At high incidence, low-aspect-ratio wings present a unique set of aerodynamic characteristics, including flow separation, vortex shedding, and unsteady force production. Furthermore, low-aspect ratio wings exhibit a highly impactful tip vortex, which introduces strong spanwise gradients into an already complex flow. In this work, we explore the interaction between leading edge flow separation and a strong, persistent tip vortex over a Reynolds number range of $600 \leq Re \leq 10,000$. In performing this study, we aim to bridge the insight gained from existing low Reynolds number studies of separated flow on finite wings ($Re \approx 10^2$) and turbulent flows at higher Reynolds numbers ($Re \approx 10^4$). Our study suggests two primary effects of Reynolds number. First, we observe a break from periodicity, along with a dramatic increase in the intensity and concentration of small-scale eddies, as we shift from $Re = 600$ to $Re = 2,500$. Second, we observe that many of our flow diagnostics, including the time-averaged aerodynamic force, exhibit reduced sensitivity to Reynolds number beyond $Re = 2,500$, an observation attributed to the stabilizing impact of the wing tip vortex. This latter point illustrates the manner by which the tip vortex drives flow over low-aspect-ratio wings, and provides insight into how our existing understanding of this flowfield may be adjusted for higher Reynolds number applications.
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）
Four well-resolved LESs of the turbulent boundary layers around a NACA4412 wing section, with Rec ranging from 100,000 to 1,000,000, were performed at 5 degree angle of attack. By comparing the turbulence statistics with those in ZPG TBLs at approximately matching Re_tau, we find that the effect of the adverse pressure gradient (APG) is more intense at lower Reynolds numbers. This indicates that at low Re the outer region of the TBL becomes more energized through the wall-normal convection associated to the APG. This is also reflected in the fact that the inner-scaled wall-normal velocity is l…
Linear modal instabilities of flow over finite-span untapered wings have been investigated numerically at Reynolds number 400, at a range of angles of attack and sweep on two wings having aspect ratios 4 and 8. Base flows have been generated by direct numerical simulation, marching the unsteady incompressible three-dimensional Navier-Stokes equations to a steady state, or using selective frequency damping to obtain stationary linearly unstable flows. Unstable three-dimensional linear global modes of swept wings have been identified for the first time using spectral-element time-stepping solver…
Reynolds-number effects in the adverse-pressure-gradient (APG) turbulent boundary layer (TBL) developing on the suction side of a NACA4412 wing section are assessed in the present work. To this end, we analyze four cases at Reynolds numbers based on freestream velocity and chord length ranging from Rec = 100, 000 to 1,000,000, all of them with 5 degree angle of attack. The results of four well-resolved large-eddy simulations (LESs) are used to characterize the effect of Reynolds number on APG TBLs subjected to approximately the same pressure-gradient distribution (defined by the Clauser pressu…
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…
Wing-body junction flows occur when a boundary layer encounters an airfoil mounted on the surface. The corner flow near the trailing edge is challenging for the linear eddy viscosity Reynolds Averaged Navier-Stokes (RANS) models, due to the interaction of two perpendicular boundary layers which leads to highly anisotropic Reynolds stress at the near wall region. Recently, Xiao et al. proposed a physics-informed Bayesian framework to quantify and reduce the model-form uncertainties in RANS simulations by utilizing sparse observation data. In this work, we extend this framework to incorporate th…
Forward-swept wings offer unique advantages in the aerodynamic performance of air vehicles. However, the low-Reynolds-number characteristics of such wings have not been explored in the past. In this work, we numerically study laminar separated flows over forward-swept wings with semi aspect ratios $sAR=0.5$ to 2 at a chord-based Reynolds number of 400. Forward-swept wings generate wakes that are significantly different from those of backward-swept wings. For low-aspect-ratio forward wings, the wakes remain steady due to the strong downwash effects induced by the tip vortices. For larger aspect…
Adaptive mesh refinement (AMR) in the high-order spectral-element method code Nek5000 is demonstrated and validated with well-resolved large-eddy simulations (LES) of the flow past a wing profile. In the present work, the flow around a NACA 4412 profile at a chord-based Reynolds number $Re_c=200,000$ is studied at two different angles of attack: 5 and 11 degrees. The mesh is evolved from a very coarse initial mesh by means of volume-weighted spectral error indicators, until a sufficient level of resolution is achieved at the boundary and wake regions. The non-conformal implementation of AMR al…
