Hydrofoil Surface Research Articles

Optimization of a novel biomimetic vortex generator structure based on cavitation intensity and stability control

Cavitation phenomena in the fields of hydraulic machinery and underwater submersibles have brought numerous negative impacts, such as vibration noise and mechanical damage. To suppress cavitation intensity and reduce the negative effects of cavitation instability, a biomimetic vortex generator (BVG), arranged on the surface of hydrofoils, is proposed in this study. The renormalization group k-ε turbulence model with density correction and the Ffowcs Williams and Hawkings acoustic model are employed. The cavitation intensity and cavitation stability of the BVG hydrofoil at different arrangement densities are analyzed. Cavitation control performance can be enhanced by reducing the spacing between structures on the hydrofoil. However, an excessively high BVG arrangement density may cause large-scale cavities to collapse prematurely, promoting the formation of small-scale cavities. This exacerbates cavitation instability, intensifies high-frequency pressure oscillations, and consequently amplifies noise. To mitigate performance degradation in hydrofoils caused by high-density BVG arrangements, the effects of structural height on the reentrant jet and surface vortices are analyzed. As a result of BVG structural optimization, cavitation intensity is further reduced, and cavitation stability is improved. Compared to the baseline hydrofoil, the time-averaged vapor volume over three cavitation cycles is reduced by 22.68%, the overall sound pressure level at receiver F decreases by 5.7 dB, and the dominant frequency of S3h2 hydrofoil cavitation decreases by 1.87 Hz. Ultimately, the optimization of the BVG structure enhances cavitation stability and significantly reduces high-frequency noise caused by pressure fluctuations on the hydrofoil surface.

Reconstructing Multiphase Flow Fields with Limited Pressure Observations Based on an Improved Transformer Model

In practical applications, the implementation of active cavitation control can significantly enhance the hydrodynamic performance of underwater vehicles. However, the sparsity of sensor information poses a substantial challenge to acquiring flow field states. Recent advances in deep learning offer reliable solutions to this problem. Specifically, deep learning methods, through the construction of sparse reconstruction models, establish connections between sparse observational information and flow field states with minimal or no prior knowledge. To reconstruct multiphase flow fields from sparse pressure observations on the hydrofoil surface, this work proposes a Transformer-based sparse reconstruction model. Test results on cavitation datasets demonstrate that the model's predictions of cavity contours, cavity lengths, and cavity volumes are highly consistent with actual results during the sheet cavity growth and cavity shedding stages. However, due to the highly unsteady nature of cavitation flow and the lack of far-field information, the model's prediction performance is limited during the cloud cavity aggregation and collapse stages. This model exhibits potential in the sparse reconstruction of multiphase flow fields, providing support for the observation of flow field states and active cavitation control.

Cavitation analysis of plunging hydrofoils using large eddy simulations

This study employs numerical analysis to investigate the behavior of the National Advisory Committee for Aeronautics (NACA)66 modified (mod) hydrofoil under plunging motion, considering various cavitation numbers. The Large Eddy Simulation (LES) method is utilized to model turbulence. The hydrofoil's plunging motion leads to an increase in lift force and a decrease in drag force. Our research indicates that increasing the speed of the hydrofoil's heaving motion delays the onset of cavitation and enhances the formation of cavity clouds. Furthermore, during the peak oscillatory motion of the hydrofoil in the plunging phase, the detachment length of cavitation bubbles decreases. Additional investigations reveal that cavitation on the hydrofoil's surface accelerates the transition from a laminar to a turbulent boundary layer, strengthening the turbulent boundary layer and postponing the onset of flow separation. This research involves an in-depth investigation of the terms in the vorticity transport equation in cavitation inception, finding a correlation between vapor volume fraction and vorticity dilatation near the hydrofoil surface. This correlation proves crucial to the initial stages of the cavitation inception process.

