Blade Element Method Research Articles

Cavitation simulation on horizontal axis marine current turbines

In this paper, the occurrence of cavitation on horizontal axis marine current turbine blades has been investigated by numerical methods. To implicate the effects of cavitation on turbine performance, a momentum blade element method was used in conjunction with a boundary element method which adopts the section cavity lengths as inputs and computes the lift and drag coefficients of cavitating blade sections. Distribution of cavitation along the blades of marine current turbines was also modelled using a vortex lattice method. In order to assess the capability of the methods, marine current turbines tested previously under certain conditions were analyzed and the results were compared with the experimental data available in literature. Satisfactory agreement validated that the distribution of cavitation along the blade and the length of cavity at each blade section can be predicted adequately for a cavitating marine current turbine. Using the methods presented in this study, up to 30% theoretical loss in generated power is predicted for the particular case of a model turbine subjected to cavitation under specific test conditions.

Aerodynamic dissipation effects on the rotating blades of floating wind turbines

Due to the flexibility of their mooring systems, floating wind turbines are susceptible to large oscillations, which may compromise their performance and structural stability. Dissipation effects from wind–blade interactions and other sources are thus an important factor. In the design process the aerodynamic effects are often simulated through a quasi-static approach, whose accuracy is not guaranteed. In this study we numerically examine the aerodynamically generated added-mass and damping effects on the blades using a quasi-static blade-element method and an unsteady boundary-element method. The results based on unsteady simulation suggest that there exists a phase shift in the aerodynamic force as frequency increases, causing a switching from dissipation-dominated behavior in low frequency to a mixture of dissipation and inertia effects in high frequency. This is consistent with predictions via a simplified model with Theodorsen's theory. The quasi-static method, on the other hand, cannot predict this potentially important phenomenon. We also show that compared with other dissipation effects such as the wave radiation damping and the damping from the mooring system, the aerodynamic damping is smaller in magnitude and thus negligible in the responses of the platform itself. Nevertheless, its effect on the structural vibration of the tower may still be significant.

Flight Dynamics Analyses of a Propeller-Driven Airplane (I): Aerodynamic and Inertial Modeling of the Propeller

This paper focuses on aerodynamic and inertial modeling of the propeller for its applications in flight dynamics analyses of a propeller-driven airplane. Unsteady aerodynamic and inertial loads generated by the propeller are formulated using the blade element method, where the local velocity and acceleration vectors for each blade element are obtained from exact kinematic relations for general maneuvering conditions. Vortex theory is applied to obtain the flow velocities induced by the propeller wake, which are used in the computation of the aerodynamic forces and moments generated by the propeller and other aerodynamic surfaces. The vortex lattice method is adopted to obtain the induced velocity over the wing and empennage components and the related influence coefficients are computed, taking into account the propeller induced velocities by tracing the wake trajectory trailing from each of the propeller blades. Aerodynamic forces and moments of the fuselage and other aerodynamic surfaces are computed by using the wind tunnel database and applying strip theory to incorporate viscous flow effects. The propeller models proposed in this paper are applied to predict isolated propeller performances under steady flight conditions. Trimmed level forward and turn flights are analyzed to investigate the effects of the propeller on the flight characteristics of a propeller-driven light-sports airplane. Flight test results for a series of maneuvering flights using a scaled model are employed to run the flight dynamic analysis program for the proposed propeller models. The simulations are compared with the flight test results to validate the usefulness of the approach. The resultant good correlations between the two data sets shows the propeller models proposed in this paper can predict flight characteristics with good accuracy.

Comparative CFD study of the effect of the presence of downstream turbines on upstream ones using a rotational speed control system

The effect of a downstream turbine on the production of a turbine located upstream of the latter is studied in this work. This is done through the use of two CFD simulation codes, namely OpenFOAM and EllipSys3D, which solve the Navier-Stokes equations in their incompressible form using a finite volume approach. In both EllipSys3D and OpenFoam, the LES (Large Eddy Simulation) technique is used for modelling turbulence. The wind turbine rotors are modelled as actuator disks whose loading is determined through the use of tabulated airfoil data by applying the blade-element method. A generator torque controller is used in both simulation methods to ensure that the simulated turbines adapt, in terms of rotational velocity, to the inflow conditions they are submited to. Results from both simulation codes, although they differ slightly, show that the downstream turbine affects the upstream one when the spacing between the turbines is small. This is also suggested to be the case looking at measurements performed at the Lillgrund offshore wind farm, whose turbines are located unusually close to each other. However, for distances used in today's typical wind farms, this effect is shown by our calculations not to be significant.

