Arbitrary Wind Research Articles

Efficient modeling of atmospheric infrasound propagation with the Semi-Analytical-Finite-Element (SAFE) method

Downward refraction in the lower atmosphere, attributed to winds and temperature inversion, can enable infrasound to efficiently propagate over long distances inside acoustic waveguides. In this study, we use the semi-analytic finite element (SAFE) method to predict this effect in stratified, inhomogeneous, moving air for range-independent noise propagation over reflective half-planes. We present solutions for different temperature and velocity profiles and compare them to direct numerical solutions of the two-dimensional linearized Euler equations. The SAFE method separates the exact two-dimensional wave equation for a stratified, inhomogeneous, moving medium by expressing the pressure field as a sum of vertical eigenmodes propagating in the range direction. This simplifies the acoustic problem into a one-dimensional eigenvalue problem. As this problem is addressed with the finite-element method, the method can accommodate arbitrary wind and temperature profiles. For large, range-independent domains, the proposed procedure proves to be much more efficient than the tested direct numerical computations. Additionally, it converges against the exact solution of the acoustic problem if enough modes are included in the calculation. Therefore, the method offers a viable procedure for benchmarking other pressure field prediction techniques.

МОДЕЛЮВАННЯ АСИНХРОННИХ МАШИН У СКЛАДІ ЕЛЕКТРОМЕХАНІЧНИХ СИСТЕМ З УРАХУВАННЯМ ВТРАТ У СТАЛІ СТАТОРА

A comparative study has been conducted on methods for accounting for the influence of losses in the stator iron of squirrel-cage induction motors on the operating parameters. A comparison was made between reference data and calculation results of the nominal mode parameters of an asynchronous motor without considering losses in the stator iron and with their consideration using equivalent resistances connected in parallel to the motor, as well as equivalent circuits of losses in the stator. The effect of the ratio of active and inductive components of the load of equivalent stator loss circuits on the results of mathematical modeling has been investigated. The study was carried out based on a universal mathematical model of an asynchronous motor of electromechanical systems with an arbitrary stator winding scheme. An algorithm for determining and adjusting the parameters of the stator loss circuits during the integration of the differential equations of electrical and mechanical balance of the asynchronous motor to a steady-state value has been developed, based on the values of losses in the stator iron (depending on the induction and frequency) and the effective value of the current of the equivalent circuit. To ensure solution stability, the use of an iteration coefficient and discretization of resistance adjustment has been justified. The application of stator iron loss circuits in the mathematical model of an asynchronous machine in generator mode has been justified, when the use of parallel connected equivalent resistances contradicts the machine's energy diagram. References 10, figure 1, table 1.

Wind Finslerian Structures: From Zermelo’s Navigation to the Causality of Spacetimes

The notion of wind Finslerian structure Σ \Sigma is developed; this is a generalization of Finsler metrics (and Kropina ones) where the indicatrices at the tangent spaces may not contain the zero vector. In the particular case that these indicatrices are ellipsoids, called here wind Riemannian structures, they admit a double interpretation which provides: (a) a model for classical Zermelo’s navigation problem even when the trajectories of the moving objects (planes, ships) are influenced by strong winds or streams, and (b) a natural description of the causal structure of relativistic spacetimes endowed with a non-vanishing Killing vector field K K (SSTK splittings), in terms of Finslerian elements. These elements can be regarded as conformally invariant Killing initial data on a partial Cauchy hypersurface. The links between both interpretations as well as the possibility to improve the results on one of them using the other viewpoint are stressed. The wind Finslerian structure Σ \Sigma is described in terms of two (conic, pseudo) Finsler metrics, F F and F l F_l , the former with a convex indicatrix and the latter with a concave one. Notions such as balls and geodesics are extended to Σ \Sigma . Among the applications, we obtain the solution of Zermelo’s navigation with arbitrary time-independent wind, metric-type properties for Σ \Sigma (distance-type arrival function, completeness, existence of minimizing, maximizing or closed geodesics), as well as description of spacetime elements (Cauchy developments, black hole horizons) in terms of Finslerian elements in Killing initial data. A general Fermat’s principle of independent interest for arbitrary spacetimes, as well as its applications to SSTK\xspace spacetimes and Zermelo’s navigation, are also provided.

