and the vortex street suddenly disappeared after reaching the critical velocity ratio αc2 ≈ 2.2. The value of αc1 was affected by the thickness of the trailing edge, and αc2 was affected by the thickness and the Reynolds number. Besides, the asymmetry of the flow velocity also affected the effectiveness of the trailing-edge trimming. This research can provide references for the design of hydraulic machinery and other submerged structures. [ABSTRACT FROM AUTHOR]

This paper presents the effects of heaving motions on the hydrodynamic characteristics, supercavitating flow regimes and vortex structures for a two-dimensional (2D) supercavitating hydrofoil. The sinusoidal heaving motion of the supercavitating hydrofoil is realized by overset grid technology. The lift coefficient, drag coefficient, supercavitating flow regime and vortex structures around the supercavitating hydrofoil are analyzed and compared among different amplitudes of the heaving motion. The predicted cavities and the hydrodynamic characteristics are in good accordance with the experiments at a stationary state. The lift coefficient and drag coefficient of the heaving hydrofoil present a sinusoidal law, which is related to the effective angle of attack. The heaving motion would affect the cavity length and its thickness. The greater the heaving amplitude, the greater the difference in cavity pattern at different heaving positions. The cavity variation would affect the shear layer and thus change the vortex shedding characteristics, which are different from those at a stationary state. [ABSTRACT FROM AUTHOR]

The flow over a hydrofoil in the wake of a marine propeller is studied using large-eddy simulation on a cylindrical grid composed of 3.8 billion points. Four angles of incidence of the downstream hydrofoil are considered, ranging from 0 ° to 15 ° . The impact of the propeller wake on the flow within the boundary layer of the hydrofoil is substantial, increasing the skin-friction and producing significant spanwise flows, associated especially with the deflection of the tip and hub vortices. This deflection is strongly influenced by the incidence angle of the hydrofoil, producing an overall expansion of the propeller wake on its pressure side and a contraction on its suction side. The tip and hub vortices are also the major source of pressure fluctuations on the surface of the hydrofoil, affecting this way its unsteady lift and drag coefficients. On the pressure side, the most significant pressure fluctuations are due to the hub vortex, while on the suction side, their maxima originate from the overlapping effects by the tip vortices and the adverse streamwise pressure gradient, promoting the instability of the boundary layer. Pressure fluctuations are an increasing function of the incidence of the hydrofoil on both its pressure and suction sides. [ABSTRACT FROM AUTHOR]

How swimming fish extract energy from environmental vortices is still an open question. In this work, fish swimming in unsteady flow is numerically investigated by using the immersed boundary lattice Boltzmann method. The swimming fish is modeled as a forced Kármán gait hydrofoil, and the vortical flow is generated by a stationary circular cylinder. We calculate the Fourier spectra of hydrodynamic forces on the hydrofoil surface and found that there is a coupling between lateral force and drag, which results from a nonlinear wave interaction. The Kármán gait hydrofoil adjusts the lateral force by applying lateral excitation to the vortical flow and improves the drag/thrust through nonlinear wave interaction. We find that suppressing the harmonic energy of the viscous mode is the key ingredient to extract energy from the passing vortex. In turn, the downstream distance LN and foil-vortex phase φ determine whether the viscous harmonic energy can be suppressed. If the viscous mode harmonic is strong, the interaction between the vortex shedding mode and the viscous mode leads to a series of combined modes, which extract energy from the fundamental mode. These combined modes that appear in the fluid force spectra reduce the efficiency of energy extraction. [ABSTRACT FROM AUTHOR]

The wake of an oscillating teardrop hydrofoil with combined heaving and pitching motion was studied numerically at Reynolds number of 8000 and Strouhal numbers of $St=0.21{-}0.94$. The lower Strouhal number exhibited high efficiency propulsion with small thrust generation. However, larger thrust generation at high $St$ required more power, which lowered the propulsive efficiency. Quantitative assessment of vortex evolution, along with qualitative investigation of the formation and interaction of primary structures, revealed the association with elliptic instability characteristics for both co-rotating and counter-rotating vortex structures in both wakes. With respect to advection of the leading-edge vortex, the pressure distribution further depicted evidence of spanwise instability with distinct temporal evolution along the suction and pressure surfaces of the oscillating foil. Three-dimensional assessment of wake structures located downstream of the trailing edge depicted the existence of dislocations associated with primary vortex 'rollers'. At low $St$ , these were limited to fine spanwise corrugations (valleys and bulges) on weaker leading edge rollers, which enlarged as the rollers advected downstream. In contrast, at high $St$ , the wake exhibited conjoint hairpin-horseshoe vortex structures that led to stronger deformations on the coupled vortex rollers. The statistical characteristics of secondary structures resembled the long wavelength mode and mode A identified previously for purely pitching and heaving foils, respectively. They also mimicked mode B for stationary cylinders. Novel wake models are introduced based on a complete vivid three-dimensional depiction of coherent wake structures. [ABSTRACT FROM AUTHOR]

