Green's function for infinite thin plate with elliptic hole under bending heat source and interaction between elliptic hole and crack under uniform bending heat flux

Green's function is derived for the bending problem of an infinite thin plate with an elliptic hole under a bending heat source. Then the interaction problem between an elliptic hole and a crack in a thin plate under uniform bending heat flux is analyzed. First, the complex variable method is developed for the thermoelastic problem of bending. Then an exact solution in explicit form is derived for the Green's function by using the complex variable method. Distributions of temperature moment, heat flux moments, bending moments along the hole edge are shown in figures. For solving the interaction problem, a solution for an infinite thin plate with an adiabatic elliptic hole under uniform bending heat flux, and two Green's functions of the plate under a bending heat source couple and a bending dislocation are given. The interaction problem then reduces into singular integral equations using the Green's functions and the principle of superposition. After the equations are solved numerically, the moment intensity factors at crack tips are presented in the figures.     

Variational multiscale methods for premixed combustion based on a progress-variable approach

In this study, novel computational techniques for the numerical simulation of premixed combustion based on a progress-variable formulation are proposed. Two new variational multiscale methods within a finite element framework are developed for the system of mass, momentum and progress-variable equations: a purely residual-based variational multiscale method and an algebraic variational multiscale-multigrid method. The proposed methods are tested for the numerical example case of a flame–vortex interaction using Arrhenius chemical kinetics. This actually laminar reactive flow problem may serve as a model problem for interactions of turbulent flows and (premixed) flames. The results obtained from this test case show that both methods are capable of accurately predicting the features expected during the progression of the flame–vortex interaction. The evolution of both a pocket of unburned gas and a secluded, drop-like structure, which detaches itself and moves upwards, are accurately predicted already for a relatively coarse discretization.     

Viscous and Aeroelastic Effects on Wind Turbine Blades. The VISCEL Project. Part II: Aeroelastic Stability Investigations

The recent introduction of ever larger wind turbines poses new challenges with regard to understanding the mechanisms of unsteady flow–structure interaction. An important aspect of the problem is the aeroelastic stability of the wind turbine blades, especially in the case of combined flap/lead–lag vibrations in the stall regime. Given the limited experimental information available in this field, the use of CFD techniques and state‐of‐the‐art viscous flow solvers provides an invaluable alternative towards the identification of the underlying physics and the development and validation of sound engineering‐type aeroelastic models. Navier–Stokes‐based aeroelastic stability analysis of individual blade sections subjected to combined pitch/flap or flap/lead–lag motion has been attempted by the present consortium in the framework of the concluded VISCEL JOR3‐CT98‐0208 Joule III project. Copyright © 2003 John Wiley & Sons, Ltd.     

Isogeometric based framework for aeroelastic wind turbine blade analysis

A framework based on isogeometric analysis is presented for parametrizing a wind turbine rotor blade and evaluating its response. The framework consists of a multi‐fidelity approach for wind turbine rotor analysis. The aeroelastic loads are determined using a low‐fidelity model. The model is based on isogeometric approach to model both the structural and aerodynamic properties. The structural deformations are solved using an isogeometric formulation of geometrically exact 3D beam theory. The aerodynamic loads are calculated using a standard Blade Element Momentum(BEM) theory. Moreover, the aerodynamic loads calculated using BEM theory are modified to account for the change in the blade shape due to blade deformation. The aeroelastic loads are applied in finite element solver Nastran, and both the stress response and buckling response are extracted. Furthermore, the capabilities of Nastran are extended such that design dependent loads can be applied, resulting in correct aeroelastic sensitivities of Nastran responses, making this framework suitable for optimization. The framework is verified against results from the commercial codes FAST and GH Bladed, using the NREL 61.5m rotor blade as a baseline for comparison, showing good agreement. Copyright © 2016 John Wiley & Sons, Ltd.     

Effect of steady deflections on the aeroelastic stability of a turbine blade

This paper deals with effects of geometric non‐linearities on the aeroelastic stability of a steady‐state deflected blade. Today, wind turbine blades are long and slender structures that can have a considerable steady‐state deflection which affects the dynamic behaviour of the blade. The flapwise blade deflection causes the edgewise blade motion to couple to torsional blade motion and thereby to the aerodynamics through the angle of attack. The analysis shows that in the worst case for this particular blade, the edgewise damping can be decreased by half. Copyright © 2010 John Wiley & Sons, Ltd.     

