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

This paper discusses several aspects of mathematical modelling relevant to the flight dynamics of insect flight in the context of insect-like flapping wing micro air vehicles (MAVs). MAVs are defined as flying vehicles ca six inch in size (hand-held) and are developed to reconnoitre in confined spaces (inside buildings, tunnels etc). 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 of reproducing the functionality of insect flight by engineering means. This can only be achieved if qualitative insight is accompanied by appropriate quantitative analysis, especially in the context of flight dynamics, as flight dynamics underpin the desirable manoeuvrability. 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 these purposes 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, focussing on a successful example of modelling hover. Such modelling progresses from first principles of fluid mechanics, but relies on simplifications justified by the known flow phenomenology and/or geometric and kinematic symmetries. In particular, this is relevant to six types of fundamental manoeuvres, which we define as those steady flight conditions for which only one component of both the translational and rotational body velocities is non-zero (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 existence of non-periodic solutions of equations of motion is of practical interest, since this allows steady recitilinear flight. Progress in both aspects of mathematical modelling for insect flight will require further advances in aerodynamics of insect-like flapping. Improved aerodynamic modelling and computational fluid dynamics (CFD) calculations are required. These theoretical advances must be accompanied by further flow visualisation and measurement to validate both the aerodynamic modelling and CFD predictions

Forcing boundary-layer transition on an inverted airfoil in ground effect and at varying incidence

Presented at 34th AIAA Applied Aerodynamics ConferenceThe influence of the laminar boundary-layer state on a wing operating in ground effect at Re = 6 × 10 has been investigated using experiments with a model that provides two-dimensional flow and computations with a panel-method code. The effect of a boundary-layer trip placed at varying distances from the leading edge was observed at various incidences in terms of on-surface characteristics, including pressure measurements, flow visualisation and hot-film anemometry, and off-surface characteristics with LDA surveys below and behind the wing. The act of forcing transition led to downforce being reduced and drag increased, moreover, it altered almost all aspects of the wing’s aerodynamic characteristics, with the effect becoming greater as the trip was placed closer to the leading edge. These aspects include the replacement of a laminar separation bubble with trailing-edge separation, a thicker boundary layer, and a thicker wake with greater velocity deficit. The importance of considering laminar phenomena for wings operating in ground effect has been show

An Efficiently Parallelized High-Order Aeroacoustics Solver Using a Characteristic-Based Multi-Block Interface Treatment and Optimized Compact Finite Differencing

This paper presents the development of a fourth-order finite difference computational aeroacoustics solver. The solver works with a structured multi-block grid domain strategy, and it has been parallelized efficiently by using an interface treatment based on the method of characteristics. More importantly, it extends the characteristic boundary condition developments of previous researchers by introducing a characteristic-based treatment at the multi-block interfaces. In addition, most characteristic methods do not satisfy Pfaff’s condition, which is a requirement for any mathematical relation to be valid. A mathematically-consistent and valid method is used in this work to derive the characteristic interface conditions. Furthermore, a robust and efficient approach for the matching of turbulence quantities at the multi-block interfaces is developed. Finally, the implementation of grid metric relations to minimise grid-induced errors has been adopted. The code was validated against a number of benchmark cases, which demonstrated its accuracy and robustness across a range of problem types

Effects of scaling on high subsonic cavity flow oscillations and control

The effects of scaling on cavity oscillations and control have been studied by measuring the unsteady pressure on the floor of three cavities of different scales. The cavities have a length-to-depth ratio of 5 and a length-to-width ratio of 2, and the corresponding linear dimensions are in the ratio0.5∶1∶2. The experiments were conducted with clean cavities and cavities fitted with leading-edge sawtooth spoilers so as to study the influence of scaling on clean cavities as well as the effectiveness of the passive control method on different sized cavities. The results showed significant variation of certain spectral characteristics of the clean cavities. The control effectiveness of the spoilers also showed variations with a change in scale of the model. It is recommended that, before implementing a passive control device for practical applications, the device should be tested in the possible range of cavity length-to-boundary-layer-thickness ratio (L/δ) that can be experienced in actual flight

Scale effects on the performance of sawtooth spoilers in transonic rectangular cavity flow

