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See detailEffect of Levels of Fidelity on Steady Aerodynamic and Static Aeroelastic Computations
Crovato, Adrien; Almeida, Hugo; Vio, Gareth; Silva, Gustavo; Prado, Alex; Breviglieri, Carlos; Güner, Hüseyin; Cabral, Pedro; Boman, Romain; Terrapon, Vincent; Dimitriadis, Grigorios

in Aerospace (2020), II

Static aeroelastic deformations are nowadays considered as early as in the preliminary aircraft design stage, where low-fidelity linear aerodynamic modeling is favored because of its low computational cost. However, transonic flows are essentially nonlinear. The present work aims at assessing the impact of the aerodynamic level of fidelity used in preliminary aircraft design. Several fluid models ranging from the linear potential to the Navier–Stokes formulations were used to solve transonic flows for steady rigid aerodynamic and static aeroelastic computations on two benchmark wings: the Onera M6 and a generic airliner wing. The lift and moment loading distributions, as well as the bending and twisting deformations predicted by the different models, were examined, along with the computational costs of the various solutions. The results illustrate that a nonlinear method is required to reliably perform steady aerodynamic computations on rigid wings. For such computations, the best tradeoff between accuracy and computational cost is achieved by the full potential formulation. On the other hand, static aeroelastic computations are usually performed on optimized wings for which transonic effects are weak. In such cases, linear potential methods were found to yield sufficiently reliable results. If the linear method of choice is the doublet lattice approach, it must be corrected using a nonlinear solution.

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See detailA modified Leishman-Beddoes model for airfoil sections undergoing dynamic stall at low Reynolds numbers
Boutet, Johan; Dimitriadis, Grigorios; Amandolese, Xavier

in Journal of Fluids and Structures (2020)

A modified Leishman-Beddoes[1] model is proposed to predict the aerodynamic load responses of airfoils undergoing dynamic stall at low Reynolds, low Mach numbers and low to very high equivalent reduced pitch rates. The modifications include using Wagner function aerodynamics for the attached flow model, defining and using a time-varying reduced pitch rate, equating the time delays applied to the normal force, the separation point location and the vortex shedding and using Sheng and Galbraith's dynamic stall onset criteria [2]. The steady and unsteady force and pitching moment measurements of three airfoils with distinct stall mechanisms (a flat plate, a NACA0012, and a NACA0018) are used to demonstrate the validity of this new model. Dynamic tests consist of oscillating the airfoils in pitch around the quarter chord with a mean angle A0 = 10 deg and with different prescribed reduced frequencies from k = 0.015, to k = 0.16, and amplitudes from A = 5 deg to 20 deg, at Reynolds numbers of the order of Re=1.8x104. The resulting equivalent reduced pitch rates range from r' = 0.001 to 0.06. The computations of the values of the different model parameters are demonstrated and it is observed that the values of the time delay parameters change continuously and smoothly with time instead of jumping discontinuously at discrete time instances as proposed by Leishman and Beddoes [1]. It is shown that the modified Leishman-Beddoes model is in good agreement with experiments for low to moderate equivalent reduced pitch rates (r'<=0.04). It also significantly improves the dynamic load prediction in this range of pitch rates, in comparison to the original Leishman-Beddoes model. Nevertheless, as for the original model, the modified model presented here becomes inaccurate at the highest equivalent reduced pitch rates of r' > 0.05.

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See detailNumerical and experimental study of the flow around a 4:1 rectangular cylinder at moderate Reynolds number
Guissart, Amandine; Andrianne, Thomas; Dimitriadis, Grigorios; Terrapon, Vincent

in Journal of Wind Engineering and Industrial Aerodynamics (2019), 189

This paper presents the results of investigations into the flow around a rectangular cylinder with a chord-to-depth ratio equal to 4. The studies are performed through wind tunnel dynamic pressure measurements along a cross section combined with two-dimensional Unsteady Reynolds-Averaged Navier-Stokes (URANS) and three-dimensional Delayed-Detached Eddy Simulation (DDES). These experimental and numerical studies are complementary and combining them allows a better understanding of the unsteady dynamics of the flow. These studies aim mainly at determining the effects of the rectangle incidence and freestream velocity on the variation of the flow topology and the aerodynamic loads, and at assessing the capability of the industrially affordable URANS and DDES approaches to provide a sufficiently accurate estimation of the flow for different incidences. The comparison of experimental and numerical data is performed using statistics and Dynamic Mode Decomposition. It is shown that the rectangular cylinder involves complex separation-reattachment phenomena that are highly sensitive to the Reynolds number. In particular, the time-averaged lift slope increases rapidly with the Reynolds number in the range 7.8e3 < Re < 1.9e4 due to the modification of the time-averaged vortex strength, thickness and distance from the surface. Additionally, it is shown that both URANS and DDES simulations fail to accurately predict the flow at all the different incidence angles considered. The URANS approach is able to qualitatively estimate the spatio-temporal variations of vortices for incidences below the stall angle alpha = 4°. Nonetheless, URANS does not predict stall, while DDES correctly identifies the stall angle observed experimentally.

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See detailUnsteady aerodynamic modeling methodology based on dynamic mode interpolation for transonic flutter calculations
Güner, Hüseyin; Thomas, David; Dimitriadis, Grigorios; Terrapon, Vincent

in Journal of Fluids and Structures (2019), 84

A new unsteady aerodynamic modeling methodology for calculating transonic flutter characteristics is presented. The main idea of the methodology is to obtain the unsteady flow response to small amplitude periodic deformations of a structure over a large range of oscillation frequencies through the interpolation of the most dominant fluid dynamic modes obtained from Dynamic Mode Decomposition (DMD) of a few reference unsteady simulations at different oscillation frequencies. These simulations can be carried out by solving the Euler or RANS equations. The methodology can then be used to obtain a frequency-domain generalized aerodynamic force matrix, and stability analysis can be performed using standard flutter analysis methods such as the p-k method. The proposed methodology provides a very good estimate of the flutter boundary for the 2D Isogai airfoil and 3D AGARD 445.6 wing models, but at a lower computational cost than the traditional higher-fidelity Fluid-Structure Interaction (FSI) simulations.

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See detailCUPyDO - An integrated Python environment for coupled fluid-structure simulations
Thomas, David; Cerquaglia, Marco Lucio; Boman, Romain; Economon, Thomas; Alonso, Juan; Dimitriadis, Grigorios; Terrapon, Vincent

in Advances in Engineering Software (2019)

CUPyDO, a fluid-structure interaction (FSI) tool that couples existing independent fluid and solid solvers into a single synchronization and communication framework based on the Python language is presented. Each coupled solver has to be wrapped in a Python layer in order to embed their functionalities (usually written in a compiled language) into a Python object, that is called and used by the coupler. Thus a staggered strong coupling can be achieved for time-dependent FSI problems such as aeroelastic flutter, vortex-induced vibrations (VIV) or conjugate heat transfer (CHT). The synchronization between the solvers is performed with the predictive block-Gauss-Seidel algorithm with dynamic under-relaxation. The tool is capable of treating non-matching meshes between the fluid and structure domains and is optimized to work in parallel using Message Passing Interface (MPI). The implementation of CUPyDO is described and its capabilities are demonstrated on typical validation cases. The open-source code SU2 is used to solve the fluid equations while the solid equations are solved either by a simple rigid body integrator or by in-house linear/nonlinear Finite Element codes (GetDP/Metafor). First, the modularity of the coupling as well as its ease of use is highlighted and then the accuracy of the results is demonstrated.

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See detailThe impact of circularity defects on bridge stay cable dry galloping stability
Benidir, Adel; Flamand, Olivier; Dimitriadis, Grigorios

in Journal of Wind Engineering and Industrial Aerodynamics (2018), 181

The present work studies the influence of circularity defects, on the aerodynamic behaviour of stay cables of cable-stayed bridges. It focuses on wind tunnel tests on High-Density Polyethylene cable covers with and without helical fillets, in a range of Reynolds numbers from the sub-critical to the critical regime. The paper considers the impact of circularity defects on the aerodynamic stability of cable sheaths by testing various amplitudes of imposed ovalization. The defects are artificially applied on real sheaths whose original cross-sections are close to circular. The experiment consists in measuring surface pressures to investigate how the amplitude of ovalization influences the flow around the sheaths, especially in the critical Reynolds number regime when transition in the boundary layer occurs. The analysis is based on bifurcation diagrams and Proper Orthogonal Decomposition. The investigation demonstrates that important circularity defects can significantly increase the bi-stable nature of the flow around a sheath at the critical regime. Nevertheless, the introduction of a helical fillet de-correlates the flow around the sheath, causing jumps in lift that have different sign along its length.

