Pitching Hydrofoil Research Articles

Numerical investigation on vortex dynamics of flow around a pitching hydrofoil via the finite-domain impulse theory

Numerical investigation on vortex dynamics of flow around a pitching hydrofoil via the finite-domain impulse theory

Numerical Study on Hydrodynamic Performance of a Pitching Hydrofoil with Chordwise and Spanwise Deformation

The hydrofoil plays a crucial role in tidal current energy (TCE) devices, such as horizontal-axis turbines (HATs), vertical-axis turbines (VATs), and oscillating hydrofoils. This study delves into the numerical investigation of passive chordwise and spanwise deformations and the hydrodynamic performance of a deformable hydrofoil. Three-dimensional (3D) coupled fluid–structure interaction (FSI) simulations were conducted using the ANSYS Workbench platform, integrating computational fluid dynamics (CFD) and finite element analysis (FEA). The simulation involved a deformable hydrofoil undergoing pitching motion with varying elastic moduli. The study scrutinizes the impact of elastic modulus on hydrofoil deformation, pressure distribution, flow structure, and hydrodynamic performance. Coefficients of lift, drag, torque, as well as their hysteresis areas and intensities, were defined to assess the hydrodynamic performance. The analysis of the correlation between pressure distribution and deformation elucidates the FSI mechanism. Additionally, the study investigated the 3D effects based on the flow structure around the hydrofoil. Discrepancies in pressure distribution along the spanwise direction result from these 3D effects. Consequently, different chordwise deformations of cross-sections along the spanwise direction were observed, contributing to spanwise deformation. The pressure difference between upper and lower surfaces diminished with increasing deformation. Peak values and fluctuations of lift, drag, and torque decreased. This study provides insights for selecting an appropriate elastic modulus for hydrofoils used in TCE devices.

Hydrodynamics and propulsion of a hydrofoil undergoing leading-edge pitching and traveling wave-based surface undulation

We numerically study the fluid–structure interaction of a free-stream flow across a hydrofoil pitching at its leading edge with superimposed traveling wave-based surface undulations. We utilize an in-house code that employs the sharp interface immersed boundary method and consider a constant pitching amplitude θ0 = 5°, a constant local amplitude-to-thickness ratio AL=0.15, and wave number K = 20 of surface undulation. We compare the effect of surface undulation on a pitching hydrofoil with that of a hydrofoil undergoing pure pitching or experiencing pure surface undulation. The findings reveal that surface undulation on the pitching hydrofoil increases thrust on the hydrofoil. The onset of asymmetry in the vortex street occurs at a lower pitching Strouhal number (St) due to the early formation of a vortex dipole. In addition to the presence of an asymmetric inverse von Kármán vortex street, higher pitching frequencies reveal re-deflection of the asymmetric inverse von Kármán vortices. We quantified dynamics of vortex dipole to explain the occurrence of asymmetric and re-deflected reverse von Kármán vortex street. Furthermore, the analysis reveals an optimum combination of St and phase speed that yields higher propulsive efficiency, as both motions compete in generating thrust. A linearly superimposed scaling analysis for the time-averaged thrust of the combined motion is also presented. The computations and scaling are found to be in good agreement.

Effect of the vortical structures on the hydrodynamic performance of a pitching hydrofoil

Effect of the vortical structures on the hydrodynamic performance of a pitching hydrofoil

Optimization of semi-active hydrofoil propulsion performance based on CFD Taguchi method and neural network

In order to improve the propulsive performance of the existing pure heaving motion hydrofoil, the effect of varying stiffness ratio K*, damping ratio C* and inertia ratio J* on the propulsive efficiency of the semi-active NACA 0012 hydrofoil is systematically investigated by using the combination of CFD, Taguchi method and neural network. The results show that the passive pitching motion can significantly affect the propulsive performance of the hydrofoil. Compared to the pure heaving hydrofoil, the propulsive efficiency of the optimized semi-active hydrofoil can be improved by up to 20.97%. Further analysis reveals that the passive pitching motion can weaken the strength of the vortex around the hydrofoil, thus reducing the thrust and lift force on the hydrofoil, which results less power consumed by the active heaving motion of the hydrofoil. Although the thrust coefficient is reduced, the energy consumed by the passive pitching hydrofoil is reduced more, which leads a higher propulsive efficiency of the semi-active hydrofoil.

