BEM Results Research Articles

Performance estimation of small‐scale horizontal axis wind turbine blade

AbstractThe extracted energy from the wind is mainly influenced by the geometry of the rotor blades. Determining the aerodynamic optimum blade shape is one of the main tasks of the wind turbine designer. In the current study, the mixed airfoil technique was employed by using “Blade‐Element‐Momentum” (BEM) and “Computational‐Fluid‐Dynamics” (CFD) analysis to predict the aerodynamic performance of a small‐scale horizontal axis wind turbine blade. The BEM was then run using the open‐source wind turbine design and performance computation program Q‐Blade. The numerical simulation is carried out by Ansys Fluent. Here, the k‐ω Shear Stress Transport (SST) model was used. The results were compared with existing experimental data on lift and drag coefficients at the optimal angle of attack. The results of the two approaches were compared for different tip speed ratio values and a good agreement between CFD and BEM results was found.

Solution of two-dimensional diffusion–advection problems for non-isotropic media with spatially variable velocity field by the boundary element method

This work presents a boundary element method formulation for the solution of the diffusion–advection problem. The formulation, developed for two-dimensional problems, for non-isotropic media, considers a spatially variable velocity field. The only way to deal with such a kind of problem is employing a steady-state fundamental solution. Consequently, the basic BEM equation presents one domain integral related to the velocity components, and another one related to the time derivative of the variable of interest, which is approximated using a backward finite difference scheme. BEM results are compared with an available analytical solution in the first part of the first example, and with the results provided by a finite element method formulation, taken as reference ones, in the second part of the first example and in the second example. From the comparisons, one can observe a good agreement between the results furnished by the proposed formulation and the analytical and reference solutions.

Linkage of logarithmic capacity in potential theory and degenerate scale in the BEM for two tangent discs

Degenerate scales of different shapes have been studied by many researchers. BEM/BIEM may lead to a degenerate scale for a two-dimensional Laplace problem. In this paper, we study the problem of the two tangent discs with different radii. We use the conformal mapping of complex variables and the unit logarithmic capacity to examine the degenerate scale. Although the degenerate scale of infinite plane containing two circular holes has been derived by using the degenerate kernel in terms of bipolar coordinates, this shape cannot be solved by using the degenerate kernel. Finally, the numerical results of BEM were also compared with those of analytical formula.

Fracture Parameters for Cracked Cylincal Shells

In this paper, 2D boundary element stress analysis is carried out to obtain the T-stress for multiple internal edge cracks in thick-walled cylinders for a wide range of cylinder radius ratios and relative crack depth. The T-stress, together with the stress intensity factor K, provides amore reliable two-parameter prediction of fracture in linear elastic fracture mechanics. T-stress weight functions are then derived from the T-stress solutions for two reference load conditions corresponding to the cases when the cracked cylinder is subject to a uniform and to a linear applied stress variation on the crack faces. The derived weight functions are then verified for several non-linear load conditions. Using the BEM results as reference T-stress solutions; the T-stress weight functions for thick-walled cylinder have also been derived. Excellent agreements between the BEM results and weight function predictions are obtained. The weight functions derived are suitable for obtaining T-stress solutions for the corresponding cracked thick-walled cylinder under any complex stress fields. Results of the study show that the two dimensional BEM analysis, together with weight function method, can be used to provide a quick and accurate estimate of T-stress for 2-D crack problems.

Buckling Analysis of Laminated Anisotropic Kirchhoff’s Plates via The Boundary Element Method

Abstract A new fundamental solution for laminated anisotropic Kirchhoff’s plates with out-of-plane and in-plane compressive loads is derived here. The multicompressed solution for both isotropic and anisotropic cases is obtained via the Radon Transform. Some fundamental kernels of the integral equations are described in detail. BEM results of displacements and critical buckling loads of several plates with different boundary conditions and geometries are presented. Comparisons with available analytical solutions and some published numerical results confirm the reliability and accuracy of the proposed formulation.

