Aeroelastic analysis of large horizontal wind turbine baldes?

A nonlinear aeroelastic analysis method for large horizontal wind turbines is described. A vortex wake method and a nonlinear ?nite element method (FEM) are coupled in the approach. The vortex wake method is used to predict wind turbine aero-dynamic loads of a wind turbine, and a three-dimensional (3D) shell model is built for the rotor. Average aerodynamic forces along the azimuth are applied to the structural model, and the nonlinear static aeroelastic behaviors are computed. The wind rotor modes are obtained at the static aeroelastic status by linearizing the coupled equations. The static aeroelastic performance and dynamic aeroelastic responses are calculated for the NH1500 wind turbine. The results show that structural geometrical nonlinearities signi?cantly reduce displacements and vibration amplitudes of the wind turbine blades. Therefore, structural geometrical nonlinearities cannot be neglected both in the static aeroelastic analysis and dynamic aeroelastic analysis.     

Progresses in application of computational ?uid dynamic methods to large scale wind turbine aerodynamics?

The computational ?uid dynamics (CFD) methods are applied to aerody-namic problems for large scale wind turbines. The progresses including the aerodynamic analyses of wind turbine pro?les, numerical ?ow simulation of wind turbine blades, evalu-ation of aerodynamic performance, and multi-objective blade optimization are discussed. Based on the CFD methods, signi?cant improvements are obtained to predict two/three-dimensional aerodynamic characteristics of wind turbine airfoils and blades, and the vorti-cal structure in their wake ?ows is accurately captured. Combining with a multi-objective genetic algorithm, a 1.5 MW NH-1500 optimized blade is designed with high e?ciency in wind energy conversion.     

Design and veri?cation of airfoil families for large-size wind turbine blades?

For the design of wind turbine blades, the use of a family of specially tailored airfoils is particularly important. The dedicated airfoils can dramatically improve the capability of capturing wind power, reduce the structural weight to save the cost of manufacturing and transportation, and lower the inertial loads as well as the loads due to gust. An overview of the world-wide wind turbine airfoil families developed since 1990’s is presented, such as the S series, the DU series, the Ris? series, and the FFA series. The design and wind-tunnel tests of the Northwestern Polytechnical University (NPU) airfoil family for megawatt-size wind turbines, called the NPU-WA series, are summarized. All tests for the NPU-WA series are carried out in the NF-3 low-speed wind-tunnel with a two-dimensional (2D) test section of 1.6 m?0.8 m and at the Reynolds number ranging from 1.6?106 to 5?106 . The research activities for further improving the NPU-WA airfoils towards lower roughness sensitivity are also reviewed. The development of the new NPU-WA series dedicated for multi-megawatt wind turbines is discussed.     

Investigation of horizontal-axis wind turbine (HAWT) blade three-dimensional rotational e?ect based on ?eld experiments?

Field experiments are performed on a two-bladed 33 kW horizontal-axis wind turbine (HAWT). The pressures are measured with 191 pressure sensors positioned around the surfaces of seven spanwise section airfoils on one of the two blades. Three-dimensional (3D) and two-dimensional (2D) numerical simulations are performed, respectively, on the rotor and the seven airfoils of the blade. The results are compared with the experimental results of the pressure distribution on the seven airfoils and the lift coe?cients. The 3D rotational e?ect on the blade aerodynamic characteristics is then studied with a numerical approach. Finally, some conclusions are drawn as follows. From the tip to the root of the blade, the experimental di?erential pressure of the blade section airfoil increases at ?rst and then decreases gradually. The calculated 3D result of the pressure distribution on the blade surface is closer to that of the experiment than the 2D result. The 3D rotational e?ect has a signi?cant impact on the blade surface ?ow and the aerodynamic load, leading to an increase of the di?erential pressure on the airfoils and their lift coe?cient than that with the 2D one because of the stall delay. The in?uence of the 3D rotational e?ect on the wind turbine blade especially takes place on the sections with ?ow separation.     

O?shore ?oating wind turbine and its dynamic problems?

Green energy sources and ocean wind power are plentiful in deep sea. More and more o?shore wind power plants are constructed in the deep water over hundred meters below the surface. While o?shore ?oating wind turbine system is working, wind turbine, ?oating foundation, and mooring system a?ect each other with wind, waves, and currents acting on them. Various o?shore ?oating wind turbine systems and the encoun-tered environmental loads are brie?y reviewed and discussed. It is di?cult and crucial to comprehensively analyze the aerodynamic-hydrodynamic-service system-structure un-der the coupling e?ect of o?shore ?oating wind turbine system. The environmental ?ow ?eld, structure scale, and rational applications of theories and approaches should be well considered in advance.     

Research status and trend of wind turbine aerodynamic noise?

The main components of the wind turbine aerodynamic noise are introduced. A detailed review is given on the theoretical prediction, experimental measurement, and numerical simulation methods of wind turbine noise, with speci?c attention to appli-cations. Furthermore, suppression techniques of wind turbine aerodynamic noise are discussed. The perspective of future research on the wind turbine aerodynamic noise is presented.     

