BEM Code Research Articles

On the influence of twist and taper of HAWT blades on the rotational augmentation phenomenon: the NREL Phase VI – Phase II comparison

The physics of 3D flows on rotating blades is currently one of the most important research fields related to wind turbines. Although many authors have studied the phenomenon thoroughly and they have proposed meaningful physical explanation of the mechanism which triggers the onset of the rotational augmentation, a universal correlation between rotor geometry, operating conditions and centrifugal pumping effects has not been derived yet. For instance, all the proposed corrections for rotational stall delay within 1D codes have demonstrated fairly good accuracy but in limited operating range or for specific airfoils or rotor geometries. In the present work the authors applied a consolidated methodology, based on the use of accurate CFD 3D models and of an inverse BEM code, to thoroughly analyze the differences in terms of rotational augmentation effects between the two widely known NREL Phase VI and Phase II HAWTs. This choice was made precisely since both the rotors used the S809 airfoil for the active part of the blade, had equal radial dimensions and the operating conditions were approximately the same. Thus, the substantial difference between the rotors was the fact that the Phase VI blade was twisted and tapered while the Phase II one had constant chord and pitch along the radial direction. In this way, the possible influence due to the twist and taper of the blade on the physics of the centrifugal pumping could be highlighted more easily. The CFD models were developed in Ansys Fluent and validated against experimental measurements available in the literature. The inverse BEM code, already implemented in a previous work, allowed the authors to extrapolate and compare sectional data obtained through the CFD simulations. The post-processing of the results demonstrated the strong influence of the twist and taper of the blade on the dynamics of the rotational augmentation. These results lead the way for a better understanding of the relation between rotor geometry and centrifugal pumping physics.

Impact of turbulence and blade surface degradation on the annual energy production of small‐scale wind turbines

AbstractSmall‐scale horizontal axis wind‐turbines (SHAWTs) are acquiring relevance within the regulatory policies of the wind sector aiming at net‐zero emissions, while reducing visual and environmental impact by means of distributed grids. SHAWTs operate transitionally, at Reynolds numbers that fall between . Furthermore, environmental turbulence and roughness affect the energetic outcome of the turbines. In this study, the combined effect of turbulence and roughness is analysed via wind tunnel experiments upon a transitionally operating NACA0021 airfoil. The combined effects cause a negative synergy, inducing higher drops in lift and efficiency values than when considering the perturbing agents individually. Besides, such losses are Reynolds‐dependent, with higher numbers increasing the difference between clean and real configurations, reaching efficiency decrements above 60% in the worst‐case scenario.Thus, these experimental measurements are employed for obtaining the power curves and estimating the annual energy production (AEP) of a 7.8‐kW‐rated SHAWT design by means of a BEM code. The simulations show a worst‐case scenario in which the AEP reduces above 70% when compared to the baseline configuration, with such a loss getting attenuated when a pitch‐regulated control is assumed. These results highlight the relevance of performing tests that consider the joint effect of turbulence and roughness.

An Optimization Strategy to Position CHIEF Points in Boundary-Element Acoustic Problems

The use of boundary elements in the analysis of exterior acoustic problems poses challenges at specific frequencies, since fictitious eigenfrequencies may arise at the internal resonances of cavities, leading to inaccurate results or even unstable behavior. To filter out these fictitious eigenfrequencies, a scheme based on the combined Helmholtz integral equation formulation (CHIEF) can be used to prevent the so-called non-uniqueness problem, although it requires additional equations and points. The BEM formulation final accuracy will, however, depend on the correct choice of these points. Here, a strategy to help in defining good approximations for the position and number of such points is proposed, based on an optimization process which maximizes the system matrix’s smallest singular value. The accuracy of the method for exterior radiation problems is investigated using different examples. With low computational cost and simple implementation, the two proposed algorithms automatically circumvent the non-uniqueness problem, aiding the implementation of more stable BEM codes.

