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An analysis is undertaken to provide a simple analytic expression to estimate the stroke averaged lift of a hovering insect based on geometric and kinematic data. The expression should prove useful in the conceptual design of biologically inspired microaerial vehicles. The study includes estimation of the average vortex lift developed. The leading-...
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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 optimizing thrust production. In this work, the unsteady vortex lattice...
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... where C lα,2d is the two-dimensional section lift curve slope, and in this work is assigned a value of 0.09 deg −1 based on experimental flat plate lift curve slope values at typical insect Reynolds numbers [28,29]. The symbol α i denotes the induced angle of attack resulting from the induced downwash velocity and is function of time, as it is through this term the model will capture the transient variations of the induced angle of attack due to the wake capture velocity field. ...
Flapping wings may encounter or ‘capture’ the wake from previous half-stroke, leading to local changes in the instantaneous aerodynamic force on the wing at the start of each half-stroke. In this paper, I developed a simple approach to integrating prediction of these wake capture effects into existing analytical quasi-steady models for hovering insect flapping flight. The local wake flow field is modelled as an additional induced velocity component normal to the stroke plane of the flapping motion that is blended/switched in at the start of each half-stroke. Comparison of model results against experimental data in the literature shows satisfactory agreement in predicting the wake capture lift and drag variations for eight different test cases. Sensitivity analysis shows that the form of the translation velocity time history has a significant effect on the magnitude of wake capture forces. Profiles that retain high translational velocity right up to stroke reversal evoke a much larger effect from wake capture compared with sinusoidal. This result is significant because while constant flapping translation velocity profiles can be generated in the laboratory, the very high accelerations required near stroke reversals incur high mechanical cost that prevents practical adoption in nature or engineered flapping flight vehicles.
... There are uncertainties concerning whether the Polhamus model can be fully applicable to the conditions of insect and samara flights, where the maximum operating α are much higher (α ≈ 45°, 80°, respectively). Nonetheless, a few researchers [23,27,63] have applied the Polhamus model to describe the lift and drag of low aspect ratio flapping/revolving wings. ...
Autorotating samaras such as Sycamore seeds are capable of descending at exceptionally slow speeds and the secret behind this characteristic is attributed to a flow mechanism known as the leading edge vortex (LEV). A stable LEV is known to increase the maximum lift coefficient attainable at high angles of attack and recent studies of revolving and flapping wings have proposed suitable lift and drag coefficient models to characterise the aerodynamic forces of the LEV. For the samara, however, little has been explored to properly test the suitability of these low-order lift and drag coefficient models in describing the aerodynamic forces produced by the samara. Thus, in this paper, we aim to analyse the use of two proposed aerodynamic models, namely, the normal force and Polhamus models, in describing the sectional aerodynamic lift of a samara that is producing a LEV. Additionally, we aim to quantify the aerodynamic parameters that can describe the lift and drag of the samara for a range of wind speed conditions. To achieve this, the study first examined the samara flight data available in the literature, and from it, the profiles of the lift coefficient curves were investigated. Subsequently, a numerical Blade Element-Momentum model (BEM) of the autorotating samara encompassing different lift profiles was developed and validated against a comprehensive set of samara flight data, which were measured from wind tunnel experiments conducted at the University of Bristol for three different Sycamores. The results indicated that both the normal force and Polhamus lift models combined with the normal force drag can be used to describe the two-dimensional lift characteristics of a samara exhibiting an LEV. However, the normal force model appeared to be more suitable, since the Polhamus relied on many assumptions. The results also revealed that the aerodynamic force parameters can vary with windspeed and with the samara wing characteristics, as well as along the span of the samara wing. Values of the lift curve slope, zero-lift drag coefficient, and maximum lift coefficient are predicted and presented for different samaras. The study also showed that the low-order BEM model was able to generate a good agreement with the experimental measurements in the prediction of both rotational speed and thrust. Such a validated BEM model can be used for the initial design of bio-inspired rotors for micro-air vehicles.
... The two-dimensional aerofoil lift curve slope, C lα,2d , takes a value of 5.16 rad −1 for flat plate wings at typical Reynolds numbers for insects [33]. The parameter E is the quotient of the wing semi-perimeter to its length, and is included to correct the lifting line expression for low aspect ratio effects [34]. ...
This work aims to develop an integrated conceptual design process to assess the scalability and performance of propulsion systems of resonant motor-driven flapping wing vehicles. The developed process allows designers to explore the interaction between electrical, mechanical and aerodynamic domains in a single transparent design environment. Wings are modelled based on a quasi-steady treatment that evaluates aerodynamics from geometry and kinematic information. System mechanics is modelled as a damped second-order dynamic system operating at resonance with nonlinear aerodynamic damping. Motors are modelled using standard equations that relate operational parameters and AC voltage input. Design scaling laws are developed using available data based on current levels of technology. The design method provides insights into the effects of changing core design variables such as the actuator size, actuator mass fraction and pitching kinematics on the overall design solution. It is shown that system efficiency achieves peak values of 30–36% at motor masses of 0.5–1 g when a constant angle of attack kinematics is employed. While sinusoidal angle of attack kinematics demands more aerodynamic and electric powers compared with the constant angle of attack case, sinusoidal angle of attack kinematics can lead to a maximum difference of around 15% in peak system efficiency.