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See detailA combined Multiple Time Scales and Harmonic Balance approach for the transient and steady-state response of nonlinear aeroelastic systems
Berci, Marco; Dimitriadis, Grigorios

in Journal of Fluids and Structures (2018), 80

The majority of methods for calculating the dynamic response of nonlinear aeroelastic systems considers only steady-state periodic behaviour. An exception is the Multiple Time Scales method, which can estimate both the transient and steady-state solutions of such systems; nevertheless, this approach is only accurate close to the Hopf bifurcation. This paper proposes a novel combined approach whereby the transient response is obtained from the Multiple Time Scales method and the asymptotic periodic behaviour is corrected using the Harmonic Balance method. This consistent and efficient framework mutually empowers both techniques and accounts for large parameter variations around the critical condition. The effect of cubic aero-structural nonlinearities on the dynamic response of a generic aeroelastic system is then investigated. Both the Multiple Time Scales and Harmonic Balance methods are adopted and perfect agreement of the explicit results is demonstrated, albeit near the system instability. In contrast, the proposed combined solution is valid for a wider range of perturbations, is analytical and has negligible computational cost while retaining accuracy. The role of key parameters and terms on the core mechanism of the dynamic behaviour is rigorously identified and discussed, from both physical and mathematical points of view. Galloping is finally considered as the simplest but complete application to a fundamental yet practical problem, featuring full conceptual complexity while exploiting the solid synthesis capability of the newly proposed analytical approach. Excellent agreement was found in all cases with results from the numerical integration of the nonlinear equations of motion in the time domain.

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See detailA Modal Frequency-Domain Generalised Force Matrix for the Unsteady Vortex Lattice Method
Dimitriadis, Grigorios; Giannelis, N. F.; Vio, G. A.

in Journal of Fluids and Structures (2018), 76

The unsteady Vortex Lattice method is becoming an increasingly popular aerodynamic modelling method for incompressible aeroelastic problems, such as flexible low-speed aircraft, wind turbines and flapping flight. It leads to discrete time aeroelastic state space equations, which must be solved in a time-marching framework. Eigenvalue or singular value decompositions of the discrete time equations can be used in order to perform stability analysis but such procedures must be accompanied by model order reduction because the size of the equations is large. This work proposes a modal frequency domain implementation of the Vortex Lattice method, resulting in a modal generalised force matrix. Model order reduction is implicit in the modal approach and stability analysis can be carried out using industry-standard flutter analysis techniques, such as the p-k method. The approach is validated by comparison to wind tunnel flutter data obtained from rectangular cantilever flat plate wings of different aspect ratios and sweep angles. It is found that the aeroelastic model predictions follow the experimental trends for both flutter speed and frequency but tend to be moderately conservative.

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See detailUnsteady Lifting Line Theory Using theWagner Function for the Aerodynamic and Aeroelastic Modeling of 3D Wings
Boutet, Johan; Dimitriadis, Grigorios

in Aerospace (2018), 5(3), 92

A method is presented to model the incompressible, attached, unsteady lift and pitching moment acting on a thin three-dimensional wing in the time domain. The model is based on the combination of Wagner theory and lifting line theory through the unsteady Kutta–Joukowski theorem. The results are a set of closed-form linear ordinary differential equations that can be solved analytically or using a Runge–Kutta–Fehlberg algorithm. The method is validated against numerical predictions from an unsteady vortex lattice method for rectangular and tapered wings undergoing step or oscillatory changes in plunge or pitch. Further validation is demonstrated on an aeroelastic test case of a rigid rectangular finite wing with pitch and plunge degrees of freedom.

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See detailExperimental and Numerical Study of Mini-UAV Propeller Performance in Oblique Flow
Theys, Bart; Dimitriadis, Grigorios; Hendrick, Patrick; De Schutter, Joris

in Journal of Aircraft (2017), 54(3), 1076-1084

This paper presents the modelling of the performance of small propellers used for Vertical Take Off and Landing Micro Aerial Vehicles (VTOL MAVs) operating at low Reynolds numbers and in oblique flow. Blade Element Momentum Theory (BEMT), Vortex Lattice Method (VLM) and momentum theory for oblique flow are used to predict propeller performance. For validation, the predictions for a commonly used propeller for VTOL MAVs are compared to a set of wind tunnel experiments. Both BEMT and VLM succeed in predicting correct trends of the forces and moments acting upon the propeller shaft, although accuracy decreases significantly in oblique flow. For the dataset analysed here, combining the available data of the propeller in purely axial flow with momentum theory for oblique flow and applying a correction factor for the wake skew angle results in more accurate performance estimates at all elevation angles.

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See detailExperimental passive flutter suppression using a linear tuned vibration absorber
Verstraelen, Edouard; Habib, Giuseppe; Kerschen, Gaëtan; Dimitriadis, Grigorios

in AIAA Journal (2017), 55(5), 1707-1722

The current drive for increased efficiency in aeronautic structures such as aircraft, wind turbine blades and helicopter blades often leads to weight reduction. A con- sequence of this tendency can be increased flexibility, which in turn can lead to un- favourable aeroelastic phenomena involving large amplitude oscillations and non- linear effects such as geometric hardening and stall flutter. Vibration mitigation is one of the approaches currently under study for avoiding these phenomena. In the present work, passive vibration mitigation is applied to a nonlinear experimental aeroelastic system by means of a linear tuned vibration absorber. The aeroelastic apparatus is a pitch and flap wing that features a continuously hardening restoring torque in pitch and a linear restoring torque in flap. Extensive analysis of the sys- tem with and without absorber at pre-critical and post-critical airspeeds showed an improvement in flutter speed of around 36%, a suppression of a jump due to stall flutter, and a reduction in LCO amplitude. Mathematical modelling of the exper- imental system is used to demonstrate that optimal flutter delay is achieved when two of the system modes flutter at the same flight condition. Nevertheless, even this optimal absorber quickly loses effectiveness as it is detuned. The wind tunnel mea- surements showed that the tested absorbers were much slower to lose effectiveness than those of the mathematical predictions.

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See detailVortex Lattice simulations of attached and separated flows around flapping wings
Lambert, Thomas; Abdul Razak, Norizham; Dimitriadis, Grigorios

in Aerospace (2017), 4(2), 22

Flapping flight is an increasingly popular area of research, with applications to micro-unmanned air vehicles and animal flight biomechanics. Fast but accurate methods for predicting the aerodynamic loads acting on flapping wings are of interest for designing such aircraft and optimising thrust production. In this work, the unsteady Vortex Lattice method is used in conjunction with three load estimation techniques in order to predict the aerodynamic lift and drag time histories produced by flapping rectangular wings. The load estimation approaches are the Katz, Joukowski and simplified Leishman-Beddoes techniques. The simulations' predictions are compared to experimental measurements from a flapping and pitching wing presented by Razak and Dimitriadis [1]. Three types of kinematics are investigated, pitch-leading, pure flapping and pitch lagging. It is found that pitch-leading tests can be simulated quite accurately using either the Katz or Joukowski approaches as no measurable flow separation occurs. For the pure flapping tests, the Katz and Joukowski techniques are accurate as long as the static pitch angle is greater than zero. For zero or negative static pitch angles these methods underestimate the amplitude of the drag. The Leishman-Beddoes approach yields better drag amplitudes but can introduce a constant negative drag offset. Finally, for the pitch-lagging tests the Leishman-Beddoes technique is again more representative of the experimental results, as long as flow separation is not too extensive. Considering the complexity of the phenomena involved, in the vast majority of cases the lift time history is predicted with reasonable accuracy. The drag (or thrust) time history is more challenging.

