Showing papers on "Blade element momentum theory published in 2014"

Aerodynamic Damping and Seismic Response of Horizontal Axis Wind Turbine Towers

Abstract: Aerodynamic damping has an important effect on the seismic response of horizontal axis wind turbines (HAWTs). Some researchers have estimated that aerodynamic damping in operational HAWTs is ∼5% of critical in the fore-aft direction (i.e., perpendicular to the rotor and parallel to the prevailing wind). In most recent studies, dynamic analyses of HAWT towers under seismic loads have neglected aerodynamic damping, and this assumption has significant implications in the predicted seismic response. This paper presents a closed-form solution for the aerodynamic damping of HAWTs responding dynamically in the fore-aft and side-to-side directions. The formulation is intended as a convenient method for structural earthquake engineers to include the effect of aerodynamic damping in the seismic analysis of HAWTs. The formulation is based on blade element momentum theory and is simplified by assuming a rigid rotor subjected to a steady and uniform wind oriented perpendicular to the rotor plane. This paper ex...

Effect of Blade Skew Strategies on the Operating Range and Aeroacoustic Performance of the Wells Turbine

Abstract: One of the most intensively studied principles of harnessing the energy from ocean waves is the oscillating water column (OWC) device. The OWC converts the motion of the water waves into a bidirectional air flow, which in turn drives an air turbine. The bidirectional axial Wells turbine as a candidate for OWC power takeoff systems was the object of considerable research conducted in the last decades. The vast majority of the investigations focused on the aerodynamic performance. However, aiming at minimizing the overall environmental impact of this technology requires a new effort to reduce the aeroacoustic noise associated with a Wells turbine's operation. As for other turbomachinery, rotor blade skew is hypothesized to affect aeroacoustic noise sources favorably. Because of the unique symmetry of the blade shape of any Wells turbine, skew here means an inclination of the stagger line exclusively in circumferential direction and hence incorporates a combination of blade sweep and dihedral. Based on a blade element momentum theory, a new blade design methodology for a Wells turbine with skewed blades is established. Then, the effect of blade skew is assessed systematically by numerical simulations and experiments. As compared to a state-of-the-art rotor with straight blades, optimal backward/forward blade skew from hub to tip delays the onset of stall and increases the range of unstalled operation by approximately 5% in terms of static pressure head. As a Wells turbine in an OWC power plant operates cyclically along its characteristic, any extension of stall-free operating range has the potential of improving the energy yield. The flow-generated sound in unstalled operation was decreased up to 3 dB by optimal backward/forward blade skew. However, the predominate noise benefit in terms of equivalent sound power along complete operating cycles is due to the extended operating range without excessive sound due to stall.

On the Impact of Geometric Variability on Fan Aerodynamic Performance, Unsteady Blade Row Interaction, and Its Mechanical Characteristics

Abstract: The focus of the present study is to assess and quantify the uncertainty in predicting the steady and unsteady aerodynamic performance as well as the major mechanical characteristics of a contrarotating turbofan, primarily due to geometric variations stemming from the manufacturing process. The basis of this study is the optically scanned blisk of the first rotor, for which geometric variations from blade to blade are considered. In a first step, selected profile sections of the first rotor were evaluated aerodynamically by applying the 2D coupled Euler/boundary-layer solver mises. Statistical properties of the relevant flow quantities were calculated firstly based on the results of the nine manufactured blades. In a second step, the geometric variations were decomposed into their corresponding eigenforms by means of principal component analysis (PCA). These modes were the basis for carrying out Monte Carlo (MC) simulations in order to analyze in detail the blade's aerodynamic response to the prescribed geometric variations. By means of 3D-computational fluid dynamics (CFD) simulations of the entire fan stage for all the nine scanned rotor 1 blade geometries, the variation of the overall stage performance parameters will be quantified. The impact of the instrumentation will be discussed, here partly doubling the standard deviation of the major performance indicators for the instrumented blades and also triggering a premature laminar/turbulent transition of the boundary layer. In terms of the unsteady blade row interaction, the standard deviation of the resulting blade pressure amplitude shall be discussed based on unsteady simulations, taking advantage of a novel harmonic balance approach. It will be shown that the major uncertainty in terms of the predicted blade pressure amplitude is in the aft part of the front rotor and results from upstream shock/blade interaction. Apart from the aerodynamic performance, an analysis of the mechanical properties in terms of Campbell characteristics and eigenfrequencies was carried out for each of the scanned blades of rotor 1, reflecting the frequency scattering of each eigenmode due to geometric variability.