How to improve open rotor aerodynamics at cruise and take-off

AbstractA key challenge in open rotor design is getting the optimum aerodynamics at both the cruise and take-off conditions. This is particularly difficult because the operation and the requirements of an open rotor are very different at cruise compared to takeoff. This paper uses CFD results to explore the impact of various design changes on the cruise and take-off flow-fields. The paper then considers how a given open rotor design is best operated at take-off to minimise noise whilst maintaining high thrust. The main findings are that various design modifications can be applied to control the flow features that lead to lost efficiency at cruise and increased noise emission at take-off. A breakdown of the lost power terms from CFD solutions demonstrates how developments in open rotor design have led to reduced aerodynamic losses. At take-off, the operating point of the open rotor should be set such that the non-dimensional lift is as high as possible, without causing significant flow separation. This can be achieved through suitable amounts of re-pitch and speed up applied to a design. Comparisons with fully three-dimensional CFD show that the amount of re-pitch required can be determined using simplified methods such as two-dimensional CFD and a Blade Element Method.

A methodology for the transient behavior of horizontal axis hydrokinetic turbines

In recent years, increasing attention is being given to the study of hydrokinetic turbines for power generation due to the use of clean energy by using renewable sources. This paper aims to present a general methodology for the efficient design of horizontal axis hydrokinetic turbines with variable rotation. The approach uses the Blade Element Method (BEM) for determining the power coefficient of the turbine. The modeling of the hydrokinetic rotor is coupled with the model of the drive line of the system, including the multiplier and the electric generator. Therefore, the modeling of the whole system comprises the hydrodynamic information of the rotor and the characteristics of the inertia of whole system, frictional losses and electromagnetic torque of the generator. The results of numerical simulation are obtained for the rotational speed of the rotor as well as the results of the torque, mechanical and electrical power.

Improving actuator disk wake model

The wind energy industry has traditionally relied on simple wake models for estimating Wind Turbine (WT) wake losses. Despite limitations, low requirements in terms of detailed rotor information makes their use feasible, unlike more complex models, such as Blade Element Method (BEM) or Actuator Line. Froude's Actuator Disk (AD) does not suffer the simpler model's limitation of prescribing the wake through a closed set of equations, while sharing with them the low rotor data requirements. On the other hand they require some form of parametrization to close the model and calculate total thrust acting on the flow. An Actuator Disk model was developed, using an iterative algorithm based on Froude's one-dimensional momentum theory to determine the WT's performance, proving to be successful in estimating the performance of both machines in undisturbed flow and in the wake of an upstream machines. Before Froude's AD limitations compared to more complex rotor models, load distributions emulating those of a BEM model were tested. The results show that little impact is obtained at 3 rotor diameters downstream and beyond, agreeing with common definition of a far-wake that starts at 1-2 diameters downstream, where rotor characteristics become negligible and atmospheric flow effects dominate.

Hierarchical Methodology for the Numerical Simulation of the Flow Field around and in the Wake of Horizontal Axis Wind Turbines: Rotating Reference Frame, Blade Element Method and Actuator Disk Model

A hierarchy of computational methods for Horizontal Axis Wind Turbine (HAWT) flow field is proposed, focusing on rotor models for Reynolds-Averaged Navier-Stokes simulations. Three models are systematically compared to determine their adequacy to capture performance and wake dynamics, and the trade-offs between accuracy and computational cost. The Rotating Reference Frame model is prescribed for detailed flow field studies, specifically at the root and blade tip. The Blade Element Model does not reproduce the near wake region but successfully predicts the velocity deficit in the axisymmetric far wake, and the power and torque coefficients. The Actuator Disk Model underestimates the velocity deficit in the far wake, but can be corrected to perform simulations of large wind farms. This methodology is applied to a canonical rotor and compared against experimental data. These models span three orders of magnitude in computational time and cost for the study of HAWT aerodynamic performance and wake interaction.