Aerodynamic optimization of a 5 Megawatt wind turbine blade

Wind power has been widely considered in recent years as an available and a clean renewable energy source. The cost of wind energy production is currently the main issue, and increasing the size of wind turbines can reduce wind energy production costs. Hence, megawatt wind turbines are being rapidly developed in recent years. In this paper, an aerodynamic analysis of the NREL 5MW turbine is carried out using the modified blade element momentum theory (BEM). The genetic algorithm (GA) as an optimization method and the Bezier curve as a geometry parameterization technique are used to optimize the original design. The modified BEM results are compared with the NREL published results for verification. Cost of energy (COE) is considered an objective function, which is one of the most important and common choices of objective function for a megawatt wind turbine. Besides, the optimization variables involve chord and twist distributions variation along the blade span. The optimal blade shape is investigated for the minimum cost of energy with considered constant rotor diameter and airfoil profiles. Then the objective function is improved and a new optimum geometry is compared with the original geometry. Although the Annual Energy Production and rated power are reduced by 2% and 3% respectively, the net cost of wind energy production is decreased by 15%, showing the importance of such optimization studies.

Earth Pressure and Settlement Analysis of Trench Ducts Backfilled with Controlled Low Strength Materials

Recently trench ducts for allocating conveying pipes for various hydraulic or electric lines are tremendously constructed due to rapid growth of life and communication demand. Graded sands and concrete are usually in conventional excavation and backfill operation. Controlled low-strength material (CLSM) has been proposed as a suitable substitute for this construction. However, exact and reliable analysis is required to assure the stress and settlement limitation. This paper presents static analysis of trench duct backfilled with sustainable materials and conventional materials using boundary element (BE) method. The Young's moduli of CLSM are obtained from laboratory tests for two different binder mixtures, CLSM B-130/30% and CLSM B-8-/30%, respectively. Two-dimensional planar strain is employed in the BE formulation of static analysis and comparison study of 4 kinds of backfill materials, i.e., graded sand, CLSM B130-30%, CLSM B130-80%, and concrete. Emphasis is put on the lateral pressure on the side wall, settlement at the top of trench duct, vertical displacement along the centerline of duct and top of pipe cover, induced by three wheel surcharges: concentrated, strip and uniform lane loads. Convergence tests of BEM results are first conducted. Numerical results show that the settlement and lateral pressure of CLSM backfills are acceptable to assure the applicability of CLSM as a suitable sustainable material employed for trench duct design and backfill construction.

An experimental study on the absorption characteristics of a three-dimensional permeable membrane space sound absorber

In this study, we propose a rectangular and cylindrical three-dimensional space sound absorber using a permeable membrane and the absorption characteristics which are examined experimentally by reverberation room method. As a pilot study, a two-dimensional boundary element (2-D BEM) analysis is also conducted to predict the absorption characteristics of the absorbers. The experimental study revealed that the absorption coefficient is low at low frequencies and gradually increases with frequency. The absorption coefficient converges to 0.5 at the maximum which is similar to a single-leaf permeable membrane. The flow resistance and the surface density of the permeable membrane mainly affect the absorption characteristics at middle to high frequencies. At low frequencies, the heavy membrane contributes to the higher absorption performance. In the experiment specimens with high flow resistance produce higher absorptivity. Also, the cylindrical absorber shows slightly higher absorption coefficient than the rectangular absorber mainly at low frequencies. The 2-D BEM results show similar frequency characteristics as the measured values when the membrane's flow resistance and surface density are low, but the numerical values overestimate overall the absorptivity of the absorbers.

Simulation of 2D symmetry and asymmetry wedge water entry by smoothed particle hydrodynamics method

This article presents a study of fluid–solid interaction in a free surface flow by smoothed particles hydrodynamics method. Different cases of symmetry and asymmetry wedge water entries are presented. All cases are performed at constant speed, considering the effect of gravity. First-order density filter, turbulence modeling and a pressure filter have been utilized. Through these compiling options, low-pass pressure filter has been able to eliminate the undesirable fluctuation of pressure, and good results have been achieved. Pressure distribution and free surface profiles have been produced in all cases. In the cases of symmetry wedge water entries, the obtained results were compared against the results of BEM, similarity and asymptotic solutions, but in the cases of asymmetry wedge water entry, the obtained results were compared against those of analytical work. Through these comparisons, it was found that although the general trend of the computed pressure distributions follows the results of the previous studies, there still exist some differences among them. Main difference between the obtained results and other studies is related to the position of the pressure peak. It was concluded that this may indeed be attributed to the nature of the applied methods and due to the methodology of cutting the edges in schemes like BEM to overcome the abrupt flow at the edge. Vertical force in particular symmetry and asymmetry cases was also computed and presented. It was found that the global behavior of the vertical force in both the symmetry and asymmetry wedge water entry is the same and that there are some differences among them in terms of decreasing rate as well as the maximum value of the force.