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See detailInduced Drag Calculations with the Unsteady Vortex Lattice Method for Cambered Wings
Lambert, Thomas; Dimitriadis, Grigorios

in AIAA Journal (2017), 55(2), 668-672

The Unsteady Vortex Lattice Method (UVLM) is an approach widely used to estimate the aerodynamic loads in unsteady subsonic flows. It is based on modeling the camber surface of a lifting body by means of bound vortex rings. Even though this method has been known and used for several decades, there is little discussion of the modeling of the leading-edge suction in the literature. To address this concern, Simpson et al. [1] presented a comparison of two different ways to model this effect for the case of uncambered airfoils and wings in harmonic pitch or plunge motions. They concluded that the Joukowski method converges significantly faster than the Katz technique as the number of chorwise panels is increased. The present paper is an extension of the study by Simpson et al. to cambered lifting surfaces. It shows that the presence of camber can change radically the convergence performance of the two methods. For cambered wings, the Katz approach converges significantly faster than the Joukowski technique.

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See detailTwo-domain and three-domain limit cycles in a typical aeroelastic system with freeplay in pitch
Verstraelen, Edouard; Dimitriadis, Grigorios; Dal Ben Rossetto, Gustavo; Dowell, Earl H.

in Journal of Fluids and Structures (2017), 69

Freeplay is a significant source of nonlinearity in aeroelastic systems and is strictly regulated by airworthiness authorities. It splits the phase plane of such systems into three piecewise linear subdomains. Depending on the location of the freeplay, limit cycle oscillations can result that span either two or three of these subdomains. The purpose of this work is to demonstrate the existence of two-domain cycles both theoretically and experimentally. A simple aeroelastic system with pitch, plunge and control deflection degrees of freedom is investigated in the presence of freeplay in pitch. It is shown that two-domain and three-domain cycles can result from a grazing bifurcation and propagate in the decreasing airspeed direction. Close to the bifurcation, the two limit cycle branches interact with each other and aperiodic oscillations ensue. Equivalent linearization is used to derive the conditions of existence of each type of limit cycle and to predict their amplitudes and frequencies. Comparisons with measurements from wind tunnel experiments demonstrate that the theory describes these phenomena with accuracy.

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See detailApplication of a 3D unsteady surface panel method with flow separation model to horizontal axis wind turbines
Prasad, Chandra Shekhar; Dimitriadis, Grigorios

in Journal of Wind Engineering and Industrial Aerodynamics (2017), 166

This work describes the development and application of a 3D unsteady surface panel method with a separation model to the problem of simulating the flow around the blades of a horizontal axis wind turbine. The present method is intended as a design tool to capture the 3D time-dependent characteristics of both attached and separated flow conditions and is an extension of previous 2D approaches. Flow separation is modelled using a loose coupling procedure between the inviscid panel method and a quasi-3D viscous boundary layer solution. A separated wake is shed at the predicted separation points and propagated at the local flow velocity, just like the trailing edge wake. The methodology is demonstrated on the NREL phase-VI wind turbine test case and the model predictions are compared to experimental measurements.

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See detailAeroservoelastic Simulations for Horizontal Axis Wind Turbines
Prasad, Chandra Shekhar; Chen, Qiong Zhong; Bruls, Olivier; D'Ambrosio, Flavio; Dimitriadis, Grigorios

in Proceedings of the Institution of Mechanical Engineers. Part A, Journal of Power and Energy (2017), 231(2), 103-117

This paper describes the development of a complete methodology for the aeroservoelastic modeling of horizontal axis wind turbines at the conceptual design stage. The methodology is based on the implementation of unsteady aerodynamic modeling, advanced description of the control system and nonlinear finite element calculations in the SWT wind turbine design package. The aerodynamic modeling is carried out by means of fast techniques, such as the Blade Element Method and the unsteady Vortex Lattice Method, including a free wake model. The complete model also includes a description of a doubly fed induction generator and its control system for variable speed operation. The SWT software features a non-linear finite element solver with multi-body dynamics capability. The full methodology is used to perform complete aeroservoelastic simulations of a realistic 2MW wind turbine model. The interaction between the three components of the approach is carefully analyzed and presented here.

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See detailPIV-based estimation of unsteady loads on a flat plate at high angle of attack using momentum equation approaches
Guissart, Amandine; Bernal, Luis; Dimitriadis, Grigorios; Terrapon, Vincent

in Experiments in Fluids (2017), 58(5), 53

This work presents, compares and discusses results obtained with two indirect methods for the cal culation of aerodynamic forces and pitching moment from 2D Particle Image Velocimetry (PIV) measurements. Both methodologies are based on formulations of the momentum balance: the integral Navier-Stokes equations and the “flux equation” proposed by Noca et al. (1999), which has been extended to the computation of moments. The indirect methods are applied to spatio-temporal data for different separated flows around a plate with a 16:1 chord-to-thickness ratio. Experimental data are obtained in a water channel for both a plate undergoing a large amplitude imposed pitching motion and a static plate at high angle of attack. In addition to PIV data, direct measurements of aerodynamic loads are carried out to assess the quality of the indirect calculations. It is found that indirect methods are able to compute the mean and the temporal evolution of the loads for two-dimensional flows with a reasonable accuracy. Nonetheless, both methodologies are noise sensitive and, the parameters impacting the computation should thus be chosen carefully. It is also shown that results can be improved through the use of Dynamic Mode Decomposition (DMD) as a pre-processing step.

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See detailThe influence of flight style on the aerodynamic properties of avian wings as fixed lifting surfaces
Lees, John J.; Dimitriadis, Grigorios; Nudds, Robert L.

in PeerJ (2016), 4:e2495

The diversity of wing morphologies in birds reflects their variety of flight styles and the associated aerodynamic and inertial requirements. Although the aerodynamics underlying wing morphology can be informed by aeronautical research, important differences exist between planes and birds. In particular, birds operate at lower, transitional Reynolds numbers than do most aircraft. To date, few quantitative studies have investigated the aerodynamic performance of avian wings as fixed lifting surfaces and none have focused upon the differences between wings from different flight style groups. Dried wings from 10 bird species representing 3 distinct flight style groups were mounted on a force/torque sensor within a wind tunnel in order to test the hypothesis that wing morphologies associated with different flight styles exhibit different aerodynamic properties. Morphological differences manifested primarily as differences in drag rather than lift. Maximum lift coefficients did not differ between groups, whereas minimum drag coefficients were lowest in undulating flyers (Corvids). The lift to drag ratios were lower than in conventional aerofoils and data from free-flying soaring species; particularly in high frequency, flapping flyers (Anseriformes), which do not rely heavily on glide performance. The results illustrate important aerodynamic differences between the wings of different flight style groups that cannot be explained solely by simple wing-shape measures. Taken at face value, the results also suggest that wing-shape is linked principally to changes in aerodynamic drag, but, of course, it is aerodynamics during flapping and not gliding that is likely to be the primary driver.

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See detailExperimental and numerical study of the flight of geese
Dimitriadis, Grigorios; Gardiner, James; Tickle, Peter; Codd, Jonathan; Nudds, Robert

in Aeronautical Journal (2015), 119(1217), 1-30

The 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 100 W to 240 W. Finally, it was observed that tandem flying can be very expensive for the trailing bird.

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See detailImpact of roughness and circularity-defect on bridge cables stability
Benidir, Adel; Flamand, Olivier; Gaillet, Laurent; Dimitriadis, Grigorios

in Journal of Wind Engineering and Industrial Aerodynamics (2015), 137

The stay cables on cable-stayed bridges have been the subject of considerable research in order to understand the origins of the dry galloping phenomenon. Surface irregularity is one of the last parameters that have not been thoroughly examined. This paper focuses on static wind tunnel tests on original High Density Polyethylene cable covers in a range of Reynolds numbers from the sub-critical regime to the critical, corresponding to values ranging from Re = 9.6x104 to Re = 3.3x105. The experiment consists in testing cable covers of various diameters in order to investigate the effect of surface irregularity (roughness and circularity defect) on the mechanism of dry galloping excitation. Previous studies reported that dry galloping is caused by the appearance of a negative pressure bubble on one side of the circular cylinder at the critical Reynolds number range, leading to a rapid drop in the drag coefficient and the appearance of a non-negligible lift force. The results of the present investigation demonstrate that there is a clear correlation between the single bubble pressure pattern and the circularity defect along the tube. They further show that surface roughness has little effect on the location of the bubble. The paper also treats the spatial and temporal correlation of the instantaneous pressure pattern along the tube with respect to the circularity defect.

