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Compliant lift-generating surfaces have widespread applications as marine propellers, hydrofoils and control surfaces, and the fluid–structure interactions (FSI) of such systems have important effects upon their performance and stability. Multi-phase flows like cavitation and ventilation alter the hydrodynamic and hydroelastic behaviours of lifting surfaces in ways that are not yet completely understood. This paper describes experiments on one rigid and two flexible variants of a vertical surface-piercing hydrofoil in wetted, ventilating and cavitating conditions. Tests were conducted in a towing tank and a free-surface cavitation channel. This work, which is Part 1 of a two-part series, examines the passive, or flow-induced, fluid–structure interactions of the hydrofoils. Four characteristic flow regimes are described: fully wetted, partially ventilated, partially cavitating and fully ventilated. Hydroelastic coupling is shown to increase the hydrodynamic lift and yawing moments across all four flow regimes by augmenting the effective angle of attack. The effective angle of attack, which was derived using a beam model to account for the effect of spanwise twisting deflections, effectively collapses the hydrodynamic load coefficients for the three hydrofoils. A generalized cavitation parameter, using the effective angle of attack, is used to collapse the lift and moment coefficients for all trials at a single immersed aspect ratio, smoothly bridging the four distinct flow regimes. None of the hydrofoils approached the static divergence condition, which occurs when the hydrodynamic stiffness negates the structural stiffness, but theory and experiments both show that ventilation increases the divergence speed by reducing the hydrodynamic twisting moment about the elastic axis. Coherent vortex shedding from the blunt trailing edge of the hydrofoil causes vortex-induced vibration at an approximately constant Strouhal number of 0.275 (based on the trailing edge thickness), and leads to amplified response at lock-in, when the vortex-shedding frequency approaches one of the resonant modal frequencies of the coupled fluid–structure system.

In this paper, we provide new experimental data of the wave-induced steady forces (the added resistance, wave-induced steady lateral force, and yaw moment) acting on a full hull ship in regular waves, and we verify the validity of existing prediction methods for wave-induced steady forces by performing comparisons with results obtained experimentally. For the prediction methods, we consider the zero-speed three-dimensional panel method (3DPM) and the method based on formulas of the wave-induced steady forces that are expressed using the Kochin-function assuming a slender ship (strip theory-based Kochin-function method: SKFM). The results show that the calculation accuracy obtained using 3DPM and SKFM for added resistance and steady lateral force is acceptable for practical purposes although the accuracy is insufficient for the steady yaw moment. In order to confirm the applicability of both methods to the problem of maneuvering in waves, we predict the turning motions of the ship in irregular waves using the calculation results obtained by 3DPM and SKFM for the wave-induced steady forces, and we compare the turning motions with the free-running model test results. Both methods are useful for predicting turning motions in irregular waves.

This work is dedicated to systematically studying and predicting the wake characteristics of a yawed wind turbine immersed in a turbulent boundary layer. To achieve this goal, wind tunnel experiments were performed to characterize the wake of a horizontal-axis wind turbine model. A high-resolution stereoscopic particle image velocimetry system was used to measure the three velocity components in the turbine wake under different yaw angles and tip-speed ratios. Moreover, power and thrust measurements were carried out to analyse the performance of the wind turbine. These detailed wind tunnel measurements were then used to perform a budget study of the continuity and Reynolds-averaged Navier–Stokes equations for the wake of a yawed turbine. This theoretical analysis revealed some notable features of the wakes of yawed turbines, such as the asymmetric distribution of the wake skew angle with respect to the wake centre. Under highly yawed conditions, the formation of a counter-rotating vortex pair in the wake cross-section as well as the vertical displacement of the wake centre were shown and analysed. Finally, this study enabled us to develop general governing equations upon which a simple and computationally inexpensive analytical model was built. The proposed model aims at predicting the wake deflection and the far-wake velocity distribution for yawed turbines. Comparisons of model predictions with the wind tunnel measurements show that this simple model can acceptably predict the velocity distribution in the far wake of a yawed turbine. Apart from the ability of the model to predict wake flows in yawed conditions, it can provide valuable physical insight on the behaviour of turbine wakes in this complex situation.