Decoupled incremental nonlinear dynamic inversion control for aircraft autonomous landing with ground-effect

Due to motion coupling and increased model dependence, the use of nonlinear controllers in real-time applications for aircraft is extremely constrained. This explains why proportional, derivative, and integral (PID) controls are frequently used in practice. However, fast changes in the commanded path and the requirement for high accuracy and tracking performance limit use of PID in landing. This paper presents a design of a decoupled incremental nonlinear dynamic inversion (INDI) controller for performing autonomous landing of a fixed-wing aircraft. The investigation is carried out using the ground effect model and is compared without it. A carrot chasing guidance algorithm is implemented for waypoint navigation to generate the command for the proposed controller's outer loop. The navigational state estimate issue has been resolved using the Cubature Kalman Filter (CKF) approach. Two decoupled CKF algorithms named complementary Cubature Kalman Filter (CCKF) and Integrated Cubature Kalman Filter (I-CKF) are proposed to estimate aircraft navigational states comprised of attitudes, navigational position in terms of latitude, longitude altitudes, and North-East-down velocities. The mathematical model for flare and approach trajectory is designed and commanded to follow the same by the proposed INDI controller. The effectiveness of INDI have been evaluated in a simulation environment by landing the aircraft in the same runway position at arbitrary wind conditions. The performance of the proposed INDI controller is juxtaposed with a conventional proportional integrator and derivative (PID) based landing controller. The simulation findings demonstrate that the INDI has a competitive edge over traditional PID approaches due to its robust performance, less dependence on model dynamics, and fast command tracking capability required during the flare phase.

An open-source project for wind instrument modeling using digital waveguides

Digital waveguide methods for time-domain modeling of acoustic structures comprised of interconnected piece-wise one-dimensional cylinders, cones and toneholes have been well reported in the past. In this work, an open-source Matlab class is presented that can be used to model arbitrary wind instrument air column structures, defined by length, radii and hole geometric parameters, using digital waveguide methods. Fractional-delay filtering can be enabled or disabled, with support for both Thiran and Lagrange filter types of specified order. Thermoviscous losses can be modeling using either a discrete-time least squares or a shelf-filter fit, both of arbitrary order. Three different tonehole model options are provided (two-port, three-port or wave digital filter). End boundary conditions include closed, anechoic, ideally open, open flanged and open unflanged. The class object can be used either in single-sample iterative contexts (for example, with an attached excitation model) or with arbitrarily-sized input signals (for example, to compute a reflection function or impedance). The modeled geometry can be constructed manually by iteratively adding segments or holes, or a complete geometry can be specified in a file. This project is bundled together with a parallel and previously reported open-source project for frequency-domain transfer matrix modeling of air columns (https://github.com/garyscavone/acmt).

A shear stress parametrization for arbitrary wind farms in conventionally neutral boundary layers

In the context of large off-shore wind farms, power production is influenced greatly by the turbine array's interaction with the atmospheric boundary layer. One of the most influencing manifestations of such complex interaction is the increased level of shear stress observed within the farm. This leads to higher momentum fluxes that affect the wind speed at the turbine locations and in the cluster wake. At the wind farm entrance, an internal boundary layer (IBL) grows due to the change in effective roughness imposed by the wind turbines, and for large enough clusters, this can reach the unperturbed boundary layer height in what is referred to as the fully developed regime. Downwind, a second IBL starts growing, while the shear stress profile decays exponentially to its unperturbed state. In the present study, we propose a simple analytical model for the vertical profile of the horizontal shear stress components in the three regions identified above. The model builds upon the top-down model of Meneveau (J. Turbul., vol. 13, 2012, N7), and assumes that the flow develops in a conventionally neutral boundary layer. The proposed parametrization is verified successfully against large-eddy simulations, demonstrating its ability to capture the vertical profile of horizontal shear stress, and its evolution both inside and downwind of the wind farm. Our findings suggest that the developed model can prove extremely useful to enhance the physical grounds on which new classes of coupled wind farm engineering models are based, leading to a better estimation of meso-scale phenomena affecting the power production of large turbine arrays.