Cavitation flow characteristics on the surface of hydrofoil with microjet structure

A hydrofoil physical model is established based on the surface microstructure to mitigate the detrimental effects of cavitation phenomena on hydrodynamic machinery, such as cavitation erosion or surface damage. Tangential microjet structures are arranged on the hydrofoil's surface, and the modified k-omega shear stress transport (SST k–ω) turbulence model is employed to simulate the hydrofoil numerically. This simulation aims to analyze the effects of different chordwise positions and widths of microjet structures on the cavitation flow and performance of hydrofoils. The mechanism of cavitation suppression is revealed by coupling the chordwise position and width of the microjet structures. The results indicated that the chordwise position of the microjet structures near the trailing edge of the hydrofoil has a minimal impact on the hydraulic properties. The optimal chordwise positions are 0.5c and 0.6c, with the deviation rate of the lift-drag ratio within 3%. The optimum jet width is 0.5 mm, and the cavitation suppression is approximately 15% of the prototype hydrofoil. The microjet structures with tangential jets suppress cavitation by creating obstruction and suppression of the re-entrant jet. The tangential jet ratio of 0.3 represents the most effective tangential jet hydrofoil scheme, and the addition of tangential jets produces a significant inhibitory effect on the shedding of large-scale cavitation.

Enhanced hydrofoil pressure field reconstruction through phase-informed sensing and sensor optimization

This study proposes a cost-effective mixed-learning method for the cavitation behavior on hydrofoils, aiming to predict the global pressure field on the hydrofoil surface with sparse placed pressure sensors and the variation of the cavity outline captured by the high-speed cameras. The method integrates CS (compressed sensing) and deep learning techniques. Firstly, within the framework of CS, the Particle Swarm Optimization (PSO) algorithm is utilized to identify the best measuring points and achieve the initial reconstruction accordingly. Subsequently, in combination with the phase information, the final reconstructions are obtained within the deep learning framework. Through validation, the proposed mixed-learning model demonstrates significantly improved reconstruction performance compared to a single source of pressure information and an unoptimized measurement point position and significantly reduces the number of sensors. This provides a novel and effective approach for accurately predicting the pressure field on hydrofoil surfaces. Furthermore, the study evaluates the robustness concerning hydraulic sensor measurement errors, sensor placement deviations, missing measuring points, reconstruction performance under various cases and hydrofoil surface regions, and the contribution of optimized measuring points to the global field. Results show that the mixed-learning model exhibits robustness against typical measurement errors, position deviations of hydraulic sensors and missing measuring points on the suction side. Additionally, a positive correlation exists between the average pressure gradient under different conditions and regions and the reconstruction error, with the pressure side region significantly contributing to global field reconstruction. These findings underscore the mixed model's superiority in predicting pressure fields on hydrofoils and offer guidance for rational sensor installation.

Numerical simulation study of cavitation characteristics of jet hydrofoil surface

To mitigate the adverse effects of cavitation on the performance degradation and chemical corrosion of hydraulic machines, a jet hydrofoil physical model based on the structure of a guide vane model of a high-pressure mixed-flow hydraulic turbine was established. A density correction turbulence model based on filters was adopted to numerically simulate the cavitation characteristics on the surface of the jet hydrofoil. The results demonstrate that when the jet speed is 12 m/s and the jet angle is −15°, the scheme exhibits the best cavitation suppression effect among all combinations of jet angles and speeds. Cavities near the jet structure are prematurely collapsed after being pressurized, and the cavitation suppression effect in the low-pressure area at the trailing edge is also satisfactory. The time-averaged bubble volume fraction reaches its minimum at 2.17%, with the time-averaged bubble volume fraction being 27.3% of the prototype hydrofoil. At flow speeds of 2.4 m/s and 7.2 m/s, small-angle jet fluid accumulated will stick to the closed cavities on the surface of the hydrofoil and cause them to rupture, while the jet fluid at the jet angle of 60° and speeds of 7.2 m/s and 12 m/s will directly cut off the bubbles.

