Arbitrary Wind Research Articles

Dynamic wind turbine output power reduction under varying wind speed conditions due to inertia

ABSTRACTThe inertia of wind turbines causes a reduction in their output power due to their inability to operate at the turbine maximum co‐efficient of performance point under dynamic wind conditions. In this paper, this dynamic power reduction is studied analytically and using simulations, assuming that a steady‐state optimal torque control strategy is used.The concepts of the natural and actual turbine time‐constant are introduced, and typical values for these parameters are examined. It is shown that for the typical turbine co‐efficient of performance curve used, the average turbine speed can be assumed to be determined by the average wind speed. With this assumption, analytical expressions for the power reduction with infinite and then finite turbine inertia are determined for sine‐wave wind speed variations. The results are then generalized for arbitrary wind speed profiles.A numerical wind turbine system simulation model is used to validate the analytical results for step and sine‐wave wind speed variations. Finally, it is used with real wind speed data to compare with the analytical predictions. Copyright © 2012 John Wiley & Sons, Ltd.

A unified analytical solution of the steady-state atmospheric diffusion equation

A unified analytical solution of the steady-state atmospheric diffusion equation for a finite and semi-infinite/infinite media was developed using the classic integral transform technique (CITT) which is based on a systematized method of separation of variable.The solution was obtained considering an arbitrary mean wind velocity depending on the vertical coordinate (z) and a generalized separable functional form for the eddy diffusivities in terms of the longitudinal (x) and vertical coordinates (z).The examples described in this article show that the well known closed-form analytical solutions, available in the literature, for both finite and semi-infinite/infinite media are special cases of the present unified analytical solution. As an example of the strength of the developed methodology, the Copenhagen and Prairie Grass experiments were simulated (finite media with the mean wind speed and the turbulent diffusion coefficient described by different functional forms). The results indicate that the present solutions are in good agreement with those obtained using other analytical procedures, previously published in the literature. It is important to note that the eigenvalue problem is associated directly to the atmospheric diffusion equation making possible the development of the unified analytical solution and also resulting in the improvement of the convergence behavior in the series of the eigenfunction-expansion.

Methods for Computing Minimum-Time Paths in Strong Winds

This paper describes methods for computing minimum-time flight paths at high altitudes in the presence of strong horizontal wind s. The first method shows how to calculate nonlinear feedback (“dynamic programming”) solutions for minimum-time flight paths. To do this the Zermelo Problem for arbitrary winds is extended from a flat earth model to a spherical earth model as a two-state problem (latit ude and longitude) with one control (heading angle). Many minimum-time paths are calculated backwards from New York JFK Airport and San Francisco International Airport to points in the continental U.S. Then the optimal heading angle and the minimum-time can be found by interpolation given the current latitude and longitude using an interpolant created by Delaunay triangulation. The second method is based on an analytical neighboring optimal control solution that computes neighboring optimal heading commands as a function of the winds along a nominal flight path. As an example, minimum-time paths to New York and San Francisco are determined for the actual jet stream winds on 14 February 2001 at 36 kft.

Energy-Based Long-Range Path Planning for Soaring-Capable Unmanned Aerial Vehicles

To enable long-distance, long-duration flights by small soaring-capable uninhabited aircraft, a graph-based method for planning energy-efficient trajectories over a set of waypoints is presented. It introduces the energy map, which is an upper bound on the minimum energy required to reach a goal from anywhere in the environment while accounting for arbitrary three-dimensional wind fields. The energy map provides the path to the goal as a sequence of waypoints, the optimal speeds to fly for each segment between waypoints, and the heading required to fly along a segment. Trajectories computed using the energy map are compared with trajectories planned using an A * -based approach. Results are presented for simple wind fields representative of orographic lift. Finally a high-fidelity numerical simulation of a realistic wind field (ridge lift and wave over complex terrain) is used as a test case. The energy-map approach is shown to perform very well without the need for the heuristics associated with A * .

Rainwater rivulets running on a stay cable subject to wind

Stay cables are likely to vibrate under the combined effect of rain and wind in the so-called phenomenon rain–wind-induced vibrations (RWIVs). Rain takes part in the phenomenon in the shape of water rivulets that run along the cables. In previous articles, the authors investigated the conditions under which such rivulets can be formed. Using a lubrication model, it was shown for a particular wind–cable configuration that rivulets can only be exhibited above a critical wind speed for which gravity is overcome. The rivulets’ position was also predicted with the model. The results were validated by experiments. In this paper, the wind speed at which rivulets appear and their position are expressed for an arbitrary wind–cable orientation. A maximum wind speed for the rivulets’ existence is then estimated as the result of a balance between the drag force and the surface tension. A wind speed interval is consequently obtained for the rivulets’ appearance and maintenance on a cylinder. The boundaries of this interval are expressed in term of Weber numbers, comparing the surface tension and wind effect. These predictions are successfully compared with all the measurements that have been published in the literature.