Wind-induced responses for cable net structures considering punching rate of reflecting panels

The datum surface of the active reflector of the Five-hundred-meter Aperture Spherical radio Telescope (FAST) is a spherical crown with a radius of 300 m and an aperture of 500 m. The reflector is supported on a cable net structure. Due to its sensitivity to wind loads, it is imperative to investigate its aerodynamic characteristics and wind-induced vibration response. This paper explores the aerodynamic characteristics of the reflecting panel through computational fluid dynamics (CFD). Compared with the nonporous panel, the drag coefficient of the reflecting panel with a punching rate of approximately 50% increases by approximately 51%, and the main reason is that the resistance changes little, but the projected area decreases by 50%. On this basis, the calculation method of the aerodynamic coefficient of the reflecting panel under arbitrary wind direction angle is established. Then, the simulation model of the active reflector system is established, and the wind-induced vibration response is analyzed under different wind speed conditions. The displacement and stress responses of the cable net structure, ring beams, and lattice columns are studied, and the gust response factors (GRFs) are calculated. The results show that the wind load has a very strong effect on the nodal displacement and column bottom stress but has little effect on the stress of the cable net structure; the displacement GRFs of the cable net structure, ring beams, and lattice columns increase with increasing wind speed, of which the simulated results can provide a reference for the design of similar projects.

Fast Analytical Loss Model for Litz Wire in Transformers With Arbitrary Winding Arrangements

Fast Analytical Loss Model for Litz Wire in Transformers With Arbitrary Winding Arrangements

Experimental Study of the Transient Behavior of a Wind Turbine Wake Following Yaw Actuation

Wind tunnel experiments were performed to investigate the response of a wind turbine model immersed in a replicated atmospheric boundary layer to dynamic changes in the yaw angle. Both the flow field in the wake and the operating properties of the turbine, namely its thrust force, torque, and angular velocity, were monitored during repeated yaw maneuvers for a variety of yaw angles. It was observed that the characteristic time scale of the transient experienced by the turbine scalar quantities was one order of magnitude larger than that of the yaw actuation and depended primarily on the inertia of the rotor and the generator. Furthermore, a Morlet wavelet analysis of the thrust signal showed a strong peak at the rotation frequency of the turbine, with the transient emergence of high activity at a lower frequency during the yaw maneuver. The insights provided by the proper orthogonal decomposition analysis performed on the wake velocity data enabled the development of a simple reduced-order model for the transient in the flow field based on the stationary states before and after the yaw maneuver. This model was then further improved to require only the final state, extending its applicability to any arbitrary wind farm as a dynamical surrogate of the farm behavior.

Development of a Three-Phase Power-Flow Calculation Method for Distribution Systems with Automatic Handling of Arbitrary Winding Connections of Transformers

Development of a Three-Phase Power-Flow Calculation Method for Distribution Systems with Automatic Handling of Arbitrary Winding Connections of Transformers

Local flow and loads estimation on wake-affected wind turbines using graph neural networks and PyWake

