Unsteady Vortex Lattice Method Research Articles

Extended Unsteady Vortex-Lattice Method for Insect Flapping Wings

An extended unsteady vortex-lattice method is developed to study the aerodynamics of insect flapping wings while hovering and during forward flight. Leading-edge suction analogy and vortex-core growth models are used as an extension, which is incorporated into a conventional unsteady vortex-lattice method in an effort to overcome the challenges that arise when simulating insect aerodynamics such as wing–wake interaction and leading-edge effects. A convergence analysis was carried out to derive an optimal aerodynamic mesh and a time-step size for flapping-wing models. A parallel computing technique was used to reduce computational time. The aerodynamics of hawkmoth (Manduca sexta) wing models was simulated, and the results were validated against previous numerical and experimental data.

Effects of leading-edge tubercles on wing flutter speeds

The dynamic aeroelastic effects on wings modified with bio-inspired leading-edge (LE) tubercles are examined in this study. We adopt a state-space aeroelastic model via the coupling of unsteady vortex-lattice method and a composite beam to evaluate stability margins as a result of LE tubercles on a generic wing. The unsteady aerodynamics and spanwise mass variations due to LE tubercles have counteracting effects on stability margins with the former having dominant influence. When coupled, flutter speed is observed to be 5% higher, and this is accompanied by close to 6% decrease in reduced frequencies as an indication of lower structural stiffness requirements for wings with LE tubercles. Both tubercle amplitude and wavelength have similar influences over the change in flutter speeds, and such modifications to the LE would have minimal effect on stability margins when concentrated inboard of the wing. Lastly, when used in sweptback wings, LE tubercles are observed to have smaller impacts on stability margins as the sweep angle is increased.

Dynamic Load Alleviation in Wake Vortex Encounters

This paper introduces an integrated approach for flexible-aircraft time-domain aeroelastic simulation and controller design suitable for wake encounter situations. The dynamic response of the vehicle, which may be subject to large wing deformations in trimmed flight, is described by a geometrically nonlinear finite-element model. The aerodynamics are modeled using the unsteady vortex lattice method and include the arbitrary time-domain downwash distributions of a wake encounter. A consistent linearization in the structural degrees of freedom enables the use of balancing methods to reduce the problem size while retaining the nonlinear terms in the rigid-body equations. Numerical studies on a high-altitude, long-endurance aircraft demonstrate the reduced-order modeling approach for load calculations in wake vortex encounters over a large parameter space. Closed-loop results finally explore the potential of combining feedforward/feedback control and distributed control surfaces to obtain significant load reductions.

Experimental investigation of linear and nonlinear aeroelastic behavior of a cropped delta wing with store in low subsonic flow

The present paper aims to investigate flutter phenomenon for cropped delta wing with an external store using numerical and experimental methods in a subsonic and incompressible flight regime. Wing structure is modeled based on von Karman plate theory. The unsteady vortex lattice method is applied to wing aerodynamic model and a slender-body theory is used for store aerodynamic model. The experimental tests have been conducted in an incompressible subsonic wind tunnel. The comparison indicates a satisfactory agreement between the experimental results and the theoretical analyses. Moreover, the effects of different parameters such as wing thickness, wing aspect ratio, spanwise store position, store mass, the aerodynamics of the store, underwing clearance and store center of gravity on both flutter speed and instability boundary of the wing are studied both analytically and experimentally. Also, the system behaviors and the oscillation amplitude are examined experimentally for post-flutter where time history simulation and phase portrait are obtained for various velocities. The FFT analysis of time history measured data shows that beside the dominant harmonic frequency, both superharmonic and subharmonic frequencies are clearly identifiable. The results obtained from experimental bifurcation diagram indicate the presence of hysteresis loop regions corresponding to the stable LCOs.