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See detailThe aerodynamic cost of head morphology in bats: maybe not as bad as it seems
Vanderelst, Dieter; Peremans, Herbert; Abdul Razak, Norizham; Verstraelen, Edouard; Dimitriadis, Grigorios

in PLoS ONE (2015), 10(3), 0118545

At first sight, echolocating bats face a difficult trade-off. As flying animals, they would benefit from a streamlined geometric shape to reduce aerodynamic drag and increase flight efficiency. However, as echolocating animals, their pinnae generate the acoustic cues necessary for navigation and foraging. Moreover, species emitting sound through their nostrils often feature elaborate noseleaves that help in focussing the emitted echolocation pulses. Both pinnae and noseleaves reduce the streamlined character of a bat’s morphology. It is generally assumed that by compromising the streamlined charactered of the geometry, the head morphology generates substantial drag, thereby reducing flight efficiency. In contrast, it has also been suggested that the pinnae of bats generate lift forces counteracting the detrimental effect of the increased drag. However, very little data exist on the aerodynamic properties of bat pinnae and noseleaves. In this work, the aerodynamic forces generated by the heads of seven species of bats, including noseleaved bats, are measured by testing detailed 3D models in a wind tunnel. Models of Myotis daubentonii, Macrophyllum macrophyllum, Micronycteris microtis, Eptesicus fuscus, Rhinolophus formosae, Rhinolophus rouxi and Phyllostomus discolor are tested. The results confirm that non-streamlined facial morphologies yield considerable drag forces but also generate substantial lift. The net effect is a slight increase in the lift-to-drag ratio. Therefore, there is no evidence of high aerodynamic costs associated with the morphology of bat heads

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See detailReduced Order Analysis of Aeroelastic Systems with Freeplay using an Augmented Modal Basis
Silva, Gustavo H. C.; Dal Ben Rossetto, Gustavo; Dimitriadis, Grigorios

in Journal of Aircraft (2015), 52(4), 1312-1325

Freeplay in aircraft control surface actuators is a common source of nonlinearity that can cause undesirable aeroelastic phenomena and, as a consequence, certification authorities place strict limits on the size of the deadband gaps of actuators. In recent years many authors have worked on determining the effects of freeplay on the dynamic behavior of aeroelastic systems; these efforts have yielded significant improvements in the understanding of the phenomena, but have concentrated on simple models. Investigations of industry-relevant aeroelastic models of complete aircraft with freeplay in the actuators have been much rarer, the main difficulty being the selection of an appropriate modal basis that can represent the full range of possible dynamic phenomena. This work presents a novel implementation of the residual vectors approach to create consistent and numerically stable reduced order models suitable for industrial-standard aeroelastic models of aircraft. The methodology relies on the piecewise linear nature of freeplay to create a single reduction basis that represents the dynamics of the system both inside and outside the freeplay deadband gap. The method is demonstrated on an Embraer generic test bench aircraft, showing that the resulting reduced order model is efficient and effective. Nonlinear analysis is carried out using equivalent linearization as well as time integrations of the full nonlinear system. It is shown that, while equivalent linearization is an indispensable tool for a preliminary mapping of the main aeroelastic instabilities, the time integration-based nonlinear analysis is an essential complementary tool to confirm the characteristics of the system behavior.

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See detailEmpirical modelling of the bifurcation behaviour of a bridge deck undergoing across-wind galloping
Andrianne, Thomas; Dimitriadis, Grigorios

in Journal of Wind Engineering and Industrial Aerodynamics (2014), 135

This work presents an empirical model capable to describe the galloping bifurcation behaviour of a bridge deck. It is based on a general polynomial form proposed by Novak, which we limit to the 5th order. The advantage of choosing this function for modelling the vertical force coefficient is that asymmetry of the even terms is enforced in order to reproduce the sub-critical aeroelastic behaviour of the bridge deck. The coefficients of the polynomial are identified from several pairs of displacement amplitudes and the corresponding airspeeds, measured in a wind tunnel during dynamic tests on the sectional bridge model. The identification is carried out using a first order harmonic balance technique. A stability analysis is presented in order to highlight the need of such a model to catch the complete bifurcation behaviour of the system. The resulting force coefficient of this full order model is compared to the well known models of Parkinson and Novak. Finally, the concept universal curve is used in order to discuss the galloping responses of square and rectangular cylinders, in comparison with the one of the bridge deck.

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See detailExperimental study of wings undergoing active root flapping and pitching
Abdul Razak, Norizham; Dimitriadis, Grigorios

in Journal of Fluids and Structures (2014), 49

This paper presents the results of experiments carried out on mechanical wings undergoing active root flapping and pitching in the wind tunnel. The objective of the work is to investigate the effect of the pitch angle oscillations and wing profile on the aerodynamic forces generated by the wings. The experiments were repeated for different reduced frequency, airspeed, flapping and pitching kinematics, geometric angle of attack and wing sections (one symmetric and two cambered airfoils). A specially designed mechanical flapper was used, modelled on large migrating birds. It is shown that, under pitch leading conditions, good thrust generation can be obtained at a wide range of Strouhal numbers if the pitch angle oscillation is adjusted accordingly. Consequently, high thrust was measured at both the lowest and the highest tested Strouhal numbers. Furthermore, the work demonstrates that the aerodynamic forces can be sensitive to the Reynolds number, depending on the camber of the wings. Under pitch lagging conditions, where the effective angle of attack amplitude is highest, the symmetric wing was affected by the Reynolds number, generating less thrust at the lowest tested Reynolds value. In contrast, under pure flapping conditions, where the effective angle of attack amplitude was lower but still significant, it was the cambered wings that demonstrated Reynolds sensitivity.

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See detailExperimental and numerical investigations of the torsional flutter oscillations of a 4:1 rectangular cylinder
Andrianne, Thomas; Dimitriadis, Grigorios

in Journal of Fluids and Structures (2013), 41

The torsional flutter oscillations of a 4:1 rectangular cylinder around its pitching axis are investigated through wind tunnel experiments and numerical simulations. The rectangle’s responses to different initial conditions and turbulence excitations at various wind tunnel airspeeds are recorded. Timeresolved Particle Image Velocimetry measurements are taken at two different airspeeds, when the rectangle undergoes Limit Cycle Oscillations. Aeroelastic simulations are carried out using the Discrete Vortex Method and the resulting responses are compared to the experimental measurements. The Common-base Proper Orthogonal Decomposition method is used to analyse and compare the measured and simulated unsteady flow fields around the rectangle. A discussion of the participation of each mode in the different states of the flow-field is presented, at two different amplitudes of oscillation. The Motion Induced Vortex (MIV) is identified as the fundamental cause of the torsional flutter phenomenon and its role over a complete cycle is studied. MIV-induced oscillations can be started either by a suitable initial disturbance or by a second, nearly linear self-excited instability that causes negative aerodynamic damping. The combination of these two instabilities results in a complete description of the torsional flutter of the rectangle.

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See detailIntegrating Experimental and Computational Fluid Dynamics approaches using Proper Orthogonal Decomposition Techniques
Andrianne, Thomas; Yasue, Kanako; Guissart, Amandine; Terrapon, Vincent; Dimitriadis, Grigorios; Kuchi-Ishi, Shigeru; Watanabe, Shigeya

in Progress in Aerospace Sciences (2013)

The concept of Proper Orthogonal Decomposition (POD) is used to integrate Experimental Fluid Dynamics (EFD) and Computational Fluid Dynamics (CFD) approaches. The key idea is to take advantage of the optimality of the POD technique and its capability to extract the most energetic patterns of complex aerodynamic flow fields. First, the concept of Modal Assurance Criterion (MAC) is used to obtain a simple quantitative criterion to compare EFD measurements to CFD results. The comparison is based on the POD modes, extracted from each set of data. The analysis of the energy content of the modes allows to draw important conclusions about the role of the latter. The method is applied in the study of the flow field around a rectangular cylinder, which is either static or oscillating in a low-speed flow field. The second EFD/CFD integration technique deals with the reconstruction of a flow field from measured data, making use of CFD simulation results. The POD modes are first extracted from several CFD data sets, using a snapshot POD approach. Then the entire flow field of measured data can be reconstructed using a gappy POD method. The technique is applied to the transonic flow around a civil aircraft type wind tunnel model. The EFD measurements consist in pressure coefficient data from pressure ports or pressure-sensitive paint. It is shown that the complete flow field can be reconstructed from the pressure data with satisfactory accuracy and at relatively low computational cost. The work demonstrates the potential of the POD technique to integrate EFD and CFD data, leading to a combined, validated and complete analysis of the flow under consideration.