The estimation of the flow conditions throughout a modern wind farm is a relevant albeit complex problem involving several different modelling scales. In this context, recent years have seen the rise of the demand - normally industry-driven - of quick, computationally inexpensive, wind farm flow field simulators upon which further calculations might be undertaken (e.g. power output, fatigue loads, etc.). Naturally, the trustworthiness of such models hinges upon their ability to accurately estimate wakes, under the evident trade-off between computational time and accuracy. One such simulator that has been recently gaining traction within the wind community is PyWake, a Python-based flow solver, with several possible add-ons and modularity options. Based on runs from PyWake, this contribution studies the applicability of graph neural networks (GNN) as a simultaneous wind turbine fleet, wind inflow and loads surrogate. As graphs are discrete mathematical sets of dependent objects, one can see how the layout-dependent interaction between wind turbines’ aerodynamics, from which wake arises, lends itself to be modelled as a graph. Thus, we introduce the use of GNNs for layout-agnostic joint modelling of rotor-averaged wind speed, turbulence intensity, power production and damage equivalent loads (DEL) on individual turbines of wind farms. To this end, probabilistic samples of inflow conditions from a Weibull distribution for wind speed, uniform wind direction and conditional normal distributions of wind shear and nacelle yaw angles are generated as main inflow properties in the numerical simulations. Additionally, arbitrary wind farm layouts are created based on varied geometric shapes with random parametrization (varying orientations, length/width ratio). Both the arbitrary layouts and the random inflow conditions are then used as inputs for PyWake. PyWake’s output, namely, rotor averaged wind speed, turbulence intensity, power production and DELs of each individual wind turbine in the wind farms, are used to train a general GNN model. We elect to implement an Encode-Process-Decode GNN as a graph learning model. We compare the performance of various approaches of the relational dependency representation (edge-forming techniques) amongst the nodes (wind turbines) on the graph, such as Delaunay triangulation, KNN, radius-based methods and fully connected scheme. In our analysis, we evaluate the accuracy of GNNs and its ability to generalize their joint predictions for unseen layouts and varying inflow conditions.

Analytical modelling of high‐frequency losses in toroidal inductors

AbstractToroidal inductors are widely used in power electronic systems. With the increasing switching frequency of power devices, the AC losses of high‐frequency inductor windings have become an issue that cannot be ignored in design. A method with low computational time cost and high accuracy is urgently needed by designers. This paper proposes a modified analytical method for winding loss calculation of toroidal inductors based on the one‐dimensional Dowell method and the two‐dimensional Ferreira method, and proposes a compensated analytical model considering the proximity effect of inter‐turn conductors of toroidal windings. The analytical method calculates the non‐linear porosity of toroidal windings, and can accurately solve the AC losses of toroidal inductors with arbitrary porosity winding encapsulation. The analytical results are in good agreement with the finite element method (FEM) and experimental data. The experimental measurement data verifies the validity of the proposed model within 1‐MHz frequency, the calculation error of the modified analytical method is less than 25%, and the calculation error of the compensated analytical model is reduced to 10%.

Analytical Hybrid Quasi-3D Transformer Leakage Inductance Model

Fast and accurate models of the transformer leakage inductance are crucial for optimization-based design of isolated converters. This article proposes an analytical hybrid Quasi-3D (HQ3D) model for E/U/ER/UR-core type transformers that combines the best suited submodels for each winding section of the transformer. A submodel is developed that directly calculates the leakage inductance contribution of curved winding sections based on the integration of the radially weighted magnetic energy density. The HQ3D model can describe arbitrary winding positions and its fully analytical nature guarantees optimal geometrical scalability. The only restriction is that the windings need to be parallel to the core edges. The HQ3D model is in the accuracy range of 3D finite-element method and verified with measurements on nine transformer prototypes with significantly different geometry ranges. The HQ3D model is rapidly executable, and therefore, well suited for optimizations of galvanically isolated converters.

Time-Fuel-Optimal Navigation of a Commercial Aircraft in Cruise With Heading and Throttle Controls Using Pontryagin’s Maximum Principle

In this research, we consider the commercial aircraft trajectory optimization problem for a general cruise model with arbitrary spatial wind fields to be solved using the Pontryagin’s maximum principle. The model features two fundamental controls, namely “throttle setting” (appearing as a singular control) and “heading angle” (appearing as a regular control). For a problem with state-inequality constraints and minimum time-fuel objective, we show that the optimal “heading angle” can be described through the classic Zermelo’s navigation identity. We also demonstrate, by analyzing the switching function, that the singular “throttle setting” can be characterized through a feedback function that relies on both the optimal states and “heading angle”. The switching-point algorithm is employed to solve a case study where we inspect the optimality conditions and graph the optimal controls together with the optimal state and co-state variables.