... Some flying animals use flapping in order to generate and sustain LEVs leading to lower pressure (suction) and greater lift [3] [4]. It has also been suggested that a spanwise flow along the vortex core may be responsible for Traub's semi-empirical model (quasi-steady model with empirical corrections) in order to compute the effect of LEVs [12]. This was Polhamus' leading-edge suction analogy [13] originally developed for delta wings, but also used successfully in models for insect flight [12] [14] and lift generation of avian tails [15], among others. ...
... It has also been suggested that a spanwise flow along the vortex core may be responsible for Traub's semi-empirical model (quasi-steady model with empirical corrections) in order to compute the effect of LEVs [12]. This was Polhamus' leading-edge suction analogy [13] originally developed for delta wings, but also used successfully in models for insect flight [12] [14] and lift generation of avian tails [15], among others. Polhamus' model has been discussed along with LEVs by Nabawy [16], who suggested LEVs increase the suction and thus the effective lift coefficient as well as increase the stall angle, thereby enlarging the flight envelope. ...
This article presents a development of a simple analytical aerodynamic model capable of describing the effect of leading-edge vortices (LEVs) on the lift of rotating samara wings. This analytical model is based on the adaptation of Polhamus’ method to develop a sectional two-dimensional lift function, which was implemented in a numerical blade element model (BEM) of a rotating samara blade. Furthermore, wind tunnel experiments were conducted to validate the numerical BEM and to assess the validity of the newly developed analytical lift function. The results showed good agreement between the numerical model and the experimental measurements of rotational speed and rate of descent of the samara wing. The results were also compared with numerical predictions using BEM but adopting different lift coefficient expressions available in literature. This research contributed towards efficient aerodynamic modelling of the lift generated by LEVs on rotating samara wings for performance prediction, which could potentially be used in the design of bio-inspired rotary micro-air vehicles.
... Recently, many researchers have contributed greatly to the development of unsteady models. 5,51,60,61,[84][85][86][87][88][89][90][91][92][93][94][95][96] These models for flapping flight are relatively new, and the origin and progression of these methods cannot be identified. Ansari et al. 26 reviewed the development of unsteady and representative models. ...
The special aerodynamic characteristics of insects have attracted the interest of biologists and engineers. In this paper, aerodynamic modeling methods for flapping flight are systematically reviewed in detail, especially those methods developed in the past ten years. The differences among kinds of methods, the development of each type of methods, and their applications for different flight conditions are discussed in detail. First, steady-state and several representative models are presented. The applicability of this simple model decreases when it is applied to predict the loads on small insects. Next, this paper provides a detailed description of quasi-steady (QS) models and divides these models into three groups: Osborne, Walker, and Dickinson models. Osborne models are suitable for cases with a low flight speed and flapping amplitude. Walker and Dickinson models rely on experimental and numerical data to improve the QS models for predicting nonlinear aerodynamic forces. The total forces in Walker models are divided into circulatory and non-circulatory parts. Dickinson models are established according to different high-lift mechanisms. A representative Dickinson model consists of translational, rotational, added-mass, and wake-capture components. These models provide reasonable predictions, except that their accuracy depends on empirical constants. Finally, unsteady models based on the traditional theory are examined, and several representative models are addressed. The assumption of Kutta–Joukowski conditions may not be suitable for high stroke amplitudes and flapping frequencies. Further challenges to improve aerodynamic modeling methods are mainly due to the present limited understanding of the flow complexities of various insects at low Reynold numbers.
... Similarly, the circulatory forces in the quasi-steady falling card force model have been corrected for aspect ratio variations by accounting for the influence of the trailing vortex system (Wang et al. 2013). Numerous other quasi-steady models have been proposed for flapping flight (Traub 2004;Ansari et al. 2006;Wang et al. 2016;Han et al. 2017;Wang et al. 2017;Moriche et al. 2017). Although most of these models incorporate added mass effects, they are described as quasi-steady models since they generally do not incorporate wake induced effects. ...
Scaling laws for the propulsive performance of three-dimensional pitching propulsors – ADDENDUM - Volume 873 - Fatma Ayancik, Qiang Zhong, Daniel B. Quinn, Aaron Brandes, Hilary Bart-Smith, Keith W. Moored
... Similarly, the circulatory forces in the quasi-steady falling card force model have been corrected for aspect ratio variations by accounting for the influence of the trailing vortex system (Wang et al. 2013). Numerous other quasi-steady models have been proposed for flapping flight (Traub 2004;Ansari,Żbikowski & Knowles 2006;Wang, Goosen & Van Keulen 2016;Han, Chang & Han 2017;Moriche, Flores & García-Villalba 2017;Wang, Goosen & van Keulen 2017). Although most of these models incorporate added mass effects, they are described as quasi-steady models since they generally do not incorporate wake-induced effects. ...