Actuator Disk Theory—Steady and Unsteady Models

In this paper, the classical work on steady actuator disk theory is recalled and the interpretation of the flow as the continuous shedding of vortex rings of constant strength that causes the slip stream is shown to be consistent with the classical model, yet offers a different approach that provides more flexibility for the extension to unsteady flow. The ring model is in agreement with the conservation law theorems which indicate that the axial inductance inside the streamtube, far downstream, is twice that at the rotor disk. The actuator disk relationship between the power and the axial inductance at the rotor plane has been used previously to construct the prescribed wake in the 3D vortex line model (VLM) of the author. The local pitch of the vortex sheet helices is based on the axial inductance along the streamtube, therefore, it is important to be able to calculate the axial inductance in all cases. In unsteady flow, the strength of the shed rings varies with power absorbed by the rotor and a new relationship between the two is derived to first-order, using the unsteady Bernoulli equation, which allows to calculate the inductance at the rotor and in the wake with the Biot-Savart law, even in cases where the Betz limit is exceeded. This more rigorous model can replace the semi empirical models such as dynamic stall and dynamic inflow used in the blade element method (BEM). The proposed new model has been incorporated in the VLM and applied to two sets of experiments, the Tjaereborg in-field tests and the NREL wind tunnel campaign, for which test data has been collected and serves for the comparison. The simulations show an overall good agreement with the experimental data. In some tests, the power coefficient exceeds the Betz limit, in which cases there are no solutions to the steady actuator disk theory, but the new model provides a solution for the inductance even in this case.

OffWindSolver: Wind farm design tool based on actuator line/actuator disk concept in OpenFoam architecture

Wind energy is a good alternative to meet the energy requirements in some parts of the world; however the efficiency of wind farm depends on the optimized location of the wind turbines. Therefore a software tool that is capable of predicting the in-situ performance of multiple turbine installations in different operating conditions with reliable accuracy is needed. In present study wind farm layout design tool OffWindSolver is developed within the OpenFoam architecture. Unsteady PisoFoam solver is extended to account for wind turbines, where each turbine is modeled as a sink term in the momentum equation. Turbine modeling is based on actuator line concepts derived from SOWFA code, where each blade of the turbine is represented as a line. The loading on each line/blade of the turbine is estimated using the Blade Element Method (BEM). The inputs for the solver are tabulated airfoil aerodynamic data, dimension and height of the wind turbines, wind magnitude and direction. OffWindSolver is validated for a real wind farm - Lillgrund offshore facility in Sweden/Denmark operated by Vattenfall Vindkraft AB. Because of the scale of the computation, we only examine the effect of wind from one direction at one speed. In the absence of time dependent Marine Atmospheric Boundary Layer (MABL), a log wind profile with surface roughness of 0.04 is used at the inlet. The simulated power production of each turbine is compared to the field data and large-eddy simulation. The overall power of the wind farm is well predicted. The simulation shows the significant decreases of the power for those turbines that were in the wake.

Stability and power optimality in time-periodic flapping wing structures

This paper investigates the nonlinear dynamics of a vehicle with two flexible flapping wings. The body dynamics and the wings’ deformation are monolithically grouped into a single system of equations, with aerodynamics accounted for by a quasi-steady blade element method. A periodic shooting method is then used to locate closed orbits of this non-autonomous system, and Floquet multipliers assess the linearized stability about the nonlinear orbit. This framework is then exposed to a gradient based optimizer, in order to quantify the role of wing planform variables, wing structure variables, and kinematic actuation variables in obtaining vehicles with superior open-loop stability characteristics, and/or low-power requirements.

Experimental and numerical study of flow around a wind turbine rotor

An improved model of an actuator surface is proposed, representing the flow around a wind turbine. This model was developed in conjunction with a Navier-Stokes solver using a blade element method for the calculation of power and wake development. Blades have been replaced with thin surfaces, and a boundary condition of ‘pressure discontinuity’ has been applied with rotor inflow and blade-section characteristics. The proposed improvement consists of applying tangential body forces along the chord, in addition to normal body forces resulting from pressure discontinuity along the blade cross-section. The proposed model has been validated for the flow around a horizontal-axis wind turbine. The results obtained from the proposed model are compared with the experimental results obtained from PIV-wind tunnel techniques. The comparison has displayed the necessity of the proposed model for accurate reproduction of the wake behind rotor. The rapidity of calculation, in comparison to full-geometry modelling, appears to be promising for wind farm simulations.