A simple method of fast evaluating full-field wake velocities for arbitrary wind turbine arrays on complex terrains

Wind energy is an important option of renewable energy and plays more and more an irreplaceable role in many regions. A technical and meanwhile a scientific problem directly relevant to selecting the wind farm site, optimizing the wind farm layout and evaluating the power output, is to calculate accurately the wake effects generated behind wind turbines, which affect the wind velocity distribution of downstream turbines and reduce the power output of a wind farm. Through modifications of near-field and far-field empirical wake models and the wake model on a complex terrain, a unified wake model is developed to calculate the full-field wake velocity distribution over a wind farm with arbitrary turbine arrays located on flat or complex terrains. The derived wake velocity is formulated in an explicit and concise form to obtain the wind velocity at any position within the turbine arrays. The velocity distribution over the whole array can be fast acquired by implementing a simple procedure and occupying the least computing resources. Compared to the CFD modelling, the present method performs superiorly in both easiness and efficiency, which would be a powerful tool in designing and optimizing a large wind farm composed of numerous and variably deployed turbines of different densities on complex terrains. With this solution, it becomes feasible to construct the wind turbine arrays at the sites of restricted space, specifically the offshore islands and the large floating structures.

Application of the finite element method to atmospheric sound propagation over impedance discontinuities

Outdoor noise propagation typically involves the propagation of sound over mixed ground conditions, including variations in the surface impedance. Diffraction occurs at the interface between different ground conditions, and this can significantly affect local sound attenuation. Popular approaches to modelling impedance discontinuities include the boundary integral method, parabolic equations, and semi-empirical methods. This paper presents an alternative approach that takes advantage of the generality of the finite element method. It was shown recently that the semi analytic finite element method can be used to solve the exact governing wave equation for atmospheric sound propagation in a complex vertically stratified medium. This allows for the inclusion of arbitrary temperature and wind profiles provided the problem is range independent. It is shown here that it is relatively straightforward to extend this approach to include multiple surface impedance discontinuities, provided each discrete surface is uniform in the axial direction. This is achieved using point collocation to enforce the axial boundary conditions over each discontinuity. Predictions are generated for single and multiple discontinuities, and comparisons are made against predictions obtained using other computational methods.

A Tutorial and Review on Flight Control Co-Simulation Using Matlab/Simulink and Flight Simulators

Flight testing in a realistic three-dimensional virtual environment is increasingly being considered a safe and cost-effective way of evaluating aircraft models and their control systems. The paper starts by reviewing and comparing the most popular personal computer-based flight simulators that have been successfully interfaced to date with the MathWorks software. This co-simulation approach allows combining the strengths of Matlab toolboxes for functions including navigation, control, and sensor modeling with the advanced simulation and scene rendering capabilities of dedicated flight simulation software. This approach can then be used to validate aircraft models, control algorithms, flight handling chatacteristics, or perform model identification from flight data. There is, however, a lack of sufficiently detailed step-by-step flight co-simulation tutorials, and there have also been few attempts to evaluate more than one flight co-simulation approach at a time. We, therefore, demonstrate our own step-by-step co-simulation implementations using Simulink with three different flight simulators: Xplane, FlightGear, and Alphalink’s virtual flight test environment (VFTE). All three co-simulations employ a real-time user datagram protocol (UDP) for data communication, and each approach has advantages depending on the aircraft type. In the case of a Cessna-172 general aviation aircraft, a Simulink co-simulation with Xplane demonstrates successful virtual flight tests with accurate simultaneous tracking of altitude and speed reference changes while maintaining roll stability under arbitrary wind conditions that present challenges in the single propeller Cessna. For a medium endurance Rascal-110 unmanned aerial vehicle (UAV), Simulink is interfaced with FlightGear and with QGroundControl using the MAVlink protocol, which allows to accurately follow the lateral UAV path on a map, and this setup is used to evaluate the validity of Matlab-based six degrees of freedom UAV models. For a smaller ZOHD Nano Talon miniature aerial vehicle (MAV), Simulink is interfaced with the VFTE, which was specifically designed for this MAV, and with QGroundControl for the testing of advanced H-infinity observer-based autopilots using a software-in-the-loop (SIL) simulation to achieve robust low altitude flight under windy conditions. This is then finally extended to hardware-in-the-loop (HIL) implementation on the Nano Talon MAV using a controller area network (CAN) databus and a Pixhawk-4 mini autopilot with simulated sensor models.