Cavitation flow of hydrofoil surface and turbulence model applicability analysis

To improve the simulation accuracy of hydrofoil unsteady cavitation, a user-defined density function is used to correct a variety of turbulence models and combined with a hydrofoil with an angle of attack of 8° for numerical simulation of unsteady cavitation. This study aims to find the optimal turbulence model and apply it to other hydrofoil types to verify its applicability. The results show that the corrected RNG k-ε turbulence model and SST k-ω turbulence model can better fit the experimental results in terms of cavitation morphology and cavitation shedding frequency. The frequency error of cavitation detachment for the corrected SST k-ω turbulence model is just 0.3% compared to the experimental results, and it shows an improvement of approximately 67% over the uncorrected SST k-ω turbulence model. The corrected SST k-ω turbulence model can more accurately capture the shedding cavitation due to the re-entrant jet, better capture the generation of the attached cavitation edge of the U-shape, the shedding of large-scale cavities, and the collapse of the shedding cavitation downstream. Furthermore, the optimal turbulence model has a good applicability in different dimensions and on different hydrofoil types.

Cavitating flow around a low aspect ratio NACA0012 hydrofoil with regular grooves

Abstract The purpose of this work is to study the influence of the periodic grooves applied to the surface of the hydrofoil as passive control method on the cavitation dynamics and development. The cavitating flow in the slit channel around NACA 0012 hydrofoil is investigated. An experimental study of the flow was carried out using the high-speed visualization followed by image processing of acquired data. Attached cavity length is substantially reduced by 25% - 30% by using grooves on hydrofoil surface. However, cavitation inception for grooved hydrofoil occurs at almost two-time lower flowrate.

Effect of branch-like structures created by vortex generators on cavitation dynamics at high angle of attack

When hydraulic machines operate away from their design condition, the angle between the inflow and the blade's leading edge increases significantly, causing severe cavitation. To address this, this investigation focuses on cavitation flow around hydrofoil with a high incidence angle. The effects of the vortex generators (VGs) on cavitation evolution, pressure fluctuations, and flow-induced noise were discussed. Experiments and simulations were jointly employed in this work. The results indicate that under current conditions, cavitation initiates upstream of the VGs, closer to the leading edge. The branch-like vortex cavitation induced by the VGs enhances the stability of the shedding cavities in the midstream of the hydrofoil, leading to a 15.24% reduction in the primary frequency of cavitation shedding. With the addition of the VGs, the amplitude of pressure fluctuations on the hydrofoil surface is reduced. Also, the acoustic power drops over the entire spectrum, especially in the high-frequency range. The sound pressure corresponding to the main frequency of cavitation noise is reduced by 7 dB.

Effects of cavitation on the vortex shedding behind a truncated hydrofoil subjected to forced oscillation

Abstract Cavitating vortex shedding behind a truncated NACA 0009 hydrofoil subjected to forced oscillation has been numerically investigated using a one degree-of-freedom (1 DOF) model coupled with a homogeneous mixture cavitation model. The pitching motion of the hydrofoil has been prescribed using a sinusoidal function with a fixed amplitude and variable frequencies ranging from lock-off values below the vortex shedding frequency to values well above it and passing through the lock-in condition. The obtained results have permitted us to study the change in the dynamics and morphology of the shed-vortex structures with varying hydrofoil oscillation frequencies when cavitation takes place. More specifically, it has been found that the frequency regime of the lock-in condition is altered due to the occurrence and development of cavitation. Also, two distinct wake patterns have been observed for oscillating frequencies below and above the vortex shedding frequency. Furthermore, the phase angle between the applied torque and the hydrofoil surface acceleration has been estimated as a function of the excitation frequency and the cavitation number, which has helped to understand the effects of cavitation on the dynamic behaviour of the shed vortices.