Aerodynamic Performance Investigation of a Small Horizontal Axis Wind Turbine with Multi-Airfoil Blade Profiles of SD2030 and E231 Using Wind Tunnel Experiments and BEM Theory Method

The goal of this study is to investigate the performance of a small horizontal axis wind turbine blade at wind speeds of lower than 5 m/sec numerically and experimentally. The rotor blade has a diameter of 0.7m and consists of two airfoils profile: the thin airfoil SD2030 selected at the outboard region, and the thick airfoil E231 at the inboard region. The former airfoil, SD2030, is highly recognized for aerodynamic performance as it is suitable for low Reynolds number (Re), while the latter airfoil E231 is likewise appropriate for low Re flow but has a higher thickness-to-chord ratio which acts as structural support and good strength at the hub. The selected airfoils were analyzed using QBlade software based on XFOIL and Blade Element Theory (BEM) for different Reynolds number. Using a low-speed wind tunnel and Reynolds number ranging from 1x105 to 5x105, experiments at pitch angles of 5ο were conducted to determine the variation in torque and predict blade performance. The results reveal that the turbine with two hybrid different airfoil profiles have achieved a better start-up response at low wind speed of 1.5 m/s and a high-power coefficient of 0.34 with 3.7 tip speed ratio. The turbine can be used to generate a power of 0.5W at 1.5 m/s and a maximum power harvest of up to 20W at a wind speed of 7m/sec. The turbine's performance compared to other small wind turbines from the literatures demonstrate good performance and the results obtained from wind tunnel data were found in satisfactory agreement with the results provided by the BEM code.

How to extrapolate 3D aerodynamic coefficients from HAWT CFD simulations: an inverse BEM approach

In the present work the authors developed a methodology based on an inverse BEM method, to easily extrapolate 3D aerodynamic coefficients from HAWT CFD 3D simulation results. Specifically, since the BEM method was based on the solution of a discrete number of blade radial sections, the CFD model was implemented in Ansys Fluent in such a way to split the surface of one of the blades in a certain number of sections already at the CAD level. Therefore, the normal and tangential aerodynamic forces were calculated for each radial section and subsequently provided directly within the modified BEM code developed in Matlab. Thus, the BEM code iterated for the axial and tangential induction factors and calculated the lift and drag coefficients, the related local angle of attack, the torque, the power and the power coefficient for each specific operating condition simulated. The methodology proposed here was validated using the NREL Phase VI rotor geometry for which a very good agreement between numerical and experimental data was found. Furthermore, this allowed for an insight into the 3D effects over the blade since it was possible to compare the experimental 2D and the 3D lift and drag coefficients section by section.

Aerodynamic Performance of a 100 W Single-Rotor Wind Turbine in Comparison with Multi-Rotor Wind Turbines of the Same Capacity

Large-scale wind turbines come with great costs and logistic difficulties in transportation and installation. This work presents a solution by using Multi-Rotor Systems (MRS) wind turbines. Four different configurations of wind turbines with one, two, three, and four rotors of the same turbine capacity of 100 W have been studied. An in-house BEM code has been verified and used for the current study. The study has shown that the total mass of the rotor/nacelle assembly is 70%, 57%, and 50% for the twin-rotor, tri-rotor, and quad-rotor respectively as a percentage of the total mass of the single rotor. Torque load has also shown a significant decrease down to 50% of the quad-rotor compared to single-rotor showing the great advantage of MRS compared to single-rotor wind turbines. Based on the rotor/nacelle performance solely, increasing the number of rotors results in better performance with less mass and accordingly cost.

A simple model to predict the energy loss due to leading edge roughness

In this paper a simple model to predict losses in annual energy production due to leading edge roughness or leading edge erosion from wind turbines is presented. Because detailed information about wind turbines not always are available, the input to this model requires only a few parameters: rated power, rotor radius, two Weibull parameters and categories of local damages. Therefore, some assumptions are made in the model. It was validated against a common implementation of a BEM code and showed good agreement in the loss of annual energy production.Also, a categorisation methods was proposed. The categories ranged between a and e corresponding to an undamaged blade and a severely damaged blade, respectively. This categorisation was made locally on the blade. The blade is divided into annular elements and each annular element is graded with a category. By summing up the annular elements on the blade, each with their categories, the total loss in energy production was predicted.

Wind turbine performances prediction using BEM approach with Jonkman-Buhl brake state model coupled to CFD method

In wind turbine design, it's essential to study the flow behavior around the rotor blades and evaluate the aerodynamic loads. However, due to the complicated nature of the flow, predicting the aerodynamic characteristics remains a difficult task. For this reason, a new simplified numerical code was developed by the authors using the BEM (Blade Element Theory) theory coupled to 2D-CFD (Computational Fluid Dynamics) calculations to evaluate power and calculate loads acting on the rotor blades. A steady state, 2D calculations were conducted for the S809 profil to simulate the flow field around the airfoil. The fluid equations were numerically solved using the SST k-ω turbulence model. Through a linking program between Matlab and Ansys, the two-dimensional parameters retrieved from this simulation, were inserted into the classical BEM program to predict power. Simulation findings were compared then to experimental measurements, and slight discrepancies were found. To improve the numerical method's accuracy, several corrections were adopted: the classical BEM code was substituted by a modified BEM approach with Jonkman-Buhl brake state model and stall delay models. The results were then compared with experimental data and good agreement was found. This new approach is very useful for engineering applications since it uses fewer resources and computation time compared to experimental measurements.