Progress in wind tunnel experimental techniques for wind turbine?

Based on the unsteady aerodynamics experiment (UAE) phase VI and the model experiment in controlled conditions (MEXICO) projects and the related research carried out in China Aerodynamic Research and Development Center (CARDC), the recent progress in the wind tunnel experimental techniques for the wind turbine is sum-marized. Measurement techniques commonly used for di?erent types of wind tunnel ex-periments for wind turbine are reviewed. Important research achievements are discussed, such as the wind tunnel disturbance, the equivalence of the airfoil in?ow condition, the three-dimensional (3D) e?ect, the dynamic in?ow in?uence, the ?ow ?eld structure, and the vortex induction. The corresponding research at CARDC and some ideas on the large wind turbine are also introduced.     

Status of large scale wind turbine technology development abroad?

To facilitate the large scale (multi-megawatt) wind turbine development in China, the foreign e?orts and achievements in the area are reviewed and summarized. Not only the popular horizontal axis wind turbines on-land but also the o?shore wind turbines, vertical axis wind turbines, airborne wind turbines, and shroud wind turbines are discussed. The purpose of this review is to provide a comprehensive comment and assessment about the basic work principle, economic aspects, and environmental impacts of turbines.     

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.     

网络最短的最优解集结构

The shortest path problem in a network G is to find shortest paths between some specified source vertices and terminal vertices when the lengths of edges are given. The structure of the optimal solutions set on the shortest paths is studied in this paper. First,the conditions of having unique shortest path between two distinguished vertices s and t in a network G are discussed;Second,the structural properties of 2-transformation graph (?) on the shortest-paths for G are presented heavily.     

On the Winding of Stationary Diffusions

In this paper, the winding of stationary diffusions are studied. It is shown that, differently from Brownian motions,stationary diffusions wind up to time t angles in order of t, while Brownian motions wind up angles in order of logt,and the winding rates tend to , where c, an-i c2 are constants and is a Cauchy random variable.Moreover, it is proved that a stationary diffusion is reversible iff c2=0 for the winding around every point.     

On cubic Hermite coalescence hidden variable fractal interpolation functions

Hermite interpolation is a very important tool in approximation theory and numerical analysis, and provides a popular method for modeling in the area of computer aided geometric design. However, the classical Hermite interpolant is unique for a prescribed data set,and hence lacks freedom for the choice of an interpolating curve, which is a crucial requirement in design environment. Even though there is a rather well developed fractal theory for Hermite interpolation that offers a large flexibility in the choice of interpolants, it also has the shortcoming that the functions that can be well approximated are highly restricted to the class of self-affine functions. The primary objective of this paper is to suggest a C1-cubic Hermite interpolation scheme using a fractal methodology, namely, the coalescence hidden variable fractal interpolation, which works equally well for the approximation of a self-affine and non-self-affine data generating functions. The uniform error bound for the proposed fractal interpolant is established to demonstrate that the convergence properties are similar to that of the classical Hermite interpolant. For the Hermite interpolation problem, if the derivative values are not actually prescribed at the knots, then we assign these values so that the interpolant gains global C2-continuity. Consequently, the procedure culminates with the construction of cubic spline coalescence hidden variable fractal interpolants. Thus, the present article also provides an alternative to the construction of cubic spline coalescence hidden variable fractal interpolation functions through moments proposed by Chand and Kapoor [Fractals, 15(1)(2007), pp. 41-53].     

The Mindlin-Medick Plate Theory and Its Application Under Flexoelectricity and Temperature Effects北大核心CSCD

Based on the Hamiltonian variational principle, the 2D field equations and boundary conditions for flexoelectricity were derived, and the corresponding governing equations were obtained through substitution of the constitutive relation and geometric equations into the field equation. The in⁃plane tensile deformation, thick⁃ ness⁃stretch deformation, symmetric thickness⁃shear deformation, and their coupled flexoelectric polarization of flexoelectric nanoplates caused by inhomogeneous temperature changes, were studied. The displacement fields and electric potential fields were solved with the double Fourier series method. The results demonstrate that, all fields are sensitive to the temperature load, which raises the prospect of controlling the mechanical and electrical behaviors of flexoelectric nanoplates by means of the temperature field. The effects of the thermal field and mechanical field on the displacement field were compared and examined. The work extends the Mind⁃ lin⁃Medick plate structure analysis theory in view of the flexoelectric and temperature effects, and provides a reference for the structural design of micro⁃ and nano⁃scale devices. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

A new class of three-variable orthogonal polynomials and their recurrences relations

A new class of three-variable orthogonai polynomials,defined as eigenfunctions of a second order PDE operator,is studied.These polynomials are orthogonal over a curved tetrahedron region, which can be seen as a mapping from a traditional tetrahedron,and can be taken as an extension of the 2-D Steiner domain.The polynomials can be viewed as Jacobi polynomials on such a domain.Three- term relations are derived explicitly.The number of the individual terms,involved in the recurrences relations,are shown to be independent on the total degree of the polynomials.The numbers now are determined to be five and seven,with respect to two conjugate variables z,(?) and a real variable r, respectively.Three examples are discussed in details,which can be regarded as the analogues of the Chebyshev polynomials of the first and the second kinds,and Legendre polynomials.     