Aeroelastic analysis of a wind turbine blade using the harmonic balance method

An aeroelastic model for wind turbine blades derived from the unsteady Navier‐Stokes equations and a mode shape–based structural dynamics model are presented. For turbulent flows, the system is closed with the Spalart‐Allmaras turbulence model. The computation times for the aerodynamic solution are significantly reduced using the harmonic balance method compared to a time‐accurate solution. This model is significantly more robust than standard aeroelastic codes that rely on blade element momentum theory to determine the aerodynamic forces. Comparisons with published results for the Caradonna‐Tung rotor in hover and the classical AGARD 445.6 flutter case are provided to validate the aerodynamic model and aeroelastic model, respectively. For wind turbines, flutter of the 1.5 MW WindPACT blade is considered. The results predict that the first flapwise and edgewise modes dominate flutter at the rotor speeds considered.     

Effects of extreme wind shear on aeroelastic modal damping of wind turbines

Wind shear is an important contributor to fatigue loads on wind turbines. Because it causes an azimuthal variation in angle of attack, it can also affect aerodynamic damping. In this paper, a linearized model of a wind turbine, based on the non‐linear aeroelastic code BHawC, is used to investigate the effect of wind shear on the modal damping of the turbine. In isotropic conditions with a uniform wind field, the modal properties can be extracted from the system matrix transformed into the inertial frame using the Coleman transformation. In shear conditions, an implicit Floquet analysis, which reduces the computational burden associated with classical Floquet analysis, is used for modal analysis. The methods are applied to a 2.3 MW three‐bladed pitch‐regulated wind turbine showing a difference in damping between isotropic and extreme shear conditions at rated wind speed when the turbine is operating closest to stall. The first longitudinal tower mode decreases slightly in damping, whereas the first flapwise backward whirling and symmetric modes increase in damping. This change in damping is attributed to an interaction between the periodic blade mode shapes and the azimuth‐dependent local aerodynamic damping in the shear condition caused by a beginning separation of the flow. Copyright © 2012 John Wiley & Sons, Ltd.     

Comparing different dynamic stall models

The dynamic stall phenomenon and its importance for load calculations and aeroelastic simulations is well known. Different models exist to model the effect of dynamic stall; however, a systematic comparison is still lacking. To investigate if one is performing better than another, three models are used to simulate the Ohio State University measurements and a set of data from the National Aeronautics and Space Administration Ames experimental study of dynamic stall and compare results. These measurements were at conditions and for aerofoils that are typical for wind turbines, and the results are publicly available. The three selected dynamic stall models are the ONERA model, the Beddoes–Leishman model and the Snel model. The simulations show that there are still significant differences between measurements and models and that none of the models is significantly better in all cases than the other models. Especially in the deep stall regime, the accuracy of each of the dynamic stall models is limited. Copyright © 2012 John Wiley & Sons, Ltd.     

水电站水库群与地下水资源系统联合运行多目标管理模型

本文对水电站水库群与地下水资源系统联合运行多目标管理问题进行研究,建立起联合运行多目标管理模型,并提出一种求解大规模多目标决策问题的模糊带权目标协调法。实例计算与分析论证表明,所建立的模型和提出的方法具有实用性和通用性。     

TWO CRACK GROWTHS IN A FUNCTIONALLY GRADED PLATE UNDER THERMAL SHOCK

This article examines the problem of two thermal cracks under a transient temperature field in a ceramic/metal functionally graded plate. When the functionally graded plate is subjected to thermal shock, multiple cracks often occur on the ceramic surface. It is shown that the crack paths are influenced by interaction between multiple cracks and a compositional profile of the functionally graded plate. Transient thermal stresses are treated as a linear quasi-static thermoelastic problem for a plane strain state. The crack paths of two cracks are obtained using the finite element method with mode I and mode II stress intensity factors.     

