Grigorios Dimitriadis

Bifurcation Behavior of Airfoil Undergoing Stall Flutter Oscillations in Low-Speed Wind Tunnel

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 systems 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.

A Comparison of Blade Tip-Timing Data Analysis Methods

Abstract 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.

Flutter Prediction from Flight Flutter Test Data

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 flutter 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.

Flutter and stall flutter of a rectangular wing in a wind tunnel

The aeroelastic behavior of a rectangular wing with pitch and plunge degrees of freedom was observed experimentally using pressure, acceleration, and particle image velocimetry measurements. The wing was set at different static angles of attack and wind-tunnel airspeeds. The wing’s dynamic behavior was governed by a twoparameter bifurcation from steady to limit cycle oscillations, with 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 supercriticalHopf bifurcation at higher angles. The latterwas combinedwith a fold bifurcation at intermediate angles of attack. All limit cycle oscillations observed were either low-amplitude oscillations with timevarying amplitude or high-amplitude oscillations with nearly steady amplitude. They were caused by two different types of dynamic stall phenomena. During low-amplitude limit cycle oscillations the periodically stalled flow covered only the rear part of the wing. During high-amplitude limit cycle oscillations, trailing-edge and leading-edge separation occurred. Trailing-edge separation was characterized by a significant amount of unsteadiness, varying visibly from cycle to cycle. The occurrence of leading-edge separation was muchmore regular and had the tendency to stabilize the amplitude of the limit cycle oscillation motion.

Continuation of Higher-Order Harmonic Balance Solutions for Nonlinear Aeroelastic Systems

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 were 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 subcritical and supercritical 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 free-play stiffness nonlinearity in the control surface. It is shown that high-order harmonic balance solutions will accurately capture 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.

A Class of Methods for the Analysis of Blade Tip Timing Data from Bladed Assemblies Undergoing Simultaneous Resonances—Part I: Theoretical Development

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.

Identification of a Nonlinear Wing Structure Using an Extended Modal Model

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.

A potential role for bat tail membranes in flight control.

Wind tunnel tests conducted on a model based on the long-eared bat Plecotus auritus indicated that the positioning of the tail membrane (uropatagium) can significantly influence flight control. Adjusting tail position by increasing the angle of the legs ventrally relative to the body has a two-fold effect; increasing leg-induced wing camber (i.e., locally increased camber 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 pitching moment (nose-down) produced. However, removing the tail membrane significantly reduced the change in pitching moment with increasing leg angle, but it had no significant effect on the level of lift produced. The drag on the model also significantly increased with the removal of the tail membrane. 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.

Limit Cycle Oscillation Control and Suppression

The prediction and characterisation of the limit cycle oscillation (LCO) behaviour of non-linear aeroelastic systems has become of great interest recently. However, much of this work has concentrated on determining the existence of LCOs. We concentrate on LCO stability. By considering the energy present in different 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 non-linear aeroelastic system

The aerodynamics of big ears in the brown long-eared bat Plecotus auritus

Abstract 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.