Hydrofoil Shape Research Articles

Numerical Study of Sediment Erosion of a Francis Turbine with change in guide vane design

Abstract The guide vane is a primary component influencing the sediment erosion of the turbines. For the current work, Francis turbine installed in the Bhilangana-III hydroelectric plant is numerically modelled to investigate the effect of guide vane design on turbine erosion. The existing guide vane profile has been modified to adopt an unsymmetrical hydrofoil shape. Two numerical models of the scaled turbine are developed using the commercial code ANSYS CFX. The first model is prepared with the existing guide vane, whereas the second model incorporates the modified guide vane. The erosion rate density is determined using a modified Grant and Tabakoff erosion model for different operating conditions and a sediment concentration range of 500 – 2500 PPM. The turbine with modified guide vanes showed a reduction in wear of guide vanes and runner by 12-23 % in comparison to that of the existing guide vanes. Further, the erosion is higher for both the part and high load conditions as compared to the best efficiency point operation.

Investigation on transition characteristics of hydrofoil boundary layer based on algebraic local-correlation-based transition modeling model

Hydrofoil shapes are used for the marine turbine blades to capture kinetic energy from water currents effectively. Predicting transitions is a critical concern when studying the hydrofoil boundary layer. This paper analyzed the transitional behavior of the boundary layer in the National Advisory Committee of Aeronautics (NACA) hydrofoil, NACA0009, with a blunt trailing edge using the Algebraic Local-Correlation-based Transition Modeling (Algebraic LCTM) model. First, through sensitivity analysis, the effects of the maximum y+ (the dimensionless distance y to the wall), grid expansion ratio, number of normal and streamlined grids, and timescale on transition prediction were studied. The results indicate that finer y+ value and appropriate grid expansion ratios can improve the accuracy of transition prediction, while the influence of timescale on the prediction results is relatively small within the range of Courant number theory values. Second, further analysis was conducted on the transition prediction performance under different Reynolds numbers. It was found that the model predictions were consistent with experimental values at low Reynolds numbers, but the predicted transition position was advanced at high Reynolds numbers, mainly because of the significant disparity in eddy viscosity coefficients within the free flow field. In the study of leading-edge roughness bands' impact on boundary layer transition for hydrofoil, the introduction of roughness significantly expedited the transition process. The Algebraic LCTM model outperformed the gamma (γ) transition model, reducing prediction errors by 5–40% for boundary layer parameters and maintaining errors between 0.005 and 4% for wake vortex shedding frequency, as opposed to the γ model's 0–23%. The results of this study provide a theoretical basis for hydrofoil design.

Harnessing tidal energy efficiency: A comprehensive analysis of tandem flapping hydrofoils for maximizing power generation from low-level currents

Harnessing natural water currents for renewable energy generation holds significant promise. Flapping foil hydrokinetic turbines (FHTs), inspired by aquatic organisms' propulsion mechanisms, leverage undulating motion to extract energy from flowing water. This study investigates the impact of hydrofoil shape and mechanical parameters on oscillating tandem hydrofoil systems' performance for energy harvesting, focusing on Persian Gulf tidal currents. Computational Fluid Dynamics (CFD) in a 2D domain is employed for analysis. Parameters include hydrofoil profiles (IFS, NACA 0015, HSVA, and flat plate), damping coefficient, and initial pitch angle optimized for low-level currents around 1 m/s, derived from HYCOM data. Numerical simulations highlight the superior hydrodynamic efficiency of the IFS hydrofoil. Through RANS equations in unsteady conditions, an optimal configuration with a 75-degree initial angle and damping coefficient of 4 achieves a maximum power efficiency of approximately 66.77%. Efforts have been made to ensure data accuracy, including rounding reported efficiencies appropriately and conducting thorough uncertainty analyses.

Orca hydrofoil shape optimization using Bezier curve and artificial neural network – Multiple objective genetic algorithm for low flow velocity

Tidal energy is a clean and predictable power source commonly harnessed using horizontal-axis tidal turbines. The power generation process of these turbines is influenced by various elements, including the hydrofoil performance metrics such as the lift coefficient, drag coefficient, and lift-to-drag ratio. This study introduces the utilization of the Orcinus Orca hydrofoil for horizontal-axis tidal turbines. The Orcinus Orca geometry was obtained by modifying the NACA0021 airfoil. Subsequently, Bézier curve parameterization was employed to achieve a smooth hydrofoil profile. The study further deployed an artificial neural network coupled with a multi-objective genetic algorithm, targeting hydrofoil shape optimization at a low flow velocity of 0.5 m/s. The aim of this optimization was to augment the lift coefficient and decrease the drag coefficient, thereby amplifying the lift-to-drag ratio. The findings reveal a significant enhancement in performance, as the optimized Orcinus Orca hydrofoil exhibits a remarkable increase of 42.78 % and 27.93 % compared to the original Orcinus Orca and the Bézier-modified Orcinus Orca hydrofoils, respectively.

