The influence of fluid–structure interaction on cloud cavitation about a rigid and a flexible hydrofoil. Part 3

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.

Experimental Study on the Relationship Between Cavitation and Lift Fluctuations of S-Shaped Hydrofoil

In order to study the energy loss of bi-directional hydraulic machinery under cavitation conditions, this paper uses high-speed photography combined with six-axis force and torque sensors to collect cavitating flow images and lift signals of S-shaped hydrofoils simultaneously in a cavitation tunnel. The experimental results show that the stall angle of attack of the S-shaped hydrofoil is at ±12° and that the lift characteristics are almost symmetrical about +1°. Choosing α = +6° and α = −4° with almost equal average lift for comparison, it was found that both cavitation inception and cloud cavitation inception were earlier at α = −4° than at α = +6°, and that the cavitation length at α = −4° grew significantly faster than at α = +6°. When α = +6°, the cavity around the S-shaped hydrofoil undergoes a typical cavitation stage as the cavitation number decreases: from incipient cavitation to sheet cavitation to cloud cavitation. However, when α = −4°, as the cavitation number decreases, the cavitation phase goes through a developmental process from incipient cavitation to sheet cavitation to cloud cavitation to sheet cavitation to cloud cavitation, mainly because the shape of the S-shaped hydrofoil at the negative angle of attack affects the flow of the cavity tails, which is not sufficient to form re-entrant jets that cuts off the sheet cavitation. The formation mechanism of cloud cavitation at the two different angles of attack (α = +6°、−4°) is the same, both being due to the movement of the re-entrant jet leading to the unstable shedding of sheet cavity. The fast Fourier analysis reveals that the fluctuations of the lift signals under cloud cavitation are significantly higher than those under non-cavitation, and the main frequencies of the lift signals under cloud cavitation were all twice the frequency of the cloud cavitation shedding.

Statistical analysis of vapor distribution in a cavitation flow based on an ensemble of instantaneous liquid velocity fields

A new method was developed for statistical analysis of ensembles of instantaneous velocity fields measured by PIV in liquid (continuous phase) to determine the distribution of the vapor phase in cavitating flow. The method is based on two main principles: the absence of tracers used for PIV measurements in vapor, and the statistical independence of individual measurements. This allowed establishing an exponential dependence of repeatability of the vapor phase at a certain point of a cavitating flow. Compliance with this theoretical law was verified using the Pearson chi-square test. All theoretical distributions were divided into several groups depending on the time-averaged local vapor content calculated over the entire ensemble of realizations and the probability of a single event. As a result, dimensions of the stationary part of an attached cavity and the place of detachments of cloud cavities from the hydrofoil surface were determined using the new method of statistical analysis for an unsteady cloud cavitation regime.

Study of unsteady cavitating flow around Clark-Y hydrofoil using nonlinear PANS model with near-wall correction

In this paper, we describe the use of a new nonlinear partially-averaged Navier–Stokes (PANS) model with near-wall correction for simulating the cavitating flow around a Clark-Y hydrofoil. For comparison, the standard [Formula: see text]–[Formula: see text] PANS model is also used. The results demonstrate that compared to [Formula: see text]–[Formula: see text] PANS and experiment, the new PANS model shows better performance for cavitation flow, including time-averaged velocity, root mean square (rms) velocity and cavity shedding processing. Through the calculation of the lift and drag coefficient at [Formula: see text] and [Formula: see text], it can be concluded that the cavitation will decrease the lift and increase the drag of the hydrofoil, resulting in a decrease of the lift-to-drag ratio. From the analysis of different terms in both the turbulent kinetic energy (TKE) and dissipation rate transport equations of the cloud cavitation, it is found that the production term and the dissipation term are dominant in the turbulent transport, and they are mainly distributed in the vapor–liquid interface and the trailing edge of the hydrofoil.

Systematic Validation Study of an Unsteady Cavitating Flow over a Hydrofoil Using Conditional Averaging: LES and PIV

We present results of Large-eddy simulations (LES) modeling of steady sheet and unsteady cloud cavitation on a two-dimensional hydrofoil which are validated against Particle image velocimetry (PIV) data. The study is performed for the angle of attack of 9∘ and high Reynolds numbers ReC of the order of 106 providing a strong adverse pressure gradient along the surface. We employ the Schnerr–Sauer and Kunz cavitation models together with the adaptive mesh refinement in critical flow regions where intensive phase transitions occur. Comparison of the LES and visualization results confirms that the flow dynamics is adequately reproduced in the calculations. To correctly match averaged velocity distributions, we propose a new methodology based on conditional averaging of instantaneous velocity fields measured by PIV which only provides information on the liquid phase. This approach leads to an excellent overall agreement between the conditionally averaged fields of the mean velocity and turbulence intensity obtained experimentally and numerically. The benefits of second-order discretization schemes are highlighted as opposed to the lower-order TVD scheme.

Unsteady cavities near the hydrofoil with a small aspect ratio

Using digital processing of high-speed visualization data on a cavitation flow near NACA hydrofoil with critically low aspect ratio, the frequencies of the formation and separation of cavities in the flow are identified. It is shown that in the case of development of cloud cavitation the main dimensionless frequency varies within 0.4, which corresponds to the type of internal instability. The Strouhal number corresponds to the frequency of attached cavity occurrence and varies in range from 0.6 to 0.8. The Strouhal numbers calculated in third mode exceed 1. This mode corresponds to the forming of very small cavities near the leading edge of hydrofoil.

Investigation of Water Injection Influence on Cloud Cavitating Vortical Flow for a NACA66 (MOD) Hydrofoil

Re-entrant jet causes cloud cavitation shedding, and cavitating vortical flow results in flow field instability. In the present work, a method of water injection is proposed to hinder re-entrant jet and suppress vortex in cloud cavitating flow of a NACA66 (MOD) hydrofoil (Re = 5.1 × 105, σ = 0.83). A combination of filter-based density corrected turbulence model (FBDCM) with the Zwart–Gerber–Belamri cavitation model (ZGB) is adopted to obtain the transient flow characteristics while vortex structures are identified by Q criterion & λ2 criterion. Results demonstrate that the injected water flow reduces the range of the low-pressure zone below 1940 Pa on the suction surface by 54.76%. Vortex structures are observed both inside the attached and shedding cavitation, and the water injection shrinks the vortex region. The water injection successfully blocks the re-entrant jet by generating a favorable pressure gradient (FPG) and effectively weakens the re-entrant jet intensity by 46.98%. The water injection shrinks the vortex distribution area near the hydrofoil suction surface, which makes the flow in the boundary layer more stable. From an energy transfer perspective, the water injection supplies energy to the near-wall flow, and hence keeps the steadiness of the flow field.