Free Wake Model Research Articles

Development and application of a dynamic stall model for rotating wind turbine blades

In unsteady conditions of wind turbines, both the dynamic stall phenomenon and the three-dimensional (3D) rotational effect affect the rotor aerodynamics. The dynamic stall mechanism for rotating wind turbine blades is first investigated. Through the comparison of the aerodynamic data between the rotating blade and the two-dimensional (2D) airfoil, the normal force slope in the attached flow and the separation point expression in the separated flow are modified in the Beddoes-Leishman (B-L) dynamic stall model for rotating NREL wind turbine blades. The modified model is validated by the comparison between the calculation results and the experimental results of the lift and drag coefficients at different radial positions. Both the hysteresis loop shapes and the calculation values are closer to the experiment than the 2D dynamic stall model. The present dynamic stall model is then coupled to a free vortex wake model. The coupled model is used to calculate the unsteady blade aerodynamic loads and the low speed shaft torque of the NREL wind turbine in a yawed condition. The accuracy is greatly improved by the corrections presented in the paper.

Validation of a three-dimensional viscous–inviscid interactive solver for wind turbine rotors

MIRAS is a newly developed computational model that predicts the aerodynamic behavior of wind turbine blades and wakes subject to unsteady motions and viscous effects. The model is based on a three-dimensional panel method using a surface distribution of quadrilateral singularities with a Neumann no penetration condition. Viscous effects inside the boundary layer are taken into account through the coupling with the quasi-3D integral boundary layer solver Q3UIC. A free-wake model is employed to simulate the vorticity released by the blades in the wake. In this paper the new code is validated against measurements and/or CFD simulations for five wind turbine rotors, including three experimental model rotors [20–22], the 2.5 MW NM80 machine [23] and the NREL 5 MW virtual rotor [24]. Such a broad set of operational conditions and rotor sizes constitutes a very challenging validation matrix, with Reynolds numbers ranging from 5.0⋅104 to 1.2⋅107.

Multibody analyses for performance and aeromechanics of a rotor in low-speed flight

Purpose – This paper aims to correlate the flexible multibody analysis for the performance, blade airloads, rotor pitch control angles, and blade structural loads of a full-scale utility helicopter rotor in low-speed forward flight with wind tunnel test and flight test data. Design/methodology/approach – A nonlinear flexible multibody dynamics analysis code, DYMORE, is used to analyze the performance and aeromechanics of a utility helicopter rotor in low-speed forward flight. The main rotor system is modeled using various multibody elements such as rigid bodies, nonlinear elastic beams, mechanical joints, and elastic springs/dampers. The freewake model is used to capture rotor wakes more elaborately in low-speed forward flight. Findings – Fair to good correlations of rotor performance such as figure of merit in hover, rotor power, propulsive force, and lift in low-speed forward flight are achieved with sweeps of the thrust, rotor shaft tilting angle, and advance ratio, against wind tunnel test data. The b...

Theoretical modelling of wakes from retractable flapping wings in forward flight

A free-wake method is used to simulate the wake from retractable, jointed wings. The method serves to complement existing experimental studies that visualise flying animal wakes. Simulated wakes are shown to be numerically convergent for a case study of the Rock Pigeon in minimum power cruising flight. The free-wake model is robust in simulating wakes for a range of wing geometries and dynamics without requiring changes to the numerical method. The method is found to be useful for providing low order predictions of wake geometries. However, it is not well suited to reconstructing 3d flowfields as solutions are sensitive to the numerical mesh node locations.

Loosely coupled multibody dynamics–CFD analysis for a rotor in descending flight

This paper conducts a loose-coupling analysis using the nonlinear flexible multibody dynamics, DYMORE, and the computational fluid dynamics (CFD), KFLOW, for a rotor correlation with the wind tunnel test data in descending flight. The present study investigates the three test cases of the HART II (second Higher-harmonic control Aeroacoustic Rotor Test): baseline (BL), minimum noise (MN), and minimum vibration (MV). The DYMORE/KFLOW coupled analysis uses two different models: an isolated rotor model and a rotor–fuselage model. The coupled analysis results are correlated with both the measured data and the stand-alone DYMORE analysis with the freewake model. Among the predicted sets of results, the coupled analysis using a rotor–fuselage model shows good agreement of the section normal forces and gives reasonable prediction of the trim control angles, against the measured data. As compared with the coupled analysis using an isolated rotor model, the rotor–fuselage model improves the phase of blade elastic torsion deformations in the BL case. In all three test cases, the coupled analyses show improved predictions on the flap bending moment than those by the stand-alone DYMORE analysis, while the inclusion of a fuselage model has only marginal effect on the blade structural loads predictions between the coupled analyses. It is observed that the inclusion of a fuselage model in the coupled analysis induces stronger upwash over the front disk region resulting in a close agreement with the measured data for the vortex positions, especially in the advancing side.