Yawing wind turbines has emerged as an appealing method for wake deflection. However, the associated flow properties, including the magnitude of the transverse velocity associated with yawed turbines, are not fully understood. In this paper, we view a yawed turbine as a lifting surface with an elliptic distribution of transverse lift. Prandtl’s lifting line theory provides predictions for the transverse velocity and magnitude of the shed counter-rotating vortex pair known to form downstream of the yawed turbine. The streamwise velocity deficit behind the turbine can then be obtained using classical momentum theory. This new model for the near-disk inviscid region of the flow is compared to numerical simulations and found to yield more accurate predictions of the initial transverse velocity and wake skewness angle than existing models. We use these predictions as initial conditions in a wake model of the downstream evolution of the turbulent wake flow and compare predicted wake deflection with measurements from wind tunnel experiments.

This work is dedicated to studying the similarity between wakes of wind turbines with different yaw angles and tip speed ratios under different turbulent inflows using large-eddy simulations with actuator surface models. Simulation results show that wake characteristics from cases with different yaw angles overlap with each other when normalized properly, which include the streamwise variations of the wake deflection, the centreline velocity deficit, the widths of the wakes, the standard deviations of instantaneous wake centre positions and the instantaneous wake widths. Different scalings are proposed for the streamwise velocity deficit and the transverse velocity. The similarities observed between cases with different yaw angles and the different scalings suggest that it is proper to decompose the wake of a yawed wind turbine into a streamwise wake and a lateral wake deflection, which is critical for developing analytical models. The mean of the instantaneous wake widths and the mean of the instantaneous centreline streamwise velocity are observed as being smaller than those of the time-averaged wake. These quantities are then related by using two analytical expressions proposed in this work. The observed similarities together with the proposed analytical expressions provide a better understanding of wakes of yawed wind turbines and can be employed to develop physics-based dynamic wake models.

The yaw moment of wind turbine rotors has never been in the focus of wind turbine aerodynamics. With the increasing activities in the development of support structures for Floating Offshore Wind Turbines (FOWT), which passively align with the wind, the interest has shifted, as an accurate determination of the yaw moment is a crucial issue for a successful design of such power plants. A downwind coned rotor is a promising option to increase the yaw moment and therefore the self‐alignment capability of a passively yawing FOWT. Unfortunately, experimental and numerical studies on the estimation of the yaw moment of wind turbine rotors are rare. This is especially the case for downwind coned rotors. The aim of the present work is to provide reliable knowledge in this field. For this purpose, an extensive experimental and numerical study is carried out to determine the yaw moment of a downwind coned rotor. The results obtained from measurements in the wind tunnel are compared to those of simulations using a high fidelity RANS method and a blade element momentum theory (BEMT) method. BEMT is widely applied and can be considered as state of the art for predicting aerodynamic loads on FOWTs. However, the basic assumptions of BEMT do not account for a realistic influence of the skewed wake, so that the application of a correction method is necessary. In this work, the frequently used wake skew correction method based on Pitt and Peters is utilised and its influence on the calculation of the yaw moment is investigated. It is shown that this correction method yields a significant overprediction of the yaw moment in comparison to the measurements and consequently even impairs the quality of the simulation in this case. In contrast to this, the wake‐resolving RANS method is capable of reproducing the measurements with reasonable accuracy and provides valuable insight into the role of the lateral force for the measurement of the yaw moment.

X rudder is particularly important for submarine maneuverability, but its influence on wake flow field remains largely unknown. In this study, the X rudder was scaled down three-dimensionally to 80%, 85%, 90%, 95% and 100% of the original rudder area with unchanged aspect ratio and installation position of rudder shaft. Next, the effects of X rudder area on the horizontal mechanical properties and wake flow field of the submarine with a tail control plane were analyzed using the CFD method. The results showed that when the X rudder area was reduced by 20%, the resistance was not significantly affected, and the yaw torque was still larger than that of cross-shaped rudder submarine. At the rudder angles of 0°, 2° and 5°, the velocity non-uniformity coefficients of S1 were reduced by about 9%, 25% and 71%, respectively, when compared to those of S5.