PIV measurement of cavitating flow around a pitching hydrofoil

Particle Image Velocimetry (PIV) and hydrodynamic measurements were applied to investigate the cavitating flow of a pitching hydrofoil in the form of triangular wave motion (mean incidence α 0=10°, amplitude Δα=5° and pitching frequency f*=2Hz). The Reynolds number is Re=4.5×105. The cavitation number is set to σ=2.3, 1.36. Different typical cavity patterns are observed by PIV images in the whole pitching period, including sub cavitation, inception cavitation, sheet cavitation and cloud cavitation. As the σ decreases, the cavity area increases. And the the corresponding time and position of cavitation patterns also changed significantly. In the instantaneous velocity field of an oscillating hydrofoil, the low velocity zone (LVZ) and the mainstream zone (MZ) are observed. The LVZ corresponds to the cavitation region and changes with the change of cavitation morphology. Meanwhile, the LVZ has a large velocity gradient. The velocity gradient in the MZ is larger along the direction parallel to the incoming flow, and the velocity tends to increase first and then decrease gradually downstream. With the decrease of cavitation number, the area of LVZ increases. And the distribution of LVZ is more uneven, which is mainly caused by oscillation motion and uneven water vapor mixing.

Numerical investigation of hydrodynamic damping of a pitching hydrofoil at different flow regimes

Due to the development of intermittent renewable energy resources, hydropower plants are mostly operated under off-design conditions. This may lead to natural frequency excitation shortening the turbine life-span. To accurately estimate the fatigue life, it is necessary to evaluate the hydrodynamic damping parameters. In the present study, different flow regimes and their relationship with hydrodynamic damping are analyzed numerically using the γ - Reθt transition SST ĸ - ω turbulence model. The test case is a NACA0009 hydrofoil pitching around its center of mass. A good agreement between the present and previous numerical results is obtained. Consistent with the literature, hydrodynamic damping coefficient demonstrate consistently two different regions. The phase shift between the displacement and moment increases with the rise of the pitching frequency. After reaching a peak value at a reduced frequency of around κ = 5, the phase shift starts to decrease, and eventually approaches zero again. The damping behavior demonstrates an opposite trend. First, it reduces in spite of the phase shift increase, and after the inflection point, where the flow field changes from the drag mode to the thrust mode, it rises due to the torque development. The maximum of the damping occurs at the low frequencies.

Revealing the mechanism and scaling laws behind equilibrium altitudes of near-ground pitching hydrofoils

A classic lift decomposition (Von Kármán & Sears, J. Aeronaut. Sci., vol. 5, 1938, pp. 379–390) is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behaviour provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for ${A{\kern-4pt}R}\ {\rm (aspect\ ratio)} <1.5$ occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within $20\,\%$ of its value when $St\ {\rm (Strouhal\ number)} < 0.45$ . For $St \ge 0.45$ there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effects, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization.

Large eddy simulation of cavitating flow around a pitching hydrofoil

This numerical investigation employs advanced computational fluid dynamics techniques to examine the intricate physics of cavitating flows around a pitching NACA 66 hydrofoil. Unsteady simulations are conducted using both large eddy simulation (LES) and K-Omega SST turbulence models. The pitching motions range from 0 to 15°, encompassing four cavitation numbers (3.25, 3.5, 3.75, 4) and a Reynolds number of 750,000. The study comprehensively analyzes various flow field characteristics, including pressure distribution, velocity, vorticity, shear stress, vapor volume fraction, and turbulence kinetic energy. The kinematics of pitching significantly influence hydrodynamic loads and the surrounding flow structures in cavitating conditions. Flow visualizations illustrate the evolution of sheet/cloud cavitation, reentrant jet, and vortex dynamics throughout a pitching cycle. Notable findings demonstrate the impact of cavitation number on cavity shape and the relationship between angle of attack, reentrant jet location, and vortex size. Additionally, negative vorticity dilatation is observed to be correlated with cavity size.