Comprehensive multibody dynamics analysis for rotor aeromechanics predictions in descending flight

AbstractThis paper studies the rotor aeromechanics in descending flight using a nonlinear flexible multibody dynamic analysis code, DYMORE. A freewake model is included in DYMORE to improve the rotor wake modelling. The wind-tunnel test data of the Higher-harmonic Aeroacoustics Rotor Test (HART) II rotor, with and without higher harmonic pitch control (HHC), and the flight test data of the full-scale utility helicopter rotor in descent are used for the aeromechanics correlation at an advance ratio of 0·15. The blade-vortex interaction (BVI) airloads are reasonably predicted for both the HART II and utility helicopter rotors, although some BVI peaks are missed on the advancing sides for both the rotors. The flap deflections and elastic torsion deformations at the blade tip are fairly correlated against the measured data of the HART II rotor. The correlation of blade structural moments for both HART II and utility helicopter rotors are not as good as the lift predictions; however, a reasonable prediction is obtained for the utility helicopter rotor.

Unsteady Aerodynamic Analysis and Wake Simulation of Helicopter Rotors using the Time-Domain Panel Method

An unsteady panel method based on potential flow theory is developed for unsteady aerodynamic analysis of helicopter rotors. The panel method uses a piecewise constant source and doublet singularities in the solution. This potential-based panel method is based on the Dirichlet boundary condition coupled with a time-stepping method. The proposed method uses a time-stepping loop to simulate the unsteady motion of helicopter rotors. A free wake model is used for the wake simulation of a helicopter rotor. The proposed method is validated by comparing our results with experimental data. The incompressible results of the proposed method for helicopter rotors are in good agreement with the experimental data for hovering and forward flight. The proposed method can be used for practical applications such as aerodynamic designs and the analysis of various helicopter rotor configurations.

Influence of Wake Effects and Inflow Turbulence on Wind Turbine Loads

Wind turbines are emerging as an exciting and rapidly expanding form of renewable energy. However, there are numerous technological challenges that must be overcome before wind energy provides a significant amount of power in the United States. One of the primary challenges in wind turbine design and analysis is accurately accounting for the wake. This study represents an initial step towards including wake effects in wind turbine design and analysis codes. A free wake model is developed using a time marching vortex line method, and subsequently verified and validated against existing results. The model is then used to examine time step requirements in the presence of inflow turbulence. Finally, comparisons are made between the developed free wake model and typical aerodynamic modeling approaches such as Blade Element Momentum Theory and Dynamic Inflow. For the configurations considered, blade time step sizes of 10° in azimuthal angle are adequate for capturing the effect of inflow turbulence on the wake. Finally, the inability of Blade Element Moment Theory and Dynamic Inflow to predict blade loads with combined inflow turbulence and wake effects is demonstrated.

Wake Effects of Free-Wake Model on Aeroelastic Behavior of Hovering Rotors

The wake effects on aeroelastic deflections and aerodynamics for the isotropic and composite rotor blades have been investigated. To take into account the large deflections and rotations of rotor blades, a large-deflection beam modelwas used. A free-wake model basedon vortex-lattice method wasused to obtain the aerodynamic forces while considering wake effects. Newton–Raphson iteration method was applied to the aeroelastic analysis to obtain the numericalsolutions.The flap,lag,andtorsiondeflectionsconsideringwakeeffectsbyusingthefree-wakemodelwere investigated and compared with the results using two-dimensional quasi-steady model. Finally, aerodynamic changes after aeroelastic deflections were investigated.