Hydrodynamic damping is a key factor that influencing the amplitude of structural vibration under resonance conditions. In this study, the one-way FSI energy balance method by loading structure mode onto flow field is applied to simulate the hydrodynamic damping. Based on the good solution of vortex shedding frequency, structure natural frequency and mode shape, it provides a good accuracy on both flow field and structural field by predicting the hydrodynamic damping well with deviations less than 10.4%. On the basis, the hydrodynamic damping characteristics of different vibration displacements and the lock-in region are studied and analyzed in detail. Results found that the hydrodynamic damping ratio increases with the increasing of vibration displacement. A displacement interval within 6 × 10−5 m–1.2 × 10−4 m can be detected when the hydrodynamic damping ratio is slightly affected by vibration displacement. It is proved that the value of hydrodynamic damping depends on the combined area of hydrodynamic force and structural velocities. The hydrodynamic damping in the lock-in region changes nonlinearly. Under the resonance condition, the disturbance of the fluid domain increases, and a negative damping value will appear, which will increase the structure vibration amplitude. • The one way method can well predict the hydrodynamic damping. • The hydrodynamic damping increases with the increase of vibration displacement. • There is a vibration displacement interval that the damping values are similar. • Negative damping value appears in the lock-in region. • The damping depends on the combined area of flow force and structure velocity. [ABSTRACT FROM AUTHOR]

A comprehensive two-dimensional numerical investigation has been undertaken to calculate the energetic cost of propulsion and the various flow transitions of a fish-like body undulation mechanism based on a National Advisory Committee for Aeronautics 0012 hydrofoil. This covers a wide range of Strouhal (0 ≤ S t ≤ 1.4) and Reynolds (500 ≤ R e ≤ 5000) numbers from simulations based on a level-set function immersed-interface method. It is found that the time-averaged thrust coefficient displays a quadratic relationship with increasing St, and increases significantly with Re. Additionally, the time-averaged input power coefficient exhibits a cubic dependence with increasing St but is independent of Re. Both St dependences agree with those previously observed experimentally and numerically for an oscillating foil; however, for similar ranges of governing parameters, comparisons suggest that the body undulation mechanism possesses a higher propulsive efficiency. The S t ∝ R e − 0.19 scaling for the drag-to-thrust transition is consistent with that found for a wide variety of fish and birds in nature. Interestingly, for cases with an undulation wave-speed below the free-stream speed, the time-averaged drag coefficient is found to be higher than that of a stationary hydrofoil at the same Re. Furthermore, the time-averaged input power coefficient is negative, indicating the potential for the undulation mechanism to extract energy from the free-stream. Eight different wake patterns/transitions are documented for the parameter space; these have been assembled into a wake-regime parameter-space map. The present findings should aid in predicting and understanding different hydrodynamic forces and wake patterns for undulating kinematics. [ABSTRACT FROM AUTHOR]

We present the dynamics of a hydrofoil free to oscillate in a plane as it interacts with vortices that are shed from a cylinder placed upstream. We consider cases where the cylinder is (i) fixed, (ii) forced to rotate constantly in one direction or (iii) forced to rotate periodically. When the upstream cylinder is fixed, at lower reduced velocities, the hydrofoil oscillates with a frequency equal to the frequency of vortices shed from the cylinder, and at higher reduced velocities with a frequency equal to half of the shedding frequency. When we force the cylinder to rotate in one direction, we control its wake and directly influence the response of the hydrofoil. When the rotation rate goes beyond a critical value, the vortex shedding in the cylinder's wake is suppressed and the hydrofoil is moved to one side and remains mainly static. When we force the cylinder to rotate periodically, we control the frequency of vortex shedding, which will be equal to the rotation frequency. Then at lower rotation frequencies, the hydrofoil interacts with one of the vortices in its oscillation path in the positive crossflow (transverse) direction, and with the second vortex in the negative crossflow direction, resulting in a 2:1 ratio between its inline and crossflow oscillations and a figure-eight trajectory. At higher rotation frequencies, the hydrofoil interacts with both shed vortices on its positive crossflow path and again in its negative crossflow path, resulting in a 1:1 ratio between its inline and crossflow oscillations and a linear trajectory. [ABSTRACT FROM AUTHOR]

Hydrofoil is the core unit of energy conversion for axial-flow pumps and hydro-energy turbines. The dynamic characteristics of hydrofoil significantly affect the operation stability of pumps and turbines, especially under the critical stall condition. In this paper, the unsteady flow field of NACA66 hydrofoil under critical stall condition at Reynolds number 0.75 × 10E6 is investigated by IDDES method. The low-frequency oscillations (LFO) under critical stall condition characterized by two typical frequencies with Strouhal number (St) 0.031 and 0.065 are reported in pressure pulsation and lift coefficient respectively. It is found that the merging phenomenon of separation vortices are the main reason of the wave peak of LFO with St 0.031, while the phenomenon of generation and shedding of separation vortices exist at the moment corresponding to the wave trough. The reason of the LFO of lift coefficient with St 0.065 is found to be the long-short switching of streamwise coverage of the leading edge separation vortex. The change of streamwise coverage is corresponding to the movement of the reattachment point of the separation area. The revelation of LFOs flow mechanism in hydrofoil under critical stall can provide reference for its unsteady flow control and applications. • LFO characteristic of hydrofoil NACA66 under critical stall condition is reported. • Two typical low-frequencies dominate the transient pressure and lift respectively. • The separation vortex merging fosters the first low-frequency. • Long-short switching of LE separation vortex leads to the second low-frequency. [ABSTRACT FROM AUTHOR]