Experiment investigation of the tip vortex cavitation around a pitching hydrofoil

Experimental research was carried out to investigate the characteristics of tip vortex cavitation (TVC) caused by tip vortex in an oscillating hydrofoil. Shanghai Shipping and Research Institute's looped cavitation tunnel served as the site of the experiments. The hydrofoil used as the test was NACA (National Advisory Committee for Aeronautics) 63820. Two high-speed cameras, one torque sensor, and six hydrophones were employed to capture the cavitation patterns, the torque exerted on the hydrofoil, and the cavitation noise, respectively. The cavitation flow under static angle of attack (AoA) and the dynamic AoA have all been investigated in order to have a better knowledge of the differences between the TVC surrounding these two conditions. The AoA of 8.5°, 10°, and 14.5° and the AoA range of 1.8°–16° were selected for the static condition research and the dynamic condition study, respectively. A tip vortex flow was created between the tip of the stationary hydrofoil and the ceiling of the tunnel test section. To investigate the impact of the cavitation number on the growth of TVC surrounding the pitching hydrofoil, various pressure environments were built up. As for the experiment environment, cavitation numbers 2.47, 2.00, and 1.66 were used. The results indicate: (1) under static conditions, decreasing cavitation and increasing AoA lead to increased stability and topological complexity of TVC. (2) Comparing and analyzing cavitation patterns during the ascending, static, and descending processes reveal that the strongest cavitation intensity during the descending process, followed by static conditions, with the least intensity during the ascending process. (3) The frequency properties under pitching motion include those of each static AoA condition, although the acoustic characteristic of higher AoA has a stronger influence on that of dynamic condition.

Cavitation induced hysteresis of a pitching hydrofoil near free surface

Cavitation induced hysteresis of a pitching hydrofoil near free surface

Qualitative and quantitative analysis of interaction between cavitation patterns and vortices of a pitching hydrofoil from Lagrangian viewpoint

The evolution of transient flow structures and mass transport in cavitating flow around a pitching hydrofoil is investigated qualitatively and quantitatively, and the interaction between cavitation patterns and vortices is elucidated from Lagrangian viewpoint. First, turbulence effects are estimated by the density-corrected k–ω model to account for the local compressibility of the multiphase flow at Reynolds number Re=6.4×105. Then, the formation and evolution of vorticity structures during the whole pitching cycle are analyzed using Lagrangian averaged vorticity deviation method. By comparing the flow structures and hydrodynamic properties at varying angles of attack, the cavitating flow is divided into two distinct stages, namely multi-scale cloud cavitation phase from α+=10° to α−=8°, and traveling sheet cavitation phase from α−=8° to α+=10°. Specifically in cloud cavitation, the formation of the cavitation pattern is closely related to the development of the main vortex. Furthermore, the quantitative analysis method based on Lagrangian flow network is developed to deeply analyze the transport and mixing processes. Importantly, the coherence ratio and the mixing parameter are proposed as transport indicators to precisely quantify the spatial connectivity behavior. Finally, the correlations between vapor fraction, codelength, global coherence ratio and global mixing parameter are evaluated. As the conclusion, it is shown that Lagrangian methods are powerful tool for both qualitative and quantitative analysis, and the results obtained could provide a key and important understanding of the flow structure and changing mechanism between cavitation and vortices in marine hydro and propulsion systems.