Validation of comprehensive dynamics analysis predictions for a rotor in descending flight

PurposeThe purpose of this paper is to evaluate the prediction capability of comprehensive structural dynamics (CSD) analysis codes for the higher harmonic control aeroacoustic rotor test (HART) II data.Design/methodology/approachA nonlinear flexible multibody dynamics analysis code DYMORE, as well as the comprehensive analytical model of rotorcraft aerodynamics and dynamics (CAMRAD) II, are used to perform the task. The predicted results on rotating free vibration analysis, airloads, blade elastic motions, and structural moments are correlated with the measured data for the baseline, minimum noise, and minimum vibration cases.FindingsThe DYMORE analysis results with a free wake model show a good performance in capturing blade vortex interaction peaks in the prediction of section normal forces but apparently with a phase shift problem. The high‐frequency behavior in the airloads signal does not affect much on the aeroelastic response and structural moments of the rotor.Originality/valueThe present approach uses two separate CSD codes to systematically validate the HART II data. The accuracy of each code on structural dynamic aspects of HART II rotor is assessed using a consistent set of inputs. The effects of blade tip deflections on the interaction of blades and their trailed vortices leading to a reduced noise emission are also investigated.

Wind turbine aerodynamics and loads control in wind shear flow

Wind turbine is subjected to some asymmetrical effects like wind shear, which will lead to unsteady blade airloads and performance. Fatigue loads can lead to damage of turbine components and eventually to failures. It is evident that the variation of the velocity over the rotor disc has an influence on the blade and introduces both flap-wise and edge-wise fatigue damage on the blade as a result of moment fluctuations in the two directions. The flap-wise moments on the blade are the origin of the rotor yaw and tilt moments which transmit to the turbine structure through the drive train to the yaw system and the tower. A lifting surface method with time marching free wake model is used to investigate the periodic unsteady nature in the wind shear. Individual pitch control (IPC) that is applied nowadays is the most advanced active control to reduce the fatigue. The blade airloads and performance of the turbine are also predicted under IPC control. It is found that IPC of the fluctuating blade root flap-wise moment can reduce the flap-wise fatigue damage remarkably while the blade root edge-wise moments are less sensitive to the varying blade pitch than the blade root flap-wise moments.

Fractal boundaries of basin of attraction of Newton–Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries.

General momentum theory for wind turbines at low tip speed ratios

ABSTRACTGeneral momentum theory is used to study the behaviour of the ‘classical’ free vortex wake model of Joukowsky. This model has recently attained considerable attention as it shows the possibility of achieving a power performance that greatly exceeds the Lanchester‐Betz limit for rotors running at low tip speed ratios. This behaviour is confirmed even when including the effect of a centre vortex, allowing azimuthal velocities and the associated radial pressure gradient to be taken into account in the axial momentum balance without any simplifying assumptions. It is shown that the most likely explanation for the anomalous behaviour at small tip speed ratios is that the influence of the lateral component of pressure and friction is neglected in the axial momentum theorem. A refined model is proposed that remedies the problem of using the axial momentum theorem and by which the power coefficient never exceeds the Lanchester‐Betz limit and which tends to zero at zero tip speed ratio. Copyright © 2010 John Wiley & Sons, Ltd.

Correlation study of a rotor in descending flight using DYMORE with a freewake model

In this work, the Blade Vortex Interaction (BVI) airloads characteristic for a rotor in descending flight condition is investigated using a nonlinear flexible multibody dynamics analysis code DYMORE. A free vortex wake model is incorporated into the comprehensive analysis system and improvement of airloads prediction as well as collective and cyclic pitch control settings is obtained over the finite-state dynamic inflow model that is adopted in the conventional DYMORE analysis. The three test conditions in the HART (Higher harmonic control Aeroacoustic Rotor Test) II are considered to illustrate the present investigation. It is found that the BVI airloads characteristic is significantly influenced by the higher harmonic pitch control inputs. The influence of BVI oscillatory peaks along with the miss-distance between the blade and the vortices is studied in detail to identify the mechanism of reducing noise and vibration in the HART II experiment.

Comprehensive Code Validation on Airloads and Aeroelastic Responses of the HART II Rotor

In this work, the comprehensive structural dynamics codes including DYMORE and CAMRAD II are used to validate the higher harmonic control aeroacoustic rotor test (HART) II data in descending flight condition. A total of 16 finite elements along with 17 aerodynamic panels are used for the CAMRAD II analysis; whereas, in the DYMORE analysis, 10 finite elements with 31 equally-spaced aerodynamic panels are utilized. To improve the prediction capability of the DYMORE analysis, the finite state dynamic inflow model is upgraded with a free vortex wake model comprised of near shed wake and trailed tip vortices. The predicted results on aerodynamic loads and blade motions are correlated with the HART II measurement data for the baseline, minimum noise and minimum vibration cases. It is found that an improvement of solution, especially for blade vortex interaction airloads, is achieved with the free wake method employed in the DYMORE analysis. Overall, fair to good correlation is achieved for the test cases considered in this study.