Influence of surface slip on hydrodynamics and flow field around a two-dimensional hydrofoil at a moderate Reynolds number

In the present study, the effects of surface slip on the hydrodynamics and flow around a two-dimensional National Advisory Committee for Aeronautics 0012 hydrofoil are systematically investigated by numerical methods. The objective is to fully understand the effects of surface slip on the streamlined body. Three slip positions (both surfaces, the upper surface, the lower surface) and eight slip lengths (in a wide range from 1 to 500 μm) under 0°–10° angles of attack are fully investigated at a moderate Reynolds number of 1.0 × 106. Surface slip has been found to increase lift and reduce drag by postponing the flow transition, laminar separation bubble, and flow separation on the hydrofoil surface under both surfaces and the upper surface slip conditions. Slip has also been found to induce upshift of the mean velocity profile, decrease the displacement thickness, and mitigate the turbulent kinetic energy in the flow field. However, counterintuitive phenomenon occurs under the lower surface slip condition, where the total drag of the hydrofoil is increased compared to that under the no slip condition. Total drag increase is found mainly due to the increase in the pressure drag under small slip lengths and relatively large angles of attack. Flow maps demonstrating the complex interaction between different surface slip conditions and the flow field are further presented. The results suggest that surface slip can not only reduce drag, but also increase the drag of the streamlined body, which shall provide valuable insights for practical applications of slippery materials.

Assessment of cavitation erosion on an asymmetric hydrofoil based on energy conversion via a multiscale approach

Cavitation erosion is a long-standing issue, which plays a pivotal role in the material damage of much hydraulic machinery. However, despite abundant numerical research on cavitation erosion assessment, bubble dynamics has been commonly overlooked. Consequently, we develop an improved cavitation erosion model based on energy conversion and assess an ALE15 hydrofoil surface by its incorporation into a multiscale approach. Our erosion model stands out in considering the bubble behaviors throughout its entire lifespan to eliminate the influence of bubble oscillation on cavitation erosion. Using the bubble information in the well reproduced cavitating flow, we evaluate both the cumulative and instantaneous cavitation erosion, and the results show satisfactory agreement with the experimental pattern. Our findings demonstrate that frequent vapor-liquid alternations, induced by the collaborative effects of upstream pressure gradients and main flow, increase the potential for erosion risk at the hydrofoil leading edge. Downstream erosion primarily results from secondary shedding and the collapse of U-shaped cavities’ legs. By contrast, the acoustic energy emitted by the shedding cavities traveling farther and upwards away from the hydrofoil leads to negligible erosion on the surface.

Fully passive model-based numerical analysis of the trailing-edge flexibility of hydrofoil on energy harvesting performance

The oscillating hydrofoil, a device used for collecting environmentally friendly tidal energy, is the focus of the study. The flexibility of the hydrofoil's trailing edge can impact its surface pressure distribution, lift, and moment characteristics. To improve the energy harvesting performance of oscillating hydrofoils, it is important to conduct thorough research on their energy harvesting mechanism. Therefore, numerical analysis is employed to develop a numerical model of the fully passive oscillating hydrofoil with the flexible trailing edge. The dynamic development behavior of surface vortices on hydrofoils is analyzed, demonstrating that the fluid–structure interaction between the hydrofoil and the surrounding fluid alters the hydrofoil's motion. The vortex patterns and pressure distribution on the hydrofoil surface are also affected, ultimately influencing the energy harvesting performance. By optimizing the flexibility coefficient of the fully passive oscillating hydrofoil with a flexible trailing edge, the energy harvesting performance of the oscillating hydrofoil is improved. When the maximum chord offset δm= 0.1c and the flexibility coefficient n= 2, the energy harvesting efficiency is 31.37%, and the average power coefficient is 1.17. Therefore, increasing the tail flexibility can be considered to enhance energy harvesting performance when designing the fully passive oscillating hydrofoil. The research provides a comprehensive analysis of energy harvesting performance, addressing the dynamic problem of the fully passive oscillating hydrofoils with flexible trailing edges. The findings of this study may provide guidance for the design and optimization of tidal energy harvesting devices with similar structures.

Adaptive estimation model: Robust full-state prediction through sparse observations with variable layout and quantity

Recovering the full-state from limited observation data is crucial because it provides a reliable reference for active control. Advances in deep learning technology further enable building robust and high-precision estimators. In this work, we proposed a robust estimator capable of adapting to the number and layout of observation points, enabling precise reconstruction of the pressure distribution from sparse observations on the hydrofoil surface. The ability for adaptive and accurate reconstruction stems from carefully designed steps of randomly masking inputs in the training stage and Transformer models with enhanced feature extraction capabilities. An impact analysis was conducted to assess the influence of the number of observation points on reconstruction performance. Furthermore, tests to evaluate the performance under conditions with missing observation points were also conducted. These assessments validated the robust reconstruction performance of the proposed model. Noise tests further highlighted the strengths of the proposed model, but also revealed stability issues that can be improved.