Hydrodynamic characteristics of a pitching hydrofoil in unsteady uniform inflow with special emphasis on the hysteresis effect

Numerical flow simulations on a Clark-Y pitching hydrofoil are carried out to study the effect of an unsteady uniform inflow on the dynamic characteristics and the corresponding flow structure. The representative hysteresis phenomenon of pitching hydrofoil is observed and analyzed emphatically. In this study, the pitching motion trajectory is a triangular wave with mean incidence of α0 = 10° and amplitude of Δα0 = 5° at a pitching frequency f* of 2 Hz. The amplitude of unsteady uniform velocity ΔU is set 0, 0.75, 1.50, 3.0 respectively, and the frequency of unsteady uniform velocity f of 1, 2, 4 were chosen. The numerical method is validated through the experimental results at ΔU = 0. Results revealed that pitching motion and unsteady uniform inflow both lead to the occurrence of hysteresis effect, and two hysteresis effect quantization parameters (the hysteresis parameter εCL and hysteresis area SCL) were defined. Results showed that the relationship between ΔU, f and the two parameters is respectively linear and nonlinear. Meanwhile, the values of ΔU, f directly determine the contribution of unsteady uniform inflow to hydrodynamic hysteresis effect. In addition, ΔU and f have a significant impact on the flow structures and the development of vortices. However, ΔU and f don't change vortex structure directly, but affect the formation and dwell time of vortex structure significantly, thus leading to the different hydrodynamic characteristics.

Dynamic responses of pitching hydrofoil in laminar–turbulent transition regime

Recently, the problem of a transitional boundary layer around a pitching foil has been attracting increasing attention. To determine the underlying physical mechanisms, in this study, a pitching hydrofoil is numerically investigated using the shear stress transport (SST) k–ω turbulence model coupled with the γ–Re˜θt transition model. First, the prediction of the static performance is compared with the experimental measurements and XFOIL data to validate and verify the numerical accuracy of the proposed method. Subsequently, the flow morphologies induced by sinusoidal and non-sinusoidal pitching laws are analyzed and compared in different reduced frequencies. The results indicate that reducing the empirical coefficient, A1, in the SST k–ω turbulence model can generate the flow separation in advance, thus improving the prediction of the hydraulic performance at a high angle of attack. The dynamic behavior of the laminar separation bubble is strongly associated with the pitching method and velocity. The collapse of the laminar separation bubble can destabilize the local boundary layer, generating multi-laminar separation bubbles. When new separation bubbles form and shed, a turbulent boundary layer moves downstream and is adsorbed on the surface simultaneously. The turbulence flow passes through the trailing edge, destroying the local vortex, contributing to a transiently elevated hydrodynamic lift. During a rapid pitching down, a counterclockwise trailing edge vortex becomes increasingly unstable, repeating the processes of inception, development, and shedding. The Theodorsen model fails to produce a reasonable hysteresis loop owing to the assumption of a fully attached flow. The results of a hybrid of the Theodorsen and Øye models show noticeable improvement in the dynamic lift prediction. The empirical coefficient, ks, of the Snel model is optimized, improving the predictions of low-frequency pitching significantly. All dynamic stall models present the same trend: low-frequency motions show better agreement than high-frequency ones. In the former, modeling of a non-sinusoidal pitching is closer to the transient numerical results than that of a sinusoidal motion.

A robust and accurate finite element framework for cavitating flows with moving fluid-structure interfaces