• Reliable numerical simulation for vortex shedding frequency on truncated hydrofoil. • The effect of upstream for a vortex shedding frequency on the truncated hydrofoil. • The effect of propeller in front of a truncated hydrofoil on the vortex shedding frequency. • The comparison of vortices on the 2D truncated hydrofoil and the isolated 2D truncated hydrofoil. • High accuracy of propeller performance based on the sliding mesh method. [ABSTRACT FROM AUTHOR]

A hydrofoil blade design (HBD) is proposed to suppress the unsteady pressure pulsations in a centrifugal pump. Numerical simulation is carried out using the SST k‐ω model to obtain the unsteady flow field in the pump both with HBD and the conventional blade design (CBD). The pressure pulsations with the two types of blade profiles are compared at the nominal flow rate, whereas the jet‐wake flow patterns and vortex structures are analyzed to clarify the effect of the HBD on the flow field. The pressure pulsation amplitudes at the blade frequency (fBPF) are significantly reduced with the HBD, especially near the volute tongue, with a reduction of 72%. It is evident that HBD can effectively suppress the pressure pulsation. It is for these reasons that the relative velocities in the jet region at the impeller outlet are reduced, and the velocity gradients between the pressure and suction side are decreased, which contributes to improving the flow uniformity at the impeller outlet. Besides, the vorticities at the impeller outlet are reduced, and the high energy vortices shedding from the blade trailing edge are restrained. The combined effects of the uniform flow field and low vorticities contribute to the reduction of pressure amplitude with the HBD. The findings would serve as a reference for the pump designs with low noise and vibration. [ABSTRACT FROM AUTHOR]

Large eddy simulations are presented on the wake flow of a notional propeller (the INSEAN E1658), upstream of a NACA0020 hydrofoil of infinite spanwise extent, mimicking propeller–rudder interaction. Results show that the flow physics is dominated by the interaction between the coherent structures populating the wake of the propeller and the surface of the hydrofoil. The suction and pressure side branches of the tip vortices move towards inner and outer radii, respectively. The hub vortex is split into two branches at the leading edge of the hydrofoil. The two branches of the hub vortex shift in the opposite direction, compared to the tip vortices, towards the rudder suction sides. As a result, a contraction of the propeller wake on the suction sides occurs, leading to increased levels of shear stress and turbulence. At downstream locations along the hydrofoil the spanwise deflection of the suction side branches of the tip vortices affects the trajectory of the overall propeller wake, including also the smaller helical vortices across the span of the wake of each blade and the two branches of the hub vortex on the two sides of the hydrofoil. This cross-stream shift persists, producing a strong anti-symmetry of the overall wake. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the hydrodynamic characteristics and corresponding flow structures of a pitching Clark-Y hydrofoil with special emphasis on the added force effect. The experiments were performed in the looped cavitation tunnel, and the hydrodynamic characteristics are obtained by the dynamic moment measurement system. The average angle of attack and amplitude of pitching hydrofoil are 10° and 5°, respectively. The whole oscillatory motion is divided into two stages, namely the up stage and down stage. The pitching rate is set with the Reynolds number Re = 4.4 × 105. The incompressible URANS equations are solved by using the coupled k-ω SST turbulence model and γ - Re θ transition model. It can be shown that the numerical results agree well with the experimental measurements. Compared to the static hydrofoil, the lift of the pitching case is higher in the up stage because of the positive added lift. Meanwhile, the center of pressure is closer to the pitching axis. For the down stage, the lift of the pitching case is lower caused by the negative added lift and the pressure center is further away from the pitching axis. The main reason is that the different pitching direction corresponds to specific position of the added lift relative to the pitching axis, causing the pressure center to move in different directions. When the stall happens, the evolution of lift and the pressure center fluctuates due to the shedding vortex structures. Results show that the added force effect on the hydrodynamic force is negligible compared with the contributions from the vorticity within the flow in the stall phase. As the pitching rate increases, the added force effect becomes more significant, thus leading to the higher lift of the up stage and the lower lift of the down stage. Besides, for the stall phase, the dynamic stall angle is delayed for the fast pitching rate, which is due to the generation and development of the counterclockwise trailing edge vortex. • Compared with static hydrofoil, the lift of pitching hydrofoil increases in the up stage and decreases in the down stage. • Compared with static hydrofoil, the pressure center is closer to pitching axis in the up stage, the down stage is opposite. • The added force effect becomes more significant with the increase of the pitching rate. [ABSTRACT FROM AUTHOR]