Numerical investigations of the effects of different arrays on power extractions of horizontal axis tidal current turbines

As the tidal current industry grows, power extraction from tidal sites has received widespread attention. In this paper, a blade element actuator disk model that is coupled with the blade element method and a three-dimensional Navier–Stokes code is developed to analyse the relationship between power extraction and the layout of turbine arrays. First, a numerical model is constructed to simulate an isolated turbine and the model is validated using experimental data. Then, using this validated model, the power extraction of horizontal axis tidal current turbines using different tidal turbine arrays and rotation directions is predicted. The results of this study demonstrate that staggered grid array turbines can absorb more power from tidal flows than can rectilinear grid array turbines and that staggered grid array turbines are less affected by the rotation of upstream turbines. In addition, for staggered gird arrays, the relationships between power coefficients, lateral distance and longitudinal distance are discussed. The appropriate lateral distance is approximately 2.5 turbine diameters, whereas for the longitudinal distance, the largest value possible should be used. The relative power coefficient can achieve 3.74 when the longitudinal distance is 6 times the turbine diameter. To further increase the power extraction, this study suggests an improved staggered grid array layout. The relative power coefficient of the improved four-row turbine arrays is approximately 3–4% higher than that of the original arrays and will increase as the distance between the second-row and third-row increases. Considering only the first two rows of turbines, the total power extraction can be 11% higher than for an equivalent number of isolated turbines.

Actuator Disk 모델 기반의 로터 유입류 해석을 위한 OpenFOAM 알고리즘 확장

The purpose of current study is to develop and verify the newly developed solver for analyzing rotor flow using the open-source code. The algorithm of standard solver, OpenFOAM, is improved to analyze the rotor inflow with and without fuselage. For the calculation of the rotor thrust, the virtual blade method based on the blade element method is employed. The inflow velocities on the rotor disk used to specify the effective angle of attack, have been included in the solver. The results of the current rotor inflow analysis are verified by comparing with other experimental and numerical results. It was confirmed that the modified solver provides satisfactory results for rotor-fuselage interaction problem.

동적 유입류 모델을 이용한 회전익기 전진비행 공탄성 해석

본 논문에서는 비정상 공기력을 모델링하기위해 Peters-He의 동적유입류모델을 고려한 2차원 준정상 공기력 이론을 적용하여 회전익기 전진비행에 대한 공탄성 해석을 수행하였다. 또한, 공력탄성학적 안정성 해석을 수행하기 위하여, 전진비행 시 주기적인 특성을 갖는 비선형 정적 트림 해를 얻기 위해 동체 평형을 고려한 연계 트림 해석을 통한 완전 유한요소 방정식을 이용하였다. 동적유입류모델의 공력과 구조 특성을 검증하기 위해 유도 유입류와 깃끝에서의 구조변형을 타 수치해석결과와 비교하였다. 또한, 공탄성 안정성을 검증하기 위해 두 모델의 래그 감쇠값을 비교하였다. In this study, the aeroelastic analysis of rotorcraft in forward flight has been performed using dynamic inflow model to handle unsteady aerodynamics. The quasi-steady airload model based on the blade element method has been coupled with dynamic inflow model developed by Peters and He. The nonlinear steady response to periodic motion is obtained by integrating the full finite element equation in time through a coupled trim procedure with a vehicle trim for stability analysis. The aerodynamic and structural characteristics of dynamic inflow model are validated against other numerical analysis results by comparing induced inflow and blade tip deflections(flap, lag). In order to validate aeroelastic stability of dynamic inflow model, lag damping are also compared with those of linear inflow model.

Development of an Unsteady Aerodynamic Analysis Module for Rotor Comprehensive Analysis Code

The inherent aeromechanical complexity of a rotor system necessitated the comprehensive analysis code for helicopter rotor system. In the present study, an aerodynamic analysis module has been developed as a part of rotorcraft comprehensive program. Aerodynamic analysis module is largely classified into airload calculation routine and inflow analysis routine. For airload calculation, quasi-steady analysis model is employed based on the blade element method with the correction of unsteady aerodynamic effects. In order to take unsteady effects - body motion effects and dynamic stall - into account, aerodynamic coefficients are corrected by considering Leishman-Beddoes's unsteady model. Various inflow models and vortex wake models are implemented in the aerodynamic module to consider wake induced inflow. Specifically, linear inflow, dynamic inflow, prescribed wake and free wake model are integrated into the present module. The aerodynamic characteristics of each method are compared and validated against available experimental data such as Elliot's induced inflow distribution and sectional normal force coefficients of AH-1G. In order to validate unsteady aerodynamic model, 2-D unsteady model for NACA0012 airfoil is validated against aerodynamic coefficients of McAlister's experimental data.