In the current work, we present a variational mechanics framework for the coupled numerical prediction of cavitating turbulent flow and structural motion via a stabilized finite element formulation. To model the finite mass transfer rate in cavitation phenomena, we employ the homogenous mixture-based approach via phenomenological scalar transport differential equations given by the linear and nonlinear mass transfer functions. Stable linearizations of the finite mass transfer terms for the mass continuity equation and the reaction term of the scalar transport equations are derived for the robust and accurate implementation. The linearized matrices for the cavitation equation are imparted a positivity-preserving property to address numerical oscillations arising from high-density gradients typical of two-phase cavitating flows. The proposed formulation is strongly coupled in a partitioned manner with an incompressible 3D Navier-Stokes finite element solver, and the unsteady problem is advanced in time using a fully-implicit generalized-α time integration scheme. We first verify the implementation on the benchmark case of the Rayleigh bubble collapse. We demonstrate the accuracy and convergence of the cavitation solver by comparing the numerical solutions with the analytical solutions of the Rayleigh-Plesset equation for bubble dynamics. We find our solver to be robust for large time steps and the absence of spurious oscillations/spikes in the pressure field. The cavitating flow solver is coupled with a hybrid URANS-LES turbulence model. We validate the coupled solver for a very high Reynolds number turbulent cavitating flow over a NACA0012 hydrofoil section. Finally, the proposed method is applied in an Arbitrary Lagrangian-Eulerian framework to study turbulent cavitating flow over a pitching hydrofoil section and the characteristic features of cavitating flows such as re-entrant jet and periodic cavity shedding are discussed.

Characteristics of vortex shedding from a sinusoidally pitching hydrofoil at high Reynolds number

This experimental study characterizes vortex shedding from a sinusoidally pitching hydrofoil at high Reynolds number, reveals the effects of pitching amplitude, reduced frequency, and Reynolds number on the dynamic force responses beyond the linear inviscid theory, and sheds light on the correlation between vortex shedding regimes and dynamic force responses for a high Reynolds number pitching hydrofoil.

Dynamics of flow around a pitching hydrofoil

This paper presents a parametric study on a forced pitching hydrofoil. The non-dimensional frequency (Strouhal number, Std) and amplitude ratio (A∗) of the hydrofoil pitching are varied as 0.21 ≤Std≤ 0.33 and 0.55 ≤A∗≤ 0.8, respectively. The numerical solution of the problem is obtained using unsteady Navier–Stokes equations. Coefficients of thrust, power, and efficiency of the hydrofoil are calculated and presented on the Std – A∗ plane. The evolution of the flow structure around the pitching hydrofoil is clarified for the conditions corresponding to both drag and thrust generations. A flow model is hypothesized. A mathematical analysis of the flow model, involving Euler, Coriolis and centrifugal accelerations in a non-inertial frame, is developed to assimilate the physical insight into the thrust generation and power input. The analysis provides theoretical relationships of thrust, power, and efficiency as functions of Strouhal number and/or amplitude ratio. The data from the numerical simulation tangibly support the relationships. This subject would be handy for undergraduate and postgraduate studies.

The interaction between the transient cavitating flow and hydrodynamic performance around a pitching hydrofoil

The interaction between the unsteady cavitating flow and hydrodynamic performance around a pitching Clark-Y hydrofoil is investigated experimentally and numerically. The experiments were conducted in the looped cavitation tunnel, and the cavitation patterns are documented by two high-speed digital cameras, and the moment of hydrofoil is measured by the moment sensor. The pitching hydrofoil is controlled from α+ = 10° to α+ = 15° firstly, and goes back to α− = 5° from α+ = 15°, then goes back to α+ = 10° from α− = 5° at Re = 4.4∗105. The upstream velocity U∞ and the cavitation number σ is fixed at 6.3 m/s and 1.38, respectively. And the pitching rate is α˙=40∘/s,α˙∗=0.086. The numerical investigations were performed by solving the incompressible UNRANS equations via the commercial code CFX using the Merkle cavitation model, the coupled k-ω SST turbulence model and γ-Reθ transition model. The predicted cavity patterns and moment coefficients agree well with the experimental results. The results showed there are two distinct cavitation patterns (Multi-scale cloud cavitation and Traveling sheet cavitation). For the Multi-scale cloud cavitation phase (α+ = 10°-α- = 10°), the re-entrant flow is the main factor on the stability of cavitating flow structures, which is responsible for different shedding patterns. According to the breaking position and re-entrant flow thickness, this stage is divided into three different patterns of the cavity development and shedding. For the Traveling sheet cavitation phase (α− = 10°-α+ = 10°), the shedding of cavity mainly results from the interaction of the re-entrant flow and the fluctuation of the gas liquid interface, thus leading to the irregular breaking points. The cavitating flow structure of different phases were further investigated using the LESs, which will be help to identify the dynamic behavior of flow structures effectively.