Experimental and numerical study of the flight of geese

AbstractThe flight of barnacle geese at airspeeds representing high-speed migrating flight is investigated using experiments and simulations. The experimental part of the work involved the filming of three barnacle geese (Branta Leucopsis) flying at different airspeeds in a wind tunnel. The video footage was analysed in order to extract the wing kinematics. Additional information, such as wing geometry and camber was obtained from a 3D scan of a dried wing. An unsteady vortex lattice method was used to simulate the aerodynamics of the measured flapping motion. The simulations were used in order to successfully reproduce the measured body motion and thus obtain estimates of the aerodynamic forces acting on the wings. It was found that the mean of the wing pitch angle variation with time has the most significant effect on lift while the difference in the durations of the upstroke and downstroke has the major effect on thrust. The power consumed by the aerodynamic forces was also estimated; it was found that increases in aerodynamic power correspond very closely to climbing motion and vice versa. Root-mean-square values of the power range from 100W to 240W. Finally, it was observed that tandem flying can be very expensive for the trailing bird.

Aerodynamic load control in horizontal axis wind turbines with combined aeroelastic tailoring and trailing‐edge flaps

ABSTRACTThis paper presents an aeroservoelastic modeling approach to investigate dynamic load alleviation in large wind turbines with composite blades and trailing‐edge aerodynamic surfaces. The tower and rotating blades are modeled using geometrically non‐linear composite beams and linearized about reference rotating conditions with potentially arbitrarily large structural displacements. The aerodynamics of the rotor are represented using a linearized unsteady vortex lattice method, and the resulting aeroelastic system is written in a state‐space description that is both convenient for model reductions and control design. A linear model of a single blade is then used to design an regulator, capable of providing load reductions of up to 13% in closed loop on the full wind turbine non‐linear aeroelastic model. When combined with passive load alleviation through aeroelastic tailoring, dynamic loads can be further reduced to 35%. While the separate use of active flap controls and passive mechanisms for load alleviation has been well‐studied, an integrated approach involving the two mechanisms has yet to be fully explored and is the focus of this paper. Finally, the possibility of exploiting torsional stiffness for active load alleviation on turbine blades is also considered. Copyright © 2014 John Wiley & Sons, Ltd.

Computational Study of a Transverse Rotor Aircraft in Hover Using the Unsteady Vortex Lattice Method

This paper presents the simulation of a two-rotor aircraft in different geometric configurations during hover flight. The analysis was performed using an implementation of the unsteady vortex-lattice method (UVLM). A description of the UVLM is presented as well as the techniques used to enhance the stability of results for rotors in hover flight. The model is validated for an isolated rotor in hover, comparing numerical results to experimental data (high-Reynolds, low-Mach conditions). Results show that an exclusion of the root vortex generates a more stable wake, without affecting results. Results for the two-rotor aircraft show an important influence of the number of blades on the vertical thrust. Furthermore, the geometric configuration has a considerable influence on the pitching moment.

An unsteady vortex lattice method model of a horizontal axis wind turbine operating in an upstream rotor wake

An unsteady formulation of the vortex lattice method, VLM, is presented that uses a force- free representation of the wake behind a horizontal axis wind turbine, HAWT, to calculate the aerodynamic loading on a turbine operating in the wake of an upstream rotor. A Cartesian velocity grid is superimposed over the computational domain to facilitate the representation of the atmospheric turbulence surrounding the turbine and wind shear. The wake of an upstream rotor is modelled using two methods: a mean velocity deficit with superimposed turbulence, based on experimental observations, and a purely numeric periodic boundary condition. Both methods are treated as frozen and propagated with the velocity grid.Measurements of the mean thrust and blade root bending moment on a three bladed horizontal axis rotor modelling a 5 MW HAWT at 1:250 scale were carried out in a wind tunnel. Comparisons are made between operation in uniform flow and in the wake of a similarly loaded rotor approximately 6.5 diameters upstream. The measurements were used to validate the output from the VLM simulations, assuming a completely rigid rotor. The trends in the simulation thrust predictions are found to compare well with the uniform flow case, except at low tip speed ratios where there are losses due to stall which are yet to be included in the model. The simple wake model predicts the mean deficit, whilst the periodic boundary condition captures more of the frequency content of the loading in an upstream wake. However, all the thrust loads are over-predicted. The simulation results severely overestimate the bending moment, which needs addressing. However, the reduction in bending due to the simple wake model is found to reflect the experimental data reasonably well.

