Recent improvements of actuator line-large-eddy simulation method for wind turbine wakes

In a large wind farm,the wakes of upstream and downstream wind turbines can interfere with each other,affecting the overall power output of the wind farm.To further improve the numerical accuracy of the turbine wake dynamics under atmosphere turbulence,this work proposes some improvements to the actuator line-large-eddy simulation(AL-LES)method.Based on the dynamic k-equation large-eddy simulation(LES),this method uses a precursor method to generate atmospheric inflow turbulence,models the tower and nacelle wakes,and improves the body force projection method based on an anisotropic Gaussian distribution function.For these three improvements,three wind tunnel experiments are used to validate the numerical accuracy of this method.The results show that the numerical results calculated in the far-wake region can reflect the characteristics of typical onshore and offshore wind conditions compared with the experimental results.After modeling the tower and nacelle wakes,the wake velocity distribution is consistent with the experimental result.The radial migration velocity of the tip vortex calculated by the improved blade body force distribution model is 0.32 m/s,which is about 6%different from the experimental value and improves the prediction accuracy of the tip vortex radial movement.The method proposed in this paper is very helpful for wind turbine wake dynamic analysis and wind farm power prediction.

STRESS INTENSITY FACTORS CALCULATION IN ANTI-PLANE FRACTURE PROBLEM BY ORTHOGONAL INTEGRAL EXTRACTION METHOD BASED ON FEMOL

For an anti-plane problem, the differential operator is self-adjoint and the corresponding eigenfunctions belong to the Hilbert space. The orthogonal property between eigenfunctions （or between the derivatives of eigenfunctions） of anti-plane problem is exploited. We developed for the first time two sets of radius-independent orthogonal integrals for extraction of stress intensity factors （SIFs）, so any order SIF can be extracted based on a certain known solution of displacement （an analytic result or a numerical result）. Many numerical examples based on the finite element method of lines （FEMOL） show that the present method is very powerful and efficient.

Simulation of electrically driven jet using Chebyshev collocation method

The model of electrically driven jet is governed by a series of quasi 1D dimensionless partial differential equations(PDEs).Following the method of lines,the Chebyshev collocation method is employed to discretize the PDEs and obtain a system of differential-algebraic equations(DAEs).By differentiating constrains in DAEs twice,the system is transformed into a set of ordinary differential equations(ODEs) with invariants.Then the implicit differential equations solver 'ddaskr' is used to solve the ODEs and post-stabilization is executed at the end of each step.Results show the distributions of radius,linear charge density,stretching ratio and also the horizontal velocity at a time point.Meanwhile,the spiral and expanding projections to X-Y plane of the jet centerline suggest the occurring of bending instability.

STUDY ON THREE-DIMENSIONAL FINITE BODIES CONTAINING CRACKS USING THE FINITE ELEMENT METHOD OF LINES

The three-dimensional finite element method of lines is presented, and the basic processing description of 3D FEMOL in cracking questions is given in detail. Applications to 3D bodies with cracks indicate that good accuracy can be obtained with relatively coarse girds. In particular, application to the tension specimen shows very good agreement with the evaluation of stress intensity factors, which is better than the results of other methods. This implies a considerable potential for using this method in the 3D analysis of finite geometry solids and suggests a possible extension of this technique to nonlinear material behavior.

Cracking analysis of fracture mechanics by the finite element method of lines(FEMOL)

The Finite Element Method of Lines （FEMOL） is a semi-analytic approach and takes a position between FEM and analytic methods. First, FEMOL in Fracture Mechanics is presented in detail. Then, the method is applied to a set of examples such as edge-crack plate, the central-crack plate, the plate with cracks emanating from a hole under tensile or under combination loads of tensile and bending. Their dimensionless stress distribution, the stress intensify factor （SIF） and crack opening displacement （COD） are obtained, and comparison with known solutions by other methods are reported. It is found that a good accuracy is achieved by FEMOL. The method is successfully modified to remarkably increase the accuracy and reduce convergence difficulties. So it is a very useful and new tool in studying fracture mechanics problems.

A numerical approach based on the meshless collocation method in elastodynamics

In this paper, a collocation technique with the modified equilibrium on line method （ELM） for imposition of Neumann （natural） boundary conditions is presented for solving the two-dimensional problems of linear elastic body vibrations. In the modified ELM, equilibrium over the lines on the natural boundary is satisfied as Neumann boundary condition equations. In other words, the natural boundary conditions are satisfied naturally by using the weak formulation. The performance of the modified version of the ELM is studied for collocation methods based on two different ways to construct meshless shape functions： moving least squares approximation and radial basis point interpolation. Numerical examples of two-dimensional free and forced vibration analyses show that by using the modified ELM, more stable and accurate results would be obtained in comparison with the direct collocation method.

