Predicting wind turbine blade loads using vorticity transport and RANS methodologies

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

Aerodynamic Response of a Hovering Rotor to Ramp Changes in Pitch Input

Under transient conditions, a helicopter rotor generates a complex, time-dependent pattern of shed and trailed vorticity in its wake that has profound eects on its loading. To examine these eects, the response of a two-bladed hovering rotor to a ramp change in collective pitch is investigated using three dierent computational approaches. Solutions obtained using a Compressible Reynolds Averaged Navier{Stokes ap- proach are compared to results obtained from lifting-line theory coupled to an Eulerian Vorticity Transport Model, and from a simple single-state dynamic in ow model. The dierent numerical approaches yield very similar predictions of the thrust response of the rotor to ramp changes in collective pitch, as long as the ramp rates are small. This suggests that the basic underlying ow physics is properly represented by all the approaches. For more rapid ramp rates, an additional delay in the aerodynamic response of the rotor, that is related to the nite extent of the wake during its early history, is predicted by the Navier{Stokes and Vorticity Transport approaches. Even though the evolution of the wake of the rotor is strongly three dimensional and highly unsteady, the predictions of the Navier{Stokes and lifting-line models agree very closely as long as the blades of the rotor do not stall. In the pre-stall regime, a quasi two-dimensional representation of the blade aerodynamics thus appears adequate for predicting the performance of such systems even under highly transient conditions. When ow separation occurs, the resulting three dimen- sionality of the blade aerodynamics forces the predictions of the Navier{Stokes and lifting-line approaches to diverge, however. The characterization of the wake interactions and stall propagation mechanisms that are presented in this study oers some insight into the fundamental uid dynamic mechanisms that govern the transient aerodynamic response of a rotor to control inputs, and provides some quantication of the limits of applicability of some popular current approaches to rotor aerodynamic analysis

Wake dynamics and rotor-fuselage aerodynamic interactions

The unsteady loads experienced by a helicopter are known to be strongly influenced by aerodynamic interactions between the rotor and fuselage; these unsteady loads can lead to deficiencies in handling qualities and unacceptable vibratory characteristics of the rotorcraft. This work uses a vorticity-based computational model to study the governing processes that underpin this aerodynamic interaction and aims to provide greater understanding of the wake dynamics in the presence of a fuselage, as well as an appreciation of how the geometry of the wake affects the loading on the fuselage. The well-known experiments using NASA's ROBIN fuselage are used to assess the accuracy of the computations. Comparisons of calculations against results from smoke visualization experiments are used to demonstrate the ability of the model to reproduce accurately the geometry of the rotor wake, and comparisons with inflow data from the experiments show the method to capture well the velocity field near to the rotor. The fuselage model is able to predict accurately the unsteady fuselage loading that is induced by blade passage and also by the inviscid interaction between the main rotor wake and fuselage

Predicting the wake structure of the HART II rotor using the vorticity transport model

Brown’s Vorticity Transport Model has been used to predict the wake structure and resultant blade loading of the rotor that was studied during the HART II experimental programme. The descending flight condition of the experiment yields significant high-frequency content to the blade loading due to the presence of blade-vortex interactions. PIV images of the wake structure were compared against numerical predictions of the detailed geometry of the rotor wake using three different computational resolutions of the flow. This was done to investigate the origin of inaccuracies exposed in an earlier study of the system in capturing the effects of blade vortex interactions on the loading on the rotor. The predicted positions of the vortex cores agree with measured data to within a fraction of the blade chord, and the strength of the vortices is preserved to well downstream of the rotor, essentially independently of the resolution of the calculation. Nevertheless the amplitude of the loading impulses induced on the blade by vortex interaction are strongly influenced by the resolution of the calculation through the effect of cell density on the minimum vortex core size that can be supported. It would appear thus that the inaccuracies in predicting the high-frequency loading on the rotor are not due to any inherent deficiency in the representation of the wake, although viscous effects may need to be considered in future in order to decouple the vortex core size from the cell size, but rather due to the inherent deficiencies of the lifting line approach used to model the blade aerodynamics

A rational approach to comparing the performance of coaxial and conventional rotors