APPLICATION OF MINIMUM PROJECTION UNIFORMITY CRITERION IN COMPLEMENTARY DESIGNS

In this article, we consider the characterization problem in design theory. The objective is to characterize minimum projection uniformity for two-level designs in terms of their complementary designs. Here, the complementary design means a design in which all the Hamming distances of any two runs are the same, which generalizes the concept of a pair of complementary designs in the literature. Based on relationships of the uniformity pattern between a pair of complementary designs, we propose a minimum projection uniformity （MPU） rule to assess and compare two-level factorials.     

Double penalized variable selection procedure for partially linear models with longitudinal data

Based on the double penalized estimation method,a new variable selection procedure is proposed for partially linear models with longitudinal data.The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components.Under some regularity conditions,the rate of convergence and asymptotic normality of the resulting estimators are established.In addition,to improve efficiency for regression coefficients,the estimation of the working covariance matrix is involved in the proposed iterative algorithm.Some simulation studies are carried out to demonstrate that the proposed method performs well.     

Vectorial variational principle with variable set-valued perturbation

We give a general vectorial Ekeland's variational principle, where the objective function is defined on an F-type topological space and taking values in a pre-ordered real linear space. Being quite different from the previous versions of vectorial Ekeland's variational principle, the perturbation in our version is no longer only dependent on a fixed positive vector or a fixed family of positive vectors. It contains a family of set-valued functions taking values in the positive cone and a family of subadditive functions of topology generating quasi-metrics. Hence, the direction of the perturbation in the new version is a family of variable subsets which are dependent on the ob jective function values. The general version includes and improves a number of known versions of vectorial Ekeland's variational principle. From the general Ekeland's principle, we deduce the corresponding versions of Caristi–Kirk's fixed point theorem and Takahashi's nonconvex minimization theorem. Finally, we prove that all the three theorems are equivalent to each other.     

Recent progresses in studies on wave-current loads on foundation structure with piles and slab?

The foundation structure with piles and slab is widely used in o?shore wind farm construction in shallow water. Experimental studies on the hydrodynamic loads acting on the piles and slab under irregular waves and currents are summarized with discussion on the e?ects of pile grouping on the wave forces and wave impact loads on the slab locating near the free surface. By applying the theoretical solution of the wave di?racted by the slab and using the Morison equation to evaluate the wave force on the piles, the e?ects of the slab on the wave forces acting on the piles are analyzed. Based on the Reynolds-averaged Navier-Stokes (RANS) equations and the volume of ?uid (VOF) method, a numerical wave basin is developed to simulate the wave-structure interaction. The computed maximum wave force on the foundation structure with piles and slab agrees well with the measured data. The violent deformation, breaking, and run-up of the wave around the structure are presented and discussed. Further work on the turbulent ?ow structures and large deformation of the free surface due to interaction of the waves and foundation structures of o?shore wind farms needs more e?cient approaches for evaluating hydrodynamic loads under the e?ects of nonlinear waves and currents.     

Distribution estimation with smoothed auxiliary information

Distribution estimation is very important in order to make statistical inference for parameters or its functions based on this distribution.In this work we propose an estimator of the distribution of some variable with non-smooth auxiliary information,for example,a symmetric distribution of this variable.A smoothing technique is employed to handle the non-differentiable function.Hence,a distribution can be estimated based on smoothed auxiliary information.Asymptotic properties of the distribution estimator are derived and analyzed.The distribution estimators based on our method are found to be significantly efficient than the corresponding estimators without these auxiliary information.Some simulation studies are conducted to illustrate the finite sample performance of the proposed estimators.     

A variational formulation for physical noised image segmentation

Image segmentation is a hot topic in image science. In this paper we present a new variational segmentation model based on the theory of Mumford-Shah model. The aim of our model is to divide noised image, according to a certain criterion, into homogeneous and smooth regions that should correspond to structural units in the scene or objects of interest. The proposed region-based model uses total variation as a regularization term, and different fidelity term can be used for image segmentation in the cases of physical noise, such as Gaussian, Poisson and multiplicative speckle noise. Our model consists of five weighted terms, two of them are responsible for image denoising based on fidelity term and total variation term, the others assure that the three conditions of adherence to the data, smoothing, and discontinuity detection are met at once. We also develop a primal-dual hybrid gradient algorithm for our model. Numerical results on various synthetic and real images are provided to compare our method with others,these results show that our proposed model and algorithms are effective.