A deep learning approach for hydrofoil optimization of tidal turbines

Hydrofoil optimization plays a crucial role in improving the hydrodynamic performance of tidal turbines. However, the high-dimensional representations in hydrofoil design space require significant Computational Fluid Dynamics (CFD) simulations, increasing computational load and time expenditure. This paper proposes a hydrofoil optimization framework based on deep learning to achieve an effective mapping between design parameters, pressure fields, and hydrodynamic characteristics. The designed hydrofoil represented using the Signed Distance Function (SDF) is input to Convolutional Neural Networks (CNN) for fast prediction of hydrodynamic coefficients and pressure field. Due to the effective integration of the prediction model and genetic optimization algorithm, this framework can generate a large number of smooth hydrofoils and rapidly predict their hydrodynamic performance to achieve efficient optimization of hydrofoils. The optimized hydrofoil shapes obtained based on the above framework exhibit a higher lift-to-drag ratio than common hydrofoils. Furthermore, the optimized hydrofoils are applied to design tidal energy turbine blades. The simulation results demonstrate that the hydrodynamic performance of tidal turbines can be effectively improved through hydrofoil design optimization. The proposed framework enhances the design efficiency of the tidal turbine rotor and provides turbine hydrofoils with higher power coefficients.

Tidal turbine hydrofoil design and optimization based on deep learning

The optimal design of hydrofoils is critical to improve the hydrodynamic performance of the tidal turbine. However, the global optimization of hydrofoils is limited by the high dimensionality of the design space, which requires extensive computational fluid dynamics simulations. This paper proposes an interactive framework for hydrofoil design and optimization based on deep learning. Generative adversarial networks are used to parameterize the hydrofoil design, which automatically learns representations from existing hydrofoils and controls new hydrofoil generation using fewer variables to reduce optimization dimensions. Moreover, the surrogate model based on convolutional neural networks is constructed, which realizes the mapping of hydrofoil design and operating parameters to hydrodynamic performance parameters. The framework can generate a large number of smooth and realistic hydrofoils with three design variables and quickly predict the performance, enabling effective optimization design of hydrofoils. The results show that the optimized hydrofoil shapes have larger lift-to-drag ratios than those of the common hydrofoils. Furthermore, the optimized hydrofoil is applied to the design of 3D horizontal axis tidal turbine blades. The simulation results show that the framework is effective and stable, which can facilitate the design of tidal turbine rotors and provide hydrofoils with higher power coefficients.

Surrogate modelling for high-lift multi-element hydrofoil shape optimization of a hydrokinetic turbine blade

The hydrodynamic shapeof a blade is one of the most important factorsin the design process of a horizontal axis hydrokinetic turbinethat influencesits performance. The present work is focused on thedesign and hydrodynamic analysis of a high-lift system using the optimization methodof surrogate models and computational fluid dynamics(CFD)analysis.The parameters that affectthe amount of the lift and the drag force thata hydrofoil cangenerate are the gap, the overlap, the flap deflection angle(δ), the flap chord length(C2) andthe angle of attackof the hydrofoil(α). These factors were varied to examine theturbine performancein terms ofthe ratio between the lift (CL) and the dragcoefficient(CD), and the minimum negative pressure coefficient (min Cpre) in order toavoid the cavitation inception. For this propose, surrogatemodels were implemented to analyse the CFDresultsand find the optimal combination of the design parameters of the high-lift hydrofoil.ThetraditionalEppler 420 hydrofoil was utilized for the design of the multi-element profile, which wascomposed of a main element and a flap. The multi-element design selected as optimal had a gap of 2.825 %C1, an overlap of 8.52 %C1, a δ of 19.765 ̊, a C2of 42.471 %C1and a αof -4 ̊, where C1refers to the chord length of the main element.In comparison with the traditionalEppler 420hydrofoil,CL/CDratio increasesfrom 39.050 to 42.517.