Vortex shedding of freely rotating hydrofoils and the fluctuations in hydrodynamic loads are typical problems in marine engineering. Hence, the hydrodynamic mechanism should be investigated in detail. In this study, the Reynolds-averaged Navier–Stokes method is used to analyze the unsteady flow characteristics of a two-dimensional freely rotating hydrofoil in uniform flow at different Reynolds numbers. The accuracy of the numerical simulation method is verified through convergence analysis of the simulation results. According to the mechanical characteristics and flow field distributions, the effects of three Reynolds numbers from 5 × 104 to 1.2 × 106 and five rotation centers from 0.2c to 0.4c on the dynamic stall of the hydrofoil are analyzed. The results show that the rotation center considerably influences the dynamic stall characteristics of the hydrofoil. As the rotation center approaches 0.4c, the amplitudes of the drag and lift coefficients and the rotation angle of the hydrofoil clearly increase by at least 206%, 10.5%, and 185%, respectively, along with the vortex shedding frequency, which also leads to the increase in the Strouhal number by at least 17.3%. Furthermore, the recovery of the drag and lift coefficients is delayed, resulting in an evident hysteresis effect. Simultaneously, this dynamic stall results in the decrease in the velocity distribution amplitude in the wake field and the increase in the pressure difference between the upper and lower surfaces. The continuous shedding of strong vortices from the trailing edge also leads to more complicated flow field characteristics. [ABSTRACT FROM AUTHOR]

In order to investigate the turbulence-induced acoustic characteristics of hydrofoils, the flow and sound field for a model NH-15-18-1 asymmetric hydrofoil were calculated based on the mixed method of large eddy simulation (LES) with Lighthill analogy theory. Unsteady fluid turbulent stress source around the hydrofoil were selected as the inducements of quadrupole sound. The average velocity along the mainstream direction was calculated for different Reynolds numbers (R e). Compared to experimental measurements, good agreement was seen over a range of R e. The results showed that the larger the R e , the larger the vortex intensity, the shorter the vortex initial shedding position to the leading edge of the hydrofoil, and the higher the vortex shedding frequency (f s). The maximum sound pressure level (SPL) of the hydrofoil was located at the trailing edge and wake of the hydrofoil, which coincided with the velocity curl (ω) distribution of the flow field. The maximum SPL of the sound field was consistent with the location of the vortex shedding. There were quadratic positive correlations between the total sound pressure level (TSPL) and the maximum value of the vortex intensity (Γ max) and velocity curl, which verified that shedding and diffusion of vortices are the fundamental cause of the generation of the quadrupole source noise. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to use the NACA 0015 symmetric hydrofoil as the research subject and control cloud cavitation on hydrofoils. Design/methodology/approach: Based on observed distribution of caudal fin spines on fish, a bionic structure of fin-like spines is arranged on the hydrofoil suction surface, which maintains the cavitation in a quasi-steady state stage by eliminating the cyclic shedding process of cloud cavitation. Based on the modified shear stress transport k-ω turbulence model and the Zwart–Gerber–Belamri cavitation model, this paper compares and analyzes the NACA 0015 hydrofoil and the bionic NACA 0015 hydrofoil under condition of an angle of attack of 8° and a cavitation number of 0.8. Findings: The results show that the average drag of the hydrofoil is reduced but the lift is decreased, and the lift-drag ratio is increased after arranging the bionic structure. The bionic structure can effectively reduce the turbulent kinetic energy and make the flow more stable; it also can effectively control the hydrofoil surface side-entrant jet and the vortex shedding process of the near wall region. Originality/value: Based on the above conclusions, the bionic structure of fin-like spines can achieve a significant passive control in the hydrofoil cloud cavitation process. [ABSTRACT FROM AUTHOR]

• A new two-dimensional model for lock-in research is proposed. • Frequency locking is reproduced in simulating the elastic vibration of two-dimensional hydrofoil. • Analyze the causes of lock-in through the frequency spectrum characteristics of solid and fluid systems. Vortex-induced vibration (VIV) has always been a significant research topic in relation to marine structures, with structural resonance and locking vibrations liable to occur at particular Reynolds numbers. To investigate this problem, fluid–structure coupling simulations of an elastic hydrofoil within a viscous flow are conducted. The correlation between the structural response and vortex shedding was explored. By analyzing the frequency eigenvalues, the structural response and vortex shedding at different frequencies can be decoupled. The findings suggest that the self-sustainability of natural vibration plays a significant role in frequency lock-in once structural resonance has been triggered. The phase difference between the lift pulsation and vortex shedding is determined, and is confirmed to be a significant factor influencing the resonant vibration of elastic foils. This phase difference can be used to determine whether the lock-in phenomenon has occurred. It is also found that veering phase, the resonance appears as forced vibration, while at locking phase, the resonance appears as self-sustained vibration at a natural frequency. [ABSTRACT FROM AUTHOR]

In more recent years, supercavitation has attracted intensive attention due to its potentials in drag reduction for underwater vehicles. Ventilation is acknowledged as an efficient way to enhance cavitation when vehicles work under low speed. That means natural and ventilated cavitation may coexist in the flow and the interaction between the natural cavitation and ventilated cavitation has to be considered. In this paper, ventilated cavitating flow with natural cavitation around a base-ventilated hydrofoil is solved by a multi-phase cavitation solver based on OpenFOAM. The Partially-Averaged Navier-Stokes method is utilized for resolving turbulence. Lengths of the natural cavities are investigated under non-ventilation and ventilation conditions. Cavity shape evolution and interface deformation have also been studied under different angle of attack. Results show that ventilation cavitation at the base of the hydrofoil tends to depress the natural cavitation on the hydrofoil surface. As the increase of the attack angle, the shedding cavity of natural cavitation have a great impact on the interface shape of the ventilation cavity. Furthermore, the research also finds that the re-entry jet is the reason for natural cavitation shedding process and the interface deformation of the ventilated cavity arises from the vortex structures induced by the shedding natural cavitation. [ABSTRACT FROM AUTHOR]