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See detailDamping identification of lightly damped linear dynamic systems using Common-base Proper Orthogonal Decomposition
Andrianne, Thomas; Dimitriadis, Grigorios

in Mechanical Systems and Signal Processing (2012), 28

This paper presents a new technique to identify the damping of linear systems. It is developed from the Proper Orthogonal Decomposition (POD) of the free response of the system and extended to the recently proposed Common-base POD (CPOD). The present application of CPOD considers simultaneously several free responses of the system to different initial conditions. The eigen-decomposition of the co-variance matrix leads to a unique vector basis which is likely to contain more information about the dynamics of the system than a vector basis obtained by the classic POD technique. The ability of the technique to estimate the mode shapes and the modal damping is demonstrated on a simulated mass-spring-damper system. Two different distributions of masses are considered in order to confront the CPOD analysis to the intrinsic limitation of POD, i.e. that the mode shapes are identified exactly only if the mass matrix is proportional to the identity matrix. It is shown that the identification of the damping is still possible when the modes are not orthonormal. The robustness of the technique is demonstrated in the presence of noise in the responses of the system and through an experimental application with comparison with other identifications techniques.

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See detailA potential role for bat tail membranes in flight control
Gardiner, James D; Dimitriadis, Grigorios; Codd, Jonathan R; Nudds, Robert L

in PLoS ONE (2011), 6(3), 18214

Wind tunnel tests conducted on a model based on the long-eared bat Plecotus auritus, indicated that the position of the tail membrane (uropatagium) can significantly influence flight control. Adjusting tail position by increasing the angle of the legs relative to the body, has a two-fold effect; increasing leg-induced wing camber (i.e. locally increased camber and angle of attack of the inner wing surface) and increasing the angle of attack of the tail membrane. We also used our model to examine the effects of flying with and without a tail membrane. For the bat model with a tail membrane increasing leg angle increased the lift, drag and nose-down pitching moment produced. However, removing the tail membrane significantly reduced the change in pitching moment with increasing leg angle, but it had a much smaller effect on the level of lift and drag produced. The tail membrane, therefore, is potentially important for controlling the level of pitching moment produced by bats and an aid to flight control, specifically improving agility and manoeuvrability. Although the tail of bats is different from that of birds, in that it is only divided from the wings by the legs, it nonetheless, may, in addition to its prey capturing function, fulfil a similar role in aiding flight control.

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See detailShooting-Based Complete Bifurcation Prediction for Aeroelastic Systems with Freeplay
Dimitriadis, Grigorios

in Journal of Aircraft (2011), 48(6), 1864-1877

In recent years there have been several applications of numerical continuation approaches to aeroelastic systems with freeplay. While some of these have been successful, the general application of the method to such systems remains problematic. Numerical continuation can fail in the presence of complex bifurcations, numerous nearby periodic solution branches and other factors. In this paper, a three-part procedure for applying numerical continuation to aeroelastic systems with freeplay is proposed, designed to ensure that the complete periodic behavior is identified, even for systems with very complex bifurcation diagrams. First, the equivalent linearization approach is used to determine approximations to the periodic solutions of the nonlinear system. Then, a shooting-based technique is applied separately to each linearized approximation in order to pinpoint the nearest exact periodic solution. This process results in a cloud of periodic solutions, representing points on all the solution branches and sub-branches. Finally, a branch-following shooting procedure is applied to this cloud of points in order to obtain a complete description of every branch of periodic solutions. The methodology is applied to a simple aeroelastic system with three degrees of freedom and freeplay in the control surface. This system has been often studied but never fully characterised. It is shown that the proposed method succeeds in describing the complete bifurcation behaviour of the system and explaining its limit cycle response.

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See detailFlutter and stall flutter of a rectangular wing in a wind tunnel
Norizham, Abdul Razak; Andrianne, Thomas; Dimitriadis, Grigorios

in AIAA Journal (2011), 49(10), 2258-2271

The aeroelastic behavior of a rectangular wing with pitch and plunge degrees of freedom was observed experimentally using pressure, acceleration and PIV measurements. The wing was set at different static angles of attack and wind tunnel airspeeds. The wing's dynamic behavior was governed by a two-parameter bifurcation from steady to Limit Cycle Oscillations (LCO), the two parameters being the airspeed and the static angle of attack. At the lowest static angle, the wing underwent a classical flutter phenomenon that was transformed into a supercritical Hopf bifurcation at higher angles. The latter was combined with a fold bifurcation at intermediate angles of attack. All LCOs observed were either low amplitude oscillations with time-varying amplitude or high amplitude oscillations with nearly steady amplitude. They were caused by two different types of dynamic stall phenomena. During low amplitude LCOs the periodically stalled flow covered only the rear part of the wing. During high amplitude LCOs, trailing edge and leading edge separation occured. Trailing edge separation was characterized by a significant amount of unsteadiness, varying visibly from cycle to cycle. The occurrence of leading edge separation was much more regular and had the tendency to stabilize the amplitude of the LCO motion.

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See detailSubcritical, nontypical and period doubling bifurcations of a Delta Wing in a low speed wind tunnel
Korbahti, Banu; Kagambage, Emile; Andrianne, Thomas; Norizham, Abdul Razak; Dimitriadis, Grigorios

in Journal of Fluids and Structures (2011), 27(3), 408-426

Limit Cycle Oscillations (LCOs) involving Delta wings are an important area of research in modern aeroelasticity. Such phenomena can be the result of geometric or aerodynamic nonlinearity. In this paper, a flexible half-span Delta wing is tested in a low speed wind tunnel in order to investigate its dynamic response. The wing is designed to be more flexible than the models used in previous research on the subject in order to expand the airspeed range in which LCOs occur. The experiments reveal that this wing features a very rich bifurcation behavior. Three types of bifurcation are observed for the first time for such an aeroelastic system: subcritical bifurcations, period doubling/period halving and nontypical bifurcations. They give rise to a great variety of LCOs, even at very low angles of attack.The LCOs resulting from the nontypical bifurcation display Hopf-type behavior, i.e. have fundamental frequencies equal to one of the linear modal frequencies. All of the other LCOs have fundamental frequencies that are unrelated to the underlying linear system modes.

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See detailBifurcation Behavior of Airfoil Undergoing Stall Flutter Oscillations in Low-Speed Wind Tunnel
Dimitriadis, Grigorios; Li, Jing

in AIAA Journal (2009), 47(11), 2577-2596

Stall flutter is a nonlinear aeroelastic phenomenon that can affect several types of aeroelastic systems such as helicopter rotor blades, wind turbine blades, and highly flexible wings. Although the related aerodynamic phenomenon of dynamic stall has been the subject of many experimental studies, stall flutter itself has rarely been investigated. This paper presents a set of experiments conducted on a NACA0012 airfoil undergoing stall flutter oscillations in a low-speed wind tunnel. The aeroelastic responses are analyzed with the objective of characterizing the local bifurcation behavior of the system. It is shown that symmetric stall flutter oscillations are encountered as a result of a subcritical Hopf bifurcation, followed by a fold bifurcation. The cause of these bifurcations is the occurrence of dynamic stall, which allows the transfer of energy from the freestream to the wing. A second bifurcation occurs at the system’s static divergence airspeed. As a consequence, the wing starts to undergo asymmetric stall flutter bifurcations at only positive (or only negative) pitch angles. The dynamic stall mechanism itself does not change but the flow only separates on one side of the wing.

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See detailIdentification of multi-degree of freedom non-linear systems using an extended modal space model
Platten, Michael F; Wright, Jan Robert; Dimitriadis, Grigorios; Cooper, Jonathan E

in Mechanical Systems and Signal Processing (2009), 23(1), 8-29

The identification of non-linear dynamic systems is an increasingly important area of research, with potential application in many industries. Current non-linear identification methodologies are, in general, mostly suited to small systems with few degrees of freedom and few non-linearities. In order to develop a practical identification approach for real engineering structures, the capability of such methods must be significantly extended. In this paper, it is shown that such an extension can be achieved using multi-exciter techniques in order to excited specific modes or degrees of freedom of the system under investigation. A novel identification method for large non-linear systems is presented, based on the use of a multi-exciter arrangement using appropriated excitation applied in bursts. This proposed Non-linear Resonant Decay Method is applied to a simulated system with 5 degrees of freedom and an experimental clamped panel structure. The technique is essentially a derivative of the Restoring Force Surface method and involves a non-linear curve fit performed in modal space. The effectiveness of the resulting reduced order model in representing the non-linear characteristics of the system is demonstrated. The potential of the approach for the identification of large continuous non-linear systems is also discussed.

