The accurate prediction of the aerodynamics and performance of vertical-axis wind turbines is essential if their design is to be improved but poses a significant challenge to numerical simulation tools. The cyclic motion of the blades induces large variations in the angle of attack of the blades that can manifest as dynamic stall. In addition, predicting the interaction between the blades and the wake developed by the rotor requires a high-fidelity representation of the vortical structures within the flow field in which the turbine operates. The aerodynamic performance and wake dynamics of a Darrieus-type vertical-axis wind turbine consisting of two straight blades is simulated using Brown's Vorticity Transport Model. The predicted variation with azimuth of the normal and tangential force on the turbine blades compares well with experimental measurements. The interaction between the blades and the vortices that are shed and trailed in previous revolutions of the turbine is shown to have a significant effect on the distribution of aerodynamic loading on the blades. Furthermore, it is suggested that the disagreement between experimental and numerical data that has been presented in previous studies arises because the blade-vortex interactions on the rotor were not modelled with sufficient fidelity. Copyright (C) 2010 John Wiley & Sons, Ltd.

Accurate aerodynamic modelling of vertical-axis wind turbines poses a significant challenge. The rotation of the turbine induces large variations in the angle of attack of its blades that can manifest as dynamic stall. In addition, interactions between the blades of the turbine and the wake that they produce can result in impulsive changes to the aerodynamic loading. The Vorticity Transport Model has been used to simulate the aerodynamic performance and wake dynamics of three different vertical-axis wind turbine configurations. It is known that vertical-axis turbines with either straight or curved blades deliver torque to their shaft that fluctuates at the blade passage frequency of the rotor. In contrast, a turbine with helically twisted blades delivers a relatively steady torque to the shaft. In this article, the interactions between helically twisted blades and the vortices within their wake are shown to result in localized perturbations to the aerodynamic loading on the rotor that can disrupt the otherwise relatively smooth power output that is predicted by simplistic aerodynamic tools that do not model the wake to sufficient fidelity. Furthermore, vertical-axis wind turbines with curved blades are shown to be somewhat more susceptible to local dynamic stall than turbines with straight blades.

Accurate aerodynamic modeling of vertical-axis wind turbines poses a significant challenge, but is essential if the performance of such turbines is to be predicted reliably. The rotation of the turbine induces large variations in the angle of attack of its blades that canmanifest as dynamic stall. In addition, interactions between the blades of the turbine and the wake that they produce can exacerbate dynamic stall and result in impulsive changes to the aerodynamic loading on the blades. The Vorticity Transport Model has been used to simulate the aerodynamic performance and wake dynamics of vertical-axis wind turbines with straight-bladed, curved-bladed and helically twisted configuration. It is known that vertical-axis wind turbines with either straight or curved blades deliver torque to their shaft that fluctuates at the blade passage frequency of the rotor. In contrast, a rotor with helically twisted blades delivers a relatively steady torque to the shaft. In the present paper, the interactions between helically twisted blades and the vortices within their wake are shown to result in localized perturbations to the aerodynamic loading on the rotor that can disrupt the otherwise relatively smooth power output that is predicted by simplistic aerodynamic tools that do not model the wake to sufficient fidelity. Furthermore, vertical-axis wind turbines with curved blades are shown to be somewhat more susceptible to local dynamic stall than turbines with straight blades.

The tail rotor of a helicopter with a single main rotor configuration can experience a significant reduction in thrust when the aircraft operates in crosswind flight. Brown's vorticity transport model has been used to simulate a main rotor and tail rotor system translating at a sideslip angle that causes the tail rotor to interact with the main rotor tip vortices as they propagate downstream at the lateral extremities of the wake. The tail rotor is shown to exhibit a distinct directionally dependent mode during which tail rotors that are configured so that the blades travel forward at the top of the disk develop less thrust than tail rotors with the reverse sense of rotation. The range of flight speeds over which this mode exists is shown to vary considerably with the vertical location of the tail rotor. At low flight speeds, the directionally dependent mode occurs because the tail rotor is immersed within not only the downwash from the main rotor but also the rotational flow associated with clusters of largely disorganized vorticity within the main rotor wake. At higher flight speeds, however, the tail rotor is immersed within a coherent supervortex that strongly influences the velocity field surrounding the tail rotor.

