Kevin Knowles

Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 1: Methodology and analysis:

Abstract The essence of this two-part paper is the analytical, aerodynamic modelling of insect-like flapping wings in the hover for microair vehicle applications. A key feature of such flapping-wing flows is their unsteadiness and the formation of a leading-edge vortex in addition to the conventional wake shed from the trailing edge. What ensues is a complex interaction between the shed wakes which, in part, determines the forces and moments on the wing. In an attempt to describe such a flow, two-novel coupled, non-linear, wake-integral equations are developed in this first part of the paper, and these form the foundation upon which the rest of the work stands. The circulation-based model thus developed is unsteady and inviscid in nature and essentially two-dimensional. It is converted to a ‘quasi-three-dimensional’ model using a blade-element-type method, but with radial chords. The main results from the model are force and moment data for the flapping wing and are derived as part of this article using the method of impulses. These forces and moments have been decomposed into constituent elements. The governing equations developed in the study are exact, but do not have a closed analytic form. Therefore, solutions are found by numerical methods. These are described in the second part of this paper.

Non-linear unsteady aerodynamic model for insect-like flapping wings in the hover. Part 2: Implementation and validation

Abstract The essence of this two-part paper is the analytical, aerodynamic modelling of insect-like flapping wings in the hover for micro-air-vehicle applications. A key feature of such flapping-wing flows is their unsteadiness and the formation of a leading-edge vortex in addition to the conventional wake shed from the trailing edge. What ensues is a complex interaction between the shed wakes, which, in part, determines the forces and moments on the wing. In an attempt to describe such a flow, two novel coupled, non-linear, wake integral equations were developed in the first part of the paper. The governing equations derived were exact, but did not have a closed analytical form. Solutions were, therefore, to be found by numerical methods and implemented in Fortran. This is the theme of the second part of the paper. The problem is implemented by means of vortex methods, whereby discrete point vortices are used to represent the wing and its wake. A number of numerical experiments are run to determine the best values for numerical parameters. The calculation is performed using a time-marching algorithm and the evolution of the wakes is tracked. In this way, both flow field and force data are generated. The model is then validated against existing experimental data and very good agreement is found both in terms of flow field representation and force prediction. The temporal accuracy of the simulations is also noteworthy, implying that the underlying flow features are well captured, especially the unsteadiness. The model also shows the similarity between two-dimensional and three-dimensional flows for insect-like flapping wings at low Reynolds numbers of the order of Re ε 200.

Insectlike Flapping Wings in the Hover Part II: Effect of Wing Geometry

The aerodynamic design of a flapping-wing micro air vehicle requires a careful study of the wing design space to ascertainthebestcombinationofparameters.Anonlinearunsteadyaerodynamic modeldevelopedbytheauthorsis used to make such a study for hovering insectlike flapping wings. The work is characterized, in particular, by the insights it provides into flapping-wing flows and the use of these insights for aerodynamic design. The effects of wing geometry on the aerodynamic performance of such flapping wings are investigated by comparing the influence on a numberofsyntheticplanformshapeswhilevaryingonlyoneparameteratatime.Bestperformanceappearstobefor wingshapesthathavenearlystraight leadingedges andmoreareaoutboard,where flowvelocities arehigher.Other important trends are also identified and practical considerations are noted. When possible, comparisons are also drawn with quasi-steady expectations and discrepancies are explained.