An experimental study was conducted on the effectiveness of sawtooth spoilers at suppressing acoustic tones within a rectangular cavity with a length-to-depth ratio of five and a width-to-depth ratio of two, operating at a freestream Mach number of 0.71. Whereas previous research has focussed on the ratio of spoiler height to boundary-layer thickness (h/δ), this study also considers the effect of the ratio of cavity length to boundary-layer thickness (L/δ). Using a combination of unsteady pressure measurements and particle image velocimetry, it was established that consideration of the magnitude of both parameters is important when designing passive control methods for transonic cavities. A correlation was developed which suggests that in order to suppress fully the cavity tones, a critical spoiler height, h cr, is defined such that h cr/δ = 0.065 ≤ L/δ ≤ 0.082

Modelling boundary-layer transition on wings operating in ground effect at low Reynolds numbers

The transition-sensitive, three-equation k-kL-ω eddy-viscosity closure model was used for simulations of three-dimensional, single-element and multi-element wing configurations operating in close proximity to the ground. The aim of the study was to understand whether the model correctly simulated the transitional phenomena that occurred in the low Reynolds number operating conditions and whether it offered an improvement over the classical fully turbulent k-ω shear stress transport model. This was accomplished by comparing the simulation results to experiments conducted in a 2.7 m × 1.7 m closed-return, three-quarter-open-jet wind tunnel. The model was capable of capturing the presence of a laminar separation bubble on the wing and predicted sectional forces and surface-flow structures generated by the wings in wind tunnel testing to within 2.5% in downforce and 4.1% in drag for a multi-element wing. It was found, however, that the model produced insufficient turbulent kinetic energy during shear-layer reattachment, predicted turbulent trailing-edge separation prematurely in areas of large adverse pressure gradients, and was found to be very sensitive to inlet turbulence quantities. Despite these deficiencies, the model gave results that were much closer to wind-tunnel tests than those given by the fully turbulent k-ω shear stress transport model, which tended to underestimate downforce. Significant differences between the transitional and fully turbulent models in terms of pressure field, wake thickness and turbulent kinetic energy production were found and highlighted the importance of using transitional models for wings operating at low Reynolds numbers in ground effect. The k-kL-ω model has been shown to be appropriate for the simulation of separation-induced transition on a three-dimensional wing operating in ground effect at low Reynolds number

Forcing boundary-layer transition on a single-element wing in ground effect

The transition from a laminar to turbulent boundary layer on a wing operating at low Reynolds numbers can have a large effect on its aerodynamic performance. For a wing operating in ground effect, where very low pressures and large pressure gradients are common, the effect is even greater. A study was conducted into the effect of forcing boundary-layer transition on the suction surface of an inverted GA(W)-1 section single-element wing in ground effect, which is representative of a racing-car front wing. Transition to a turbulent boundary layer was forced at varying chordwise locations and compared to the free-transition case using experimental and computational methods. Forcing transition caused the laminar separation bubble, which was the unforced transition mechanism, to be eliminated in all cases and trailing-edge separation to occur instead. The aerodynamic forces produced by the wing with trailing-edge separation were shown to be dependent on trip location. As the trip was moved upstream the separation point also moved upstream, this led to an increase in drag and reduction in downforce. In addition to significant changes to the pressure field around the wing, turbulent energy in the wake was considerably reduced by forcing transition. The differences between free- and forced-transition wings were shown to be significant, highlighting the importance of modelling transition for ground-effect wings. Additionally, it has been shown that whilst it is possible to reproduce the force coefficient of a higher Reynolds number case by forcing the boundary layer to a turbulent state, the flow features, both on-surface and off-surface, are not recreated

Characteristics of boundary-layer transition and Reynolds-number sensitivity of three-dimensional wings of varying complexity operating in ground effect

The influence of Reynolds number on the aerodynamic characteristics of various wing geometries was investigated through wind-tunnel experimentation. The test models represented racing car front wings of varying complexity: from a simple single-element wing to a highly complex 2009-specification formula-one wing. The aim was to investigate the influence of boundary-layer transition and Reynolds-number dependency of each wing configuration. The single-element wing showed significant Reynolds-number dependency, with up to 320% and 35% difference in downforce and drag, respectively, for a chordwise Reynolds number difference of 0.81 × 105. Across the same test range, the multi-element configuration of the same wing and the F1 wing displayed less than 6% difference in downforce and drag. Surface-flow visualization conducted at various Reynolds numbers and ground clearances showed that the separation bubble that forms on the suction surface of the wing changes in both size and location. As Reynolds number decreased, the bubble moved upstream and increased in size, while reducing ground clearance caused the bubble to move upstream and decrease in size. The fundamental characteristics of boundary layer transition on the front wing of a monoposto racing car have been established