Engineering applications prove that the modification of the trailing edge shape of a blade can effectively reduce the amplitude of the vortex-induced vibration, but the mechanism behind it is still not fully understood. In this investigation, unsteady CFD and two-way FSI numerical simulation methods are performed on three-dimensional (3D) NACA 0009 hydrofoils with blunt and Donaldson trailing edges. The vortex shedding formation process, the added mass and the hydrodynamic damping ratio at different flow velocities are investigated. The relative deviations in the vortex shedding frequency, the natural frequency in water, and the hydrodynamic damping ratio obtained by simulation are within 12.88%, 4.62% and 8.82%, respectively, compared with the experimental results. As the flow velocity increases, the added mass for blunt and Donaldson trailing edge hydrofoils remains almost constant and gradually decreases, respectively. The hydrodynamic damping ratio of the hydrofoil increases linearly as the flow velocity increases with both blunt and Donaldson trailing edges involving a slope of 0.0032 and 0.005, respectively. At a flow velocity of 20 m/s, the maximum amplitude is reduced to 57% after Donaldson trailing edge modification. The results show that the hydrodynamic damping ratio of the Donaldson trailing edge is significantly increased when the flow velocity is greater than 20 m/s. The reason for this is the collision between the upper and lower trailing edge vortexes, which leads to the faster dissipation of vortex intensity. [ABSTRACT FROM AUTHOR]

Effects of slip on the flow around a symmetrical hydrofoil with a blunt trailing-edge are numerically investigated at Reynolds numbers of R e = 5 × 10 6 , 12.5 × 10 6 and 25 × 10 6 based on the free-stream velocity and chord length. The simulations are performed by applying a two-dimensional Unsteady Reynolds–Averaged Navier–Stokes (URANS) approach and SST k–ω turbulence model. Furthermore, the Navier boundary condition with different slip lengths ( L s = 2 , 35 and 7 0 µm) is employed on the surfaces. The results indicate that the Ls has a considerable effect on the integral parameters and a moderate influence on the wake flow structure. As such, a massive drag reduction (up to 47%) is observed, and an increase of Ls causes the increase of both frictional and pressure drag reduction rate. It is shown that a noticeable drag reduction can be achieved when the non-dimensional slip length is larger than one. The increment of slip length also leads to increase the amplitude of force fluctuations and frequency of vortex shedding; besides, the strength of vortex structures and the turbulence intensities are augmented. [ABSTRACT FROM AUTHOR]

• The turbulent cavitating flow around a hydrofoil is simulated by LES. • The three equation method is used to assess the LES results in cavitating flow. • The effect of verification and validation in cavitating flow is discussed. • The vortex structure and spectrum characteristic during cavity shedding is clarified. This study uses implicitly filtered Large Eddy Simulation with a homogenous cavitation model to investigate the transient turbulent cavitating flow around a Clark-Y hydrofoil with emphasis on Verification and Validation (V&V). The numerical results indicate that the present simulation can predict the time evolution process of the periodic cavity shedding and agree reasonably with the available experimental data. This study presents the first practical application of LES V&V in a transient cavitating flow. The three-equation method is used to assess the LES error magnitudes in unsteady cavitating flow. The results show that a noticeable difference can be observed between the modeling error and numerical error, and the former has a larger magnitude than the latter in cavitating flow. It is demonstrated that the unsteady cavitation has a big impact on the LES errors. Additionally, compared with non-cavitating flow, the unsteady cavitation increases the values and fluctuation amplitudes of numerical, modeling, and total errors. Grid requirement for modeling the cavitating flow has been discussed from the viewpoint of LES V&V. The numerical results also reveal that the periodic cavity shedding causes the complex and turbulent flow feature by vortex and spectrum analyses, and this has a great influence on the simulation accuracy. [ABSTRACT FROM AUTHOR]

In nature, the locomotion and maneuvering force of fish with thunniform mode crucially originate from the flapping foil as a principal component to produce thrust. Aiming to investigate the thrust performance and hydromechanical efficiency of flapping hydrofoil, a very large eddy simulation (VLES) method is introduced into dynamic mesh technique to solve the unsteady flow past flapping hydrofoil. The method can broaden the simulation of complex separated flow along with excellent compromise of accuracy and computing resources. In addition, the feasibility and validation of the method are verified to be well fit for dynamic mesh technique. The optimal propulsion performance is explored through varying the Strouhal (St) number and maximum angle of attack (α0) in an incoming flow condition of Re = 40,000. The temporal evolution of the angle of attack has a significant impact on lateral force coefficient, moment coefficient and the structure of shedding corotating vortices in the wake for high St number. The α0 exerts evident effect on the leading-edge separation. With the increase of St, the low-pressure values of suction surface become greater and the low-pressure areas become wider, hence producing more vortex-augmented thrusts and longer active time. The highest efficiency is equipped with the higher growth rate of thrust coefficient and moderate wake vortex strength. Furthermore, the temporal evolution of angle of attack has little effect, as does the leading-edge separation. In reality, an insight about high efficiency combined with high thrust should be considered in order to arrive to well-behaved propulsion system. [ABSTRACT FROM AUTHOR]