Insectlike Flapping Wings in the Hover Part I: Effect of Wing Kinematics

A GILE flight inside buildings, caves, and tunnels is of significant military and civilian value and is an attractive application for micro air vehicles (MAVs), defined here as flying machines of the order of 150 mm in size. Indoor flight imposes particular design and performance requirements, including small size, low speed, hovering capability, high maneuverability at low speeds, and (for covert operations) small acoustic signature, among other things. As discussed elsewhere [1–4], insectlike flapping is a solution thatmeets these requirements and is proven in nature. Although a number of elements characterize the design of a flapping-wing MAV, the focus here is on its wing aerodynamic design. This is crucial because for a flapping-wing MAV (FMAV) the wings are not only responsible for lift, but also for propulsion and maneuvers. Although insect flapping wings offer a proven solution and are abundant in nature (there are over 170,000 species of flying insects), little is known about the optimality of their wing design. Unlike forfixed or rotarywings, the parametric space associatedwith flapping wings is largely unexplored. A study that addresses the effects of both wing kinematics and wing geometry on the aerodynamic performance of flapping wings is required, and the former forms the underlying theme of this paper. The effect of wing geometry is considered elsewhere [5]. This work also provides insights into flapping-wing flow physics and uses these insights for aerodynamic design. Although Ellington’s [6] seminal work rejuvenated interest in insect flight, it is only recently that attention has been directed toward the design of vehicles that use insectlike flapping wings, particularly at the MAV scale [1–3]. In a later study, Ellington [7] proposed design guidelines based on scaling fromnature, but this does not give physical insight or allow design optimization. Dickinson et al. [8] investigated the effect of advancing or delaying pitch rotation of the flapping wing with respect to its translational motion, using experiments on Dickinson’s Robofly: a scaled-up mechanical model of the fruit fly Drosophila. Ramamurti and Sandberg [9] used a computational fluid dynamics (CFD) method to demonstrate this effect and presented some useful flow visualization. Sun and Tang [10] also used a CFD code to investigate the effect of advancing and delaying pitch rotation on insectlike flapping flight and the effect of varying the duration of stroke reversals [11]. In an earlier study [12], they investigated the effect of Reynolds number and the duration of wing stroke reversal. They also studied the effect of advance ratio (the ratio of flight speed to wing mean tip speed) in forward flapping flight [13]. Yu and Tong [14] used an aerodynamic modeling approach [15] to study forward flapping flight at various advance ratios by varying asymmetries between upand downstrokes. However, none of the preceding studies aimed to produce an optimized wing aerodynamic design. Milano and Gharib [16] made probably the only study thus far aimed at optimizing wing kinematics. They used a genetic algorithm paired with digital particle-image velocimetry experiments on a flapping wing in a water-filled towing tank. By using insectlike kinematics, they optimized for average lift over four flapping cycles and found a number of convergent solutions in the parameter space. They noted that the optimally efficient solutions all tended to generate leading-edge vortices ofmaximum strength. However, their Received 26 October 2007; revision received 11 June 2008; accepted for publication 13 June 2008. Copyright

Turbulence measurements in radial wall-jets

An experimental study was carried out into a single circular jet impinging onto a flat ground board. The jet was running at a fixed nozzle pressure ratio (NPR) of 1.05 (Reynolds number of 90,000 based on nozzle exit conditions), the nozzle to ground board separation (Hn) varying between 2 and 10 diameters (Dn). Measurements were performed in the free and wall-jets using cross-wire hot-wire anemometry, mean velocity, normal and shear stress results being presented. Nozzle height was found to affect the initial thickness of the wall-jet leaving the impingement region, increasing Hn/Dn increasing the wall-jet thickness. Nozzle height was also found to have a large effect on the peak level of turbulence found in the wall-jet up to a radial distance of r/Dn≈4.5, after which the profiles became self-similar, the peak value occurring around r/Dn=2.0. Lower Hn/Dn caused an increase in the peak level measured in all the turbulent stresses within the impingement region. This was attributed to greater shearing of the flow at the lower nozzle height due to a thinner wall-jet leaving the impingement region.

A review of jet mixing enhancement for aircraft propulsion applications

Abstract This article reviews techniques applicable to enhancing the mixing of jets, with particular emphasis on infrared (IR) signature reduction of high-speed jets. Following a brief introduction to the IR signature of jet plumes and the fundamentals of jet mixing, this paper discusses rapid mixing technologies under the categories of: geometric modifications (to the nozzle); high shear stress mixing; normal stress mixing; self-acoustic excitation; external acoustic excitation; mechanically oscillated; self-oscillated. It is shown that mixing enhancements of the order of 100 per cent are possible with some techniques and that by combining techniques this can be increased by at least as much again. Simple geometric calculations are presented which demonstrate that with rectangular nozzles such high levels of mixing enhancement may be necessary in order to reduce IR signature. Some apparent rapid mixing technologies, however, have been shown to increase jet spreading without increasing entrainment, whereas other techniques can reduce entrainment as easily as they can increase it.