Prediction of gust induced cycle counts and fatigue damage of structures

Structural vibrations caused by turbulent wind and their contributions to fatigue are still difficult to predict concisely. With regard to fatigue life prognosis, different methods have been discussed in recent years - but general reliable guidance for the determination of stress cycle counts allowing for damage accumulation concepts (besides individual calculations in the time-domain) is still not available. A parameter study in time and frequency domain has been performed to discover the dependencies of wind conditions and structural properties on the resulting cycle count distributions. The findings allowed to formulate of a first simplification approach (level 1), connecting significant parameters to realistic cycle count distributions for arbitrary wind conditions and dynamic properties of the structure. At this stage, the usage of arbitrary Δσ-N resistance curves is preserved to determine the expected structural damage, but a detailed calculation in time- or frequency domain can be waived on this level.In a second (level 2) simplification, a unique Δσ-N resistance curve with a constant slope and no fatigue endurance limit has been assumed. Due to this restriction, the damage prediction derived is functionally dependent on the ratio of present maximum structural stress Δsmax and the detail category Δσc. Consequently, damage equivalence factors KF are introduced on this level, which allows for a straightforward and safe-side estimation of the expected fatigue damage.Recommendations have been compared to detailed time domain solutions, and examples have been provided to apply both introduced concepts.

Effect of Wind Loads on Low-Rise Pitched and Circular Arch Roof Structures: A Comparative Study based on Numerical Simulation

Through numerical simulations based on Computational Fluid Dynamics (CFD), this study examines the effect of wind load operating on a pitched roof and a circular arch roof of an identical plan area of a storage structure with one wall opening. Many numerical simulations have been performed by other researchers for other types of roofs to understand the behavior of wind flow associated with them. Also, the wind standards of multiple countries have provided the Coefficients of Pressures for standard building shapes. However, there is lack of similar work for structures having one wall opening. Ansys CFX fluid flow software has been used to carry out the simulations using a standard k-ε turbulence model. The simulations have been carried out for 7 wind incidence angles at an interval of 30ᵒ. Pressure, Force, Moment, Drag and Lift Coefficients generated on the roofs were compared. It was found that, although variation in these coefficients w.r.t the wind incidence angles are similar for both the roofs types, the sharp-edged rooftop of the pitched roof contributes to higher magnitudes of these coefficients as compared to the smooth arch roof. Mathematical modules between the face average of pressure coefficients and the wind incidence angles were established in a polynomial form which could be used to find the face average of pressure coefficients and corresponding pressures and forces for arbitrary wind incidence angles.

IPTVisual: Visualisation of the Spatial Energy Flows in Inductive Power Transfer Systems with Arbitrary Winding Shapes

Mid-ranged wireless power transfer by induction or inductive power transfer (IPT), including the strong magnetic resonance method, has been widely adopted, in numerous applications where wires are restricted. The energy flow in space, of course, is invisible to engineers. The windings are often required to be irregular shapes to accommodate the industrial designs of the products, thus, a visualisation method for energy transfer paths could greatly help the design and optimization of such systems. A time-efficient methodology, including the model, analysis and plot of the three-dimensional energy flow for IPT systems, is proposed in this paper. Algorithms of fast describing arbitrarily shaped windings are proposed and the time complexities are evaluated. A software tool, IPTVisual, is developed. It takes the inputs of key coordinates of the windings, the assignments of voltage and/or current sources, any compensation capacitors and auxiliary circuits, and the required observation points to generate the 3D models of the windings and the Poynting vectors, rendered in web browsers for the most extendable compatibility. Several example scenarios have been tested and the results match with the expected operations.