Abstract The objective of this paper is to investigate the cavitating flow patterns around a specific hydrofoil (Tulin hydrofoil) via combined experimental and numerical studies, and to better understand the vortex-cavitation interactions in transient cavitating flows. The experimental studies were carried out in the closed-loop cavitation tunnel, and a high-speed digital camera is applied to document the cavitation patterns. The numerical investigations are performed using a large-eddy simulation method and the Zwart cavitation model. The results showed that the predicted cavity formation and evolution agree well with the experimental observation. With decreasing of the cavitation number, different cavitating flow patterns occur around the hydrofoil, namely inception cavitation (σ = 1.57), vortex cavitation (σ = 1.27), cavitating vortex street (σ = 1.07), cloud cavitation (σ = 0.87), mixture supercavitation (σ = 0.67), and developed supercavitation (σ = 0.54). Especially, the flow structures of vortex cavitation, cavitating vortex street and cloud cavitation were further investigated with the Euler and Lagrangian method. For vortex cavitation, the cavitating vortex forms and sheds at the leading and trailing edge of the foil alternatively, with a pair of asymmetric vortex structures observed. The trailing edge cavitating vortex has a regular vortex shape and a clear boundary between the vortex structures. For cavitating vortex street, vortex shedding process is not independent, instead, the vortex braid between the trailing edge cavitating vortexes and the so called "cat's eye" vortex row can be obviously observed. The center of circulation region is corresponding to low finite-time Lyapunov exponent (FTLE) value, and the bridges of the FTLE is concentrated in the boundary of the vortex structure and curling in the dynamic surrounding of the circulation region. The trajectory of the points well presents the dynamic flow pattern. For cloud cavitation pattern, the cavity develops to cover the entire suction surface, and the cloud cavity sheds downstream periodically. Highlights • Analyze the formation, development and collapse of different vortex cavitating flow patterns. • Improve the understanding of the vortex-cavitation interactions around a Tulin hydrofoil. • Explore a new method, Lagrangian Coherent Structures (LCS), for the analysis of transient vortex structures. [ABSTRACT FROM AUTHOR]

Highlights • Further insight into unsteady cavitating flows characteristics involved thermal effects are investigated. • Local thermal characteristics in the cavitation region around hydrofoil are obtained. • Dynamics evolution mechanism in thermos-sensitive fluids is addressed. • Interactions between the vortex structure and cavitation evolution are presented. Abstract Cavitation shedding is of a great practical interest since the unsteady flow features can induce significant fluctuations around the body where cavitation occurs, especially in thermo-sensitive fluid. The present paper numerically studies the unsteady cavitating flows over a NACA0015 hydrofoil in thermo-sensitive fluid of fluoroketone with special emphasis on the cavitation shedding dynamics. Comparisons between numerical predictions and available experimental data are performed to validate the numerical framework and help us further understand the physical feature. The results show that the predicted cavity evolution and pressure distribution are in good agreement with the experimental data. It is observed that the cavitating flows over the hydrofoil undergo more complex unsteady periodic evolution, including the cavity formation, growth, break-off, collapse and shedding. Two propagation patterns of the re-entrant flow appear along the chordwise direction and the spanwise direction, which are responsible for the unsteady cavity evolution. Note that the temperature distribution around the hydrofoil is closely related to the cavity evolution. The temperature around the hydrofoil undergoes a strong evolution that is contributed by the local evaporation and condensation processes. Meanwhile, the thermal effects on cavitating flows are associated with temperature-dependent physical properties of the fluid media. Interestingly, compared to the isothermal cavitation, thermal effects suppress the intensity of cavitation and show a potential to reduce the pressure pulsation peak. Furthermore, there is a strong interaction between the complex vortex structure and cavitation evolution. In one typical cycle, the rotation effect and the shear effect co-dominate the cavity growth, break-off and shedding of the unsteady cavitating flows. [ABSTRACT FROM AUTHOR]