Numerical study on the cavitation instability from the perspectives of pressure change and hydrodynamics evolution in the cavitating flow over a hydrofoil

The objective of this study is to investigate cavitation instability by analyzing the pressure change and hydrodynamics evolution in the cavitating flow over a hydrofoil. Two-dimensional (2D) simulation results indicate that the multi-peak pressure features are influenced by the position on the hydrofoil surface. The increased cavitation number in a certain range aggravates the oscillation of partial cavitation and promotes the cavity change, then leads to the occurrence of higher peak pressure and more complicated fluctuation frequency. The lift coefficient presents a near-linear increasing trend due to the extended low-pressure area on the suction surface and the suppression on the vortex generation in the stable development stage of sheet cavity. The interaction between the vortex with different directions on the trailing edge dominates the fluctuation of lift coefficient. The differences in three-dimensional (3D) cavitating flows with constant velocity inlet and sinusoidal velocity inlet are the flow separation point distribution and vortex changes. More separation points form in the downstream of the hydrofoil due to more cloud cavity reattachment behaviours for sinusoidal velocity inlet. Furthermore, the sinusoidal velocity inlet promotes a more violent cavity detachment and the large-scale vortex formation, which enhances the fluctuations of pressure change, lift and drag coefficient.

Enhancing hydrofoil velocity estimation through residual learning

Recovering flow states from limited observations provides supports for flow control and super-resolution. Advances in deep learning have made it possible to construct precise state estimators. In this work, a deep learning estimator with an initialization branch and a residual branch is proposed to predict velocity fields from sparse pressure on the hydrofoil surface. In detail, on the one hand, the pre-trained proper orthogonal decomposition-based model as an initialization branch is employed to generate initial predictions. On the other hand, the U-shaped neural network-based model as the residual branch is trained to learn the residual between the initial predictions and the ground truth. Compared to previous models, the proposed model not only enhances prediction accuracy but also improves the interpretability of the model. Furthermore, the incorporation of the initialization branch has little influence on training and inference speed. Test results illustrate that residual learning provides additional model capacity for improving the prediction of transverse velocity fields and flow details. Moreover, even in the presence of intense velocity fluctuations near the trailing edge, predictions from the improved model are more consistent with ground truth. Visualization of feature maps underscores a significant advantage of the improved model over the baseline model in terms of structural features and increased distinctiveness among features, thereby facilitating interpretability enhancements.

Numerical prediction of cavitation nuisance on hydrofoils: Combined analysis of cavity dynamics and the aggressiveness of collapsing cavitating structures

The unsteady cavitating flow past a three-dimensional twisted hydrofoil is numerically investigated by a large eddy simulation to obtain in-depth insight into the bubble dynamics near the cavitation erosion region. Macroscopic cavity evolution is captured by a multiphase flow computing frame, while the bubble oscillations in the cavitating flow are computed by solving the Gilmore bubble dynamic model, in which the driving force for the bubble movement is exported through the application of a discrete phase model. The cavitation erosion potential is then computed by a robust indicator developed based on the energy balance hypothesis. The relevance between the dynamics and the destructive essence of a cavitation bubble and the erosion intensity is thoroughly analyzed. The results show that the unsteadiness involved in the turbulent cloud cavitation is well reproduced, and the main cavitation erosion risk in the middle region of the hydrofoil is also accurately predicted comparing with the painting test results. A localized high-pressure region is identified near the rear part of the attached cavity where the mainstream encounters the primary reentrant jet flows. The peak bubble internal pressure can reach 487 MPa near the middle plane of the hydrofoil, during the stage when the surrounding liquid pressure is continuously increased. The bubbles with the smallest radius, ranging from 23.1 to 26.3 μm after compressing from their initial sizes (R0 = 100–700 μm) in the near wall region, are associated with the extremely high internal pressure, and they are responsible for the cavitation erosion damage on the hydrofoil surface.