GPU Accelerated Marine Data Visualization Method

The study of marine data visualization is of great value. Marine data, due to its large scale, random variation and multiresolution in nature, are hard to be visualized and analyzed. Nowadays, constructing an ocean model and visualizing model results have become some of the most important research topics of ‘Digital Ocean'. In this paper, a spherical ray casting method is developed to improve the traditional ray-casting algorithm and to make efficient use of GPUs. Aiming at the ocean current data, a 3D view-dependent line integral convolution method is used, in which the spatial frequency is adapted according to the distance from a camera. The study is based on a 3D virtual reality and visualization engine, namely the VV-Ocean. Some interactive operations are also provided to highlight the interesting structures and the characteristics of volumetric data. Finally, the marine data gathered in the East China Sea are displayed and analyzed. The results show that the method meets the requirements of real-time and interactive rendering.

Empirical Line Method Using Spectrally Stable Targets to Calibrate IKONOS Imagery

By using speetrally stable targets, the empirical line （EL） method was tested to correct the multispectral IKONOS imagery acquired over Putuo Mountain, Zhejiang, China. A series of calibration targets, which were spectrally stable over time, were selected to establish the linear predicted equation. Subsequently, a series of spectrally stable validation targets were selected to assess the accuracy of the equations. And, validation targets, which were speetrally unstable over time, were used to test the feasibility of using the EL method to calibrate the archival remotely sensed data. Ground reflectance measurements for each target were made using an ASD FieldSpec spectroradiometer. A Trimble GeoXTTM GPS unit with sub-meter accuracy was used to estimate the target position accurately. Linear regression equations for four tKONOS bands were derived. The coefficients of determination for the blue, green, and red bands were all greater than 0.9800 and it was 0.9697 for the near infrared band. It was concluded that reasonable results could be obtained by using speetrally stable targets.

Assessment of Three Methods for Estimating Abundance of Ungulate Populations

The accuracy of three methods (pellet group count, inverse line transect method and track count) for estimat-ing the density of ungulate population was assessed, based on a wapiti population with the known size in the enclosure of500 hm2 on Tonghe Hunting Farm, Heilongjiang province, China, during 1992-1993. The estimation of population densityusing the Pelld group count method was the closeSt to the actual value, whereas the density of the wapiti population wasunderestimated by the inverse line transect method and overestimated by the track count method. No signilicant differenceexisted the estimated and actual values for the pellet group method and the inverse line transed method, but thesignificant differen was found for the track count method. Therefore, it is suggested that the pellet group method should begiven the priority in the survey of ungulate population abundance in practice.

THE VIBRATION AND STABILITY ANALYSIS OF MODERATE THICK PLATES BY THE METHOD OF LINES

The method of lines based on Hu Hai-chang 's theory for the vibration and stability of moderate thick plates is developed. The standard nonlinear ordinary differential equation (ODE) system for natural frequencies and critical load is given by use of ODE techniques, and then any indicated eigenvalue could be obtained directly from ODE solver by employing the so-called initial eigenfunction technique instead of the mode orthogonality condition. Numerical examples show that the present method is very effective and reliable.

Refined empirical line method to calibrate IKONOS imagery

To extract quantitative biophysical parameters such as leaf biomass and leaf chlorophyll concentration from the remotely sensed imagery, the effect of atmospheric attenuation must be removed. The refined empirical line （REL） method was used to calibrate the IKONOS multispectral imagery. The IKONOS digital numbers （DN） were converted to the at-satellite reflectance, then the linear relation between at-satellite reflectance and surface spectral reflectance （ρA） was derived from six bright targets of known reflectance in the image, and modelled estimates of the image reflectance at ρA=0. Validation targets were used to test the feasibility of REL method. The mean relative errors between ρA retrieved from IKONOS image using REL method and ground-measured ρA were 11%, 13%, 3% and 5% in the IKONOS blue, green, red and near-infrared （NIR） respectively. When dark targets are unavailable or measurement of dark target is inconvenient, the REL method was most crucial for retrieving surface spectral reflectance. The REL offers a simple approach for quantitative retrieval of biophysical parameters from IKONOS imagery.

Method of lines for functionally gradient materials

The method of lines(MOL) for solving the problems of functionally gradient materials(FGMs) was studied. Navier’s equations for FGMs were derived, and were semi-discretized into a system of ordinary differential (equations(ODEs)) defined on discrete lines with the finite difference. By solving the system of ODEs, the solutions to the problem can be obtained. An example of three-point bending was given to demonstrate the application of MOL for a crack problem in the FGM. The computational results show that the more accurate results can be obtained with less computational time and resources. The obvious difficulties of numerical method for crack problems in FGMs, such as the effect of material nonhomogeneity and the existence of high gradient stress and strain near a crack tip, can be overcome without additional consideration if this method is adopted.

