Free Wake Model Research Articles

Numerical investigation of full scale coaxial main rotor aerodynamics in hover and vertical descent

The original free vortex wake model was used for numerical investigation. Calculation of the aerodynamic characteristics in hover and vertical descent modes in the range of vertical descent speed of 0–30 m/s including the Vortex Ring State (VRS) area was performed. The calculations were carried out under the condition of variable blade pitch angle values providing a fixed time-average thrust value. Visualization data of free vortex wake shapes, flow structures, and velocity fields were obtained and analyzed. The time-dependences of the rotor’s thrust and torque coefficients were obtained and analyzed. The obtained data allows determining the boundaries of the VRS area by various criteria such as rotor thrust and torque pulsations, growth of rotor power consumption relative to the hover, growth of rotor induced velocities relative to the hover, and growth of the required rotor blade pitch angles values. The results of the study are compared with experimental and calculated data of other authors and can significantly supplement the available results of experimental and computational studies in this area.

Comparative Study of Coaxial Main Rotor Aerodynamics in the Hover with the Usage of Two Methods of Computational Fluid Dynamics

The paper is focused on numerical modeling of the aerodynamic characteristics of a full-scale coaxial main rotor in hover. The simulation was performed using two approaches of computational fluid dynamics (CFD): the original free wake model (FWM) developed by the authors and the unsteady Reynolds-averaged Navier–Stokes (URANS) equations method based on the Ansys Fluent software. The structure of the rotor vortex wake, flow images, vorticity and induced velocity fields, total and distributed aerodynamic characteristics of the rotor, including the rotor performance and figure of merit diagrams, have been analyzed. A comparison between FWM/URANS based calculations and calculated/experimental data by other authors has been performed. A satisfactory match of these data confirms reliability of used methods when modeling the aerodynamic characteristics of coaxial rotors. The FMW demonstrates a significant advantage in speed and resources intensity when calculating the total aerodynamic characteristics of a coaxial rotor. The URANS method makes it possible to model with significant accuracy the effects associated with the blade vortex interactions and pressure distribution over the blade surface. Finally, conclusions about most effectiveness of joint application of considered methods in solving complex problems of coaxial rotor aerodynamics has been made.

MODELLING THE HELICOPTER ROTOR AERODYNAMICS AT FORWARD FLIGHT WITH FREE WAKE MODEL AND URANS METHOD

The presented work is dedicated to the numerical study of the aerodynamic characteristics of the helicopter rotor. Two approaches to modeling of the rotor are applied: the free wake model developed by the Authors with using steady airfoil characteristics and the Unsteady RANS method based on the Ansys Fluent software. The modes of hovering and horizontal flight in the range of advancing ratio μ = (0-0.45) are considered. The shapes of the rotor wake, the distributions of the normal force coefficient and the fields of inductive velocities for all considered flight modes are calculated. For a particular case with μ = 0.25 there is a comparison with experimental data. The time needed for calculation of the applied methods is estimated. Accuracy of the used methods in the framework of the solved task is analysed with taking into account used models assumptions. It is shown that in the range of μ = (0-0.25) the free wake model provides a fast and reliable calculation of the aerodynamic characteristics of the helicopter rotor. For values of μ > 0.35 it is necessary to take into account the unsteady characteristics of the airfoil.

Enhanced heat transfer research in liquid-cooled channel based on piezoelectric vibrating cantilever

In order to study the variation of vortices and heat transfer enhancement characteristics of piezoelectric vibrating cantilever in liquid-cooled channels, the effects of fluid density and viscosity, mainstream velocity, and excitation voltage on vortices were analyzed. The theoretical and numerical simulation of piezoelectric vortices was carried out by using fluid-solid coupling method. On the basis of hydrodynamic function considering the additional effect of liquid viscosity and density on piezoelectric vibrator, the vortex structure of piezoelectric vibrator was analyzed by panel method free-wake model. It is found that the larger the density of the liquid, the smaller the vortex shedding strength and the radius of the core. The larger the viscosity of the liquid, the easier to fully develop the vortex generated by the excitation. The increase of the mainstream flow velocity is beneficial to the development of the vortex structure and the increase of the vorticity intensity. Compared with the increase of the mainstream flow velocity, the excitation voltage is more conducive to the enhancement of the vorticity structure, then make it easier to mix hot and cold fluids, thus enhancing heat transfer.