Reduced Order Data-Driven Analysis of Cavitating Flow over Hydrofoil with Machine Learning

Predicting the flow situation of cavitation owing to its high-dimensional nonlinearity has posed great challenges. To address these challenges, this study presents a novel reduced order modeling (ROM) method to accurately analyze and predict cavitation flow fields under different conditions. The proposed ROM decomposes the flow field into linearized low-order modes while maintaining its accuracy and effectively reducing its dimensionality. Specifically, this study focuses on predicting cavitation on the Clark-Y hydrofoil using a combination of numerical simulation, proper orthogonal decomposition (POD), and neural networks. By analyzing different cavitation conditions, the results revealed that the POD method effectively reduces the order of the cavity flow field while achieving excellent flow field reconstruction. Notably, the zeroth- and first-order modes are associated with attachment cavitation, while the second-, third- and fourth-order modes correspond to cavitation shedding. Additionally, the fifth- and sixth-order modes along the hydrofoil surface are associated with the backward jet flow. To predict the conditions of high-energy modes, the neural network proved to be more effective, exhibiting excellent performance in stable attached cavitation. However, for cloud cavitation, the accuracy of the neural network model requires further improvement. This study not only introduces a novel approach for predicting cavitation flow fields but also highlights new challenges that will require continuous attention in future research endeavors.

The effect of three-type Vortex Generators (VGs) on NACA-0015 hydrofoil cavitation formation at different angles of attack

Cavitation, the formation of vapor bubbles on hydrofoil surfaces, poses a significant challenge to the performance and durability of marine vessels utilizing hydrofoils. Vortex generators, small structures embedded on the hydrofoil surface, have emerged as a potential solution for mitigating cavitation, but the optimal shape of vortex generators for achieving maximum cavitation resistance remains an open question. This study aims to address this challenge by systematically investigating the impact of rectangular, triangular, and circular vortex generators on the cavitation characteristics of a NACA-0015 hydrofoil. Utilizing computational fluid dynamics (CFD) simulations, the influence of these vortex generator shapes on cavitation inception and critical cavitation numbers will be evaluated under varying angles of attack and flow velocities. The findings of this study will provide valuable insights into the design and optimization of vortex generators for hydrofoil applications. Despite the effectiveness of vortex generators in mitigating cavitation, the optimal vortex generator shape for specific hydrofoil designs and operating conditions remains unclear. The precise mechanisms by which vortex generators suppress cavitation are not fully understood, requiring further investigation to optimize their design and placement. The durability and long-term performance of vortex generators under various environmental conditions, including turbulence and corrosion, warrant further evaluation. By addressing these unsolved challenges, this study will contribute to the advancement of vortex generator technology and its practical application in hydrofoil systems, leading to more efficient and reliable marine vessels.

Large eddy simulations of cavitation around a pitching–plunging hydrofoil

In this study, we numerically examine the behavior of the NACA (National Advisory Committee for Aeronautics) 66 hydrofoil under combined oscillatory motion, considering different cavitation numbers. The large eddy simulation method is used for the turbulence modeling. The vertical oscillation (combined oscillation) creates an effective angle of attack, leading to reduced drag force. Our findings indicate that increasing the speed of hydrofoil oscillation leads to a delayed onset and increased production of cavity clouds. Moreover, an increase in the angle of attack during combined oscillatory motion decreases the detachment length of cavitation bubbles. Further investigations show that cavitation on the hydrofoil's surface can accelerate the shift from a laminar to turbulent boundary layer, reinforcing the turbulent boundary layer's strength and thereby delaying the onset of flow separation. Additionally, we accurately examine the terms of the vorticity transport equation in this research. It is evident that the vorticity dilatation term forms near the boundary layers close to the hydrofoil surface and correlates well with the vapor volume fraction. This term plays a vital role in the cavitation inception process.