The merit, in terms of its efficiency and performance, of the twin, contrarotating coaxial rotor configuration over the more conventional single rotor system has long been a point of contention. Previously published comparisons yield seemingly inconsistent and conflicting conclusions. In this paper, the basis for a fair, like-for-like comparison of the performance of coaxial and single rotor systems is discussed. A comparison between experimentally measured data and numerical predictions of rotor performance obtained using the vorticity transport model shows that a computational approach can be used reliably to decompose the power consumption into induced and profile constituents. These comparisons show that a somewhat stronger similarity in geometry needs to be enforced between the two types of rotor system than previously suggested in order that the systems be directly comparable. If the equivalent single rotor system is constructed to have the same disk area, blade geometry, and total number of blades as that of the coaxial rotor, then the geometric differences between the two systems are confined to the defining characteristics of the two types of rotor system, in other words to the vertical separation between the rotor blades and their relative direction of rotation. The differences in aerodynamic performance between a coaxial rotor and an equivalent single rotor defined in this way then arise solely as a result of the differences in the detailed interaction between the blades and their wakes that arise within the two types of system. Using this form of comparison, the articulated coaxial system is shown to consume marginally less induced power than the equivalent single rotor system. The difference is small enough, however, to be obscured if the profile drag of the blades is overtly sensitive to operating condition, as for instance might be the case at low Reynolds number

Main rotor-tail rotor intraction and its implications for helicopter directional control

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

Simulating wind turbine interactions using the vorticity transport equations

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 ofturbine 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 limitsubstantially 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 wakedynamics within wind farms and the subsequent aerodynamic interaction to be evaluated over a broad range of wind farm configurations and operating conditions

Aeroacoustics of a coaxial rotor in level flight

The aeroacoustic characteristics of a coaxial system with teetering rotors in level forward °ight are com- pared to those of an equivalent articulated single rotor with the same solidity. A lifting line representation of the blade aerodynamics is coupled to Brown's Vorticity Transport Model to simulate the aerodynam- ics of the rotor systems. The acoustic ¯eld is determined using the Ffowcs Williams-Hawkings equation. Acoustic analysis shows that the principal contribution to noise radiated by both the coaxial and equivalent single rotor systems is at the fundamental blade passage frequency, but that the coaxial rotor generates higher sound pressure levels (by 10 dB for the evaluated con¯gurations) than the equivalent single rotor at all °ight speeds. The sources of blade vortex interaction (BVI) noise are investigated and the principal BVI events are identi¯ed. For the coaxial rotor, the most intense impulsive noise is seen to be generated by the inter-rotor BVI on the advancing side of the lower rotor. The impulsive noise that is generated by blade vortex interactions for the equivalent single rotor reduces in amplitude as the strength of BVI events on the rotor decreases with forward speed. Conversely, the BVI noise of the coaxial rotor intensi¯es with increasing °ight speed due to the increasing strength of the interaction between the wake of the upper rotor and the blades of the lower rotor. The impulsive noise due to BVI for the coaxial rotor is found to be higher by 20{35 dB compared to the equivalent single rotor. The overall and impulsive noise characteristics of the coaxial system are found to be weakly sensitive to changes in rotor separation and the relative phasing of the rotors

Aeroacoustic analysis of main rotor and tail rotor interaction

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

Predicting blade vortex interaction, airloads and acoustics using the vorticity transport model

Interactions between the blades and vortical structures within the wake of a helicopter rotor are a significant source of impulsive loading and noise, particularly in descending flight. Advances in the prediction and understanding of such blade vortex interactions have been aided in recent years by the extensive experimental dataset made available through the HART test programme. Brown’s Vorticity Transport Model was used to predict the rotor blade loading, the resultant wake system and the acoustic noise radiation for the HART II rotor. The vorticity conserving properties of the Vorticity Transport Model allow the detailed wake features that are associated with blade vortex interactions to be resolved. The experimental airload data, in particular the higher harmonic loading associated with blade vortex interactions, is matched well by the computations. The computed vorticity distribution in the wake also shows good correlation with the experimentally measured vortex positions. Including a representation of the fuselage within the computation yields marked improvement in the prediction of the vortex positions compared to similar calculations with an isolated rotor. An accoustic analysis, based on a Ffowcs-Williams Hawkings approach, is able to predict accurately the locations of the sound pressure maxima and the upstream attenuation of the sound radiated by the rotor. The principal discrepancies in airload, vortex position and acoustic prediction are confined almost exclusively to the rear of the advancing side of the rotor and, if errors in measuring the blade deflection can be discounted, may be due to minor inaccuracies in modelling the roll-up of the wake