A new formula describing the scaffold structure of spiral galaxies

We describe a new formula capable of quantitatively characterizing the Hubble sequence of spiral galaxies including grand design and barred spirals. Special shapes such as ring galaxies with inward and outward arms are also described by the analytic continuation of the same formula. The formula is r(phi) = A/log[B tan(phi/2N)]. This function intrinsically generates a bar in a continuous, fixed relationship relative to an arm of arbitrary winding sweep. A is simply a scale parameter while B, together with N, determine the spiral pitch. Roughly, greater N results in tighter winding. Greater B results in greater arm sweep and smaller bar/bulge while smaller B fits larger bar/bulge with a sharper bar/arm junction. Thus B controls the "bar/bulge-to-arm" size, while N controls the tightness much like the Hubble scheme. The formula can be recast in a form dependent only on a unique point of turnover angle of pitch - essentially a 1-parameter fit, aside from a scale factor. The recast formula is remarkable and unique in that a single parameter can define a spiral shape with either constant or variable pitch capable of tightly fitting Hubble types from grand design spirals to late type large-barred galaxies. We compare the correlation of our pitch parameter to Hubble type with that of the traditional logarithmic spiral for 21 well-shaped galaxies. The pitch parameter of our formula produces a very tight correlation with ideal Hubble type suggesting it is a good discriminator compared to logarithmic pitch, which shows poor correlation here similar to previous works. Representative examples of fitted galaxies are shown.

New models for wind noise measured in a flat surface under turbulent flow.

We have previously developed models for predicting the power spectral density of the wind noise pressure measured in a flat plate outdoors from the measured power spectral density of the turbulence and the measured wind velocity profile above the plate [Yu et al., Proceedings of NCAD 2008, NoiseCon2008‐ASME NCAD]. Recently we have corrected an error in the model for the logarithmic profile wind velocity gradient results and have developed an improved integration method. Also, we have developed a prediction for arbitrary wind velocity profiles using the previous single exponential model. Typical results comparing our predictions with our measurements are presented and analyzed. A simple algebraic fit to the prediction for the logarithmic profile fit form is also provided for use by others. [Research supported by the U.S. Army TACOM‐ARDEC at Picatinny Arsenal, NJ.]

English

Considerable progress has been made in the development of Velocity Prediction Programs (VPPs) suitable for analysis of racing yacht performance. In addition, investigations on yacht dynamics (i.e. optimal tacking procedure) are now available. While these tools will no doubt be further refined and computations speeded up, there is also a need to assess the performance of the yacht's helmsman and crew. The scope of the present study is the prediction of the performances of a yacht-crew system as a whole, by deriving numerical models for human behaviour alongside with those referred to the physics of yacht motion. The latter issue, the mechanical side of the problem, is analysed by solving yacht equations of motions in the time domain; crew inputs in terms of yacht steering and sail trim are considered. The yacht-crew system can sail a racecourse in an arbitrary wind pattern, according to strategic rules and given decision making schemata.

Flow in a Street Canyon for any External Wind Direction

An analytical model has been developed for the flow along a street canyon (of height H and width W), generated by an external wind blowing at any angle relative to the axis of the street. Initially, we consider the special case of a wind blowing parallel to the street. The interior of the street is decomposed into three regions, and the flow within each region is assumed to depend only on the external wind and the distance to the closest solid boundary. This decomposition leads to two different flow regimes: one for narrow streets (H/W > 1/2) and one for wide streets (H/W < 1/2). The theoretical model agrees well with results obtained from numerical simulations using a Reynolds-Averaged Navier–Stokes model. We then generalize the model to the case of arbitrary wind direction. Numerical solutions show that the streamlines of the mean flow in the street have a spiral form, and for most angles of incidence, the mass flux along the street scales on the component of the external wind resolved parallel to the street. We use this result to generalize the model derived for wind blowing parallel to the street, and the results from this model agree well with the numerical simulations. The model that has been developed can be evaluated rapidly using only very modest computing power, so it is suitable for use as an operational tool.