Scaling laws for the thrust production and energetics of self-propelled or fixed-velocity three-dimensional rigid propulsors undergoing pitching motions are presented. The scaling relations extend the two-dimensional scaling laws presented in Moored & Quinn ( AIAA J. , 2018, pp. 1–15) by accounting for the added mass of a finite-span propulsor, the downwash/upwash effects from the trailing vortex system of a propulsor and the elliptical topology of shedding trailing-edge vortices. The novel three-dimensional scaling laws are validated with self-propelled inviscid simulations and fixed-velocity experiments over a range of reduced frequencies, Strouhal numbers and aspect ratios relevant to bio-inspired propulsion. The scaling laws elucidate the dominant flow physics behind the thrust production and energetics of pitching bio-propulsors, and they provide guidance for the design of bio-inspired propulsive systems.
... This phenomenon depends partly on a strong spanwise flow that drains vorticity from the LEV toward the wing-tip vortex (analogous to the LEV on delta wings). These findings allowed the use of Polhamus's leading-edge suction analogy to take into account the extra lifting force due to the presence of an attached and stable LEV on insect wings ( [34], [41], [43], [44]). Other techniques can be used to calculate the LEV contribution to the lift, such as the Leishman-Beddoes model [35] and a leading-edge wake shed from the bound leading-edge panels [29]. ...
This work presents a three-dimensional numerical tool that is suitable for studying the aerodynamics and nonlinear dynamics of free-falling rotating seeds like samaras. The proposed simulation framework consists of a modified version of the unsteady vortex-lattice method (enhanced by including a diffusion model and the leading-edge vortex contribution by means of the Polhamus analogy) coupled with a multibody rigid dynamic model for the whole seed. The numerical scheme adopted by the aerodynamic subsystem is based on an explicit low-order integrator (Euler's explicit first-order method). On the other hand, the equations of motion associated with the structural part are integrated in the time domain using a second-order Lie group integrator based on an extension of the classical generalized- method for dynamical systems. Among the main results obtained, it is found that the predicted terminal descending velocity and angular velocity (around the vertical axis) are in close agreement with experimental results reported in the literature.
... The conical LEV created on laminar revolving/ flapping wings is similar in form to the LEV observed over delta wings at subsonic speeds and high angles of attack. This prompted several researchers [1,15,41,43] to use the 'leading edge suction' model for delta wings to analyse the revolving/flapping wing problem. Note that while at first sight revolving/flapping wings and steady delta wings appear quite different, the key similarity is that in each a stable LEV is able to form. ...
The presence of a stable leading edge vortex (LEV) on steadily revolving wings increases the maximum lift coefficient that can be generated from the wing and its role is important to understanding natural flyers and flapping wing vehicles. In this paper, the role of LEV in lift augmentation is discussed under two hypotheses referred to as 'additional lift' and 'absence of stall'. The 'additional lift' hypothesis represents the traditional view. It presumes that an additional suction/circulation from the LEV increases the lift above that of a potential flow solution. This behaviour may be represented through either the 'Polhamus leading edge suction' model or the so-called 'trapped vortex' model. The 'absence of stall' hypothesis is a more recent contender that presumes that the LEV prevents stall at high angles of attack where flow separation would normally occur. This behaviour is represented through the so-called 'normal force' model. We show that all three models can be written in the form of the same potential flow kernel with modifiers to account for the presence of a LEV. The modelling is built on previous work on quasi-steady models for hovering wings such that model parameters are determined from first principles, which allows a fair comparison between the models themselves, and the models and experimental data. We show that the two models which directly include the LEV as a lift generating component are built on a physical picture that does not represent the available experimental data. The simpler 'normal force' model, which does not explicitly model the LEV, performs best against data in the literature. We conclude that under steady conditions the LEV as an 'absence of stall' model/mechanism is the most satisfying explanation for observed aerodynamic behaviour. © 2017 The Author(s) Published by the Royal Society. All rights reserved.
... In particular, a promising method was implemented inside Traub's semi-empirical model (quasi-steady model with empirical corrections) in order to compute the effect of LEVs. This was Polhamus' leading-edge suction analogy [11], and it was originally developed for delta wings, but it was also used successfully in models for insect flight [12][13] and lift generation of avian tails [14], among others. ...
This article focuses on the development of a simple analytical aerodynamic model capable of describing the effect of Leading-Edge Vortices (LEVs) on the lift of samara wings. This was based on an adaptation of Polhamus' method to predict the lift function implemented in a numerical blade-element model for a rotating Samara blade. Furthermore, wind tunnel experiments were conducted to validate the numerical blade element model. The final results showed very good agreement between the developed numerical model and the experimental measurements in the prediction of samara wing rotational speed and rate of descent. This research furthered the understanding of the aerodynamic behaviour and modelling of LEVs on samara seeds for performance-prediction and could ultimately be used in the design of rotary micro-air vehicles.