Aerodynamic optimal design of wind turbine blades using genetic algorithm

Wind power has been widely considered and utilized in recent years as one of the most promising renewable energy sources. In the current research study, aerodynamic analysis of the upwind three-bladed horizontal axis turbine is carried out using blade element momentum theory (BEM), and a genetic algorithm (GA) is applied as an optimization method. Output power generation is considered as an objective function, which is one of the most common choices of objective function. The optimization variables also involve chord and twist distribution variations and the placement of the airfoil sections along the blade length. The optimal blade shape is investigated for the maximum output power at a specific wind speed, rotor diameter and airfoil profile. The modified BEM results are compared with an experimental measurement indicating reliable results. The results show that considering placement of the airfoils as design variables in addition to chord and twist rate has a significant effect on the optimal output power. Finally, the objective function (output power) is improved by 10% compared to the base function.

Design and Experimentation of a 1 MW Horizontal Axis Wind Turbine

In this work was carried out the aerodynamics design of a 1 MW horizontal axis wind turbine by using blade element momentum theory (BEM). The generated design was scaled and built for testing purposes in the discharge of an axial flow fan of 80 cm in diameter. Strip theory was used for the aerodynamic performance evaluation. In the numerical calculations was conducted a comparative analysis of the performance curves adding increasingly correction factors to the original equation of ideal flow to reduce the error regarding real operating values got by the experimental tests. Correction factors introduced in the ideal flow equation were the tip loss factor and drag coefficient. BEM results showed good approximation using experimental data for the tip speed ratio less than design. The best approximation of the power coefficient calculation was for tip speed ratio less than 6. BEM method is a tool for practical calculation and can be used for the design and evaluation of wind turbines when the flow rate is not too turbulent and radial velocity components are negligible.

BEM and FEM results of displacements in a poroelastic column

The dynamical investigation of two-component poroelastic media is important for practical applications. Analytic solution methods are often not available since they are too complicated for the complex governing sets of equations. For this reason, often some existing numerical methods are used. In this work results obtained with the finite element method are opposed to those obtained by Schanz using the boundary element method. Not only the influence of the number of elements and time steps on the simple example of a poroelastic column but also the impact of different values of the permeability coefficient is investigated.

Numerical Calculation of the Pressure Distributions on a Rudder Surface

This paper numerically calculates the pressure distributions of a rudder of a ship for structure strength design. The sections profile of the rudder is NACA0020 airfoil. The viscous flow is simulated by FLUENT commercial software, while the model and mesh is generated by GAMBIT software. A 2D viscous flow around a NACA0020 airfoil is calculated firstly. Some notices are given here about the magnitude of computing domain, the density distribution and the numbers of grid nodes on the airfoil surface in order to gain better results. Then, based on these experiences, the viscous flow around a 3D rudder is simulated. The calculated pressure coefficients on the rudder’s section are compared with the experiment results and BEM results of the potential theory. At the attack angles and , the three results agree well with each other. However, when the attack angle is , the viscous results from FLUENT give better agreement with the experiment results than the BEM results. This conclusion confirms that the viscosity effect is great in the case of large attack angles.

A Galerkin projection technique for the evaluation of potential derivatives on a smooth boundary in 2D BEM

Abstract A new simple and general technique for potential gradient recovery along the boundary in two-dimensional BEM is introduced and studied numerically. This technique is based on generalized Galerkin projections, and its basic formulation corresponds to a least-squares method. In preliminary numerical tests for Dirichlet and Neumann problems on smooth boundaries, this technique shows excellent accuracy. The normal flux is evaluated more accurately than direct BEM results, and the tangential flux values are calculated more accurately than with a local averaging technique.