An Efficient Solution Method for the Buoyancy Wave Equation at Variable Wind and Temperature

Abstract To solve a horizontally spectral, vertically discrete buoyancy wave equation in conditions of arbitrary wind and temperature distribution with height, a novel method is applied, which consists of a presentation of the solution in the form of a cumulative product of complex decrease factors. For decrease factors, a nonlinear, inhomogeneous, two-member recurrence formula follows that is initiated, assuming the radiative condition at the top. Singularities of the wave equation, corresponding to a critical layer in the vicinity of evanescent wind, are eliminated by turbulent friction. The estimation of minimal vertical resolution is derived, enabling solution stability and accuracy. The areas of application of the developed numerical scheme are the high-precision modeling of orographic waves for arbitrary orography in general atmospheric stratification conditions and testing of adiabatic kernels of numerical weather prediction models.

A Sequential Detector for Biochemical Release in Realistic Environments

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> We develop a sequential detector for the release of a biochemical substance, with potential applications in environmental security. The proposed detector provides online detection of the appearance of a biochemical source in realistic complex environments. To obtain optimal performance, we use an integrated approach combining statistical analysis of measurements given by an array of biochemical sensors with a physical model of the dispersion, amenable to arbitrary geometries and wind turbulence. We first focus on formulating a detector that is applicable in the presence of unknown source parameters (e.g., release time, intensity, and location). We then derive a bound on the expected delay before a false detection in order to select the threshold of the test. For a fixed false-alarm rate, we obtain the detection probability of a release as a function of its location and initial concentration. Numerical examples illustrate the applicability of our methods to real-world scenarios of an urban area and indoor ventilation duct. </para>

Comment on “Low frequency variability in globally integrated tropical cyclone power dissipation” by Ryan Sriver and Matthew Huber

Comment on “Low frequency variability in globally integrated tropical cyclone power dissipation” by Ryan Sriver and Matthew Huber

The world-sheet corrections to dyons in the Heterotic theory

All the linear alpha-prime corrections, however excluding the gravitational Chern-Simons correction, are studied in the toroidally compactified critical Heterotic string theory. These corrections are computed to the entropy for a BPS static spherical four dimensional dyonic black hole which represents a wrapped fundamental string carrying arbitrary winding and momentum charges along one cycle in the presence of KK-monopole and H-monopole charges associated to another cycle. It is verified that after the inclusion of the gravitational Chern-Simons corrections [hep-th/0608182], all the linear alpha-prime corrections to the entropy for the supersymmetric dyon can be reproduced by the inclusion of only the Gauss-Bonnet Lagrangian to the supergravity approximation of the induced Lagrangian.

Sensorless Acquisition of the Rotor Position Angle of Induction Motors With Arbitrary Stator Windings

The anisotropy of a cage rotor is utilized to determine the angular position of the rotor in an induction machine. The switching transients generated by a pulsewidth-controlled inverter serve as test signals. The response of the three-inverter terminal currents is exploited to derive a quasi-instantaneous rotor position signal. The position is sensed at the inverter through the three-phase motor cable by measuring the current derivatives. The method does not require additional wire connections. It is applicable to induction motors having stator windings connected either in wye or in delta. The results are supported by measurements from an experimental setup.

Lateral loading and response for a tall building in the non-seismic doldrums

The situation for building design against wind and earthquake effects in Singapore is apparently unique. There is no seismic design code as there is no local seismicity, yet the effects of significant regional earthquakes are frequently felt in many high rise buildings in Singapore. Whereas it has become clear that the strongest winds in Singapore originate from storms and squalls, design for wind by law requires use of an arbitrary design wind speed applied in a British loading code geared to cyclonic wind systems. A decade of monitoring of a 280 m office tower has shown that distant strong earthquakes generate dynamic response typically an order of magnitude greater than due to the strongest winds occurring during the same period. The effect is greater for high rise apartment blocks and it is becoming clear that for extreme events with similar return periods, earthquake effects should govern design for lateral load in terms of dynamic base shears under such conditions. For the present, building control authorities take code provisions for accidental eccentricity to be adequate in covering seismic loads. While there have been moves towards a more rational local code, there remains an open question about the relationship of static and dynamic effects due to wind for both cyclonic and (thunder)storm winds. In this paper, the evidence concerning the nature of the two forms of loading is presented, and the various existing and potential code provisions examined.

Free field realization of superstring theory on AdS3

The Coulomb gas representation of expectation values in SU(2) conformal field theory developed by Dotsenko is extended to the SL(2,R) WZW model and applied to bosonic string theory on AdS3 and to Type II superstrings on AdS3 x N. The spectral flow symmetry is included in the free field realization of vertex operators creating superstring states of both Ramond and Neveu-Schwarz sectors. Conjugate representations for these operators are constructed and a background charge prescription is designed to compute correlation functions. Two and three point functions of bosonic and fermionic string states in arbitrary winding sectors are calculated. Scattering amplitudes that violate winding number conservation are also discussed.