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See detailIdentification of a Nonlinear Wing Structure Using an Extended Modal Model
Platten, M. F.; Wright, J. R.; Cooper, J. E.; Dimitriadis, Grigorios

in Journal of Aircraft (2009), 46(5), 1614-1626

The nonlinear resonant decay method identifies a nonlinear dynamic system using a model based in linear modal space comprising the underlying linear system and a small number of additional terms that represent the nonlinear behavior. In this work, the method is applied to an aircraftlike wing/store/pylon experimental structure that consists of a rectangular wing with two stores suspended beneath it by means of nonlinear pylons with a nominally hardening characteristic in the store rotation degree of freedom. The nonlinear resonant decay method is applied to the system using multishaker excitation. The resulting identified mathematical model features five modes, two of which are strongly nonlinear, one is mildly nonlinear, and two are completely linear. The restoring force surfaces obtained from the mathematical model are in close agreement with those measured from the system. This experimental application of the nonlinear resonant decay method indicates that the method could be suitable for the identification of nonlinear models of aircraft in ground vibration testing.

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See detailBifurcation analysis of aircraft with structural nonlinearity and freeplay using numerical continuation
Dimitriadis, Grigorios

in Journal of Aircraft (2008), 45(3), 893-905

In recent years the aeroelastic research community has carried out substantial work on the characterization and prediction of nonlinear aeroelastic phenomena. Of particular interest is the calculation of Limit Cycle Oscillations (LCO), which cannot be accomplished using traditional linear methods. In this paper, the prediction of the bifurcation and post-bifurcation behavior of nonlinear subsonic aircraft is carried out using Numerical Continuation. The analysis does not make use of continuation packages such as AUTO or MatCont. Two different continuation techniques are detailed, specifically adapted for realistic aeroelastic models. The approaches are demonstrated on model of a simple pitch plunge airfoil with cubic stiffness and an aeroelastic model of a transport aircraft with two different types of nonlinearity in the control surface. It is shown that one of the techniques yields highly accurate predictions for LCO amplitudes and periods while the second method trades off some accuracy for computational efficiency.

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See detailContinuation of Higher Order Harmonic Balance Solutions for Nonlinear Aeroelastic Systems
Dimitriadis, Grigorios

in Journal of Aircraft (2008), 45(2), 523-537

The Harmonic Balance method is a very useful tool for characterizing and predicting the response of nonlinear dynamic systems undergoing periodic oscillations, either self-excited or due to harmonic excitation. The method and several of its variants have been applied to nonlinear aeroelastic systems over the last two decades. This paper presents a detailed description of several Harmonic Balance methods and a continuation framework allowing the methods to follow the response of dynamic systems from the bifurcation point to any desired parameter value, while successfully negotiating further fold bifurcations. The continuation framework is described for systems undergoing sub-critical and super-critical Hopf bifurcations as well as a particular type of explosive bifurcation. The methods investigated in this work are applied to a nonlinear aeroelastic model of a Generic Transport Aircraft featuring polynomial or freeplay stiffness nonlinearity in the control surface. It is shown that high order Harmonic Balance solutions will capture accurately the complete bifurcation behavior of this system for both types of nonlinearity. Low order solutions can become inaccurate in the presence of numerous folds in the Limit Cycle Oscillation branch but can still yield practical engineering information at a fraction of the cost of higher order solutions. Time domain Harmonic Balance schemes are shown to be more computationally expensive than the standard Harmonic Balance approach.

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See detailDiagnosis of Process Faults in Chemical Systems Using a Local Partial Least Squares Approach
Kruger, Uwe; Dimitriadis, Grigorios

in AIChE Journal (2008), 54(10), 2581-2596

This article discusses the application of partial least squares (PLS) for monitoring complex chemical systems. In relation to existing work, this article proposes the integration of the statistical local approach into the PLS framework to monitor changes in the underlying model rather than analyzing the recorded input/output data directly. As discussed in the literature, monitoring changes in model parameters addresses the problems of nonstationary behavior and presents an analogy to model-based approaches. The benefits of the proposed technique are that (i) a detailed mechanistic plant model is not required, (ii) nonstationary process behavior does not produce false alarms, (iii) parameter changes can be non-Gaussian, (iv) Gaussian monitoring statistics can be established to simplify the monitoring task, and (v) fault magnitude and signatures can be estimated. This is demonstrated by a simulation example and the analysis of recorded data from two chemical processes.

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See detailThe aerodynamics of big ears in the brown long-eared bat Plecotus auritus
Gardiner, James; Dimitriadis, Grigorios; Sellers, William; Codd, Jonathan E

in Acta Chiropterologica (2008), 10(2), 313-321

Wings are the most obvious adaptation bats have for powered flight and differences in wing morphology are known to correlate with flight behaviour. However, the function(s) of ancillary structures such as the ears and tail, which may also play an important role during flight, are less well understood. Here we constructed a simplified model of a bat body with ears based upon morphological measurements of a brown long-eared bat (Plecotus auritus) to examine the aerodynamic implications of flying with large ears. The forces and moments produced by the model were measured using a sensitive 6-component force and torque balance during wind tunnel testing. The large ears of the model bat produced positive lift as well as positive drag of the same order of magnitude. At small ears angles (0° to 10°), increasing the angle of the ears resulted in an increase of the lift-to-drag ratio. At higher ear angles (> 10°) separation of the flow occurred which caused a large decrease in the lift-to-drag ratio produced. To maximise the benefit from the ears (i.e., lift-to-drag ratio) our model predicts that a horizontal free flying P. auritus should hold its ears at an approximate angle of 10°. The results of the pitching moment coefficient are inconclusive in determining if the large ears are important as flight control structures. The additional drag produced by the ears has consequences for the foraging behaviour of P. auritus with reductions in its flight speed and foraging range.

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See detailDemonstrating the identification of nonlinear vibrating systems to undergraduate students
Dimitriadis, Grigorios; Vio, Gareth Arthur

in International Journal of Mechanical Engineering Education (2007), 35(4), 336-360

The identification of nonlinear dynamic systems is increasingly becoming a necessary part of vibration testing and there is significant research effort devoted to it. However, as the current methodologies are still not suitable for the identification of general nonlinear systems the subject is very rarely introduced to undergraduate students. In this paper, recent progress in developing an expert approach to nonlinear system identification is used in order to demonstrate the subject within the context of an undergraduate course or as an introductory tool for postgraduate students. The demonstration is based around a software package of an Expert System designed to apply systematically a wide range of identification approaches to the system under investigation. It is shown that the software can be used to demonstrate the need for nonlinear system identification, the complexity of the procedure, the possibility of failure and the good chances of success when enough physical information about the system is available.

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See detailA Class of Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies Undergoing Simultaneous Resonances—Part I: Theoretical Development
Gallego-Garrido, Jon; Dimitriadis, Grigorios; Wright, Jan Robert

in International Journal of Rotating Machinery (2007), 2007

Blade tip timing is a technique for the measurement of vibrations in rotating bladed assemblies. Although the fundamentals of the technique are simple, the analysis of data obtained in the presence of simultaneously occurring synchronous resonances is problematic. A class of autoregressive-based methods for the analysis of blade tip timing data from assemblies undergoing two simultaneous resonances has been developed. It includes approaches that assume both sinusoidal and general blade tip responses. The methods can handle both synchronous and asynchronous resonances. An exhaustive evaluation of the approaches was performed on simulated data in order to determine their accuracy and sensitivity. One of the techniques was found to perform best on asynchronous resonances and one on synchronous resonances. Both methods yielded very accurate vibration frequency estimates under all conditions of interest.

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See detailBifurcation analysis and limit cycle oscillation amplitude prediction methods applied to the aeroelastic galloping problem
Vio, Gareth Arthur; Dimitriadis, Grigorios; Cooper, Jonathan E

in Journal of Fluids and Structures (2007), 23(7),

A global stability and bifurcation analysis of the transverse galloping of a square section beam in a normal steady flow has been implemented. The model is an ordinary differential equation with polynomial damping nonlinearity. Six methods are used to predict bifurcation, the amplitudes and periods of the ensuing Limit Cycle Oscillations: (i) Cell mapping, {ii} Harmonic Balance, (iii) Higher Order Harmonic Balance,(iv) Centre Manifold linearization, (v) Normal Form and (vi) Numerical Continuation. The resulting stability predictions are compared with each other and with results obtained from numerical integration. The advantages and disadvantages of each technique are discussed. It is shown that, despite the simplicity of the system, only two of the methods succeed in predicting its full response spectrum. These are Higher Order Harmonic Balance and Numerical Continuation.