Evaluation of unsteady pressure fields and forces in rotating airfoils from time-resolved PIV

Abstract: The instantaneous pressure fields and aerodynamic loads are obtained for rotating airfoils from time-resolved particle image velocimetry (TR-PIV) measurements. These allowed evaluating the contribution from the local acceleration (unsteady acceleration) to the instantaneous forces. Traditionally, this term has been neglected for wind turbines with quasi-steady flows, but results show that it is a dominant term in the wake where high temporal variations in the flow field are present due to vortex shedding. Briefly, time-resolved particle image velocimetry TR-PIV measurements are used to calculate flow velocity fields and corresponding spatial and temporal derivatives. These derivatives are then used in the Poisson equation to solve for the pressure field and later used in the integral momentum equation to solve for the instantaneous forces. The robustness of the measurements is analyzed by calculating the PIV uncertainty and the independence of the calculated forces. The experimental mean aerodynamic forces are compared with theoretical predictions from the blade element momentum theory showing good agreement. The instantaneous pressure field showed dependence with time in the wake due to vortex shedding. The contribution to the instantaneous forces from each term in the integral momentum equation is evaluated. The analysis shows that the larger contributions to the normal force coefficient are from the unsteady and the pressure terms, and the larger contribution to the tangential force coefficient is from the convective term.

Powering performance of a self-propelled ship in waves

Abstract: The ability to accurately predict the powering performance of a ship when travelling in waves is of high importance for the design of new ships. Almost a century of experience exists regarding how to predict the mean resistance increase in waves compared to calm water. Despite this, improvements in numerical models are still in high demand. Traditionally, the mean increase together with the calm water resistance and propeller open water curves are used to determine the powering performance. This thesis argues that, to achieve better predictions, a more holistic approach can be taken. A RANS based numerical approach to predicting the performance of a self propelled ship in waves is presented. The model is supported by a review of previous literature as well as new experiments to determine what phenomena need to be modelled. It is concluded that the surge force amplitude in waves is something that is not well studied but that has an impact on the propeller performance. The experiments show that this is likely to be harder to predict than the mean increase. Furthermore, the inclusion of RPM control in the model is seen as important to make it better suited for predicting the performance. In developing the numerical model, it is shown that the amplitude and phase of the viscous surge force are affected to some extent by the way the RANS equations are solved numerically. Recommendations on the choice of schemes are given based on several comparative studies where a limited TVD scheme is found to give the best representation of the flow. Furthermore, detailed analysis on how the boundary layer is affected by the passing waves is presented. A framework for coupling the RANS solver with a simplified propeller model is presented. This is a powerful tool that allows for a broad range of present and future studies regarding propeller modelling and RPM control for self propelled simulations in waves. The implementation of Blade Element Momentum theory in the framework is outlined and a correction able to achieve a satisfactory run time coupling in terms of identifying the propeller induced velocities from the total wake is presented. The coupled solver is found to be a computationally efficient tool for studying ship performance in waves. It is applied to study the propulsive performance of the KCS in unsteady inflow conditions. Reasonable agreement with experiments is found both for resistance and for propeller performance. Overall, the findings and methods presented here represent a contribution towards better predictions of the performance of self propelled ships in waves.

Flapwise non-linear dynamics of wind turbine blades with both external and internal resonances

Abstract: An investigation on the non-linear aeroelastic behavior of a wind turbine blade with both external and internal resonances is presented. The external resonance is a primary resonance that appears at the first flapwise mode; it can cause severe damage to blade. The internal resonance happens at the first two flapwise modes; it can enhance the energy transfer between two modes, and change blade dynamics in primary resonance. Three aspects including blade behavior in pure primary resonance (abbr. PPR; only considering external resonance), blade behavior in combination resonance (abbr. CR; including both external and internal resonances), and the influence of internal resonance (i.e. modal interaction) on external resonance are examined. A simple Bernoulli–Euler beam model, in which geometric non-linearity and unsteady aerodynamic force are considered, is used to describe the flapwise motion of blade. The perturbation method is applied to the infinite-degree-of-freedom discrete system, which is obtained from the original continuous system via Galerkin׳s method, to get dynamic responses. Amplitude–frequency curves of resonance modes in CR and PPR are derived, and the stability of the steady state motion of blade is judged. The strongest modal interaction between two resonance modes is taken into account, and then effects of modal interaction, excitation amplitude, damping and non-linearity on non-linear vibration properties of blade are analyzed. Also, influences of three designing parameters (inflow ratio, setting angle and coning angle) and two detuning on the non-linear behavior of blade are discussed for a concrete downwind turbine.