Shape optimization of a multi-element hydrofoil for hydrokinetic turbines using response surface methodology

This paper describes the optimization procedure of a two-dimensional multi-element hydrofoil shape during its design for small horizontal axis hydrokinetic turbines using response surface methodology. JavaFoil software was used for describing the hydrofoil performance under several combinations of geometrical parameters, such as the horizontal space (overlap), h, between the drag edge of the main element and the leading edge of the second element; the vertical distance (gap), d, of the flap from the main element trailing edge; and the flap deflection angle, δ. Different experimental designs aiming at the maximization of the lift-to-drag ratio were used. The maximal lift-to-drag ratio was found to be 69.9626 for d, h and δ equal to 2.0%, 18.4619% and 20°, respectively, being δ the factor exerting a considerable influence on the response variable.

Blade optimization for hydrodynamic performance improvement of a horizontal axis tidal current turbine

This paper proposes an innovative methodology applied to blade optimization for hydrodynamic performance improvement of a horizontal axial tidal current turbine (HATCT) considering the effect of Reynolds number. Axial induction factor, tangential induction factor and angle of attack are employed for identifying the accuracy and applicability of modified Blade Element Momentum (BEM) theory. Combined with the XFoil software, the hydrofoil shape function is represented by trigonometric functions through Theodorsen method. The hydrodynamic characteristics of the hydrofoil are employed as the optimization targets, and the particle swarm optimization algorithm is used to optimize the original hydrofoil. Based on the modified BEM theory and the optimized hydrofoil, the tidal current turbine power coefficient at different tip speed ratio (TSR) is optimized according to the MATLAB function. The optimized tidal current turbine shows better performance compared with the original tidal current turbine.

Objective Functions for the Blade Shape Optimisation of a Cross-Flow Tidal Turbine under Constraints

Hydro-kinetic cross-flow tidal turbines (CFTT) are omni-directional and offer higher area-based power density compared to horizontal-axis tidal turbines, making them very attractive for tidal energy exploitation. However, the rotating motion around the vertical axis results in continuously varying angles of attack, causing alternating loads, which may lead to fatigue failure and structural damage. The OPTIDE Project addresses these challenges by implementing intracycle blade pitching to individually control the angle of attack, increasing the power coefficient CP and reducing structural loads. For this purpose a Darrieus turbine is designed with embedded actuators in each blade. Firstly a blade shape optimization will be conducted to fit the actuator at the quarter-chord position while ensuring sufficient thickness. The optimization procedure couples Computational Fluid Dynamics (CFD) with a Genetic Algorithm. The employed optimizer OPAL++ sets ten variables for each individual, which describe the hydrofoil shape, length and tip speed ratio (TSR). A smooth hydrofoil shape is generated from the variables, followed by an automatic mesh generation. Subsequently, numerical simulations of each individual at the desired TSR are conducted, while keeping the blade pitch angle constant. Simulation results provide the CP and stress acting on the turbine blades, which are the two optimization objectives (maximize CP while minimizing stress). This process is repeated during the optimization, aiming to determine the most suitable blade shape, that fits the actuator, and operating point (TSR) in a trade-off between CP and structural loads. This will lead to the increase of efficiency and a longer turbine lifetime.

Effects of hydrofoil shape and turbine solidity on the wake energy recovery in cross-flow turbines

Cross-flow turbines (CFTs) are arousing a growing interest to harvest both off-shore wind and tidal currents. A promising characteristic of CFTs could be a high power density in case of multi-device clusters or farms, achievable by shortening the distance between arrays as allowed by the fast energy recovery observed inside the wakes. However just few studies, only concerning symmetrical airfoils/hydrofoils, are found in the literature. By means of 3D Unsteady Reynolds Averaged Navier–Stokes (URANS) simulations and a momentum budget simplified approach, this author investigated the effects of blade profile and turbine solidity on the blade tip vortex generation and then on the mixing mechanisms supporting the reintroduction of streamwise momentum into the wake. Results indicate that: (a) pairs of counter-rotating vortices occurs in the wake, which rotation direction depends on blade profile and it is such as to generate positive vertical advection for camber-out profiles, but negative vertical advection for camber-in profiles; (b) camber-out profiles are much more effective in supporting the wake energy recovery due to the massive vertical advection induced by tip vortices; (c) for camber-in profiles the tip vortices poorly contribute to the wake recovery, that appears delayed and promoted by turbulent transport; (d) higher solidity implies stronger tip vortices and higher turbulent transport, therefore, a faster wake recovery.