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See detailA Class of Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies Undergoing Simultaneous Resonances—Part II: Experimental Validation
Gallego-Garrido, Jon; Dimitriadis, Grigorios; Carrington, Ian B.; Wright, Ian

in International Journal of Rotating Machinery (2007), 2007

Blade tip timing is a technique for the measurement of vibrations in rotating bladed assemblies. In Part I of this work a class of methods for the analysis of blade tip timing data from bladed assemblies undergoing two simultaneous synchronous resonances was developed. The approaches were demonstrated using data from a mathematical simulation of tip timing data. In Part II the methods are validated on an experimental test rig. First, the construction and characteristics of the rig will be discussed. Then, the performance of the analysis techniques when applied to data from the rig will be compared and analysed. It is shown that accurate frequency estimates are obtained by all the methods for both single and double resonances. Furthermore, the recovered frequencies are used to calculate the amplitudes of the blade tip responses. The presence of mistuning in the bladed assembly does not affect the performance of the new techniques.

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See detailNon-Linear Identification in Modal Space Using a Genetic Algorithm Approach for Model Selection
Platten, Michael F; Wright, Jan Robert; Worden, Keith; Dimitriadis, Grigorios; Cooper, Jonathan E

in International Journal of Applied Mathematics and Mechanics (2007), 3(1), 72-89

The Non-Linear Resonant Decay Method is an approach for the identification of non-linear systems with large numbers of degrees of freedom. The identified non-linear model is expressed in linear modal space and comprises the modal model of the underlying linear system with additional terms representing the non-linear behaviour. Potentially, a large number of these non-linear terms will exist but not all of them will be significant. The problem of deciding which and how many terms are required for an accurate identification has previously been addressed using the Forward Selection and Backward Elimination techniques. In this paper, a Genetic Algorithm optimisation is proposed as an alternative to those methods. A simulated lumped parameter non-linear dynamic system is used to demonstrate the proposed optimisation. The use of separate data sets for the identification and validation of the modal model is also investigated. It is found that the Genetic Algorithm approach yields significantly better results than the Backward Elimination and Forward Selection algorithms in many cases.

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See detailAeroelastic system identification using transonic CFD data for a wing/store configuration
Vio, Gareth Arthur; Dimitriadis, Grigorios; Cooper, Jonathan E.; Badcock, Ken J.; Woodgate, Mark A.; Rampurawala, Abdul M.

in Aerospace Science and Technology (2007), 11(2-3), 146-154

This paper is part of a study investigating the prediction of the aeroelastic behaviour of aircraft subjected to non-linear aerodynamic forces. The main objective of the work is the characterization of the dynamic response of aeroelastic models resulting from coupled Computational Fluid Dynamic and Finite Element calculations. Of interest here is the identification of the flight condition at which the response bifurcates to limited or divergent amplitude self-sustained oscillations without carrying out a comprehensive set of full, computationally expensive, time-marching calculations. The model treated in this work is a three-dimensional wing in a transonic flowfield. Short datasets of pre-bifurcation behaviour are analysed to determine the system’s stability and degree of non-linearity. It is found that the calculated responses on the run-up to a transonic Limit Cycle Oscillation show little or no evidence of non-linearity. The non-linearity appears abruptly at the bifurcation flight condition. The variation of the local Mach number over the wing’s surface in the steady-state case is used to demonstrate that the non-linearity is due to a shock wave that can move along the surface. At Mach numbers where this is not possible the system behaves in a linear manner and its stability can be analysed using linear methods.

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See detailNon-linear aeroelastic prediction for aircraft applications
Henshaw, M.J. de C.; Badcock, Ken J.; Vio, G. A.; Allen, C. B.; Chamberlaine, J.; Kaynes, I.; Dimitriadis, Grigorios; Cooper, J. E.; Woodgate, M. A.; Rampurawala, Abdul M.; Jones, D.; Fenwick, C.; Gaitonde, A. L.; Taylor, N. V.; Amor, D. S.; Eccles, T. A.; Denley, C. J.

in Progress in Aerospace Sciences (2007), 434(4-6), 65-137

Current industrial practice for the prediction and analysis of flutter relies heavily on linear methods and this has led to overly conservative design and envelope restrictions for aircraft. Although the methods have served the industry well, it is clear that for a number of reasons the inclusion of non-linearity in the mathematical and computational aeroelastic prediction tools is highly desirable. The increase in available and affordable computational resources, together with major advances in algorithms, mean that non-linear aeroelastic tools are now viable within the aircraft design and qualification environment. The Partnership for Unsteady Methods in Aerodynamics (PUMA) Defence and Aerospace Research Partnership (DARP) was sponsored in 2002 to conduct research into non-linear aeroelastic prediction methods and an academic, industry, and government consortium collaborated to address the following objectives: (1) To develop useable methodologies to model and predict non-linear aeroelastic behaviour of complete aircraft. (2) To evaluate the methodologies on real aircraft problems. (3) To investigate the effect of non-linearities on aeroelastic behaviour and to determine which have the greatest effect on the flutter qualification process. These aims have been very effectively met during the course of the programme and the research outputs include: (a) New methods available to industry for use in the flutter prediction process, together with the appropriate coaching of industry engineers. (b) Interesting results in both linear and non-linear aeroelastics, with comprehensive comparison of methods and approaches for challenging problems. (c) Additional embryonic techniques that, with further research, will further improve aeroelastics capability. This paper describes the methods that have been developed and how they are deployable within the industrial environment. We present a thorough review of the PUMA aeroelastics programme together with a comprehensive review of the relevant research in this domain. This is set within the context of a generic industrial process and the requirements of UK and US aeroelastic qualification. A range of test cases, from simple small DOF cases to full aircraft, have been used to evaluate and validate the non-linear methods developed and to make comparison with the linear methods in everyday use. These have focused mainly on aerodynamic non-linearity, although some results for structural non-linearity are also presented. The challenges associated with time domain (coupled computational fluid dynamics–computational structural model (CFD–CSM)) methods have been addressed through the development of grid movement, fluid–structure coupling, and control surface movement technologies. Conclusions regarding the accuracy and computational cost of these are presented. The computational cost of time-domain methods, despite substantial improvements in efficiency, remains high. However, significant advances have been made in reduced order methods, that allow non-linear behaviour to be modelled, but at a cost comparable with that of the regular linear methods. Of particular note is a method based on Hopf bifurcation that has reached an appropriate maturity for deployment on real aircraft configurations, though only limited results are presented herein. Results are also presented for dynamically linearised CFD approaches that hold out the possibility of non-linear results at a fraction of the cost of time coupled CFD–CSM methods. Local linearisation approaches (higher order harmonic balance and continuation method) are also presented; these have the advantage that no prior assumption of the nature of the aeroelastic instability is required, but currently these methods are limited to low DOF problems and it is thought that these will not reach a level of maturity appropriate to real aircraft problems for some years to come. Nevertheless, guidance on the most likely approaches has been derived and this forms the basis for ongoing research. It is important to recognise that the aeroelastic design and qualification requires a variety of methods applicable at different stages of the process. The methods reported herein are mapped to the process, so that their applicability and complementarity may be understood. Overall, the programme has provided a suite of methods that allow realistic consideration of non-linearity in the aeroelastic design and qualification of aircraft. Deployment of these methods is underway in the industrial environment, but full realisation of the benefit of these approaches will require appropriate engagement with the standards community so that safety standards may take proper account of the inclusion of non-linearity.

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See detailComment on Flutter Prediction from Flight Flutter Test Data
Dimitriadis, Grigorios; Cooper, Jonathan E

in Journal of Aircraft (2006), 43(3), 862-863

In a previous paper entitled “Flutter Predictions from Flight Flutter Test Data” the authors applied a number of different flutter prediction methods to data from two simulated aeroelastic aircraft models and compared the resulting flutter predictions. The two simulated models were a simple three-degree-of-freedom Hancock wing model and the Sim-2 model of a generic four-engined civil transport. One of the methods examined in the paper was the Nissim and Gilyard method (NGM). Because of difficulties encountered with the Sim-2 model, the authors failed to apply the NGM successfully to it, and only results for the Hancock model were presented in the paper. With the aid of Eli Nissim, the authors have now succeeded in applying the method to the Sim-2 model and to obtain quality flutter predictions from it. In this short Comment, the initial problems encountered will be described and then the solutions will be outlined. Finally, flutter predictions for the method will be presented and compared to the flutter predictions obtained from the other methods by Dimitriadis and Cooper.