Cavitating flow structures and corresponding hydrodynamics of a transient pitching hydrofoil in different cavitation regimes

The present paper applied experimental and numerical methods to investigate the cavitating flow structures and corresponding hydrodynamics for a transient pitching Clark-Y hydrofoil. The aims are to (1) improve the understanding of the interplay between the transient cavitating flow structures, motion of the hydrofoil, and hydrodynamic performance, (2) quantify the influence of cavitation on the hydrodynamic load coefficients and flow structures, and (3) analyze the evolution of cavitating flow during different cavitation regime. The pitching motion trajectory is a triangular wave with mean incidence of α0=10° and amplitude of Δα = 5° at a frequency of 2 Hz. The upstream velocity U∞ is fixed at 6.3 m/s, which is corresponding to Re=4.4 × 105. The cavitation patterns for different cavitation numbers are mainly documented by the high-speed photography, and the dynamic characteristics of the hydrofoil are measured by the torque sensor. The numerical investigations were performed by solving the incompressible URANS equations using the mass-transfer cavitation model, the coupled k-ω SST turbulence model and γ-Reθ transition model. The predicted cavity patterns and moment coefficients agree well with the experimental results. Four typical regimes, including sub cavitation, inception cavitation, sheet cavitation and cloud cavitation, are observed. Compared to the sub cavitation case, the hydrodynamic coefficients and flow structures are significantly affected by the incipient cavity. Results show that the leading edge (LE) cavity promotes the formation of the counterclockwise tailing edge vortex (TEV), thus leading to decline of the lift. Moreover, the LE cavity also limits the formation of the clockwise second vortex (SV), which weakens the fluctuation of the hydrodynamic load. For the sheet cavitation case, three cavitating flow patterns(Pattern A/B/C) are observed in the hydrodynamic fluctuation stage, which is corresponding to different characteristic frequency. For the cloud cavitation case, the hydrodynamic curves present four distinct stages. According to the cavity breaking position and characteristic frequency, four different patterns(Pattern I/II/III/IV) of the cavity development and shedding are observed and analyzed.

The flow regime and hydrodynamic performance for a pitching hydrofoil

The objective of this paper is to study the flow regime and hydrodynamic performance for a pitching Clark-Y hydrofoil. The aims are to (1) improve the understanding of the interplay between the hydrodynamic performance, unsteady flow structures and dynamic motion of the hydrofoil, (2) study the influence of the pitching rate on the transition of different flow regimes. The experimental investigations were conducted in the looped cavitation tunnel, and the dynamic moment measurement system was applied to obtain the hydrodynamic forces. The pitching hydrofoil is controlled to rotate from α+ = 10° to α+ = 15° firstly, then goes from α+ = 15° to α− = 5°, finally goes back to α+ = 10° from α− = 5°. The pitching rate is varying with the Reynolds number Re = 4.4 × 105. The numerical investigations were performed by solving the incompressible URANS equations using the coupled k-ω SST turbulence model and γ-Reθ transition model. The numerical results agree well with the experimental measurements. The pitching motion affects the turbulence kinetic energy distribution around the hydrofoil, leading to the delay or acceleration of the transition between different flow patterns. During the pitching process, higher level of turbulence kinetic energy distribution causes earlier transition from laminar to turbulence. Moreover, hysteresis effect of the hydrodynamic force is observed. For the upstroke stage, the higher pitching rate promotes the laminar separation slightly and intensifies the delay of turbulence separation. For the downstroke stage, the higher pitching rate promotes the turbulence separation extensively. The first leading edge vortex (LEV) and anticlockwise trailing edge vortex (TEV) are delayed with the increase of pitching rate, which is responsible to the delay of dynamic stall. The lower pitching rate shrinks the hysteresis loops and intensifies the fluctuation of the dynamic force.