Hydrodynamic design of a horizontal axis current turbine with passive flow control using vortex generator and inserted tube

ABSTRACT Energy from river currents is one of the available renewable energy sources to produce electricity. An improvement in the efficiency of the horizontal axis current turbine is required for the successful utilization of this energy. This paper compares the power production of a horizontal axis current turbine and a turbine with two passive flow control attachments, the vortex generator, and the inserted tube. Firstly, the NACA S1210 hydrofoil shape has been selected. Then the variation of chord length and twist angle along the blade span has been determined. Finally, a 5-meter-diameter, three-bladed, horizontal-axis current turbine has been designed using the blade element momentum theory.The rotor has a maximum power coefficient and a maximum power of 0.47 and 42.71 kW, respectively, at the current speed of 2.1 m/s and a tip speed ratio of 6 when the hydrofoil with tubes has been chosen to design the horizontal axis current turbine. It has been proven that including vortex generators and tubes on the turbine can help increase power production by 9.8% and 14.7%, respectively.

Dynamics of tip vortex flow over three dimensional hydrofoils by LDV measurements

Tip vortices are observed downstream of the flow past the three-dimensional hydrofoils used in propeller, wind and tidal turbines and they largely determine the forces exerted on such structures. In this study, we present the Laser Doppler Velocimetry (LDV) measurements in the flow past three-dimensional hydrofoils namely NACA 4412, NACA 16020, NACA 66(2)415 inclined at an angle of 10° with respect to the free-stream velocity, U∞. The three-dimensional hydrofoils have a semi-span, s = 60 mm, chord lengths, c = 48 mm, 60 mm & 80 mm which correspond to three aspect ratios, ∧ = 2.5, 2.0 & 1.5, respectively, at the chord length based Reynolds number, Re ranging from Re = 1.92 × 105 − 6.39 × 105. LDV measurements were performed at several coordinate points in zy−plane perpendicular to the stream-wise, x direction, measuring the mean stream-wise, u(z, y) and mean velocity component along the z-axis, w(z, y) together with the root-mean square of their fluctuations in the plane located at a stream-wise distance, x/c = 1.0. The swirling strength of the tip vortices are qualitatively evident from the measurements of z− velocity component field, w(z, y) for all the hydrofoils, at various aspect ratios and Reynolds numbers. It is observed that the magnitude of normalized axial velocity deficit, (u(z, y) − U∞)/U∞ and normalized turbulent kinetic energy, TKE(z, y) are dependent on the type of hydrofoil, their aspect ratio, ∧ and the Reynolds number, Re. TKE within the region of the wake and vortex contain about 99% of the peak magnitude of TKE observed in the x/c = 1.0 plane. The vortex center, vortex position and vortex radius are shown to be dependant on the hydrofoil shape, aspect ratio and Reynolds number.

Marine Propeller Optimization Based on a Novel Parametric Model

This paper presents a novel parametric model of marine propellers based on Non-Uniform Rational B-Splines. It involves eight parameters and five categories of spanwise parameter distributions, which are utilized for determining hydrofoil and blade shapes. 20 different hydrofoils and 5 types of well-known marine propellers are employed to detect the accuracy of the proposed parametric model. Furthermore, a propeller optimization problem was addressed with the aid of the parametric model. In the propeller optimization problem, a common AU-series propeller is treated as the baseline propeller. The proposed parametric model is used for the representation and deformation of the propeller geometric model. A hydrodynamic performance evaluation model is developed based on gene expression programming. Also, non-dominated sorting genetic algorithm II is used in the applications of the propeller optimization problem. The results demonstrate that the accuracy of the proposed parametric model satisfies the engineering requirements well, and a propeller with higher efficiency than the baseline propeller can be derived by settling the propeller optimization problem.

Fluid dynamic mechanisms for the wake energy recovery in cross-flow turbines: effects of hydrofoil shape and turbine solidity

Fluid dynamic mechanisms for the wake energy recovery in cross-flow turbines: effects of hydrofoil shape and turbine solidity

Research on tip clearance leakage flow field characteristics of tidal energy hydroelectric unit based on NACA0009 hydrofoil

In the rotor passage of tidal energy hydroelectric unit, there is a tip leakage problem between rotor and runner chamber. In order to research the flow characteristics of tidal energy hydroelectric units and explore the control method of tip leakage, based on the experimental data of NACA0009 hydrofoil, the SST-CC turbulence model was used for numerical simulation and compared with the experimental results. The characteristics of tip leakage flow and vortex were analysed under different hydrofoil shapes and gap widths. The results show that the rounded hydrofoil can effectively control the generation of tip separation vortex, but the rectangular hydrofoil has higher vortices coefficient and lower pressure coefficient in the downstream section; the tip leakage amount will increase with the increase of gap width; the tip vortex intensity will increase first and then decrease, and cavitation may occur when the vortices is maximum. The results can provide reference for studying the control method of tidal energy hydraulic machinery clearance leakage.