Impact of Tip-Vortex Modeling Uncertainty on Helicopter Rotor Blade–Vortex Interaction Noise Prediction

Free-wake models are routinely used in aeroacoustic analysis of helicopter rotors; however, their semiempiricism is accompanied with uncertainty related to the modeling of physical wake parameters. In some cases, analysts have to resort to empirical adaption of these parameters based on previous experimental evidence. This paper investigates the impact of inherent uncertainty in wake aerodynamic modeling on the robustness of helicopter rotor aeroacoustic analysis. A free-wake aeroelastic rotor model is employed to predict high-resolution unsteady airloads, including blade–vortex interactions. A rotor aeroacoustics model, based on integral solutions of the Ffowcs Williams–Hawkings equation, is utilized to calculate aerodynamic noise in the time domain. The individual analytical models are incorporated into an uncertainty analysis numerical procedure, implemented through nonintrusive Polynomial Chaos expansion. The potential sources of uncertainty in wake tip-vortex core growth modeling are identified and their impact on noise predictions is systematically quantified. When experimental data to adjust the tip-vortex core model are not available the uncertainty in acoustic pressure and noise impact at observers dominated by blade–vortex interaction noise can reach up to 25% and 3.50 dB, respectively. A set of generalized uncertainty maps is derived, for use as modeling guidelines for aeroacoustic analysis in the absence of the robust evidence necessary for calibration of semiempirical vortex core models.

Performance and Effect of Load Mitigation of a Trailing-Edge Flap in a Large-Scale Offshore Wind Turbine

As a result of the large-scale trend of offshore wind turbines, wind shear and turbulent wind conditions cause significant fluctuations of the wind turbine’s torque and thrust, which significantly affect the service life of the wind turbine gearbox and the power output stability. The use of a trailing-edge flap is proposed as a supplement to the pitch control to mitigate the load fluctuations of large-scale offshore wind turbines. A wind turbine rotor model with a trailing-edge flap is established by using the free vortex wake (FVW) model. The effects of the deflection angle of the trailing-edge flap on the load distribution of the blades and wake flow field of the offshore wind turbine are analyzed. The wind turbine load response under the control of the trailing-edge flap is obtained by simulating shear wind and turbulent wind conditions. The results show that a better control effect can be achieved in the high wind speed condition because the average angle of attack of the blade profile is small. The trailing-edge flap significantly changes the load distribution of the blade and the wake field and mitigates the low-frequency torque and thrust fluctuations of the turbine rotor under the action of wind shear and turbulent wind.

Analytical sensitivity analysis of flexible aircraft with the unsteady vortex-lattice aerodynamic theory

The unsteady vortex-lattice method provides a medium-fidelity tool for calculation of low-speed aerodynamic loads based on the potential-flow theory. It has long been favored in research on the aeroelasticity and flight dynamics for flexible aircraft with high aspect ratios. However, the unsteady vortex-lattice method is established in the discrete time domain which brings difficulties to modeling aeroelastic system for stability analysis. An analytical aerodynamic sensitivity calculation scheme is developed in this paper to formulate the aeroelastic equations of motion with UVLM aerodynamics. A free wake model is used to simulate accurate vortex shedding and subsequent wake propagation. Using a small perturbation method, the aerodynamic governing equations are linearized around the equilibrium condition, where the analytical sensitivities can be derived. The surface spline interpolation algorithm is adopted to implement the structure-aerodynamic coupling. Both aerodynamic sensitivities with respect to structural motions and circulation strengths of vortices are obtained. In numerical studies, a time-marching transient response analysis scheme is used to obtain the distributed aerodynamic loads and structural deformations. Analytical sensitivity results are validated by the finite difference method. The proposed analytical sensitivity calculation framework is demonstrated to be applicable to commonly used beam-based flexible wing models, as well as the shell-based finite element models with higher fidelity. The derived sensitivity formulations and related numerical implementations can build the foundation for further studies on aeroelastic optimization and stability analysis.

Dynamic prescribed-wake vortex method for aerodynamic analysis of offshore floating wind turbines

A prescribed-wake vortex model for evaluating the aerodynamic loads on offshore floating turbines has been developed. As an extension to the existing UMass analysis tool, WInDS, the developed model uses prescribed empirical wake node velocity functions to model aerodynamic loading. This model is applicable to both dynamic flow conditions and dynamic rotational and translational platform motions of floating offshore turbines. With this model, motion-induced wake perturbations can be considered, and their effect on induction can be modeled, which is useful for floating offshore wind turbine design. The prescribed-wake WInDS model is shown to increase computational efficiency drastically in all presented cases and maintain comparable accuracy to the free wake model. Results of prescribed-wake model simulations are presented and compared to results obtained from the free wake model to confirm model validity.