The reduced availability of sites with the requisite wind resource, planning permission and public acceptance for the placement of wind turbines poses a significant challenge to future expansion of the wind energy industry. Developers increasingly wish to site large turbines in close proximity to industrial plants, but there is uncertainty amongst environmental protection agencies on how best to measure and regulate the impact that wind turbines may have on the dispersion of the gases that are often emitted into the atmosphere from such plants. Several simplified wind turbine–flue stack configurations have been simulated using the Vorticity Transport Model. This model provides a high-fidelity representation of the vortical flow structure within both the wind turbine wake and the plume, and is able to capture the re-direction and dispersion of the plume that occurs due to interaction with the wind turbine. The impingement of the plume on the wind turbine is shown to disrupt the wake structure downwind of the wind turbine, and may induce additional unsteady loading on the turbine rotor. The velocity deficit downwind of the wind turbine influences the rate at which the plume propagates downwind, and results in an increase in the concentration of plume material (which may include pollutant gas and particulates) around the wind turbine. This localized increase in plume concentration is shown to be sensitive to the thrust coefficient at which the wind turbine is operated. The results presented in this paper show that environmental protection agencies are justified in their concerns regarding the placement of wind turbines near to industrial plants, and suggests strongly that the interaction between wind turbines and gas plumes should be investigated further.

Understanding the mechanisms that lead to the production of noise by tail rotors across a broad range of flight conditions and helicopter configurations remains an active area of research. Furthermore, designers require numerical models that are able to efficiently and accurately predict the acoustic signature of the helicopter. Predictions made using the Vorticity Transport Model in conjunction with a linear acoustics code, in which the Ffowcs Williams-Hawkings equation is solved for the sound pressure level on a horizontal observer plane beneath a scaled model of the Bo-105 helicopter, have been shown to compare well with measurements made during the HeliNOVI experiments. As the vertical distance between the tail rotor and the main rotor is reduced, the acoustic signature of the tail rotor changes considerably. Both the blade-vortex interactions that occur between the tail rotor blades and their tip vortices, and the interactions between the tail rotor blades and the tip vortices trailed behind the main rotor blades, act as major sources of loading noise. The work presented in the paper suggests strongly, however, that the apparent acoustic advantages of a tail rotor with a particular sense of rotation cannot be considered independently of the vertical location of the tail rotor with respect to the main rotor.

The perceived need to reduce mankind's impact on the global climate motivates towards a future society in which a signiflcant proportion of its energy needs will be extracted from the winds and the tides of the planet. This paper shows several examples of the application of Brown's Vorticity Transport Model, originally developed to perform simulations of helicopter aeromechanics and wake dynamics, to the analysis of the performance of renewable energy devices and their possible impact on the environment. Prediction of the loading on wind turbines introduces signiflcant additional challenges to such a model, including the need to account fully for the efiects of radial ∞ow on blade stall. The wake-mediated aerodynamic interactions that occur within a wind farm can reduce its power output signiflcantly, but this problem is very similar to that where the aerodynamic unsteadiness of the coupled wake of the main and tail rotors of a helicopter can result in signiflcantly increased pilot workload. The helicopter-related problem of brownout, encountered during operations in desert conditions, has its analogue in the entrainment of sediment into the wakes of tidal turbines. In both cases it may be possible to ameliorate the in∞uence of the rotor on its environment by careful and well-informed design. Finally, calculations of the distortion and dispersal of the exhaust plumes of a helicopter by the wake of its rotor allow insight into how wind turbines might interfere with the dispersal of pollutants from nearby industrial sites. These examples show how cross-disciplinary information transfer between the rotorcraft fleld and the renewable energy community is helping to develop the technologies that will be required by our future society, as well as helping to understand the environmental issues that might need to be faced as these technologies become more prevalent.

