Wake steering by active yawing of upstream wind turbines is a promising wind plant control technique. To enable the development of model-based wind plant control methods, there is a need for models ...that can marry the contrasting requirements of good fidelity and low computational cost. This paper presents a reduced-order model (ROM) obtained by directly compressing high-fidelity computational fluid dynamics (CFD) simulation data using the proper orthogonal decomposition (POD) method. At first, simulations of wake-interacting wind turbines are obtained for time-varying yaw settings using the lifting-line large-eddy simulation (LES) code SOWFA. Next, a ROM is synthesized from the CFD transient simulations, obtaining a discrete-time state-space model that captures the dominant dynamics of the underlying high-fidelity model with only a reduced number of states. The ROM is optionally augmented with a Kalman filter, which feeds back turbine power measurements from the plant to the model, enhancing its accuracy. Results obtained in realistic turbulent conditions show a good agreement between high-fidelity CFD solutions and the proposed POD-based ROM in terms of wake behavior and power output of waked turbines. Additionally, the ROM presents acceptable results when compared to wind tunnel experiments, including the capability of the model to partially correct for an intentionally built-in model mismatch.
Noise is an important design driver for onshore wind turbines. Therefore, there is a need to include validated noise prediction models within wind turbine and wind plant design procedures. However, ...the literature presents a multitude of different models and formulations, combined with a severe lack of publicly available experimental data. The present work presents a comparison between semi-empirical frequency-domain methods coupled to blade element momentum (BEM) aerodynamics, which is the typical approach used for the transient aeroelastic analysis of wind turbines. Among the various noise sources, only turbulent boundary layer - trailing edge and turbulent inflow noise models have been considered in the present analysis. The noise models are benchmarked in terms of emission spectra, highlighting differences and discrepancies. A time-domain Ffowcs Williams-Hawkings formulation is also coupled to the same BEM model, investigating its ability in predicting low frequency emissions. Thanks to this study, a few inconsistencies among published noise models are identified and reported.
This study integrates aeroacoustic noise emission models within a wind turbine design procedure to include overall sound pressure levels as design constraints. The proposed approach aims at the ...minimization of the cost of energy from wind, while ensuring the compliance with noise emission limits. The reference 3.35 MW onshore wind turbine developed within the international cooperation IEA Wind Task 37 is redesigned to reduce its noise emissions above and below rated wind speed, considering both single- and multi-objective design criteria. Results obtained with the proposed noise-constrained redesign methodology are compared with the simpler approach of reducing the tip speed without altering the blade shape. Results show that, while the simplistic approach causes a drop of −2.8% in annual energy production and a +2.5% increase in cost of energy, an optimized configuration fulfills the noise requirement without incurring into significant energy penalties.
This paper describes a multibody dynamics approach to the modeling of rotorcraft systems and reviews the key aspects of the simulation procedure. The multibody dynamics analysis is cast within the ...framework of nonlinear finite element methods, and the element library includes rigid and deformable bodies as well as joint elements. No modal reduction is performed for the modeling of flexible bodies. The structural and joint element library is briefly described. The algorithms used to integrate the resulting equations of motion with maximum efficiency and robustness are discussed. Various solution procedures, static, dynamic, stability, and trim analyses, are presented. Postprocessing and visualization issues are also addressed. Finally, the paper concludes with selected rotorcraft applications.
A framework for the development of robust time integration schemes for nonlinear, flexible multibody systems is presented. The proposed schemes are designed to meet four specific requirements: ...nonlinear unconditional stability of the scheme, a rigorous treatment of both geometric and material nonlinearities, exact satisfaction of the constraints, and the presence of high frequency numerical dissipation. Specific algorithms are presented for rigid bodies, cables, beams, shells, and elasto-dynamics. The kinematic nonlinearities are treated in a rigorous manner for all elements, and the material nonlinearities can be handled when the constitutive laws stem from the existence of a strain energy density function. The treatment of the constraint equations associated with the six lower pair joints are presented as well. The efficiency and robustness of the proposed approach is demonstrated with specific numerical examples.