Motivated by the need for compact descriptions of the evolution of non-classical wakes behind yawed wind turbines, we develop an analytical model to predict the shape of curled wakes. Interest in such modelling arises due to the potential of wake steering as a strategy for mitigating power reduction and unsteady loading of downstream turbines in wind farms. We first estimate the distribution of the shed vorticity at the wake edge due to both yaw offset and rotating blades. By considering the wake edge as an ideally thin vortex sheet, we describe its evolution in time moving with the flow. Vortex sheet equations are solved using a power series expansion method, and an approximate solution for the wake shape is obtained. The vortex sheet time evolution is then mapped into a spatial evolution by using a convection velocity. Apart from the wake shape, the lateral deflection of the wake including ground effects is modelled. Our results show that there exists a universal solution for the shape of curled wakes if suitable dimensionless variables are employed. For the case of turbulent boundary layer inflow, the decay of vortex sheet circulation due to turbulent diffusion is included. Finally, we modify the Gaussian wake model by incorporating the predicted shape and deflection of the curled wake, so that we can calculate the wake profiles behind yawed turbines. Model predictions are validated against large-eddy simulations and laboratory experiments for turbines with various operating conditions.

Collective wind farm flow control, where wind turbines are operated in an individually suboptimal strategy to benefit the aggregate farm, has demonstrated potential to reduce wake interactions and increase farm energy production. However, existing wake models used for flow control often estimate the thrust and power of yaw-misaligned turbines using simplified empirical expressions that require expensive calibration data and do not extrapolate accurately between turbine models. The thrust, wake velocity deficit, wake deflection and power of a yawed wind turbine depend on its induced velocity. Here, we extend classical one-dimensional momentum theory to model the induction of a yaw-misaligned actuator disk. Analytical expressions for the induction, thrust, initial wake velocities and power are developed as a function of the yaw angle ($\\gamma$) and thrust coefficient. The analytical model is validated against large eddy simulations of a yawed actuator disk. Because the induction depends on the yaw and thrust coefficient, the power generated by a yawed actuator disk will always be greater than a $\\cos ^3(\\gamma )$ model suggests. The power lost due to yaw misalignment depends on the thrust coefficient. An analytical expression for the thrust coefficient that maximizes power, depending on the yaw, is developed and validated. Finally, using the developed induction model as an initial condition for a turbulent far-wake model, we demonstrate how combining wake steering and thrust (induction) control can increase array power, compared to either independent steering or induction control, due to the joint dependence of the induction on the thrust coefficient and yaw angle.

We propose a linearized deterministic model for predicting coherent structures in the wake of a floating offshore wind turbine subject to platform motions. The model's motion-to-wake predictive capability is achieved through two building blocks: a motion-to-forcing (M2F) part and a forcing-to-wake (F2W) part. The M2F model provides a unified framework to parameterize the effects of arbitrary floating wind turbine motions as unsteady loads of a fixed actuator disk, requiring only the radial distribution of the aerodynamics force coefficient on the blade as input. The F2W model is derived based on a bi-global resolvent model obtained from the linearized Navier–Stokes equations, using the time-averaged wake of a fixed wind turbine as input. In addition to its capability of predicting sensitive frequency ranges, the model excels linear stability analysis by providing spatial modes of the wake response in a motion-specific and phase-resolved manner. The model successfully predicts the wake pulsing mode induced by surge, as well as the similarity and difference of the wake meandering modes caused by sway and yaw. Large-eddy simulations under different inflow turbulence intensities (TIs) and length scales are further conducted to analyse the wake meandering triggered by the simultaneous excitation of free-stream turbulence and sway motion. The results show distinct frequency signatures for the wake dynamics induced by ambient turbulence and sway motion. The inflow TI is found to have a stabilizing effect on the wake, reducing the motion-induced wake responses. Such a stabilizing effect is captured satisfactorily with the proposed model, provided that the effective viscosity is calibrated properly using the data from the fixed turbine wake under the corresponding turbulent inflow.