Analysis and Design of a Flap-Equipped Low-Twist Rotor for Hover

This study evaluates the potential benefits that fixed but deployable trailing-edge flaps may have on a low-twist hovering rotor using a blade-element method combined with two-dimensional and three-dimensional computational fluid dynamics. Low blade twist is beneficial in terms of forward-flight performance, which, combined with a deployable flap, could also offer good hover performance, resulting in an overall better design in comparison with a plain twisted blade. To evaluate this concept, a parametric study of flap configurations was conducted using a simple blade-element method based on computational-fluid-dynamics-generated two-dimensional aerodynamics. This simple model indicated that up to 6 deg of blade twist could be recovered at high rotor thrust by using an optimized flap configuration. Performance improvements were also obtained for outboard slotted-flap configurations. The optimum slotted-flap designs were also evaluated using three-dimensional computational fluid dynamics, which confirmed that an inboard flap combined with a low-twist ( 7 deg) rotor blade matched the performance of a plain blade with -13 deg of twist. A blended-flap configuration was also applied and evaluated. This simpler design demonstrated the equivalent performance of a clean rotor with 10 deg of blade twist, providing further evidence of the potential of the fixed inboard flap concept.

10 kW급 수평축 풍력 터빈 로터 블레이드의 공력 설계

10 kW급 수평축 풍력 터빈의 로터를 개발하기 위해 블레이드의 공력 설계 절차를 체계적으로 연구하고 실행하였다. 운동량 이론과 깃 요소법에 근거한 역 설계 방법을 확립하고, 이를 이용하여 주어진 공력 분포에 따른 근사 최적 형상을 설계하였다. 설계된 형상은 공군사관학교의 풍동에서 검증되었고, 본 설계를 통하여 실제로 제작된 로터로부터 실측 데이터를 취득하여 비교하였다. 본 연구를 통하여 저자들은 풍력 터빈 블레이드의 설계 방법에 대한 체계적 기술을 축적하고, 나아가 같은 방법을 중대형 시스템으로 확장하기 위한 기술적 노하우를 취득하였다. The procedure for the aerodynamic design of the rotor blades for 10 kW-level HAWT (horizontal axis wind turbine) has been investigated to be practiced systematically. The approximately optimal shape was designed using an inverse method based on the momentum theory and the blade element method. The configuration was tested in the wind tunnel of the Korea Air Force Academy, and the data was compared with those obtained from the real system manufactured from the present design. From this research, the authors established the systematic technolo for wind turbine blades, and set up the technical procedure which can be extended for the future design of middle and large sized wind turbines.

Actuator surface hybrid model

A hybrid model has been developed in order to represent the flow downstream a wind turbine rotor. The blades are replaced by their mean surfaces and a "pressure jump" boundary condition is applied here. The hybrid model combines CFD solver with a blade element method (BEM). The solving method is iterative: at the beginning of iteration a BEM determines the pressure discontinuities along the blade span, using the rotor inflow and the aerodynamic properties of blade sections. Then the CFD solver applies this pressure discontinuity in order to model the blade forces and the wake downstream the rotor. At the end of iteration the obtained rotor inflow, the wake development and the residuals are compared with those obtained from previous iteration. If the required precision is attained, the calculation stops. The solution is obtained after thousands of iterations, depending on the number of nodes, residuals etc. The approach of replacing blades by pressure discontinuity surfaces is validated by comparison the wakes in the cases of flat plate and the S809 airfoil. Finally, the proposed hybrid model is used to calculate the performance of NREL Phase VI wind turbine and the results obtained are satisfactory.

Further dual purpose evolutionary optimization of small wind turbine blades

Much work has been done to maximise the power extraction of wind turbine blades. However, small wind turbines are also required to be self starting and whilst blades designed for maximum power extraction can be optimised analytically, these blades often have poor starting performance. The numeric method of Differential Evolution is used here to maximise for both power and starting performance. Standard blade element theory is used to calculate the power coefficient, and a modified blade element method for starting time. The chord and twist of each blade element make up the genes for evolution. Starting times can be improved by a factor of 20 with only a small reduction in power coefficient. With the introduction of the tip speed ratio as an additional gene, up to 10% improvement in power coefficient was achieved. A second study was done in another case where analytical optimisation is not possible; the inclusion of tip losses. The inclusion resulted in only a small increase in the optimum chord in the tip region which becomes less noticeable at lower tip speed ratios.