Time-accurate aeroelastic simulations of a wind turbine in yaw and shear using a coupled CFD-CSD method

Abstract: In the present study, aeroelastic simulations of horizontal-axis wind turbine rotor blades were conducted using a coupled CFD-CSD method. The unsteady blade aerodynamic loads and the dynamic blade response due to yaw misalignment and non-uniform sheared wind were investigated. For this purpose, a CFD code solving the RANS equations on unstructured meshes and a FEM-based CSD beam solver were used. The coupling of the CFD and CSD solvers was made by exchanging the data between the two solvers in a loosely coupled manner. The present coupled CFD-CSD method was applied to the NREL 5MW reference wind turbine rotor, and the results were compared with those of CFD-alone rigid blade calculations. It was found that aeroelastic blade deformation leads to a significant reduction of blade aerodynamic loads, and alters the unsteady load behaviours, mainly due to the torsional deformation. The reduction of blade aerodynamic loads is particularly significant at the advancing rotor blade side for yawed flow conditions, and at the upper half of rotor disk where wind velocity is higher due to wind shear.

Design of Flexible Propellers with Optimized Load-Distribution Characteristics

Abstract: The mathematical model and experimental verification of flexible propeller blades are presented in this paper. The propeller aerodynamics model is based on an extended blade-element momentum model, while the Euler–Bernoulli beam theory and Saint–Venant theory of torsion are used to account for bending and torsional deformations of the blades, respectively. The proposed blade-element momentum model extends the standard blade-element momentum theory with the aim of providing a quick and robust model of propeller action capable of treating high-aspect-ratio propeller blades with a blade axis of arbitrary geometry. Based on the proposed mathematical model, a static flexible propeller blade design procedure and its associated analysis algorithm are established. Dynamic aeroelastic phenomena like propeller flutter and divergence are not covered by the presented mathematical model, design, and analysis algorithm. Experimental validation was carried out with an objective of evaluating the performance of the devel...

Design and Experimentation of a 1 MW Horizontal Axis Wind Turbine

Abstract: 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.

Development of Free Vortex Wake Method for Aerodynamic Loads on Rotor Blades

Abstract: The aerodynamics of a wind turbine is governed by the flow around the rotor, where the prediction of air loads on rotor blades in different operational conditions and its relation to rotor structural dynamics is crucial for design purposes. One of the most important challenges in wind turbine aerodynamics is therefore to accurately predict the forces on the blade, where the blade and wake are modeled by different approaches such as the Blade Element Momentum (BEM) theory, the vortex method and Computational Fluid Dynamics (CFD). A free vortex wake method, based on the potential, inviscid and irrotational flow, is developed to study the aerodynamic loads. The results are compared with the BEM method, the GENUVP code and CFD.

Modeling of the Large Torsional Deformation of an Extremely Flexible Rotor in Hover

Abstract: This paper describes the refined modeling of the large torsional deformation of extremely flexible rotor blades with negligible structural stiffness. Equations of motion including flap bending and torsion, specifically tailored toward unconventional blades with a tip mass and experiencing large elastic twist angles, are derived using the extended Hamilton’s principle. In particular, the foreshortening of the twisted blade arising from the trapeze effect (also called bifilar effect) is explicitly included. Quasi-steady aerodynamic forces are calculated using the blade element momentum theory. The nonlinear coupled equations of motion are solved using a finite-element method. The analysis is used to predict the thrust as well as the spanwise distribution of flap bending and twist of an 18-in.-diam rotor with extremely flexible blades rotating at 1200 rpm at various collective pitch angles. These predictions are correlated with the measurement of loads obtained using a load cell, and the measurement of the d...

Comparison of the lifting-line free vortex wake method and the blade-element-momentum theory regarding the simulated loads of multi-MW wind turbines

Abstract: Design load simulations for wind turbines are traditionally based on the blade- element-momentum theory (BEM). The BEM approach is derived from a simplified representation of the rotor aerodynamics and several semi-empirical correction models. A more sophisticated approach to account for the complex flow phenomena on wind turbine rotors can be found in the lifting-line free vortex wake method. This approach is based on a more physics based representation, especially for global flow effects. This theory relies on empirical correction models only for the local flow effects, which are associated with the boundary layer of the rotor blades. In this paper the lifting-line free vortex wake method is compared to a state- of-the-art BEM formulation with regard to aerodynamic and aeroelastic load simulations of the 5MW UpWind reference wind turbine. Different aerodynamic load situations as well as standardised design load cases that are sensitive to the aeroelastic modelling are evaluated in detail. This benchmark makes use of the AeroModule developed by ECN, which has been coupled to the multibody simulation code SIMPACK.