Validations of Rotor Load Analysis Using Flexible Multibody Dynamics with Multiple Wake Panels for Low-Speed Flights

Rotor load predictions of the UH-60A helicopter in low-speed flights are validated using nonlinear flexible multibody dynamic analyses with multiple wake panels. A nonlinear flexible multibody dynamic analysis code, DYMORE II, is used for predicting the blade section airloads and structural loads of the UH-60A rotor in low-speed forward and descending flights at the advance ratio of 0.15. The freewake model with multiple wake panels is integrated implicitly into DYMORE II to represent effectively the BVI (blade–vortex interaction) phenomenon of the rotor in low-speed flights. For both low-speed forward and descending flights, the multiple wake panel and single wake panel models both validate the blade section normal forces (or lift forces) moderately or well with the flight test data; however, they predict the blade section pitching moments moderately or poorly. For blade structural loads, two analyses using the multiple wake panel and single wake panel models validate the oscillatory flap bending moments moderately for both flight conditions; however, they correlate the oscillatory lead–lag bending moments poorly with the measured data. In addition, the multiple wake panel and single wake panel models both validate the oscillatory torsion moment well for the low-speed descending flight; but they predict it moderately or poorly for the low-speed forward flight. Through the present study, the analyses using multiple wake panels show better predictions of the rotor loads in low-speed flights as compared to the results with a single wake panel, along with efficient and reasonable computation resource and time.

A ring-vortex free-wake model for uniformly loaded propellers. Part I-Model description.

The paper presents a free-wake actuator disk model as applied to uniformly loaded propellers without slipstream rotation. The wake vorticity, originating from the disk edge, is represented by the superposition of a ring vortex sheet and a semi-infinite cylindrical vortex tube modelling the far wake. The shape and the density strength of the sheet are iteratively evaluated using two conditions. Firstly, the vortex sheet stability condition is strongly enforced, that is the static pressures just above and beneath the sheet are required to be equal. Secondly, the vortex sheet is constrained to align with the overall induced flow field, namely it is compelled to be a streamsurface. By doing so, the contraction of the wake is naturally accounted for in the model and no assumptions on its shape are made. The first part of this work deals with the theoretical foundations of the model and with the description of its discrete counterpart. The characteristics of the flow singularities used to model the flow induced by the wake are also presented.

A ring-vortex free-wake model for uniformly loaded propellers. Part II - Solution procedure and analysis of the results

The paper investigates the flow through a uniformly-loaded propeller by means of a free-wake ring-vortex actuator disk without wake rotation. In particular, the model represents the near wake by the superposition of N ring vortices, while the far wake is modelled by a semi-infinite vortex cylinder with uniform radius.This second part presents the iterative solution procedure of the method illustrated in the companion paper as well as the implementation of the wake boundary conditions. Then, the power coefficient, the ideal propulsive efficiency and the wake contraction ratio are presented as a function of the propeller thrust coefficient, thus revealing the relevance of the wake convergence effects. Finally, the method is used to investigate the main characteristics of the local flow field induced by such an actuator disk.

A novel hybrid free-wake model for wind turbine performance and wake evolution

Abstract A new free-wake analysis for wind turbine aerodynamics is developed to accurately predict turbine performance and downstream wake evolution. A key feature is the Constant Circulation Contour Method (CCCM) which is a novel free-wake model for wind turbine wakes. This method characterizes a turbine wake by a number of resultant vortex filaments, avoiding the numeric artifact of a vortex lattice comprised of trailing and shedding vortices. The natural capture of wake roll-up and distortion using CCCM is illustrated and its computational complexity is demonstrated to be lower than Vortex Lattice Method (VLM). For accurate blade downwash calculation, a hybrid free-wake model is developed by combining CCCM with a VLM wake immediately behind turbine blades, which transitions to CCCM further downstream. Important properties of this hybrid wake are discussed and optimized to enhance model accuracy and efficiency. Blade static stall and unsteady effects are included. The hybrid model is validated through comparison to the wind tunnel experiments UAE Phase VI and MEXICO. Simulation examples are presented showing the utilization of this free-wake analysis to investigate wake steering, demonstrating the potential application of this method to wind farm scale wake simulations.

