We report on experimental and numerical studies aimed at developing an improved paradigm to model animal flight at moderate Reynolds numbers ($ 20 k - 50k $). A series of experiments were performed to characterize the behaviors of aerodynamic forces and moment associated with a quasi-steady rectangular wing over a range of angle of attack, $α$. We demonstrate that, while the drag coefficient curve, $C_D(α)$, can be accurately modeled solely by a simple trigonometric function, the evolution of lift coefficient curve, $C_L(α)$, is governed by the sum of trigonometric and exponential functions, where the latter captures the linear variation in lift coefficient within the small-angle regime, as predicted by the linear inviscid theory. In addition, we establish an empirical relation between the location of the center of pressure and $α$, which can be used in conjunction with the proposed aerodynamic formulas (i.e., $C_L$ and $C_D$) to evaluate the pitching moment coefficient, $C_M(α)$, about any arbitrary axis. These quasi-steady formulations are then utilized within a previously tested flapping-wing code to simulate the forward flight of a pigeon and a bat at various flight speeds, and the results are compared against previously reported experimental data. We successfully demonstrate that the proposed formulas yield much better agreement with wingbeat frequency for both animals, especially at higher flight speeds. In addition, the small-angle regime proves critical in offering higher $C_L/C_D$, leading to solutions with lower power consumption and body pitching variation, both of which are important aspects in designing future flapping wing robots.
Modeling the Aerodynamic Lift Produced by Oscillating Airfoils at Low Reynolds Number
本文以Strouhal数St为控制参数，对NACA-0012翼型在1,000雷诺数Re下的绕流进行了数值模拟。非定常力的时间分布，升力和推力，以及它们的频谱分析清楚地表明，该解决方案是一个周期-1吸引低Strouhal数。研究结果表明，机翼下俯产生的气动力与机翼的初始运动条件无关，证明了极限环的存在。振荡升力中存在的频率由较高Strouhal数的基波（fs）、偶次谐波和奇次谐波（3fs）组成。利用数值模拟，脱落频率（f_s）被观察到几乎等于激励频率在所有的情况下。采用改进的vanderPol振子模型模拟了翼型下倾产生的非定常升力。利用多尺度方法和稳态CFD解的谱分析，估计了van der Pol振子模型中的频率和阻尼项。我们证明了这个模型的适用性，所有的平面运动的翼型;暴跌，俯仰和扑动。目前提出的模型的一个重要方面是捕获气动升力系数的时间平均值。
Morphing wings comprised of fixed leading sections with piezocomposite trailing control surfaces have emerged as a novel active control technique for unmanned aerial vehicles. However, the wake dynamics and aerodynamic performance of such hybrid airfoil configuration has not been thoroughly investigated. In this paper, direct numerical simulations of two-dimensional flows over hybrid airfoils comprised of NACA 0012 leading sections with piezocomposite trailing control surfaces are performed at a fixed Reynolds number of 1000. The effects of length and camber of the trailing control surface on …
We perform unsteady three-dimensional direct numerical simulations to study the aerodynamic characteristics of finite-aspect-ratio swept wings with a NACA 0015 cross-section at a chord-based Reynolds number of 400. The effects of the sweep angle ($Λ=0^{\circ}-45^{\circ}$) on the aerodynamic force coefficients are examined for finite-aspect-ratio wings ($sAR=0.5$, 1, and 2) over a wide range of angles of attack ($α=0^{\circ}-30^{\circ}$). The unsteady laminar separated flows exhibit complex aerodynamic characteristics with respect to these parameters. The introduction of sweep enhances lift for…
This paper compares the performance of two unsteady aerodynamic reduced-order models (ROMs), namely linear Volterra series and the autoregressive with exogenous input (ARX) model, on modeling dynamically linear aerodynamic behaviors. The difference between these two methods is that the latter model has an autoregressive term while the former model has only the input-related term. The first system is a plunging cylinder in a low-Reynolds number flow, where the flow stable (Re < 47). Although the training data can be fitted well with both methods, the linear Volterra method requires a higher mod…
In the present work, we investigate dynamic interaction and response of flexible bio-inspired morphing wing structure to a low Reynolds aerodynamic load. The aspects of inspiration are as follows. First, the segmentation of the wing into rigid and flexible segments. Considering a leading edge constitution of bone and muscle. In addition to a flexible trailing edge composed of feathers. Second, the material properties provided by experimental biology in literature are adopted such as the bending stiffness and Young's modulus. The development of numerical models allowing non uniform distribution…
Geese achieve stationary takeoff via synergistic wing kinematics and enhanced aerodynamics
J.C. Wu Center for Aerodynamics, School of Aeronautics and Astronautics（航空宇航学院）；Bird Aerospace Technology (Suzhou) Co., Ltd.（鸟航天科技（苏州）有限公司）；Commercial Aircraft Corporation of China（中国商用飞机有限责任公司）；Shanghai Jiao Tong University（上海交通大学）
The wind tunnel rotary-balance testing is widely used in aircraft dynamics to characterise aerodynamics at moderate and high angles of attack during stall and spin regimes. In such experiments an aircraft test model is rotated along the wind-tunnel free-stream velocity vector allowing the measurement of aerodynamic characteristics in steady rotational flow conditions with constant angle of attack and sideslip. In modified tests named as oscillatory coning, the rotation vector is tilted from the free-stream velocity vector making flow conditions with periodic variations in angle of attack and s…
Reynolds-number regimes of corrugation-induced lift enhancement in two-dimensional dragonfly-like wings
Interdisciplinary Faculty of Science and Engineering, Shimane University（岛根大学理工学综合教育faculty）；Graduate School of Integrated Sciences for Life, Hiroshima University（广岛大学生命融合科学研究生院）
Groningen Institute for Evolutionary Life Sciences, University of Groningen（格罗宁根进化生命科学研究所，格罗宁根大学）；Biomimetics group, Energy and Sustainability Research Institute Groningen, University of Groningen（仿生学小组，格罗宁根能源与可持续发展研究所，格罗宁根大学）