The objective of this study is to explore the unsteady cavitation characteristics and the mechanism of cavitation-vortex interaction around a twist hydrofoil. The cavitation conditions were simulated using the Partially-Averaged Navier-Stokes (PANS) method in conjunction with a homogeneous flow cavitation model. The numerical method employed in this study successfully captures the intricate shedding process of cavitation on the hydrofoil surface. Furthermore, the cavity morphology obtained at various time instants exhibits a remarkable agreement with the experimental results. The simulation results of the unsteady characteristics of cavitation shedding on the hydrofoil surface revealed that the shedding process could be divided into primary and secondary shedding phases. The primary shedding happened as a result of the re-entrant jet flow generated by the adverse pressure gradient at the cavitation tail. Notably, the secondary shedding was predominantly caused by the combined effects of the re-entrant jet and the side re-entrant jet flow. During the primary shedding process, the cavitation experienced disturbances from the side re-entrant jets, causing it to roll and be drawn upwards into a U -shape cavity structure. Subsequently, as the secondary shedding happened, the side re-entrant jets contributed to the formation of a secondary U -shape cavity at the cavitation tail. The investigation on the cavitation-vortex interaction around the hydrofoil showed a strong consistency between the distribution of vortices and cavitation. The foot of the primary U -shape vortex was attached to the hydrofoil surface, while the shedding vortex tail on both sides exhibited secondary U -shape vortex structures. The primary U -shape vortex formation resulted from the combined effects of suction and rotation generated by the side re-entrant jets and re-entrant jets on both sides of the hydrofoil. The secondary U -shape vortex was induced by secondary shedding cavitation which produced by rotational effects at the stable cavitation tail. • The Partially-Averaged Navier-Stokes method combined with Zwart cavitation model is used to simulate cavitation flow around the hydrofoil. • The unsteady characteristics of the cavitation shedding on the twisted hydrofoil surface are investigated. • The vortex-cavitation interference and cavitation-induced vortex structures are investigated based on the Q criterion. • The production mechanism of secondary U -shape vortex is elucidated. [ABSTRACT FROM AUTHOR]

The two-dimensional flow characteristics of the wake-structure interference between a cylinder and a freely rotating hydrofoil are analysed using the unsteady Reynolds-averaged Navier–Stokes method. The effects of different rotation centres and spacing ratios on the mechanical properties, flow-field structures, surface pressure distributions, turbulent fluctuations, vortex shedding and interference, and the resultant radiated noise and fluid resonant oscillation of the cylinder–hydrofoil system are systematically investigated. The results show that the hydrofoil decreases the shedding frequency of the cylinder wake vortex, whereas the cylinder accelerates the steady flow on the hydrofoil surface through the backward movement of the rotation centre, enhancing the dynamic stall characteristics. The turbulent vortex structures have a major suppression effect in the interaction region. At small spacing ratios, the mechanical properties of the system fluctuate considerably. As the spacing increases, the cylinder Karman vortex street is gradually released and plays a dominant role in generating turbulent fluctuations. The surface pressure increasingly recovers, and the turbulent kinetic energy and vortex intensity show jump peaks at the leading edge of the hydrofoil due to wake impingement. The primary-vortex shedding behind the cylinder impacts the hydrofoil surface, resulting in alternating shedding of the large-scale vortex street with a gradual loss in strength and coherence. This periodic variation in the hydrodynamic characteristics is reflected in the radiated noise, which is confirmed by employing a feedback model, as the system sound pressure level becomes stronger at spacing ratios of L / d = 1. 0 , 1.5, and 3.0 due to the flow resonant oscillation. [Display omitted] • The wake-structure interference of flow over a cylinder–hydrofoil system is studied. • The influence of different parameters on dynamic stall characteristics is analysed. • The noise change due to flow resonant oscillation is verified by a feedback model. [ABSTRACT FROM AUTHOR]

The wakes behind a symmetrically and a quasi-symmetrically pitching hydrofoil are numerically studied. To understand the generation mechanism of the asymmetric wake behind a symmetrically pitching hydrofoil, we shed light on the timing of vortex shedding and convection velocity of vortices in the wake. The centers of the vortices in the wake are tracked using a method based on the critical point theory. The tracks of the vortex centers reveal crucial insights into the dependence of the vortex convection velocity on pitching frequency and pitching amplitude. The vortex strength and the spatial separation between the vortices embody the wake deflection. We find the inherent inability of the shear-layer rolling up at par with the pitching motion results in an uneven temporal separation (Δ t ʹ) between two consecutive vortices, which dictates the spatial separation between the vortices. The uneven temporal separation facilitates formation of vortex dipoles, which gives rise to the asymmetric wake formation. To substantiate the hypothesis of the uneven temporal generation of vortices, we used quasi-symmetric pitching of the hydrofoil, which can even the timing of vortex shedding and can metamorphose the asymmetric wake into a symmetric wake. On the contrary, relaxing the shear-layer roll-up can transmute a symmetric wake to an asymmetric wake. The detailed analysis of symmetrically pitching hydrofoil, quasi-symmetrically pitching hydrofoil, flexible hydrofoil, and asymmetrically pitching hydrofoil reveals that Δ t ʹ = 0.5, Δ t ʹ < 0.5 and Δ t ʹ > 0.5 correspond to a symmetric wake, an upward deflected wake and a downward deflected wake, respectively. • The phase difference between vortices raises an instability. • Temporally uneven shedding of vortices leads to the formation asymmetric wake. • The asymmetric wake can be induced/suppressed by modifying the pitching motion. [ABSTRACT FROM AUTHOR]