Supercavitating vehicles are characterized by substantially reduced hydrodynamic drag, in comparison with fully wetted underwater vehicles. Drag is localized at the nose of the vehicle, where a ...cavitator generates a cavity that completely envelopes the body, at the fins, and on the vehicle after-body. This unique loading configuration, the complex and non-linear nature of the interaction forces between vehicle and cavity, the unsteady behavior of the cavity itself and memory effects associated with its formation process make the control and maneuvering of supercavitating vehicles particularly challenging. This study presents an initial effort towards the evaluation of optimal trajectories for this class of underwater vehicles. Flight trajectories and maneuvering strategies for supercavitating vehicles are obtained through the solution of an optimal control problem. Given a cost function, and general constraints and bounds on states and controls, the solution of the optimal control problem yields control time histories that maneuver the vehicle according to the desired strategy, together with the associated flight path. The optimal control problem is solved using the direct transcription method, which does not require the derivation of the equations of optimal control and leads to the solution of a discrete parameter optimization problem. Examples of maneuvers and resulting trajectories are given to demonstrate the effectiveness of the proposed methodology and the generality of the formulation.
Energy preserving schemes achieve unconditional stability for nonlinear systems by establishing discrete energy preservation statements. Several schemes have been presented by various authors within ...drastically different frameworks: finite difference schemes based on a mid-point approximation, Galerkin and time discontinuous Galerkin approximations of the equations of motion written in the symmetric hyperbolic form, finite elements in time, and 2-stage FSAL Runge—Kutta methods. Furthermore, different types of parameterization of finite rotations were used in the various formulations. This paper presents a unified, finite difference framework which readily allows comparing the various schemes and their respective properties. Numerical examples are presented and show that the predictions of two of these schemes are in very close agreement with each other.
Integrating finite rotations Bottasso, Carlo L.; Borri, Marco
Computer methods in applied mechanics and engineering,
10/1998, Letnik:
164, Številka:
3
Journal Article
Recenzirano
We study the integration of problems of evolution in the rotation group. Instead of attacking the problem in the nonlinear differential manifold SO(3) (pure rotational dynamics), as is usually done, ...we derive equations for the complete problem of motion (translational and rotational dynamics) on an extended manifold. We develop a generalization of Runge-Kutta methods that, by design, ensures that the solution will remain on the manifold for any choice of the tableau. This is obtained through configuration updates performed via the exponential map. We show how certain terms can be approximated, while retaining the order of accuracy of the scheme, and how the method conserves the total momentum of the system. Within this framework, we develop two nonlinearly unconditionally stable time integration schemes, that are associated with discrete laws of conservation/dissipation of the total energy. The dissipating algorithm generalizes to the nonlinear case the high frequency damping characteristics provided by some well-known conventional methods. We present numerical results to support our analysis, and we develop a complete application of this methodology to the nonlinear dynamics of three-dimensional rods undergoing large displacements and finite rotations, under the assumption of small strains.
This work presents a novel methodology for the dynamic analysis of general non-linear multibody systems composed of rigid and deformable bodies, the latter under the small strain assumption. In Part ...I we developed the 6-D compact representation and parameterization of motion for constrained bodies. Part II is devoted to the design of a class of modified Runge–Kutta (RK) methods dedicated to non-linear dynamics. These are capable of integrating on the configuration manifold and of preserving linear and angular momenta. Within this class of methods, two second-order algorithms are designed under the requirement of attaining non-linear unconditional stability: the energy preserving (EP) and energy decaying (ED) methods. These schemes are associated with an algorithmic law of conservation and dissipation, respectively, of the total mechanical energy of the system, together with the vanishing of the algorithmic work done by ideal, time-independent constraints. Their performances are assessed with the aid of some representative numerical applications which confirm the non-conventional properties predicted in the analysis.
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