Final results from the EU project AVATAR: Aerodynamic modelling of 10 MW wind turbines

This paper presents final results from the EU project AVATAR in which aerodynamic models are improved and validated for wind turbines on a scale of 10 MW and more. Special attention is paid to the improvement of low fidelity engineering (BEM based) models with higher fidelity (CFD) models but also with intermediate fidelity free vortex wake (FVW) models. The latter methods were found to be a good basis for improvement of induction modelling in engineering methods amongst others for the prediction of yawed cases, which in AVATAR was found to be one of the most challenging subjects to model. FVW methods also helped to improve the prediction of tip losses. Aero-elastic calculations with BEM based and FVW based models showed that fatigue loads for normal production cases were over predicted with approximately 15% or even more. It should then be realised that the outcome of BEM based models does not only depend on the choice of engineering add-ons (as is often assumed) but it is also heavily dependent on the way the induced velocities are solved. To this end an annulus and element approach are discussed which are assessed with the aid of FVW methods. For the prediction of fatigue loads the so-called element approach is recommended but the derived yaw models rely on an annulus approach which pleads for a generalised solution method for the induced velocities.

A Simplified Free Vortex Wake Model of Wind Turbines for Axial Steady Conditions

A simplified free vortex wake (FVW) model called the vortex sheet and ring wake (VSRW) model was developed to rapidly calculate the aerodynamic performance of wind turbines under axial steady conditions. The wake in the simplified FVW model is comprised of the vortex sheets in the near wake and the vortex rings, which are used to replace the helical tip vortex filament in the far wake. The position of the vortex ring is obtained by the motion equation of its control point. Analytical formulas of the velocity induced by the vortex ring were introduced to reduce the computational time of the induced velocity calculation. In order to take into account both accuracy and calculation time of the VSRW model, the length of the near wake was cut off at a 120° wake age angle. The simplified FVW model was used to calculate the aerodynamic load of the blade and the wake flow characteristic. The results were compared with measurement results and the results from the full vortex sheet wake model and the tip vortex wake model. The computational speed of the simplified FVW model is at least an order of magnitude faster than other two conventional models. The error of the low-speed shaft torque obtained from the simplified FVW model is no more than 10% relative to the experiment at most of wind speeds. The normal and tangential force coefficients obtained from the three models agree well with each other and with the measurement results at the low wind speed. The comparison indicates that the simplified FVW model predicts the aerodynamic load accurately and greatly reduces the computational time. The axial induction factor field in the near wake agrees well with the other two FVW models and the radial expansion deformation of the wake can be captured.

The unsteady aerodynamics of floating wind turbine under platform pitch motion

The aerodynamic performance of floating platform wind turbines is much more complex than fixed-base wind turbines because of the flexibility of the floating platform. Due to the extra six degrees-of-freedom of the floating platform, the inflow of the wind turbine rotors is highly influenced by the motions of the floating platform. It is therefore of interest to study the unsteady aerodynamics of the wind turbine rotors involved with the interaction of the floating platform induced motions. In the present work, a lifting surface method with a free wake model is developed for analysis of the unsteady aerodynamics of wind turbines. The aerodynamic performance of the NREL 5 MW floating wind turbine under the prescribed floating platform pitch motion is studied. The unsteady aerodynamic loads, the transient of wind turbine states, and the instability of the wind turbine wakes are discussed in detail.

Assessing Calculated Blade Loads of the Tilt Rotor Aeroacoustic Model

In an effort to assess the suitability of the U.S. Army’s Rotorcraft Comprehensive Analysis System for calculating tiltrotor aeromechanics characteristics, comparisons of rotor performance and blade loads between calculations and test data are presented for the Tilt Rotor Aeroacoustic Model rotor in helicopter mode at an advance ratio of 0.15. For rotor performance, the comparisons are with test points that form shaft angle sweeps for two different thrust levels. These calculations include those from a free vortex wake model and those from coupling the comprehensive analysis to a viscous vortex particle method. The emphasis of this work is on the comparisons of blade loads, which are analyzed in detail for two test points with a 3 deg forward shaft tilt and different thrust levels. Blade airloads calculations include the two aforementioned sets of calculations, whereas blade structural loads calculations also include those from prescribing experimentally measured airloads. The level of agreement between calculations with the free vortex wake model and test data is generally comparable with those of helicopter rotors at similar conditions. The level of agreement improves with the viscous vortex particle method. Meanwhile, some deficiencies in structural loads calculations with prescribing measured airloads are noted.