Wake-body interaction Noise Simulations by Coupling CFD and BEM

In many engineering applications, the wake-body interaction or body-vortex interaction (BVI) occurs. In the wake-body interaction, vortices shed from an upstream obstacle interact with downstream obstacle and generate noise, for example blades in a turbomachinery, tubes in a heat exchanger, rotating blades like a helicopter and wind turbine and so on. The rod-airfoil and airfoil-airfoil configurations are typical models for the wake-body interaction. A rod and an airfoil are immersed upstream of the airfoil. In this paper, we reviewed the noise mechanism generated by the wake-body interaction and show the numerical results obtained by the coupling method using commercial CFD and acoustic BEM codes. The results shows that depending on the spacing between the rod or airfoil and the airfoil, the flow patterns and noise radiation vary. With small spacing, the vortex shedding from the upstream obstacle is suppressed and it results in the suppression of the sound generation. With large spacing, the shear layer or the vortices shed from the upstream obstacle impinge on the downstream obstacle and it results in the large sound generation. The dominant peak frequency of the generated sound varies with increasing of the spacing between the two obstacles.

PRaFULL: A method for the analysis of piled raft foundation under lateral load

A new code, called PRaFULL (Piled Raft Foundation Under Lateral Load), was developed for the analysis of laterally loaded Combined Pile Raft Foundation (CPRF). The proposed code considers the contribution offered by the raft-soil contact and the interactions between all the CPRF system components. The nonlinear behaviour of the reinforced concrete pile and the soil are accounted. As shallower soil layers are of great relevance in the lateral response of a pile foundation, PRaFULL includes the possibility to consider layered soil profiles with appropriate properties. The shadowing effect on the ultimate soil pressure is accounted, when dealing with pile groups, as proposed by the Strain Wedge Model. PRaFULL BEM code obviously requires less computational resources compared to FEM (Finite Element Method) or FDM (Finite Difference Method) codes. The proposed code was validated in the linear elastic range by comparisons with the code APRAF (Analysis of Piled Raft Foundations). The reliability of the procedure to predict piled raft performance was then verified in nonlinear range by comparisons with both centrifuge tests and computer code PRAB.

Study on the Sound Radiation Efficiency of a Typical Distribution Transformer

In the realm of power grids environmental protection, low-frequency harmonic noise radiated from transformers has always been the focus of attention for decades. The existing noise control technologies, such as traditional noise barriers, sound insulation enclosures, and damping panels, not only occupying a large space but also causing difficulties in heat dissipation and daily maintenance of transformers. Therefore, explorations on the theory and design of low-noise power transformers become particularly necessary. In this paper, we started from the concept of acoustic radiation efficiency and discussed the radiation efficiency of a typical distribution transformer with radiators. It is found that the overall radiation efficiency is reduced below 230 Hz (low-frequency band) due to radiator barriers compared with that of the flat transformer tank. Furthermore, the phase effect of vibration distribution was also studied with a validated BEM code, inspired by the “acoustic short circuit” phenomenon. It is verified that the acoustic short circuit phenomenon truly exists for a typical transformer enclosure and affects its sound radiation. These supporting results might lead to a promising noise reduction technology from the perspective of radiation control of transformer tanks, i.e., acoustic metamaterials for noise source phase control.

A numerical implementation of the Coupled Criterion of Finite Fracture Mechanics for elastic interfaces

A new numerical procedure for predicting interface failures between solids is developed. The procedure is based on the Linear Elastic-(Perfectly) Brittle Interface Model (LEBIM) combined with the Coupled Criterion of the Finite Fracture Mechanics (CCFFM). Although in the present investigation this procedure is implemented in a 2D BEM code, a general pseudocode is devised allowing its implementation in any BEM or FEM code.The pull-push shear test is used as a benchmark problem, where the fracture mode II is dominant. Nevertheless, the present procedure can tackle a debond growth occurring under any fracture mode mixity. The pull-push problem is chosen since it allows us to check the obtained numerical results against an available analytical solution based on a beam model. Additionally, the numerical results are compared with some experimental data from literature. Furthermore, an inverse analysis is applied to obtain the interface strength and fracture parameters that the model needs.