Solution of Rayleighs instability equation for arbitrary wind profiles

A different approach to the solution of the singular Rayleigh equation is presented in the context of the water wave growth problem as modelled by wind-induced shear instabilities. The approach is based on the analytical solution of a Bessel equation in the vicinity of the singular point, which is obtained from Rayleigh's equation with an arbitrary wind profile. Wave growth rates are computed using an integral expression derived from the dispersion relation of the air–sea interface. Computations of the present approach agree well with those of Conte &amp; Miles (1959) for the special case of a logarithmic wind profile. Effects of the shape of the wind profile on the wave growth rate are investigated by using the 1/7-power law to represent the wind profile. Comparisons of the growth rates for the logarithmic wind profile and for the 1/7 profile reveal appreciable differences which must be investigated further, possibly using measured wind profiles within 10 m above the sea surface.

A probabilistic approach for SeaWinds data assimilation

AbstractScatterometer sea surface wind observations are being successfully assimilated into numerical weather prediction models. The quality of the winds retrieved from the new SeaWinds scatterometer (onboard the QuikSCAT satellite) depends on the subsatellite cross‐track location. In particular, the poor azimuth separation or diversity between views in the nadir region results in poor quality winds. In the QuikSCAT nadir region, where the local cost‐function minima are broad, the use of the standard procedure results in arbitrary and inaccurate winds. A new scheme, which accounts for broad cost‐function minima by allowing more ambiguous wind solutions, i.e. a multiple solution scheme (MSS), is proposed as an alternative to the standard procedure. The probability of every ambiguous solution being the ‘true’ wind is empirically derived, and used in the ambiguity‐removal procedure to make the scheme flexible enough to accept many wind solutions.A comparison between the standard wind retrieval and the MSS procedures at 100 km resolution is then performed, using independent model winds for validation. The MSS turns out to be more in agreement with the model reference than the standard procedure, especially at nadir. Moreover, it shows more spatially consistent and realistic winds by more effectively exploiting the information content of the observations. Copyright © 2004 Royal Meteorological Society

A linear upslope-time-delay model for orographic precipitation

A simple advection model is proposed for the prediction of precipitation patterns in complex terrain with arbitrary wind direction. The model includes the time delays associated with the conversion of cloud water to hydrometeors and the gravitational fallout of hydrometeors. These equations are solved using a Fast Fourier Transform. The model is tested against raingauge data from the Alps and radar data from the Lago Maggiore area of northwestern Italy, for the heavy rainfall event on September 20, 1999. Problems with these precipitation data sets are discussed. In the limit of short time delays, the model reduces to the well-known upslope method. Compared with the upslope method, the upslope-time-delay model has a significantly improved predictive skill. In the future, the method may be extended to include airflow dynamics and downslope evaporation.

Diffusion reduction in an arbitrary scale third generation wind wave model

The numerical schemes for the geographic propagation of random, short-crested, wind-generated waves in third-generation wave models are either unconditionally stable or only conditionally stable. Having an unconditionally stable scheme gives greater freedom in choosing the time step (for given space steps). The third-generation wave model SWAN (“Simulated WAves Nearshore”, Booij et al., 1999) has been implemented with this type of scheme. This model uses a first order, upwind, implicit numerical scheme for geographic propagation. The scheme can be employed for both stationary (typically small scale) and nonstationary (i.e. time-stepping) computations. Though robust, this first order scheme is very diffusive. This degrades the accuracy of the model in a number of situations, including most model applications at larger scales. The authors reduce the diffusiveness of the model by replacing the existing numerical scheme with two alternative higher order schemes, a scheme that is intended for stationary, small-scale computations, and a scheme that is most appropriate for nonstationary computations. Examples representative of both large-scale and small-scale applications are presented. The alternative schemes are shown to be much less diffusive than the original scheme while retaining the implicit character of the particular SWAN set-up. The additional computational burden of the stationary alternative scheme is negligible, and the expense of the nonstationary alternative scheme is comparable to those used by other third generation wave models. To further accommodate large-scale applications of SWAN, the model is reformulated in terms of spherical coordinates rather than the original Cartesian coordinates. Thus the modified model can calculate wave energy propagation accurately and efficiently at any scale varying from laboratory dimensions (spatial scale O(10 m) with resolution O(0.1 m)), to near-shore coastal dimension (spatial scale O(10 km) with resolution O(100 m)) to oceanic dimensions (spatial scale O(10 000 km) with resolution O(100 km).