Unsteady vortex lattice method coupled with a linear aeroelastic model for horizontal axis wind turbine

Many aerodynamic phenomena on wind turbines are extremely complicated, such as the ground boundary layer effects, directional and spatial variations in wind shear, unsteady yaw effects, and unsteady aerodynamics due to the platform motion of offshore floating wind turbines. Thus, it is unclear whether prediction of the aerodynamic load of a turbine using conventional blade element momentum theory is accurate. On the other hand, this method does not consider unsteady wake effect behind the rotor, the unsteady vortex lattice method can treat non-uniform flow effects derived from the trailing wake from the turbine. Moreover, the aeroelasticity of wind turbines is significant because of the recent scaling up of the turbine size. This induces unsteady aerodynamic phenomena because of fluctuations in the geometrical relative velocity and induced velocity. In the present work, we developed a fully coupled simulation code and analyzed the unsteady aerodynamics of wind turbines by substituting aerodynamic model from FAST's AeroDyn to the vortex lattice method. The developed code was validated with unsteady aerodynamic experimental Phase VI data from the National Renewable Energy Laboratory. Finally, the results show that the developed coupled code yields accurate values and good performance in the unsteady yaw case.

Unsteady aeroelastic behaviors of rigid airfoils with preset angles of attack

The effects of varying the angle of attack on the flutter speed and limit cycle oscillations of an aeroelastic system are investigated. This system consists of a plunging and pitching rigid airfoil supported by linear springs. The unsteady vortex lattice method is used to model the unsteady flow. The objective is to determine how the flutter boundary is affected by changing the angle of attack. To solve simultaneously and interactively the governing equations, an iterative scheme based on Hamming’s fourth order predictor–corrector model is employed. Several numerical simulations are conducted for various angles of attack to determine their effects on the dynamic behavior of the aeroelastic system and particularly on the dynamic stability or flutter speed and the nonlinear response of the system. The results show that the flutter speed increases as the angle of attack is increased. It is also determined that increasing the preset angle of attack results in a decrease in the dynamic amplitudes of the nonlinear response. In other words, increasing the angle of attack offers a way to control the system in terms of delaying flutter and reducing the limit-cycle oscillations amplitudes.

Flapping wings in line formation flight: a computational analysis

AbstractThe current understanding of the aerodynamics of birds in formation flights is mostly based on field observations. The interpretation of these observations is usually made using simplified aerodynamic models. Here, we investigate the aerodynamic aspects of formation flights. We use a potential flow solver based on the unsteady vortex lattice method (UVLM) to simulate the flow over flapping wings flying in grouping arrangements and in proximity of each other. UVLM has the capability to capture unsteady effects associated with the wake. We demonstrate the importance of properly capturing these effects to assess aerodynamic performance of flapping wings in formation flight. Simulations show that flying in line formation at adequate spacing enables significant increase in the lift and thrust and reduces power consumption. This is mainly due to the interaction between the trailing birds and the previously-shed wake vorticity from the leading bird. Moreover, enlarging the group of birds flying in formation further improves the aerodynamic performance for each bird in the flock. Therefore, birds get significant benefit of such organised patterns to minimise power consumption while traveling over long distances without stop and feeding. This justifies formation flight as being beneficial for bird evolution without regard to potential social benefits, such as, visual and communication factors for group protection and predator evasion.

Aeroservoelastic state‐space vortex lattice modeling and load alleviation of wind turbine blades

AbstractAn aeroservoelastic model, capturing the structural response and the unsteady aerodynamics of turbine rotors, will be used to demonstrate the potential of active load alleviation using aerodynamic control surfaces. The structural model is a geometrically non‐linear composite beam, which is linearized around equilibrium rotating conditions and coupled with time‐domain aerodynamics given by a linearized 3D unsteady vortex lattice method. With much of the existing work relying on blade element momentum theory with various corrections, the use of the unsteady vortex lattice method in this paper seeks to complement and provide a direct higher fidelity solution for the unsteady rotor dynamics in attached flow conditions. The resulting aeroelastic model is in a state‐space formulation suitable for control synthesis. Flaps are modeled directly in the vortex lattice description and using a reduced‐order model of the coupled aeroelastic formulation, a linear‐quadratic‐Gaussian controller is synthesized and shown to reduce root mean square values of the root‐bending moment and tip deflection in the presence of continuous turbulence. Similar trend is obtained when the controller is applied to the original non‐linear model of the turbine. Trade‐offs between reducing root‐bending moment and suppressing the negative impacts on torsion due to flap deployment will also be investigated. Copyright © 2014 John Wiley & Sons, Ltd.