Flying animals resort to fast, large-degree-of-freedom motion of flapping wings, a key feature that distinguishes them from rotary or fixed-winged robotic fliers with limited motion of aerodynamic surfaces. However, flapping-wing aerodynamics are characterised by highly unsteady and three-dimensional flows difficult to model or control, and accurate aerodynamic force predictions often rely on expensive computational or experimental methods. Here, we developed a computationally efficient and data-driven state-space model to dynamically map wing kinematics to aerodynamic forces/moments. This mod…
In the current work we numerically study the effect of traveling-wave surface morphing actuation on the suction surface of NACA0012 at Re = 1,000. Although this actuation strategy has been studied at higher Reynolds numbers for an airfoil and a rectangular flat plate, its effects at low Reynolds numbers have not yet been investigated. The kinematics of actuation are defined by wavenumber and wavespeed, both of which are varied over a wide range of values to include parameters that considerably change the lift dynamics as well as those that do not. We first study the effect of actuation at an a…
SuperWing: a comprehensive transonic wing dataset for data-driven aerodynamic design
School of Aerospace Engineering, Tsinghua University, Beijing, China（清华大学北京航空航天工程学院）；School of Computation, Information and Technology, Technical University of Munich, Germany（慕尼黑技术大学计算、信息与技术学院）
Explicit quantification of uncertainty in engineering simulations is being increasingly used to inform robust and reliable design practices. In the aerospace industry, computationally-feasible analyses for design optimization purposes often introduce significant uncertainties due to deficiencies in the mathematical models employed. In this paper, we discuss two recent improvements in the quantification and combination of uncertainties from multiple sources that can help generate probabilistic aerodynamic databases for use in aerospace engineering problems. We first discuss the eigenspace pertu…
Figuring out the right airfoil is a crucial step in the preliminary stage of any aerial vehicle design, as its shape directly affects the overall aerodynamic characteristics of the aircraft or rotorcraft. Besides being a measure of performance, the aerodynamic coefficients are used to design additional subsystems such as a flight control system, or predict complex dynamic phenomena such as aeroelastic instability. The coefficients in question can either be obtained experimentally through wind tunnel testing or, depending upon the accuracy requirements, by numerically simulating the underlying …
Resolvent analysis is performed to identify the origin of two-dimensional transonic buffet over an airfoil. The base flow for the resolvent analysis is the time-averaged flow over a NACA 0012 airfoil at a chord-based Reynolds number of 2000 and a free-stream Mach number of 0.85. We reveal that the mechanism of buffet is buried underneath the global low-Reynolds-number flow physics. At this low Reynolds number, the dominant flow feature is the von Karman shedding. However, we show that with the appropriate forcing input, buffet can appear even at a Reynolds number that is much lower than what i…
A comprehensive and detailed overview of the flow topology over a cambered NACA 65(1)-412 airfoil at Re = 20,000 is presented for angles of attack ranging from 0° to 10° using high-order direct numerical simulations. It is shown that instabilities bifurcate the flow and cause it to change at a critical angle of attack from laminar separation without reattachment over a laminar separation bubble at the trailing edge to a bubble at the leading edge. The transition of the flow regimes is governed by the Karman vortex shedding of the pressure side boundary layer at the trailing edge, Kelvin-Helmho…
We report direct numerical simulations of a pair of wings in horizontal tandem configuration, to analyze the effect of their aspect ratio on the flow and the aerodynamic performance of the system. The wings are immersed in a uniform free-stream at Reynolds number Re = 1000, and they undergo heaving and pitching oscillation with Strouhal number St = 0.7. The aspect ratios of forewing and hindwing vary between 2 and 4. The aerodynamic performance of the system is dictated by the interaction between the trailing edge vortex (TEV) shed by the forewing and the induced leading edge vortex formed on …
The number of studies related to unmanned air vehicles (UAV), micro air vehicles (MAV), wind turbines, birds and insects which operate at low Reynolds (Re) numbers have rapidly increased, recently. In this thesis, unsteady aerodynamics of low Reynolds number flows (Re=25000, 50000 and 75000) on NACA4412 airfoil shaped wing which is mainly used in wind turbines and micro air vehicles and operates at low Reynolds numbers and has aspect ratio of 1 (AR=1) was investigated by means of numerous experimental analyses at various angles of attack changing from 0° to 45°. Due to the obtained force measu…
The rise in computational capability has increased reliance on simulations to inform aircraft design. However aircraft airworthiness testing for flight certification remains rooted in real-world experiments performed after manufacturing an aircraft prototype. Leveraging multi-fidelity modeling and uncertainty quantification, we present a framework creating a stochastic representation of the aircraft, uses it to simulate flight certification maneuvers, and determines the likelihood of successfully meeting the certification requirement. We focus on uncertainties associated with Computational Flu…
A robust intermittency equation formulation for transition modeling in Spalart-Allmaras simulations of airfoil flows across a wide range of Reynolds numbers
A stochastic modeling framework to generate 2-D rough-wall high-Reynolds-number turbulent boundary layers
Saint Anthony Falls Laboratory, University of Minnesota（明尼苏达大学圣安东尼瀑布实验室）；Department of Civil, Environmental, and Geo-Engineering, University of Minnesota（明尼苏达大学土木、环境与地球工程系）