Hybrid Navier-Stokes/Free-Wake Method for Modeling Blade-Vortex Interactions

Techniques for accurate capturing of rotor blade-vortex-interaction phenomena are discussed. A number of algorithmic enhancements have been systematically examined, including geometric conservation law, refined metric and Jacobian computations, higher-order spatial and second-order temporal accuracy schemes, and embedded grids. The use of the geometric conservation law and refined metric computation were found to reduce nonphysical mass accumulation errors. These enhancements improve stability and accuracy of the higher-order schemes near far-field boundaries and in the vicinity of highly skewed cells. Embedded grids with an increased grid density were found to improve the predictions. It was also observed that the free-wake model (and, in particular, the determination of the trailing tip-vortex release point) plays a critical role in the blade-vortex-interaction prediction.

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.

A panel method free‐wake code for aeroelastic rotor predictions

AbstractA panel method free‐wake model to analyse the rotor flapping is presented. The aerodynamic model consists of a panel method, which takes into account the three‐dimensional rotor geometry, and a free‐wake model, to determine the wake shape. The main features of the model are the wake division into a near‐wake sheet and a far wake represented by a single tip vortex, and the modification of the panel method formulation to take into account this particular wake description. The blades are considered rigid with a flap degree of freedom. The problem solution is approached using a relaxation method, which enforces periodic boundary conditions. Finally, several code validations against helicopter and wind turbine experimental data are performed, showing good agreement. Copyright © 2009 John Wiley & Sons, Ltd.

회전익기 통합해석프로그램을 위한 공력해석코드 개발

본 논문에서는 회전익기 통합해석프로그램개발의 일환으로 공력해석코드를 개발 및 검증하였다. 기본적인 공력하중은 익형 공력테이블을 이용한 깃요소이론을 기반으로 계산하였고, 로터의 유도 유입류를 계산하기 위해 선형유입류 모델, 동적유입류 모델, 지정후류모델, 자유후류 모델 등 여러 유입류 예측기법을 사용하였다. 각 모델의 특성을 파악하기 위해 Elliott 등의 유도 유입류 실험결과와 AH-1G 실험결과의 국소 수직력계수를 비교 및 검증하였다. In this study, an aerodynamic performance analysis code has been developed as a part of rotorcraft comprehensive program. Airloads on rotor blades are calculated based on the blade element theory with look-up tables of aerodynamic coefficients of 2-D airfoils. In order to calculate rotor induced inflow, various inflow prediction methods such as 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 inflow distribution and sectional normal force coefficients of AH-1G.

능동 비틀림 제어기법을 이용한 복합재료 로터 블레이드의 진동 억제

능동 비틀림 제어기법을 이용한 복합재료 로터 블레이드의 헬리콥터 진동억제에 대한 수치연구를 수행하였다. 허브에 작용하는 진동하중 억제를 위해 복합재료 블레이드의 탄성 연계와 함께 압전 소재의 전단변형 메커니즘을 이용하였다. 로터 블레이드는 표면에 압전 작동기를 부착한 박벽 상자형 단면을 갖는 복합재료 보로 모델링하였다. 회전익에 대한 지배 운동방정식은 Hamilton 원리를 이용하여 구성하였고, 공력하중은 자유후류모델을 포함하는 비정상 공력 이론을 이용하여 구했다. 다양한 탄성연계 적층과 능동 작동기를 부착한 복합재료 블레이드에 대해 허브진동 하중 특성을 고찰하였다. 수치해석 결과 최적 제어 알고리듬을 적용하여 <TEX>$N_b$</TEX>/rev 진동하중을 대폭 줄일 수 있음을 보였다. In this study, an assessment is made for the helicopter vibration reduction of composite rotor blades using an active twist control concept. The piezoceramic shear actuation mechanism along with elastic couplings of composite blades is used for vibration reduction. The rotor blades are modeled as composite box-beams with actuator layers bonded on the outer surfaces of the thin-walled section. The governing equations of motion for helicopter blades are obtained using Hamilton's principle. A time domain unsteady aerodynamic theory with free wake model is used to obtain the airloads. Various rotor configurations with different elastic couplings with appropriate actuator placement are used to investigate the hub vibration characteristics. Numerical results show that a substantial reduction of <TEX>$N_b$</TEX>/rev hub vibration can be achieved using the optimal control algorithm.