Reduced-Order Aeroelastic Models for Dynamics of Maneuvering Flexible Aircraft

This paper investigates the model reduction, using balanced realizations, of the unsteady aerodynamics of maneuvering flexible aircraft. The aeroelastic response of the vehicle, which may be subject to large wing deformations at trimmed flight, is captured by coupling a displacement-based flexible-body dynamics formulation with an aerodynamic model based on the unsteady vortex lattice method. Consistent linearization of the aeroelastic problem allows the projection of the structural degrees of freedom on a few vibration modes of the unconstrained vehicle but preserves all couplings between the rigid and elastic motions and permits the vehicle flight dynamics to have arbitrarily large angular velocities. The high-order aerodynamic system, which defines the mapping between the small number of generalized coordinates and unsteady aerodynamic loads, is then reduced using the balanced truncation method. Numerical studies on a representative high-altitude, long-endurance aircraft show a very substantial reduction in model size, by up to three orders of magnitude, that leads to model orders (and computational cost) similar to those in conventional frequency-based methods but with higher modeling fidelity to compute maneuver and gust loads. Closed-loop results for a cantilever wing finally demonstrate the application of this approach in the synthesis of a robust stability augmentation system.

Consistent Structural Linearization in Flexible Aircraft Dynamics with Large Rigid-Body Motion

This paper investigates the linearization, using perturbation methods, of the structural deformations in the nonlinear flight dynamic response of aircraft with slender, flexible wings. The starting point is the coupling of a displacement-based geometrically nonlinear flexible-body dynamics formulation with a three-dimensional unsteady vortex lattice method. This is followed by a linearization of the structural degrees of freedom, which are assumed to be small in a body-fixed reference frame. The translations and rotations of that reference frame and their time derivatives, which describe the vehicle flight dynamics, can still be arbitrarily large. The resulting system preserves all couplings between rigid and elastic motions and can be projected onto a few vibration modes of the unconstrained aircraft with geometrically nonlinear static deflections at a trim condition. Equally, the unsteady aerodynamics can be approximated on a fixed lattice defined by the deformed static geometry. Numerical studies on a representative high-altitude long-endurance aircraft are presented to illustrate the approach. The results show an improvement compared to those obtained using the mean-axes approximation.

Unsteady and non-linear aeroelastic analysis of large horizontal-axis wind turbines

Analysis results, obtained from numerical simulation, for non-linear and unsteady aeroelastic behavior of large horizontal-axis wind turbines are presented in this paper. Simulations are carried out using a partitioned scheme of weak interaction that allows dealing with the fluid–structure interaction problem by using one method to solve the structural-dynamic problem and another method for the aerodynamic problem.The aerodynamic model used is the non-linear, unsteady vortex lattice method (NLUVLM). The structural model used is a system of beam finite elements and rigid bodies with finite rotation. This provides a very general tool with relatively low computational cost.The proposed method allows predicting from the operating conditions (wind speed and direction, pitch angle of blades, etc.) the aeroelastic response of wind turbines, characterized by variables such as rotation speed of the rotor, loads on the structural components and the extracted power, among others.

Lift and Thrust Characteristics of Flapping Wing Aerial Vehicle with Pitching and Flapping Motion

Development of flapping wing aerial vehicle (FWAV) has been of interest in the aerospace community with ongoing research into unsteady and low Reynolds number aerodynamics based on the vortex lattice method. Most of the previous research has been about pitching and plunging motion of the FWAV. With pitching and flapping motion of FMAV, people usually study it by experiment, and little work has been done by numerical calculation. In this paper, three-dimension unsteady vortex lattice method is applied to study the lift and thrust of FWAV with pitching and flapping motion. The results show that: 1) Lift is mainly produced during down stroke, however, thrust is produced during both down stroke and upstroke. The lift and thrust produced during down stroke are much more than that produced during upstroke. 2) Lift and thrust increase with the increase of flapping frequency; 3) Thrust increases with the increase of flapping amplitude, but the lift decreases with the increase of flapping amplitude; 4) Lift and thrust increase with the increase of mean pitching angle, but the effect on lift is much more than on thrust. This research is helpful to understand the flight mechanism of birds, thus improving the design of FWAV simulating birds.