• The mode decomposition combined with vortex identification is performed. • The roller-shaped, hairpin-shaped and horseshoe-shaped coherent structures over a ventilated hydrofoil are detected. • The modal turbulent kinetic energy transport theory is introduced and developed. • The correlation between turbulence and gas-liquid interfacial fluctuations in the ventilated wake flow is discussed. In this paper, the complex interaction of gas-vortex-turbulence in ventilated cavitation over a NACA0015 hydrofoil is investigated by using large eddy simulation. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used for analyzing the three-dimensional fluctuation modes of gas-liquid interfaces induced by turbulent coherent structures in ventilated cavitation. The results show that among the first four dominant POD modes possessing 99.5% modal kinetic energy in the ventilated cavitating flow, and the turbulent POD mode 2 contains the multi-scale coherent structures and acts as a bridge for the energy scale transition from mode 1 to mode 3 through the gas-liquid interface oscillations. The DMD modal structures are reconstructed from the roller-shaped energetic structure captured by POD mode 2, which further reveal the process of breaking down near the hydrofoil leading edge, changing into the hairpin shape and finally stretching into the horseshoe shape above the hydrofoil trailing edge for the turbulent coherent structures on the cavity interfaces. Such low-frequency wake structures are energetic but sustained by means of the high-frequency turbulent fluctuations, with the interfacial oscillation amplitude changed through the formation and transition of the multi-scale coherent structures. Further, the modal turbulent kinetic energy transport theory is introduced to describe the ventilated coherent structures. It is worth noting that the large-scale energetic structures in POD mode 2 are mainly drawing energy from mean flows through the Reynolds stress, and the modal turbulent energy stored by shedding vortex and air cavities in the ventilated wake flow is redistributed and balanced due to the turbulent and pressure diffusion effects. Besides, the uneven spatial distribution of turbulent energy caused by the vortex structures of different modal scales is proved to promote the spatial oscillation level of the ventilated cavity interfaces. This study is helpful to understand the interaction mechanism between turbulence and gas-liquid interfacial fluctuations for the ventilated wake flow. [ABSTRACT FROM AUTHOR]

The tandem configuration of two hydrofoils is an effective way to improve the power of the energy-extraction system. In such a configuration, the inter-foil spacing between two hydrofoils is one of the important configuration parameters. The effect of the inter-foil spacing on the energy-extraction power is investigated by the STAR CCM + based on an overset mesh. First, a fixed motion phase shift between two foils of −180° is proposed with adjustment of the inter-foil spacing. Then, the global phase shift is established; for keeping it constant, the motion phase shift is correspondingly changed with adjustment of the inter-foil spacing. Based on the systematical studies of the energy-extraction power of the tandem foils with spacing, it is found that in the tandem foils system, the energy extraction of the upstream foil is changed tiny. With increasing the spacing between two foils, the energy-extraction power of the downstream foil shows a very obvious periodic fluctuation when the motion phase shift is constant. Due to the loss of wake velocity, the global phase using the freestream velocity causes errors in describing the downstream foil-vortex interaction, so the wake phase model using the average wake velocity is a better choice. For the small effective angle of attack hydrofoils with only shear layer vortices, the wake energy does not change with distance, so the maximum efficiency of tandem foils with different inter-foil spacings is almost the same. But when the leading edge vortex shedding occurs, the energy extraction of the tandem foils is significantly affected by the inter-foil spacing due to the change of the wake energy. • The effect of the inter-foil spacing on the energy extraction power of two tandem foils is systematically investigated. • The maximum of the energy extraction keeps constant for different spacings provided that global phase shift is optimized. • The constant wake energy of the upstream hydrofoil results in the constant energy extraction of the tandem foils. [ABSTRACT FROM AUTHOR]

To better understand the vortex shedding mechanism and to assess the capability of our numerical methodology, we conducted numerical investigations of vortex shedding from truncated and oblique trailing edges of a modified NACA 0009 hydrofoil. The hybrid particle-mesh method and the vorticity-based subgrid scale model were employed to simulate these turbulent wake flows. The hybrid particle-mesh method combines the vortex-in-cell and the penalization methods. We have implemented numerical schemes to more efficiently use available computational resources. In this study, we numerically investigated vortex shedding from various beveled trailing edges at a Reynolds number of 106. We then compared the numerical results with the experimental data, which show good agreement. We also conducted numerical simulations of wakes behind the hydrofoil at rest in periodically varying flows. Results reveal that vortex shedding is affected by the periodicity of a free-stream flow, as well as the trailing-edge shape. [ABSTRACT FROM AUTHOR]

The unsteady cavitating flow and pressure fluctuation around the 3-D NACA66 hydrofoil were simulated and validated based on detached eddy simulation turbulence model and a homogeneous cavitation model. Numerical results show that detached eddy simulation can predict the evolution of cavity inception, sheet cavitation growth, cloud cavitation shedding, and breakup, as well as the pressure fluctuation on the surface of hydrofoil. The sheet cavitation growth, detachment, cloud cavitation shedding are responsible for the features of the pressure fluctuation. [ABSTRACT FROM AUTHOR]

The prediction accuracies of partially-averaged Navier-Stokes model and improved shear stress transport k-ω turbulence model for simulating the unsteady cavitating flow around the hydrofoil were discussed in this paper. Numerical results show that the two turbulence models can effectively reproduce the cavitation evolution process. The numerical prediction for the cycle time of cavitation inception, development, detachment, and collapse agrees well with the experimental data. It is found that the vortex pair induced by the interaction between the re-entrant jet and mainstream is responsible for the instability of the cavitation shedding flow. [ABSTRACT FROM AUTHOR]