The aerodynamic interactions that can occur within a wind farm result in the constituent turbines generating a lower power output than would be possible if each of the turbines were operated in isolation. Tightening of the constraints on the siting of wind farms is likely to increase the scale of the problem in the future. The aerodynamic performance of turbine rotors and the mechanisms that couple the fluid dynamics of multiple rotors can be understood best by simplifying the problem and considering the interaction between only two rotors. The aerodynamic interaction between two rotors in both axial and yawed wind conditions has been simulated using the Vorticity Transport Model. The aerodynamic interaction is a function of the tip speed ratio, the separation between the rotors, and the angle of yaw to the incident wind. The simulations show that the momentum deficit at a turbine operating within the wake developed by the rotor of a second turbine can limit substantially the mean power coefficient that can be developed by the turbine rotor. In addition, the significant unsteadiness in the aerodynamic loading on the rotor blades that results from the inherent asymmetry of the interaction, particularly in certain configurations and wind conditions, has considerable implications for the fatigue life of the blade structure and rotor hub. The Vorticity Transport Model enables the simulation the wake dynamics within wind farms and the subsequent aerodynamic interaction to be evaluated over a broad range of wind farm configurations and operating conditions.

The aerodynamic interactions that can occur within a wind farm can result in the constituent turbines generating a lower power output than would be possible if each of the turbines were operated in isolation. Tightening of the constraints on the siting of wind farms is likely to increase the scale of the problem in the future. The aerodynamic performance of turbine rotors and the mechanisms that couple the fluid dynamics of multiple rotors can be most readily understood by simplifying the problem and considering the interaction between only two rotors. The aerodynamic interaction between two rotors in both co-axial and offset configurations has been simulated using the Vorticity Transport Model. The aerodynamic interaction is a function of the tip speed ratio, and both the streamwise and crosswind separation between the rotors. The simulations show that the momentum deficit at a turbine operating within the wake developed by the rotor of a second turbine is governed by the development of instabilities within the wake of the upwind rotor, and the ensuing structure of the wake as it impinges on the downwind rotor. If the wind farm configuration or wind conditions are such that a turbine rotor is subject to partial impingement by the wake produced by an upstream turbine, then significant unsteadiness in the aerodynamic loading on the rotor blades of the downwind turbine can result, and this unsteadiness can have considerable implications for the fatigue life of the blade structure and rotor hub. Copyright (C) 2009 John Wiley & Sons, Ltd.

Two computational methods, one based on the solution of the vorticity transport equa- tion, and a second based on the solution of the Reynolds-Averaged Navier-Stokes equa- tions, have been used to simulate the aerodynamic performance of a horizontal axis wind turbine. Comparisons have been made against data obtained during Phase VI of the NREL Unsteady Aerodynamics Experimental and against existing numerical data for a range of wind conditions. The Reynolds-Averaged Navier-Stokes method demonstrates the potential to predict accurately the flow around the blades and the distribution of aero- dynamic loads developed on them. The Vorticity Transport Model possesses a consid- erable advantage in those situtations where the accurate, but computationally efficient, modelling of the structure of the wake and the associated induced velocity is critical, but where the prediction of blade loads can be achieved with sufficient accuracy using a lifting-line model augmented by incorporating a semi-empirical stall delay model. The largest benefits can be extracted when the two methods are used to complement each other in order to understand better the physical mechanisms governing the aerodynamic performance of wind turbines.