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See detailA time–frequency technique for the stability analysis of impulse responses from nonlinear aeroelastic systems
Dimitriadis, Grigorios; Cooper, Jonathan E

in Journal of Fluids and Structures (2003), 17(8), 11811201

A time–frequency method is proposed for the analysis of response time histories from nonlinear aeroelastic systems. The approach is based on a time-varying curve-fit of the short time Fourier transform of the impulse response. It is shown that the method can be used in order to obtain a clear picture of the sub-critical stability of a number of aeroelastic systems with a variety of structural and aerodynamic nonlinearities. Additionally, frequency and amplitude information can be obtained for both the linear and nonlinear signatures of the response signals in the sub- and postcritical regions. Finally, it is shown that, given certain types of nonlinear functions, sub-critical damping trends can be extrapolated to predict bifurcation airspeeds.

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See detailOn the use of control surface excitation in flutter testing
Wright, Jan R; Wong, Jerry; Cooper, Jonathan E; Dimitriadis, Grigorios

in Proceedings of the Institution of Mechanical Engineers. Part G, Journal of Aerospace Engineering (2003), 217(6), 317-332

Flutter testing is aimed at demonstrating that the aircraft flight envelope is flutter free. Response measurements from deliberate excitation of the structure are used to identify and track frequency and damping values against velocity. In this paper, the common approach of using a flight control surface to provide the excitation is examined using a mathematical model of a wing and control surface whose rotation is restrained by a simple actuator. In particular, it is shown that it is essential to use the demand signal to the actuator as a reference signal for data processing. Use of the actuator force (or strain) or control angle (or actuator displacement) as a reference signal is bad practice because these signals contain response information. It may also be dangerous in that the onset of flutter may not be seen in the test results.

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See detailExperimental Validation Of The Constant Level Method For Identification Of Non-Linear Multi-Degree-Of-Freedom Systems
Dimitriadis, Grigorios

in Journal of Sound and Vibration (2002), 258(5), 829-845

System identification for non-linear dynamical systems could find use in many applications such as condition monitoring, finite element model validation and determination of stability. The effectiveness of existing non-linear system identification techniques is limited by various factors such as the complexity of the system under investigation and the type of non-linearities present. In this work, the constant level identification approach, which can identify multi-degree-of-freedom systems featuring any type of non-linear function, including discontinuous functions, is validated experimentally. The method is shown to identify accurately an experimental dynamical system featuring two types of stiffness non-linearity. The full equations of motion are also extracted accurately, even in the presence of a discontinuous non-linearity.

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See detailBlade-Tip Timing Measurement Of Synchronous Vibrations Of Rotating Bladed
Dimitriadis, Grigorios; Carrington, Ian B.; Wright, Jan Robert; Cooper, Jonathan E

in Mechanical Systems and Signal Processing (2002), 16(4), 599-622

Blade-tip timing (BTT) is a promising method for the detection, measurement and analysis of blade vibrations in rotating bladed assemblies. However, the intricacies of the method when applied to real rotating structures undergoing synchronous (Engine Ordered) vibrations are not yet fully understood. In this paper, a mathematical model is developed to simulate data from typical BTT tests of rotating assemblies. The simulator is then used in order to provide a qualitative analysis of several phenomena that can be associated with the synchronous vibrations of rotating assemblies, including mistuning, coupling, excitation at multiple Engine Orders and simultaneous synchronous and asynchronous responses. It is concluded that none of these phenomena on its own will render the identification of the frequency and amplitude of blade vibrations impossible. However, there is no single BTT data analysis method that is able to deal with all of these phenomena.

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See detailFlutter Prediction from Flight Flutter Test Data
Dimitriadis, Grigorios; Cooper, Jonathan E

in Journal of Aircraft (2001), 38(2), 355-367

The most common approach to flight flutter testing is to track estimated modal damping ratios of an aircraft over a number of flight conditions. These damping trends are then extrapolated to predict whether it is safe to move to the next test point and also to determine the utter speed. In the quest for more reliable and efficient flight flutter testing procedures, a number of alternative data analysis methods have been proposed. Five of these approaches are compared on two simulated aeroelastic models. The comparison is based on both the accuracy of prediction and the efficiency of each method. It is found that, for simple aeroelastic systems, the Nissim and Gilyard method (Nissim, E., and Gilyard, G. B., “Method for Experimental Determination of Flutter Speed by Parameter Identification,” AIAA Paper 89-1324, 1989) yields the best flutter predictions and is also the least computationally expensive approach.However, for larger systems, simpler approaches such as the damping fit and envelope function methods are found to be most reliable.

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See detailA comparison of blade tip timing data analysis methods
Carrington, Ian B; Wright, Jan Robert; Cooper, Jonathan E; Dimitriadis, Grigorios

in Proceedings of the Institution of Mechanical Engineers. Part G, Journal of Aerospace Engineering (2001), 215(6), 301-312

The experimental determination of the vibration characteristics of rotating engine blades is very important for fatigue failure considerations. One of the most promising techniques for measuring the frequency of blade vibrations is blade tip timing. In this paper, three vibration analysis methods were specifically formulated and applied to the tip timing problem for the first time, using data obtained from a simple mathematical blade tip timing simulation. The results from the methods were compared statistically in order to determine which of the techniques is more suitable. One of the methods, the global autoregressive instrumental variables approach, produced satisfactory results at realistic noise levels. However, all of the techniques produced biased results under certain circumstances.

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See detailCharacterization of the Behaviour of a Simple Aeroservoelastic System with Control Nonlinearities
Dimitriadis, Grigorios; Cooper, Jonathan E

in Journal of Fluids and Structures (2000), 14(8), 1173-1193

The characterization of the behaviour of nonlinear aeroelastic systems has become a very important research topic in the Aerospace Industry. However, most work carried to-date has concentrated upon systems containing structural or aerodynamic nonlinearities. The purpose of this paper is to study the stability of a simple aeroservoelastic system with nonlinearities in the control system and power control unit. The work considers both structural and control law nonlinearities and assesses the stability of the system response using bifurcation diagrams. It is shown that simple feedback systems designed to increase the stability of the linearized system also stabilize the nonlinear system, although their effects can be less pronounced. Additionally, a nonlinear control law designed to limit the control surface pitch response was found to increase the flutter speed considerably by forcing the system to undergo limit cycle oscillations instead of fluttering. Finally, friction was found to affect the damping of the system but not its stability, as long as the amplitude of the frictional force is low enough not to cause stoppages in the motion.

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See detailLimit Cycle Oscillation Control and Suppression
Dimitriadis, Grigorios; Cooper, Jonathan E

in Aeronautical Journal (1999), 103(1023), 257-263

The prediction and characterization of the Limit Cycle Oscillation (LCO) behaviour of nonlinear aeroelastic systems has become of great interest recently. However, much of this work has concentrated on determining the existence of LCOs. This paper concentrates on LCO stability. By considering the energy present in di®erent limit cycles, and also using the Harmonic Balance Method, it is shown how the stability of limit cycles can be determined. The analysis is then extended to show that limit cycles can be controlled, or even suppressed, by the use of suitable excitation signals. A basic control scheme is developed to achieve this, and is demonstrated on a simple simulated nonlinear aeroelastic system.

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See detailA method for identification of non-linear multi-degree-of-freedom systems
Dimitriadis, Grigorios; Cooper, Jonathan E

in Proceedings of the Institution of Mechanical Engineers. Part G, Journal of Aerospace Engineering (1998), 212(4), 287-298

System identification methods for non-linear aeroelastic systems could find uses in many aeroelastic applications such as validating finite element models and tracking the stability of aircraft during flight flutter testing. The effectiveness of existing non-linear system identification techniques is limited by various factors such as the complexity of the system under investigation and the type of non-linearities present. In this work, a new approach is introduced which can identify multi-degree-of-freedom systems featuring any type of non-linear function, including discontinuous functions. The method is shown to yield accurate identification of three mathematical models of aeroelastic systems containing a wide range of structural non-linearities.