On the shape optimization of flapping wings and their performance analysis

The present work is concerned with the shape optimization of flapping wings in forward flight. The analysis is performed by combining a gradient-based optimizer with the unsteady vortex lattice method (UVLM). We describe the UVLM simulation procedure and provide the first methodology to select properly the mesh and time-step sizes to achieve invariant UVLM simulation results under mesh refinement. Our objective is to identify a set of optimized shapes that maximize the propulsive efficiency, defined as the ratio of the propulsive power over the aerodynamic power, under lift, thrust, and area constraints. Several parameters affecting flight performance are investigated and their impact is described. These include the wingʼs aspect ratio, camber line, and curvature of the leading and trailing edges. This study provides guidance for shape design of engineered flying systems.

Nonlinear analysis and enhancement of wing-based piezoaeroelastic energy harvesters

We investigate the level of harvested power from aeroelastic vibrations for an elastically mounted wing supported by nonlinear springs. The energy is harvested by attaching a piezoelectric transducer to the plunge degree of freedom. The considered wing has a low-aspect ratio and hence three dimensional aerodynamic effects cannot be neglected. To this end, the three dimensional unsteady vortex lattice method for the prediction of the unsteady aerodynamic loads is developed. A strong coupling scheme that is based on Hamming's fourth-order predictor–corrector method and accounts for the interaction between the aerodynamic loads and the motion of the wing is employed. The effects of the electrical load resistance, nonlinear torsional spring and eccentricity between the elastic axis and the gravity axis on the level of the harvested power, pitch and plunge amplitudes are investigated for a range of operating wind speeds. The results show that there is a specific wind speed beyond which the pitch motion does not pick any further energy from the incident flow. As such, the displacement in the plunge direction grows significantly and causes enhanced energy harvesting. The results also show that the nonlinear torsional spring plays an important role in enhancing the level of the harvested power. Furthermore, the harvested power can be increased by an order of magnitude by properly choosing the eccentricity and the load resistance. This analysis is helpful in designing piezoaeroelastic energy harvesters that can operate optimally at specific wind speeds.

Modified Unsteady Vortex-Lattice Method to Study Flapping Wings in Hover Flight

A numerical-simulation tool is developed that is well suited for modeling the unsteady nonlinear aerodynamics of flying insects and small birds as well as biologically inspired flapping-wing micro air vehicles. The present numerical model is an extension of the widely used three-dimensional general unsteady vortex-lattice model and provides an attractive compromise between computational cost and fidelity. Moreover, it is ideally suited to be combined with computational structural dynamics to provide aeroelastic analyses. The present numerical results for a twisting, flapping wing with neither leading-edge nor wing-tip separations are in close agreement with the results obtained in previous studies with the Euler equations and a vortex-lattice method. The present results for unsteady lift, mean lift, and frequency content of the force are in good agreement with experimental data for the robofly apparatus. The actual wing motion of a hovering Drosophila is used to compute the flowfield and predict the lift force. The downward motion of the fluid particles revealed in the graphics of the calculated wake indicates the presence of lift. Moreover, the calculated mean lift is in close agreement with the weight of a Drosophila. The results presented in this paper definitely show that the interaction between vortices is the main feature that allows insects to generate enough lift to stay aloft. The present results warrant the use of this general version of the unsteady vortex-lattice method for future studies.

Modeling and Simulation of Unsteady Aerodynamics on a Morphing Wing

Modeling and simulation method of unsteady aerodynamics on morphing wings were investigated. The Unsteady Vortex Lattice Method is employed to model the unsteady aerodynamics of 3-D potential flow field surrounding the wing. An UVLM computer code was then developed and validated for numerical simulation. A morphing wing which changes its dihedral angle with constant angular velocity was investigated by the code, and the lift, induced drag, and pitching moment coefficients time histories were obtained. The results show that the UVLM code is an effective tool for simulations of unsteady aerodynamics on morphing wings.