Study of the unsteady aerodynamics of floating wind turbines

The aerodynamic performance and instabilities of floating platform wind turbines are much more complex than fixed based wind turbines because of the flexibility of the floating platform. Due to the extra six degree-of-freedom of the floating platform, the inflow of the wind turbine rotors is highly influenced by the motions of the floating platform. In the present study, an unsteady lifting surface method with a free wake model is developed for the analysis of the wind turbine unsteady performance under the floating platform surge motion conditions. The full scale NREL 5 MW floating wind turbine is chosen as the subject of the present study. The unsteady aerodynamic performance and instabilities have been discussed in detailed. It is believed that under certain platform surge motion, the wind turbine may gain more aerodynamic power output than under steady state condition. The flow separation on the surface of the blade and the pitch control may have the potential of leading the floating wind turbine into unstable conditions during certain platform surge motion.

Three-Dimensional Aerodynamic Analysis of a Darrieus Wind Turbine Blade Using Computational Fluid Dynamics and Lifting Line Theory

Due to the rapid progress in high-performance computing and the availability of increasingly large computational resources, Navier–Stokes (NS) computational fluid dynamics (CFD) now offers a cost-effective, versatile, and accurate means to improve the understanding of the unsteady aerodynamics of Darrieus wind turbines and deliver more efficient designs. In particular, the possibility of determining a fully resolved flow field past the blades by means of CFD offers the opportunity to both further understand the physics underlying the turbine fluid dynamics and to use this knowledge to validate lower-order models, which can have a wider diffusion in the wind energy sector, particularly for industrial use, in the light of their lower computational burden. In this context, highly spatially and temporally refined time-dependent three-dimensional (3D) NS simulations were carried out using more than 16,000 processor cores per simulation on an IBM BG/Q cluster in order to investigate thoroughly the 3D unsteady aerodynamics of a single blade in Darrieus-like motion. Particular attention was paid to tip losses, dynamic stall, and blade/wake interaction. CFD results are compared with those obtained with an open-source code based on the lifting line free vortex wake model (LLFVW). At present, this approach is the most refined method among the “lower-fidelity” models, and as the wake is explicitly resolved in contrast to blade element momentum (BEM)-based methods, LLFVW analyses provide 3D flow solutions. Extended comparisons between the two approaches are presented and a critical analysis is carried out to identify the benefits and drawbacks of the two approaches.

Multiobjective Performance Optimization of a Coaxial Compound Rotorcraft Configuration

This paper presents the results of a rotorcraft preliminary design problem, solved as a multiobjective design optimization problem. A lift- and thrust-augmented coaxial compound configuration is used to demonstrate the approach. The basic optimization problem is converted into a sequence of approximate optimization problems, in which approximate Pareto frontiers are calculated based on response surfaces, obtained from radial basis function interpolation of all the designs analyzed at every step of the sequence. The Pareto frontiers are computed using a genetic algorithm. The designs are analyzed using a high-fidelity rotorcraft analysis that includes nonlinear finite element models of the rotor blade and a free vortex wake model of the rotor inflow. The results presented indicate that 1) the preliminary design problem can be effectively solved using formal numerical design optimization techniques, which therefore can complement classical design methodologies; 2) with appropriate physics-based constraints, the design optimization can be carried out by the computer completely unattended; 3) the optimization methodology is sufficiently robust to deal with multiple local optima and other numerical difficulties; and 4) the methodology is efficient enough to allow the use of high-fidelity analyses throughout the optimization, with the use of graphical processing unit computing (Compute Unified Device Architecture/Fortran) contributing to the computational efficiency.

Development of a new free wake model using finite vortex element for a horizontal axis wind turbine

The treatment of rotor wake has been a critical issue in the field of the rotor aerodynamics. This paper presents a new free wake model for the unsteady analysis for a wind turbine. A blade-wake-tower interaction is major source of unsteady aerodynamic loading and noise on the wind turbine. However, this interaction can not be considered in conventional free wake model. Thus, the free wake model named Finite Vortex Element (FVE hereafter) was devised in order to consider the interaction effects. In this new free wake model, the wake-tower interaction was described by dividing one vortex filament into two vortex filaments, when the vortex filament collided with a tower. Each divided vortex filaments were remodeled to make vortex ring and horseshoe vortex to satisfy Kelvin’s circulation theorem and Helmholtz’s vortex theorem. This model was then used to predict aerodynamic load and wake geometry for the horizontal axis wind turbine. The results of the FVE model were compared with those of the conventional free wake model and the experimental results of SNU wind tunnel test and NREL wind tunnel test under various inflow velocity and yaw condition. The result of the FVE model showed better correlation with experimental data. It was certain that the tower interaction has a strong effect on the unsteady aerodynamic load of blades. Thus, the tower interaction needs to be taken into account for the unsteady load prediction. As a result, this research shows a potential of the FVE for an efficient and versatile numerical tool for unsteady loading analysis of a wind turbine.