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

Single molecule photon counting statistics for quantum mechanical chromophore dynamics

We extend the generating function technique for calculation of single molecule photon emission statistics [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett., 90,238305 (2003)] to systems governed by multi-level quantum dynamics. This opens up the possibility to study phenomena that are outside the realm of purely stochastic and mixed quantum-stochastic models. In particular, the present methodology allows for calculation of photon statistics that are spectrally resolved and subject to quantum coherence. Several model calculations illustrate the generality of the technique and highlight quantitative and qualitative differences between quantum mechanical models and related stochastic approximations. Calculations suggest that studying photon statistics as a function of photon frequency has the potential to reveal more about system dynamics than the usual broadband detection schemes.Comment: Submitted to the Journal of Physical Chemistr

Methods for Solving Necessary Equivalences

Nonmonotonic Logics such as Autoepistemic Logic, Reflective Logic, and Default Logic, are usually defined in terms of set-theoretic fixed-point equations defined over deductively closed sets of sentences of First Order Logic. Such systems may also be represented as necessary equivalences in a Modal Logic stronger than S5 with the added advantage that such representations may be generalized to allow quantified variables crossing modal scopes resulting in a Quantified Autoepistemic Logic, a Quantified Autoepistemic Kernel, a Quantified Reflective Logic, and a Quantified Default Logic. Quantifiers in all these generalizations obey all the normal laws of logic including both the Barcan formula and its converse. Herein, we address the problem of solving some necessary equivalences containing universal quantifiers over modal scopes. Solutions obtained by these methods are then compared to related results obtained in the literature by Circumscription in Second Order Logic since the disjunction of all the solutions of a necessary equivalence containing just normal defaults in these Quantified Logics, is equivalent to that system

Representing Reflective Logic in Modal Logic

The nonmonotonic logic called Reflective Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Reflective Logic with an initial set of axioms and defaults if and only if the meaning of that set of sentences is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original Reflective Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults thus allowing such defaults to produce quantified consequences. Furthermore, this generalization properly treats such quantifiers since all the laws of First Order Logic hold and since both the Barcan Formula and its converse hold

Representing "Recursive" Default Logic in Modal Logic

The "recursive" definition of Default Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the "recursive" fixed-point equation of Default Logic with an initial set of axioms and defaults if and only if the meaning of the fixed-point is logically equivalent to a particular modal functor of the meanings of that initial set of sentences and of the sentences in those defaults. This is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and because unlike the original "recursive" definition of Default Logic, it is easily generalized to the case where quantified variables may be shared across the scope of the components of the defaults

On the Relationship between Quantified Reflective Logic and Quantified Default Logic

Reflective Logic and Default Logic are both generalized so as to allow universally quantified variables to cross modal scopes whereby the Barcan formula and its converse hold. This is done by representing both the fixed-point equation for Reflective Logic and the fixed-point equation for Default both as necessary equivalences in the Modal Quantificational Logic Z. and then inserting universal quantifiers before the defaults. The two resulting systems, called Quantified Reflective Logic and Quantified Default Logic, are then compared by deriving metatheorems of Z that express their relationships. The main result is to show that every solution to the equivalence for Quantified Default Logic is a strongly grounded solution to the equivalence for Quantified Reflective Logic. It is further shown that Quantified Reflective Logic and Quantified Default Logic have exactly the same solutions when no default has an entailment condition

Representing Autoepistemic Logic in Modal Logic

The nonmonotonic logic called Autoepistemic Logic is shown to be representable in a monotonic Modal Quantificational Logic whose modal laws are stronger than S5. Specifically, it is proven that a set of sentences of First Order Logic is a fixed-point of the fixed-point equation of Autoepistemic Logic with an initial set of axioms if and only if the meaning or rather disquotation of that set of sentences is logically equivalent to a particular modal functor of the meaning of that initial set of sentences. This result is important because the modal representation allows the use of powerful automatic deduction systems for Modal Logic and unlike the original Autoepistemic Logic, it is easily generalized to the case where quantified variables may be shared across the scope of modal expressions thus allowing the derivation of quantified consequences. Furthermore, this generalization properly treats such quantifiers since both the Barcan formula and its converse hold