Aerodynamic design of a 300 kW horizontal axis wind turbine for province of Semnan

In this research, Blade Element Momentum theory (BEM) is used to design a HAWT blade for a 300kW horizontal axis wind turbine. The airfoil is RISØ-A1-18, produced by RISØ National Laboratory, Denmark. Desirable properties of this airfoil are related to enhancement of aerodynamic and structure interactions. Design parameters considered here are wind tip speed ratio, nominal wind speed and diameter of rotor. The nominal wind speed was obtained from statistical analysis of wind speed data from province of Semnan in Iran. BEM is used for obtaining maximum lift to drag ratio for each elemental constitution of the blade. Obtaining chord and twist distribution at assumed tip speed ratio of blade, the aerodynamic shape of the blade in every part is specified which correspond to maximum accessible power coefficient. The design parameters are trust coefficients, power coefficient, angle of attack, angle of relative wind, drag and lift coefficients, axial and angular induction factors. The blade design distributions are presented versus rotor radius for BEM results. The blade shape then can be modified for ease of manufacturing, structural concerns, and to reduce costs.

805 複雑配管系における枝管の効果について : BEMによる解析と実験との比較(機械力学・計測制御V)

805 複雑配管系における枝管の効果について : BEMによる解析と実験との比較(機械力学・計測制御V)

급수 함수를 이용한 임의 형상 고정단 평판의 자유 진동 해석

A new method for free nitration analysis using series functions is proposed to obtain the eigenvalues of arbitrarily shaped, polygonal plates with clamped edges. Since a general solution used in the method satisfies the equation of motion for the transverse vibration of a plate, the method offers very accurate eigenvalues, compared to FEM or BEM results. In addition, the method can minimize the amount of numerical calculation because it has the advantage of not needing to divide the plate of interest. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM (NASTRAN) or another analytical method.

Novel meshless method for solving the potential problems with arbitrary domain

In this article, a non-singular and boundary-type meshless method in two dimensions is developed to solve the potential problems. The solution is represented by a distribution of the kernel functions of double layer potentials. By using the desingularization technique to regularize the singularity and hypersingularity of the kernel functions, the source points can be located on the real boundary and therefore the diagonal terms of influence matrices are determined. The main difficulty of the coincidence of the source and collocation points then disappears. By employing the two-point function, the off-diagonal coefficients of influence matrices are easily obtained. The numerical evidences of the proposed meshless method demonstrate the accuracy of the solutions after comparing with the results of exact solution, conventional MFS and BEM for the Dirichlet, Neumann and mix-type boundary conditions (BCs) of interior and exterior problems with simple and complicated boundaries. Good agreements with exact solutions are observed.

Analysis of Stress Singularity Fields in Three-Dimensional Joints by Three-Dimensional Boundary Element Method Using Fundamental Solution for Two-Phase Transversely Isotropic Materials.

In recent years, composite materials and ceramics-metal joints are investigated from a view of fundamental technology for producing the industrial products. In these materials, the stress concentration frequently occurs at the vicinity of joint edges and it causes cracks there. In the present study, we derived the fundamental solution for a unit force acting a point interior a two-phase transversely isotropic material, which is a bonded structure of two transversely isotropic materials with different properties. We developed a three-dimensional boundary element program using the fundamental solution. We examined the continuity of displacements and stresses at the interface of two-phase transversely isotropic materials to check the correctness of the program. We conducted the stress analysis for joints of Ti-Mg and Mg-Zn and performed the eigen value analysis based on FEM, which is formulated using a intepolation function considering stress singularity at the vertex. We showed that the results of BEM and FEM are very agreed with each other, and the stress singularities of power law and logarithmic law occur at the vertex of the three-dimensional anisotropic joints.

A quadratic boundary element implementation in orthotropic elasticity using the real variable approach

This paper revisits the real variable fundamental solution approach to the Boundary Integral Equation (BIE) method in two-dimensional orthotropic elasticity. The numerical implementation was carried out using quadratic isoparametric elements. The strong and weakly singular integrals were directly evaluated using Euler's transformation technique. The limiting process was done in intrinsic coordinates and no separate numerical treatment for strong and weak singular integrals was necessary. For strongly singular integrals a priori interpretation of the Cauchy principal value is not necessary. Two problems from plane stress and strain are presented to demonstrate the numerical efficiency of the approach. Excellent agreement between BEM results and exact solutions was obtained even with relatively coarse mesh discretizations. Copyright © 2000 John Wiley & Sons, Ltd.