Investigation of parameters affecting horizontal axis tidal current turbines modeling by blade element momentum theory

The Blade Element Momentum Theory (BEMT) is one of the most common and widely used methods in horizontal axis wind and tidal turbine performance prediction. It mainly relies on two-dimensional (2-D) hydrodynamic, lift and drag, coefficients which are used to calculate the hydrodynamic forces within the blade element section of the model. These coefficients are greatly affected by both Reynolds numbers and turbulence transition parameter (Ncrit). The performance sensitivity of scale models tidal current turbines (TCTs) to the change of Reynolds numbers and Ncrit parameter was assessed. Initially, the BEMT was validated with experimental measurements of two scale models of horizontal axis tidal current turbines. A very good agreement was seen, thus, confidence in both the implementation of the theory and the applicability of the method was built up. Lift and drag coefficients were calculated from XFoil through the use of different sets of Reynolds numbers at different Ncrit values. The best BEMT validations with experimental data were seen when the hydrodynamic coefficients were calculated at two sets of Reynolds numbers considered at optimal performance. The first set was calculated at 75% of the blade span while the second set was calculated at every local elemental position of the blade. For facilitation, reduction of time and effort, Reynolds numbers at 75% of the blade span is considered the best choice. Furthermore, the BEMT model results showed better agreements with experimental data when lift and drag coefficients were calculated at low values of Ncrit parameter. The predicted tidal turbine performances of previous experimental data by the present BEM model were compared with those derived from the academic SERG-Tidal BEM code. The present BEM model, based on the proper selection of both Reynolds number and Ncrit parameter, showed an obvious superiority over SERG-Tidal model.

A non-primitive boundary integral formulation for modeling flow through composite porous channel

In this study, we develop a non-primitive boundary integral formulation (BIF) for modeling flow through composite porous channel. We consider a planar channel having two packings that are filled with fully saturated porous media. We assume that the two porous media are isotropic and homogeneous in nature, but with different permeabilities. Brinkman equation is used to model fluid flow through porous media. Stress-jump condition is utilized at the porous-porous interface to account the flow exchange due to two layers porous media. We present BIF for steady two-dimensional flow of a viscous incompressible fluid through a composite porous channel with two layers having different permeabilities (Brinkman-Brinkman problem). The BIF developed is in terms of non-primitive variables namely, stream-function and vorticity. In the limit of large permeability Brinkman equation approaches Stokes equation. Hence, in order to assert the accuracy of our BEM code, we have considered the corresponding Stokes-Brinkman system. We derive the Brinkman layer thickness for Brinkman-Brinkman system as a function of various flow parameters. It is observed that Darcy number, stress-jump coefficients and the thickness parameter have significant effect on the flow mechanics.

Study of horizontal axis tidal turbine performance and investigation on the optimum fixed pitch angle using CFD

PurposeThe purpose of this paper is to design, investigate and optimize a horizontal axis tidal turbine (HATT) using computer-aided numerical simulation and computational fluid dynamics (CFD). This is the first step of research and development (R&D) for implementation in the Persian Gulf condition. To do so, suitable locations are reviewed. Then, the optimization is focused on determining the optimum fixed pitch angle (β) of a three-bladed HATT based on the widespread multiple reference frame (MRF) technique to calculate power and thrust coefficients at different operational rotating speeds.Design/methodology/approachTo simplify the problem and reducing the computational costs due to cyclic symmetry only one blade, accordingly one-third of the whole computational domain is considered in the modeling. Due to flow’s nature involving rotating, separation and recirculation, a realizable κ-ε turbulence model with standard wall function is selected to capture flow characteristics influenced by the rotor and near the wall region. Simulations are conducted for two free-stream velocities, then compared with their dependencies through the dimensionless tip speed ratio (TSR) parameter.FindingsThe validation process of the simulations is carried out by the use of AeroDyn BEM code, which has been evaluated by comparing with two experimental data. As results, the highest coefficient of power is achieved at ß = 19.3° at TSR = 4 with the value around 0.41 and 0.816 for thrust coefficient. Furthermore, to comprehend the rotor’s performance and simulation method, flow characteristics due to the rise in angular velocity is discussed in detail. Moreover, the major phenomenon, cavitation occurrence, is also checked at the critical situation where it is found to be safe.Originality/valueBy comparing and evaluating the results to other HATTs, it implies that the proposed rotor of this study is feasible and proved by CFD evaluation at this step. However, the current rotor is awaiting a justification through experimental assessment.