The increased restrictions placed on helicopter noise levels over recent decades have encouraged manufacturers to better understand tail rotor noise and its aerodynamic sources. A generic single main rotor and tail rotor helicopter has been simulated in high speed forward, and quartering, flight using the Vorticity Transport Model. The unsteady loads developed on the tail rotor blades and the resulting acoustic noise propagation have been computed. The sound propagation from isolated tail rotors with top-aft and top-forward senses of rotation in high speed forward flight results in impulsive sound being directed downward from the former and upward from the latter. The principal source of tail rotor noise in high speed forward flight is a periodic blade-vortex interaction between the tail rotor blades. The effect of aerodynamic interaction on tail rotor noise is highly dependent on the flight speed and trajectory, such that the noise produced as a result of interaction is, for the particular helicopter geometry simulated here, greater in quartering flight than in high speed forward flight. The sound pressure produced by periodic impulsive loads in high speed forward flight and the high frequency sound generated in quartering flight is sensitive to the scales to which the vortical features within the wake, and the radial and azimuthal distributions of blade loading, are resolved.

Aerodynamic interference between the main and tail rotor can have a strong negative influence on the flight mechanics of a conventional helicopter. Significant unsteadiness in the tail rotor loading is encountered under certain flight conditions, but the character of the unsteadiness can depend on the direction of rotation of the tail rotor. Numerical simulations, using Brown's vorticity transport model, of the aerodynamic interaction between the main and tail rotors of a helicopter are presented for a range of forward and lateral flight trajectories. Distinct differences are predicted in the behavior of the system in left and right sideward flight that are consistent with flight experience that the greatest fluctuations in loading or control input are required in left sideways flight (for a counterclockwise rotating main rotor). These fluctuations are generally more extreme for a system with tail rotor rotating top-forward than top-aft. Differences are also exposed in the character of the lateral excitation of the system as forward flight speed is varied. The observed behavior appears to originate in the disruption of the tail rotor wake that is induced by its entrainment into the wake of the main rotor. The extent of the disruption is dependent on flight condition, and the unsteadiness of the process depends on the direction of rotation of the tail rotor. In intermediate-speed forward flight and right sideward flight, the free stream delays the entrainment of the tail rotor wake far enough downstream for the perturbations to the rotor loading to be slight. Conversely, in left sideward and quartering flight, the free stream confines the entrainment process close to the rotors, where it causes significant unsteadiness in the loads produced by the system.

The mutual interaction between the main rotor and tail rotor wakes is central to some of the most problematic dynamic phenomena experienced by helicopters. Yet achieving the ability to model the growth and propagation of helicopter rotor wakes with sufficient realism to capture the details of this interaction has been a significant challenge to rotorcraft aerodynamicists for many decades. A novel computational fluid dynamics code tailored specifically for rotorcraft applications, the vorticity transport model, has been used to simulate the interaction of the rotors of a helicopter with a single main rotor and tail rotor in both hover and low-speed quartering flight, and with the tail rotor rotating both top-forward and top-aft. The simulations indicate a significant level of unsteadiness in the performance of both main and tail rotors, especially in quartering flight, and a sensitivity to the direction of rotation of the tail rotor. Although the model thus captures behaviour that is similar to that observed in practice, the challenge still remains to integrate the information from high fidelity simulations such as these into routine calculations of the X flight dynamics of helicopters.

The longitudinal flight dynamic phenomenon known as ‘pitch-up’ has caused significant problems to helicopter designers during the past 40 years. It is widely believed that pitch-up is due to the impingement of the main rotor wake on the horizontal stabilizer over a narrow range of low-speed flight conditions. Accurate simulation of pitch-up requires an accurate model of the structure and evolution of the main rotor wake as it passes close to the empennage of the helicopter. Brown’s Vorticity Transport Model has been used to analyse the aerodynamics of various typical main rotor - horizontal stabilizer configurations. The model is capable of predicting the development of the loads on the stabilizer that would induce pitch-up in a real helicopter. The range of pre-transitional advance ratios over which pitch-up is predicted correlates well with flight test data for helicopter configurations that are similar to those simulated. The overall magnitude of the down-load on the stabilizer is dependent on both the magnitude of the local velocity and the effective stabilizer angle of attack, leading to some counterintuitive behaviour, whilst the spanwise distribution of the loads along the stabilizer is modified by asymmetries in the flow-field that are induced by the main rotor wake. It is demonstrated how the physical effects that are predicted by high-resolution aerodynamic models can be incorporated into a simple flight dynamic simulation, allowing realistic representation of the effects of the interaction between the main rotor wake and stabilizer on the longitudinal dynamics of the helicopter.