Assessment of Beam and Shell Elements for Modeling Rotorcraft Blades

Abstract: A geometrically exact shell element is developed within the finite-element, multibody dynamics-based Rotorcraft Comprehensive Analysis System. The shell element accommodates transverse shear deformation as well as arbitrarily large displacements and rotations. The shell element is developed using an approach that allows for compatibility with other structural elements in the Rotorcraft Comprehensive Analysis System. It is validated by comparing its predictions with benchmark problems. The two-dimensional shell and one-dimensional beam finite-element analyses are compared for three typical blade configurations of varying slenderness ratio: a swept-tip blade, a blade with discontinuous chordwise elastic axis and center-of-gravity locations, and a blade with a flex beam. The purpose is to quantify the differences between two-dimensional-shell one-dimensional-beam finite elements for modeling rotor blades. There is good agreement between the one- and two-dimensional analyses in predicting the natural frequenc...

On the inverse problem of blade design for centrifugal pumps and fans

Abstract: The inverse problem of blade design for centrifugal pumps and fans has been studied The solution to this problem provides the geometry of rotor blades that realize specified performance characteristics, together with the corresponding flow field Here a three-dimensional solution method is described in which the so-called meridional geometry is fixed and the distribution of the azimuthal angle at the three-dimensional blade surface is determined for blades of infinitesimal thickness The developed formulation is based on potential-flow theory Besides the blade impermeability condition at the pressure and suction side of the blades, an additional boundary condition at the blade surface is required in order to fix the unknown blade geometry For this purpose the mean-swirl distribution is employed The iterative numerical method is based on a three-dimensional finite element method approach in which the flow equations are solved on the domain determined by the latest estimate of the blade geometry, with the mean-swirl distribution boundary condition at the blade surface being enforced The blade impermeability boundary condition is then used to find an improved estimate of the blade geometry The robustness of the method is increased by specific techniques, such as spanwise-coupled solution of the discretized impermeability condition and the use of underrelaxation in adjusting the estimates of the blade geometry Various examples are shown that demonstrate the effectiveness and robustness of the method in finding a solution for the blade geometry of different types of centrifugal pumps and fans The influence of the employed mean-swirl distribution on the performance characteristics is also investigated

Blade geometry transformation in optimization problems from the point cloud to the parametric form

Abstract: We consider the issues of transforming the blade geometry, which is conventionally defined as a set of points over several cross-sections, to parametric form that is necessary for the computer-aided solution of optimization problems. The method for coordinated movement of blade profile points under deformation within the optimization problem and the method of coordinated change of the profile parameters over the blade height, are proposed. An algorithm for the analytic representation of the profile specified discretely without loss of accuracy is described.

A Simplified Morphing Blade for Horizontal Axis Wind Turbines

Abstract: The aim of designing wind turbine blades is to improve the power capture ability. Since rotor control technology is currently limited to controlling rotational speed and blade pitch, an increasing concern has been given to morphing blades. In this paper, a simplified morphing blade is introduced, which has a linear twist distribution along the span and a shape that can be controlled by adjusting the twist of the blade's root and tip. To evaluate the performance of wind turbine blades, a numerical code based on the blade element momentum theory is developed and validated. The blade of the NREL Phase VI wind turbine is taken as a reference blade and has a fixed pitch. The optimization problems associated with the control of the morphing blade and a blade with pitch control are formulated. The optimal results show that the morphing blade gives better results than the blade with pitch control in terms of produced power. Under the assumption that at a given site, the annual average wind speed is known and the wind speed follows a Rayleigh distribution, the annual energy production of wind turbines was evaluated for three types of blade, namely, morphing blade, blade with pitch control and fixed pitch blade. For an annual average wind speed varying between 5~m/s and 15~m/s, it turns out that the annual energy production of the wind turbine containing morphing blades is 24.5~\% to 69.7~\% higher than the annual energy production of the wind turbine containing pitch fixed blades. Likewise, the annual energy production of the wind turbine containing blades with pitch control is 22.7~\% to 66.9~\% higher than the annual energy production of the wind turbine containing pitch fixed blades.