Energy conservation based fuzzy tracking for unmanned aerial vehicle missions under a priori known wind information

The aim of this work is to include the navigation step for the waypoint-based guidance of a UAV system and to illustrate aspects such as tracking of the reference trajectory under wind presence, while conserving total energy requirements. The mission is represented utilising graph theory tools. The mathematical modelling of an aircraft controlled by an actuator surface is presented in terms of simple analytic relationships in order to simulate the actual horizontal motion of the vehicle. Its equivalence with a Tagaki-Sugeno (T-S) fuzzy system is illustrated that can aid the control methodology involved. Additionally, the advantages of utilising such an analysis is also stressed. The model formulated is an error posture model, that depends on current and reference posture. The control law is designed through parallel distributed compensation (PDC) and the gains are computed with the help of linear matrix inequalities (LMIs). Hence stability for the system is also guaranteed provided that the state variables are bounded in a priori known compact space. Moreover the energy requirements are described. This article is contributing towards energy enhancing a UAV mission and generating safely-flyable trajectories to meet mission objectives. The control law used is calculated in the pre-flight planning and can be used in real time for any trajectory to be tracked under any environmental conditions. Provided that angular and linear velocities are bounded, the latter is feasible under the assumption that the magnitude of air speed is small compared to the ground velocity of the aerial vehicle. The methodology offers an improved visualisation to aid an analyst with the representation of a UAV mission through graph theory tools utilising energy requirements for the mission and fast computational schema using matrix analysis. A simulation example of a UAV deployed from a source to reach a destination node under windy conditions is included to illustrate the analysis. The reference trajectory used is a piecewise Bezier-Bernstein curve referred to as the Dubins path.

On mathematical modelling of insect flight dynamics in the context of micro air vehicles

We discuss some aspects of mathematical modelling relevant to the dynamics of insect flight in the context of insect-like flapping-wing micro air vehicles (MAVs). MAVs are small flying vehicles developed to reconnoître in confined spaces. This requires power-efficient, highly-manoeuvrable, low-speed flight with stable hover. All of these attributes are present in insect flight and hence the focus on reproducing the functionality of insect flight by engineering means. Empirical research on insect flight dynamics is limited by experimental difficulties. Force and moment measurements require tethering the animal whose behaviour may then differ from free flight. The measurements are made when the insect actively tries to control its flight, so that its open-loop dynamics cannot be observed. Finally, investigation of the sensory-motor system responsible for flight is even more challenging. Despite these difficulties, much empirical progress has been made recently. Further progress, especially in the context of MAVs, can be achieved by the complementary information derived from appropriate mathematical modelling. The focus here is on a means of computing the data not easily available from experiments and also on making mathematical predictions to suggest new experiments. We consider two aspects of mathematical modelling for insect flight dynamics. The first one is theoretical (computational), as opposed to empirical, generation of the aerodynamic data required for the six-degrees-of-freedom equations of motion. For this purpose we first explain insect wing kinematics and the salient features of the corresponding flow. In this context, we show that aerodynamic modelling is a feasible option for certain flight regimes, focusing on a successful example of modelling hover. Such modelling progresses from the first principles of fluid mechanics, but relies on simplifications justified by the known flow phenomenology and/or geometric and kinematic symmetries. This is relevant to six types of fundamental manoeuvres, which we define as those flight conditions for which only one component of the translational and rotational body velocities is nonzero and constant. The second aspect of mathematical modelling for insect flight dynamics addressed here deals with the periodic character of the aerodynamic force and moment production. This leads to consideration of the types of solutions of nonlinear equations forced by nonlinear oscillations. In particular, the mechanism of synchronization seems relevant and should be investigated further.

COMPUTATIONAL STUDIES OF IMPINGING JETS USINGK-ε TURBULENCE MODELS

We report numerical modelling of impinging jet flows using Rodi and Malin corrections to the k-e turbulence model, carried out using the PHOENICS finite volume code. Axisymmetric calculations were performed on single round free jets and impinging jets and the effects of pressure ratio, height and nozzle exit velocity profile were investigated numerically. It was found that both the Rodi and Malin corrections tend to improve the prediction of the hydrodynamic field of free and impinging jets but still leave significant errors in the predicted wall jet growth. These numerical experiments suggest that conditions before impingement significantly affect radial wall jet development, primarily by changing the wall jets initial thickness.

Experimental and computational investigation of an ‘open’ transonic cavity flow

Abstract This paper presents an investigation of a transonic flow (M∞=0.85) over a rectangular cavity having a length-to-depth ratio of 5. Velocities were measured inside the cavity on the central plane and two off-centre planes using a two-component particle image velocimetry system. These measurements were supported by surface flow visualization, and mean and time-varying surface pressure measurements. The flow was also simulated using an unsteady Reynolds-averaged Navier—Stokes code, with a realizable k — ε turbulence model. It is shown that this CFD model does not capture all the characteristics of the flowfield correctly. However, by using this integrated experimental and computational approach we have been able to identify three-dimensional flowfield structures within the cavity. The influence of the thickness of the approaching boundary layer is discussed.