Modelling the aerodynamics of vertical-axis wind turbines in unsteady wind conditions

Most numerical and experimental studies of the performance of vertical-axis wind turbines have been conducted with the rotors in steady, and thus somewhat artificial, wind conditions - with the result that turbine aerodynamics, under varying wind conditions, are still poorly understood. The Vorticity Transport Model has been used to investigate the aerodynamic performance and wake dynamics, both in steady and unsteady wind conditions, of three different vertical-axis wind turbines: one with a straight-bladed configuration, another with a curved-bladed configuration and another with a helically twisted configuration. The turbines with non-twisted blades are shown to be somewhat less efficient than the turbine with helically twisted blades when the rotors are operated at constant rotational speed in unsteady wind conditions. In steady wind conditions, the power coefficients that are produced by both the straight- and the curved-bladed turbines vary considerably within one rotor revolution because of the continuously varying angle of attack on the blades and, thus, the inherent unsteadiness in the blade aerodynamic loading. These variations are much larger, and thus far more significant, than those that are induced by the unsteadiness in the wind conditions

Vertical-axis wind turbines in oblique flow: sensitivity to rotor geometry

Increasing interest is being shown worldwide in the application of vertical-axis wind turbines for decentralised electricity generation within cities. The distortion of the onset air flow by buildings within the urban environment might however, under certain conditions of wind speed or direction, cause vertical-axis wind turbines to operate in oblique flow – in other words in conditions in which the wind vector is non-perpendicular to the axis of rotation of the turbine. Little is known about the effect on the operation of a vertical-axis wind turbine when the wind is perturbed from supposedly optimal conditions. In the present study, the Vorticity Transport Model has been used to simulate the aerodynamic performance and wake dynamics, both in normal and in oblique flow, of three different vertical-axis wind turbines: one with a straight-bladed configuration, another with a curved-bladed configuration and another with a helically twisted configuration. The results partly confirm previous experimental measurements that suggest that a straight-bladed vertical-axis wind turbine that operates in oblique flow might produce a higher power coefficient compared to when it is operated in normal flow. The simulations suggest, however, that significantly higher power coefficients in oblique flow are obtained only at higher tip speed ratios, and indeed only if the height of the turbine is not large compared to its radius. Furthermore, it is shown that a vertical-axis wind turbine with blades that are helically twisted around its rotational axis produces a relatively steady power coefficient in both normal and oblique flow when compared to that produced by turbines with either a straight- or a curved-bladed configuration

The influence of blade curvature and helical blade twist on the performance of a vertical-axis wind turbine

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

Simulating the aerodynamic performance and wake dynamics of a vertical-axis wind turbine

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 signifi cant 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-fi delity representation of the vortical structures within the fl ow fi eld 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 signifi cant 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

Modelling the aerodynamics of vertical-axis wind turbines

The current generation of wind turbines that are being deployed around the world features, almost exclusively, a three-bladed rotor with a horizontal-axis configuration. In recent years, however, a resurgence of interest in the vertical-axis wind turbine configuration has been prompted by some of its inherent advantages over horizontal-axis rotors, particularly in flow conditions that are typical of the urban environment. The accurate modelling of the aerodynamics of vertical-axis wind turbines poses a significant challenge. The cyclic motion of the turbine induces large variations in the angle of attack on the blades during each rotor revolution that result in significant unsteadiness in their aerodynamic loading. In addition, aerodynamic interactions occur between the blades of the turbine and the wake that is generated by the rotor. Interactions between the blades of the turbine and, in particular, tip vortices that were trailed in previous revolutions produce impulsive variations in the blade aerodynamic loading, but these interactions are notoriously difficult to simulate accurately. This dissertation describes the application of a simulation tool, the Vorticity Transport Model (VTM), to the prediction of the aerodynamic performance of three different vertical-axis wind turbines - one with straight blades, another with curved blades and a third with a helically twisted blade configuration - when their rotors are operated in three different conditions. These operating conditions were chosen to be representative of the flow conditions that a vertical-axis wind turbine is likely to encounter in the urban environment. Results of simulations are shown for each of the three different turbine configurations when the rotor is operated in oblique flow, in other words when the wind vector is non-perpendicular to the axis of rotation of the rotor, and also when subjected to unsteady wind. The performance of the straight-bladed turbine when it is influenced by the wake of another rotor is also discussed. The capability of the VTM to simulate the flow surrounding vertical-axis wind turbines has been enhanced by a dynamic stall model that was implemented in the course of this research in order to account for the effects of large, transient variations of the angle of attack on the aerodynamic loading on the turbine blades. It is demonstrated that helical blade twist reduces the oscillation of the power coefficient that is an inherent feature of turbines with non-twisted blades. It is also found that the variation in the blade aerodynamic loading that is caused by the continuous variation of the angle of attack on the blades during each revolution is much larger, and thus far more significant, than that which is induced by an unsteady wind or by an interaction with the wake that is produced by another rotor. Furthermore, it is shown that a vertical-axis turbine that is operated in oblique flow can, potentially, produce a higher power coefficient compared to the operation in conditions in which the wind vector is perpendicular to the axis of rotation, when the ratio between the height of the turbine and the radius of the rotor is sufficiently low

A case study illustrating depression from interpersonally related issues

This thesis is a single subject case study of a 20 year old, single, white female conducted in a university counseling center setting. This female presented into therapy with symptoms of major depression disorder, single episode, with moderate severity, and some mood congruent distortions. The therapy extended over a nine-week period, but with only six actual treatment sessions. Therapy consisted of an eclectic approach and individualized treatments pertaining to Cognitive-Behavioral Theory and some Interpersonal Theory elements for treating depression. This case was conceptualized through Young\u27s Early Maladaptive Schema Theory (1990) and Bowlby\u27s Attachment Theory (1969, 1973, 1980) in accordance to this client\u27s self-reported symptoms of depression, avoidance, intraparental conflict in divorce, low academic functioning, and low self-esteem and social functioning. Goals of therapy focused on 1) educating the client on symptoms and causes of depression, 2) identifying distorted schemas and maladaptive patterns pertaining to the combination of early maladaptive schemas, intraparental conflict in divorce, and attachment theory, 3) identifying individualized stressors and cues for depression, and 4) coping mechanisms and individualized cognitive-behavioral and interpersonal treatments for correcting distorted schemas and maladaptive relationship patterns eliciting her depression

Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis. The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is. Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation

Applying rotorcraft modelling technology to renewable energy research

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