Systematic micro heat sink optimization based on hydrofoil shape pin fins

Multi-objective optimization of the hydrofoil shaped pin fins for micro heat sinks was studied. Optimization tool utilized a multi objective genetic algorithm (MOGA) and a numerical model that was validated against previously obtained experimental single-phase heat transfer results on a hydrofoil shape micro scale pin fin. The numerical model was built using StarCCM + software. Several turbulence models were examined against single-phase experimental data and the Lag-EB k-epsilon turbulence model was chosen for validation. Optimization tool varied the shape of the hydrofoil pin fin through flexible parametrization utilizing an ellipse and polynomials. An algorithm coupling pin fin parametrization code, validated the 3D CFD solutions and a MOGA interface was implemented. Subsequently, multi-objective optimization was performed to maximize the heat transfer coefficient while minimizing pressure drop. A broad range of novel geometries were obtained with a tradeoff between thermal and hydraulic performance for low Reynolds number. Novel pin fin shape, bird design, is proposed as a result of the study. Additional 3D steady state conjugate CFD simulations including the bird design pin fin were performed using already verified setup, and it was shown that the enhancement in the average heat transfer coefficient dominates over the pressure drop increase at higher Reynolds numbers.

Analysis of Bulb Turbine Hydrofoil Cavitation

The influence of a bulb runner blade hydrofoil shape on flow characteristics around the blade was studied. Experimental work was performed on a bulb turbine measuring station and a single hydrofoil in a cavitating tunnel. In the cavitation tunnel, flow visualization was performed on the hydrofoil’s suction side. Cavitation structures were observed for several cavitation numbers. Cavitation was less intense on the modified hydrofoil than on the original hydrofoil, delaying the cavitation onset by several tenths in cavitation number. The results of the visualization in the cavitation tunnel show that modifying the existing hydrofoil design parameters played a key role in reducing the cavitation inception and development, as well as the size of the cavitation structures. A regression model was produced for cavitation cloud length. The results of the regression model show that cavitation length is dependent on Reynolds’s number and the cavitation number. The coefficients of determination for both the existing and modified hydrofoils were reasonably high, with R2 values above 0.95. The results of the cavitation length regression model also confirm that the modified hydrofoil exhibits improved the cavitation properties.

Inovasi Dan Desain Turbin Hidrokinetik Darrieus Berdasarkan Bentuk Distribusi Kecepatan Aliran

Darrieus turbine use blades with a hydrofoil shape, so the rotational ability is influenced by lift force. This caused the initial rotation capability to be very low when compared to the drag turbine type. The flow velocity distribution in the vertical direction indicates a small cross-sectional speed of flow approaching the base of the flow channel, then rising towards the surface. Darrieus Spinning Top turbine is the result of innovation and design based on the concept of flow velocity distribution. Darrieus Spinning Top turbine’s blade shapes are circular-arc and straight-line, adjusting flow velocity distribution of 0.2H, 0.6H and 0.8H from the top of the turbine. In this study, a performance comparison was conducted between Darrieus turbine and Spinning Top Darrieus. Darrieus turbines produce RPM and torque values of 54.59 – 67.90 and 0.014 – 0.029 Nm, respectively. Darrieus Spinning Top turbines produce RPM values and torque of 69.24 – 82.02 and 0.012 – 0.020 Nm respectively. RPM improvements in Darrieus Spinning Top turbine design increase the influence of lift force (increased λ value). This results in a high lap rate, but requires a high self starting to perform the turbine rotation cycle.

Parametric model for the reconstruction and representation of hydrofoils and airfoils

In this paper, we present a geometric parametric model that has been mainly designed to accommodate the need for an appropriate analysis model in the context of IsoGeometric Analysis (IGA) [1], but can be also employed as a universal tool for reconstructing and representing a wide range of different airfoils' and/or hydrofoils' families. This model is an extension of the parametric model employed in optimization of hydrofoils' efficiency with the aid of an isogeometric boundary element method solver (IGA-BEM), presented in [2]. Apart from its apparent use in design evaluation and optimization, the parametric model can be further employed in a wider range of relevant applications. Specifically, in this work we begin by demonstrating its use, as an alternative approach, in efficiently reconstructing airfoil and hydrofoil shapes from large sets of points appearing, mainly, in the context of reverse engineering applications. This is further investigated and the parametric model's performance in accurately representing existing airfoils is extensively benchmarked against results from pertinent methods and approaches followed in the aeronautics and aerospace research community. Finally, we demonstrate the use of the parametric model in a foil shape optimization problem. We conclude this work with a discussion on future enhancements and possible research directions.