COMPUTATION OF STRESS INTENSITY FACTORS BY THE SUB-REGION MIXED FINITE ELEMENT METHOD OF LINES

Based on the sub-region generalized variationM principle, a sub-region mixed version of the newly-developed semi-analytical ＇finite element method of lines＇ （FEMOL） is proposed in this paper for accurate and efficient computation of stress intensity factors （SIFs） of two-dimensional notches/cracks. The circular regions surrounding notch/crack tips are taken as the complementary energy region in which a number of leading terms of singular solutions for stresses are used, with the sought SIFs being among the unknown coefficients. The rest of the arbitrary domain is taken as the potential energy region in which FEMOL is applied to obtain approximate displacements. A mixed system of ordinary differential equations （ODEs） and algebraic equations is derived via the sub-region generalized variational principle. A singularity removal technique that eliminates the stress parameters from the mixed equation system eventually yields a standard FEMOL ODE system, the solution of which is no longer singular and is simply and efficiently obtained using a standard general-purpose ODE solver. A number of numerical examples, including bi-material notches/cracks in anti-plane and plane elasticity, are given to show the generally excellent performance of the proposed method.

Method of Lines for the Chiral Nonlinear Schrödinger Equation

In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically. Two numerical methods are derived using the explicit Runge-Kutta method of order four and the linear multistep method (Predictor-Corrector method of fourth order). The resulting schemes of fourth order accuracy in spatial and temporal directions. The CNSE is non-integrable and has two kinds of soliton solutions: bright and dark soliton. The exact solutions and the conserved quantities of CNSE are used to display the efficiency and robustness of the numerical methods we derived. Interaction of two bright solitons for different parameters is also displayed.

A CLASSOF NONMONOTONE CONJUGATE GRADIENT METHODSFOR NONCONVEX FUNCTIONS

This paper discusses the global convergence of a class of nonmonotone conjugate gra- dient methods(NM methods) for nonconvex object functions.This class of methods includes the nonmonotone counterpart of modified Polak- Ribière method and modified Hestenes- Stiefel method as special cases

Heat Transfer within Direct Heating Integrated Moving Bed Torrefier by Method of Lines

This work deals with the determination of the temperature profile within a direct heating moving bed torrefier in order to determine its minimum column height. A thermal model based on eulerian-eulerian two-phase solid-gas theory was performed and solved with the method of lines. In addition, this study allows to investigate the effect of the biomass particle size on the minimum torrefier column height. This investigation was performed by changing, simultaneously, the diameter of particles and the minimum fluidization velocity of the bed. Then, the calculations were made for a counter-current torrefaction reactor of 30 cm in diameter and for 5 kg/h of the feed rate of raw sugarcane bagasse. Results show that the height of the reactor column must be at least 30 cm for that are 1 mm in diameter and 108 cm for particles that are 2 mm in diameter.

Two Cases of Complicated Rectovaginal Fistula Treated by Hanging Line Method Were Reported and Reviewed in the Literature

This paper retrospectively analyzes the complicated rectovaginal fistula in 2 cases after the successful treatment. Through literatures collected, with the difficulties and contradictions of the treatment of complicated rectovaginal fistula as the starting point, the currently used hanging line method, the advantage and deficiency of surgical treatment in recent years, and the change of treatment method were reviewed. We wish to explore which current treatments could be a better choice.

A FINITE ELEMENT METHOD FOR STRESS ANALYSIS OR ELASTOPLASTIC BODY WITH POLYGONAL LINE STRAIN——HARDENING

In this paper, the stress-strain curve of material is fitted by polygonal line composed of three lines. According to the theory of proportional loading in elastoplasticity, we simplify the complete stress-strain relations, which are given by the increment theory of elastoplasticity. Thus, the finite element equation with the solution of displacement is derived. The assemblage elastoplastic stiffness matrix can be obtained by adding something to the elastic matrix, hence it will shorten the computing time. The determination of every loading increment follows the von Mises yield criteria. The iterative method is used in computation. It omits the redecomposition of the assemblage stiffness matrix and it will step further to shorten the computing time. Illustrations are given to the high-order element application departure from proportional loading, the computation of unloading fitting to the curve and the problem of load estimation.

ARBITRARILY HIGH-ORDER ENERGY-CONSERVING METHODS FOR HAMILTONIAN PROBLEMS WITH QUADRATIC HOLONOMIC CONSTRAINTS

In this paper,we define arbitrarily high-order energy-conserving methods for Hamilto-nian systems with quadratic holonomic constraints.The derivation of the methods is made within the so-called line integral framework.Numerical tests to illustrate the theoretical findings are presented.

Dynamic Modeling and Simulation of a Commercial Naphtha Catalytic Reforming Process

A first principles-based dynamic model for a continuous catalyst regeneration (CCR) platforming process, the UOP commercial naphtha catalytic reforming process, is developed in this paper. The lumping details of the naphtha feed and reaction scheme of the reaction model are given. The process model is composed of the reforming reaction model with catalyst deactivation, the furnace model and the separator model, which is capable of capturing the major dynamics that occurs in this process system. Dynamic simulations are performed based on Gear numerical algorithm and method of lines (MOL), a numerical technique dealing with partial differential equations (PDEs). The results of simulation are also presented. Dynamic responses caused by disturbances in the process system can be correctly predicted through simulations.