Fatigue design load calculations of the offshore NREL 5 MW benchmark turbine using quadrature rule techniques

A novel approach is proposed to reduce, compared with the conventional binning approach, the large number of aeroelastic code evaluations that are necessary to obtain equivalent loads acting on wind turbines. These loads describe the effect of long‐term environmental variability on the fatigue loads of a horizontal‐axis wind turbine. In particular, Design Load Case 1.2, as standardized by IEC, is considered. The approach is based on numerical integration techniques and, more specifically, quadrature rules. The quadrature rule used in this work is a recently proposed “implicit” quadrature rule, which has the main advantage that it can be constructed directly using measurements of the environment. It is demonstrated that the proposed approach yields accurate estimations of the equivalent loads using a significantly reduced number of aeroelastic model evaluations (compared with binning). Moreover, the error introduced by the seeds (introduced by averaging over random wind fields and sea states) is incorporated in the quadrature framework, yielding an even further reduction in the number of aeroelastic code evaluations. The reduction in computational time is demonstrated by assessing the fatigue loads on the NREL 5 MW reference offshore wind turbine in conjunction with measurement data obtained at the North Sea, for both a simplified and a full load case.     

Time domain prediction of power absorption from ocean waves with latching control

A three-dimensional panel method using Neumann–Kelvin method is presented for the transient wave-body interaction problems in order to absorb maximum power from the sea. The exact initial boundary value problem is linearized about a uniform flow, and recast as an integral equation using the transient free-surface Green function. The hydrodynamics part of the solution including radiation and diffraction problem is solved as impulsive velocity problem. A discrete control of latching is used to increase the bandwidth of the efficiency of the wave energy converters (WEC). When latching control is applied to WEC in the case of off-resonance condition it increases the amplitude of the motion as well as absorbed power. It is assumed that the exciting force is known in the close future and that body is hold in position during the latching time. A heaving hemisphere as a point-absorber WEC is used for the numerical prediction of the different parameters. The calculated hydrodynamics coefficients, response amplitude operator, absorbed power, relative capture width of this device compared with analytical and other published results.     

A stochastic model for the simulation of wind turbine blades in static stall

The aim of this work is to improve aeroelastic simulation codes by accounting for the unsteady aerodynamic forces that a blade experiences in static stall. A model based on a spectral representation of the aerodynamic lift force is defined. The drag and pitching moment are derived using a conditional simulation technique for stochastic processes. The input data for the model can be collected either from measurements or from numerical results from a Computational Fluid Dynamics code for airfoil sections at constant angles of attack. An analysis of such data is provided, which helps to determine the characteristics of stall. The model is applied to wind turbine rotor cases, including the stand still condition, and results are compared to experimental data. Copyright © 2009 John Wiley & Sons, Ltd.     

Thermal Fracture Analysis Of Nonhomogeneous Plate with Interfaces Under Uniform Heat Flow

The mixed-mode thermomechanical fracture problem in a nonhomogeneous material plate with two interfaces is studied in this research. Uniform heat flow conditions are considered. The interaction energy integral method for the thermal fracture problem is developed to calculate the thermal stress intensity factors (TSIFs) in nonhomogeneous materials. This method is proved to be domain independent for nonhomogeneous materials even when the integral domain is cut by one interface or many interfaces. Combining the interaction energy integral method with the extended Finite Element Method (XFEM), the temperature fields, the displacement fields, the thermal stress fields, and the TSIFs are calculated. In this article, both the edge crack and the internal crack are considered. Some examples are presented to study the influence of the material properties on the TSIFs. It can be found that the mismatch of the elastic modulus and thermal expansion coefficient can affect the TSIFs dramatically; however, the thermal conductivity interface will not arouse a kinking behavior of the TSIFs. It can be concluded that the existence of an interface (especially for elastic modulus and thermal expansion coefficient) affects the TSIFs greatly.     

Aeroelastic validation and Bayesian updating of a downwind wind turbine

Downwind wind turbine blades are subjected to tower wake forcing at every rotation, which can lead to structural fatigue. Accurate characterisation of the unsteady aeroelastic forces in the blade design phase requires detailed representation of the aerodynamics, leading to computationally expensive simulation codes, which lead to intractable uncertainty analysis and Bayesian updating. In this paper, a framework is developed to tackle this problem. Full, detailed aeroelastic model of an experimental wind turbine system based on 3‐D Reynolds‐averaged Navier‐Stokes is developed, considering all structural components including nacelle and tower. This model is validated against experimental measurements of rotating blades, and a detailed aeroelastic characterisation is presented. Aerodynamic forces from prescribed forced‐motion simulations are used to train a time‐domain autoregressive with exogenous input (ARX) model with a localised forcing term, which provides accurate and cheap aeroelastic forces. Employing ARX, prior uncertainties in the structural and rotational parameters of the wind turbine are introduced and propagated to obtain probabilistic estimates of the aeroelastic characteristics. Finally, the experimental validation data are used in a Bayesian framework to update the structural and rotational parameters of the system and thereby reduce uncertainty in the aeroelastic characteristics.     