A non-primitive boundary element technique for modeling flow through non-deformable porous medium using Brinkman equation

In this study, we develop a non-primitive boundary integral equation (BIE) method for steady two-dimensional flows of an incompressible Newtonian fluids through porous medium. We assume that the porous medium is isotropic and homogeneous, and use Brinkman equation to model the fluid flow. First, we present BIE method for 2D Brinkman equation in terms of the non-primitive variables namely, stream-function and vorticity variables. Subsequently, a test problem namely, the lid-driven porous cavity over a unit square domain is presented to assert the accuracy of our BEM code. Finally, we discuss an application of our proposed method to flows through porous wavy channel, which is a problem of significant interest in the micro-fluidics, biological domains and groundwater flows. We observe that the rate of convergence ( $$R_{c}$$ ) increases with increasing Darcy number. For low Darcy number streamlines follow the curvature of the wavy-walled channel and no circulation occurs irrespective of the wave–amplitude, while for high Darcy number the flow circulation occurs near the crest of the wavy-walled channel, when the wave–amplitude is large enough.

Numerical method for simulating tire rolling noise by the concept of periodically exciting contact force

For the numerical simulation of tire rolling noise, an important subject is the extraction of normal velocity data of the tire surface that are essential for the acoustic analysis. In the current study, a concept of periodically exciting contact force is introduced to effectively extract the tire normal velocity data. The ground contact pressure within contact patch that is obtained by the static tire contact analysis is periodically applied to the whole tread surface of stationary tire. The periodically exciting contact forces are sequentially applied with a time delay corresponding to the tire rolling speed. The tire vibration is analyzed by the mode superposition in the frequency domain, and the acoustic analysis is performed by commercial BEM code. The proposed method is illustrated through the numerical experiment of 3-D smooth tire model and verified from the comparison with experiment, and furthermore the acoustical responses are investigated to the tire rolling speed.

Accurate load prediction by BEM with airfoil data from 3D RANS simulations

In this paper, two methods for the extraction of airfoil coefficients from 3D CFD simulations of a wind turbine rotor are investigated, and these coefficients are used to improve the load prediction of a BEM code. The coefficients are extracted from a number of steady RANS simulations, using either averaging of velocities in annular sections, or an inverse BEM approach for determination of the induction factors in the rotor plane. It is shown that these 3D rotor polars are able to capture the rotational augmentation at the inner part of the blade as well as the load reduction by 3D effects close to the blade tip. They are used as input to a simple BEM code and the results of this BEM with 3D rotor polars are compared to the predictions of BEM with 2D airfoil coefficients plus common empirical corrections for stall delay and tip loss. While BEM with 2D airfoil coefficients produces a very different radial distribution of loads than the RANS simulation, the BEM with 3D rotor polars manages to reproduce the loads from RANS very accurately for a variety of load cases, as long as the blade pitch angle is not too different from the cases from which the polars were extracted.

CFD simulation of a 2 bladed multi megawatt wind turbine with flexible rotor connection

An innovative passive load reduction concept for a two bladed 3.4 MW wind turbine is investigated by a conjoint CFD and MBS - BEM methodology. The concept consists of a flexible hub mount which allows a tumbling motion of the rotor. First, the system is simulated with a MBS tool coupled to a BEM code. Then, the resulting motion of the rotor is extracted from the simulation and applied on the CFD simulation as prescribed motion. The aerodynamic results show a significant load reduction on the support structure. Hub pitching and yawing moment amplitudes are reduced by more than 50% in a vertically sheared inflow. Furthermore, the suitability of the MBS - BEM approach for the simulation of the load reduction system is shown.

Pitch Optimization in Small-size Darrieus Wind Turbines

Small Darrieus wind turbines are standing out as one of the most promising technologies in view of a widespread availability of delocalized energy production from wind. In view of a performance optimization of Darrieus rotors, the application of a pitch angle to blades has been often suggested. In the present work, the pitch modeling in an advanced BEM code has been exploited to investigate different pitch control strategies. In particular, the prospects of a pitch preset based on both the maximum power and the maximum energy extraction have been evaluated and compared to those connected to a progressive pitch variation with the turbine revolution speed. The pitch effects have been discussed both in terms of aggregated power output and of variation of the airfoil functioning conditions throughout a revolution. The analysis confirmed that the application of a proper pitch angle could definitely provide an increase of the turbine performance, especially at medium-high solidities.