The ability to model the growth and propagation of helicopter rotor wakes with sufficient realism to capture the detailed wake geometry represented by the vorticity field has been a significant challenge to rotorcraft aerodynamicists for many decades. Furthermore, modelling the mutual interaction of main rotor and tail rotor wakes has been seen as central to providing an understanding of some of the most problematic dynamic phenomena experienced by helicopters. A novel computational fluid dynamics code tailored specifically for rotorcraft applications, the Vorticity Tran sport Model, has been used to simulate such main rotor - tail rotor interactions in both hover and low-speed quartering flight, and with the tail rotor rotating with both top-forward and top-aft sense. The simulations performed indicate a significant level of unsteadiness in the performance of both main and tail rotors in the quartering flight condition. Comparison of results for the two senses of tail rotor rotation suggest some degree of sensitivity to this parameter. Analysis of the mean and fluctuating components of th e wake suggest extensive fluctuations in the wake near to the tail rotor may be a primary cause of the observed unsteadiness.

The perceived need to reduce mankind's impact on the global climate motivates towards a future society in which a significant proportion of its energy needs will be extracted from the winds and the tides of the planet. This paper shows several examples of the application of Brown's Vorticity Transport Model, originally developed to perform simulations of helicopter aeromechanics and wake dynamics, to the analysis of the performance of renewable energy devices and their possible impact on the environment. Prediction of the loading on wind turbines introduces significant additional challenges to such a model, including the need to account fully for the effects of radial flow on blade stall. The wake-mediated aerodynamic interactions that occur within a wind farm can reduce its power output significantly, but this problem is very similar to that where the aerodynamic unsteadiness of the coupled wake of the main and tail rotors of a helicopter can result in significantly increased pilot workload. The helicopter-related problem of brownout, encountered during operations in desert conditions, has its analogue in the entrainment of sediment into the wakes of tidal turbines. In both cases it may be possible to ameliorate the influence of the rotor on its environment by careful and well-informed design. Finally, calculations of the distortion and dispersal of the exhaust plumes of a helicopter by the wake of its rotor allow insight into how wind turbines might interfere with the dispersal of pollutants from nearby industrial sites. These examples show how cross-disciplinary information transfer between the rotorcraft field and the renewable energy community is helping to develop the technologies that will be required by our future society, as well as helping to understand the environmental issues that might need to be faced as these technologies become more prevalent.

Numerical simulations of the NREL phase VI wind turbine operating in yawed conditions have been performed using two computational methods; one based on the solution of the Reynolds-averaged Navier-Stokes equations (RANS) using unstructured overset meshes and one known as the Vorticity Transport Model (VTM) that is based on the solution of the vorticity transport equation. Simulations with and without the instrumentation enclosure that was present during the NREL experiments were performed. It was found that the enclosure influenced the loading significantly at the inboard part of the blade when the blade passed through the wake that was developed by the enclosure. Both the RANS and VTM codes are able to predict well the unsteady and time-averaged aerodynamic loadings on the wind turbine blades at low wind speeds. At high wind speeds, leading-edge flow separation and strong radial flow are observed on the suction surface of the blades, when the blades are at the retreating side of the rotor. Both the RANS and VTM codes provide less accurate predictions of the blade loads. However, at the advancing side of the rotor, the flow is mostly attached to the surface of the blade, and both the RANS and VTM predictions of the blade loads are in good agreement with the measured data.