Assessment of a comprehensive aeroelastic tool for horizontal‐axis wind turbine rotor analysis

This paper presents the development of a computational aeroelastic tool for the analysis of performance, response and stability of horizontal‐axis wind turbines. A nonlinear beam model for blades structural dynamics is coupled with a state‐space model for unsteady sectional aerodynamic loads, including dynamic stall effects. Several computational fluid dynamics structural dynamics coupling approaches are investigated to take into account rotor wake inflow influence on downwash, all based on a Boundary Element Method for the solution of incompressible, potential, attached flows. Sectional steady aerodynamic coefficients are extended to high angles of attack in order to characterize wind turbine operations in deep stall regimes. The Galerkin method is applied to the resulting aeroelastic differential system. In this context, a novel approach for the spatial integration of additional aerodynamic states, related to wake vorticity and dynamic stall, is introduced and assessed. Steady‐periodic blade responses are evaluated by a harmonic balance approach, whilst a standard eigenproblem is solved for aeroelastic stability analyses. Drawbacks and potentialities of the proposed model are investigated through numerical and experimental comparisons, with particular attention to rotor blades unsteady aerodynamic modelling issues. Copyright © 2016 John Wiley & Sons, Ltd.     

Development of an aeroelastic code based on three‐dimensional viscous–inviscid method for wind turbine computations

Aerodynamic and structural dynamic performance analysis of modern wind turbines are routinely estimated in the wind energy field using computational tools known as aeroelastic codes. Most aeroelastic codes use the blade element momentum (BEM) technique to model the rotor aerodynamics and a modal, multi‐body or the finite‐element approach to model the turbine structural dynamics. The present work describes the development of a novel aeroelastic code that combines a three‐dimensional viscous–inviscid interactive method, method for interactive rotor aerodynamic simulations (MIRAS), with the structural dynamics model used in the aeroelastic code FLEX5. The new code, called MIRAS‐FLEX, is an improvement on standard aeroelastic codes because it uses a more advanced aerodynamic model than BEM. With the new aeroelastic code, more physical aerodynamic predictions than BEM can be obtained as BEM uses empirical relations, such as tip loss corrections, to determine the flow around a rotor. Although more costly than BEM, a small cluster is sufficient to run MIRAS‐FLEX in a fast and easy way. MIRAS‐FLEX is compared against the widely used FLEX5 and FAST, as well as the participant codes from the Offshore Code Comparison Collaboration Project. Simulation tests consist of steady wind inflow conditions with different combinations of yaw error, wind shear, tower shadow and turbine‐elastic modeling. Turbulent inflow created by using a Mann box is also considered. MIRAS‐FLEX results, such as blade tip deflections and root‐bending moments, are generally in good agreement with the other codes. Copyright © 2017 John Wiley & Sons, Ltd.     

Investigation Methods for Thermal Shock Crack Problems of Functionally Graded Materials–Part II: Combined Analytical-Numerical Method

Fractures phenomena can be often found in functionally graded materials (FGMs) subjected to thermal shock loadings. This paper aims to develop a set of analytical-numerical methods for analyzing the mixed-mode thermal shock crack problems of a functionally graded plate (FGP). First, a domain-independent interaction energy integral method is developed for obtaining the mixed-mode transient thermal stress intensity factors (TSIFs). A perturbation method is adopted to obtain the transient temperature field. Then an analytical-numerical method combining the interaction energy integral method, a perturbation method, and the finite element method is developed to solve the present crack problem. Particularly, the influences of the materials parameters, crack length, and crack angle on the TSIFs and the crack growth angle are investigated. The results show that the present analytical-numerical method can be used to solve the thermal shock crack problem with high efficiency. The present work will be significant for the fracture mechanics analysis and design of FGM structures.