We perform direct numerical simulations of laminar separated flows over finite-aspect-ratio swept wings at a chord-base Reynolds number of $Re = 400$ to reveal a variety of wake structures generated for a range of aspect ratios ($sAR=0.5-4$), angles of attack ($α=16^{\circ}-30^{\circ}$), and sweep angles ($Λ=0^{\circ}-45^{\circ}$). Flows behind swept wings exhibit increased complexity in their dynamical features compared to unswept-wing wakes. For unswept wings, the wake dynamics are predominantly influenced by the tip effects. Steady wakes are mainly limited to low-aspect-ratio wings. Unstead…
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…
We reveal the effects of sweep on the wake dynamics around NACA 0015 wings at high angles of attack using direct numerical simulations and resolvent analysis. The influence of sweep on the wake dynamics is considered for sweep angles from $0^\circ$ to $45^\circ$ and angles of attack from $16^\circ$ to $30^\circ$ for a spanwise periodic wing at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Wing sweep affects the wake dynamics, especially in terms of stability and spanwise fluctuations with implications on the development of three-dimensional wakes. We observe that wing swee…
Icing on three-dimensional wings causes severe flow separation near stall. Standard improved delayed detached eddy simulation (IDDES) is unable to correctly predict the separating reattaching flow due to its inability to accurately resolve the Kelvin-Helmholtz instability. In this study, a shear layer adapted subgrid length scale is applied to enhance the IDDES prediction of the flow around a finite NACA (National Advisory Committee for Aeronautics) 0012 wing with leading edge horn ice. It is found that applying the new length scale contributes to a more accurate prediction of the separated sh…
The paper presents a numerical investigation of the leading-edge vortices generated by rotating triangular wings at Reynolds number $Re=250$. A series of three-dimensional numerical simulations have been carried out using a Fourier pseudo-spectral method with volume penalization. The transition from stable attachment of the leading-edge vortex to periodic vortex shedding is explored, as a function of the wing aspect ratio and the angle of attack. It is found that, in a stable configuration, the spanwise flow in the recirculation bubble past the wing is due to the centrifugal force, incompressi…
We investigate the spatial distributions and production mechanisms of vorticity and turbulent kinetic energy around a finite NACA 0018 wing with square wingtip profile at $Re_c=10^4$ and $10^{\circ}$ angle of attack with the aid of Direct Numerical Simulation (DNS). The analysis focuses on the highly inhomogeneous region around the tip and the near wake; this region is highly convoluted, strongly three-dimensional, and far from being self-similar. The flow separates close to the leading edge creating a large, open recirculation zone around the central part of the wing. In the proximity of the …
Through triglobal resolvent analysis, we reveal the effects of wing tip and sweep angle on laminar separated wakes over swept wings. For the present study, we consider wings with semi-aspect ratios from $1$ to $4$, sweep angles from $0^\circ$ to $45^\circ$, and angles of attack of $20^\circ$ and $30^\circ$ at a chord-based Reynolds number of $400$ and a Mach number of $0.1$. Using direct numerical simulations, we observe that unswept wings develop vortex shedding near the wing root with a quasi-steady tip vortex. For swept wings, vortex shedding is seen near the wing tip for low sweep angles, …
Stretching and retracting wingspan has been widely observed in the flight of birds and bats, and its effects on the aerodynamic performance particularly lift generation are intriguing. The rectangular flat-plate flapping wing with a sinusoidally stretching and retracting wingspan is proposed as a simple model of biologically-inspired dynamic morphing wings. Direct numerical simulations of the low-Reynolds-number flows around the flapping morphing wing in a parametric space are conducted by using immersed boundary method. It is found that the instantaneous and time-averaged lift coefficients of…
The scope of the present project is to quantify the effects of uniform blowing and body-force damping on turbulent boundary layers subjected to a non-uniform adverse-pressure-gradient distribution. To this end, well-resolved large-eddy simulations are employed to describe the flow around the NACA4412 airfoil at moderate Reynolds number 200, 000 based on freestream velocity and chord length. In the present paper we focus on uniform blowing and the conference presentation will include a comparison with body-force damping applied in the same region. The inner-scaled profiles of the mean velocity …
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…
Linear stability analysis of an elastically anchored wing in a uniform flow is investigated both analytically and numerically. The analytical formulation explicitly takes into account the effect of the wake on the wing by means of Theodorsen's theory. Three different parameters non-trivially rule the observed dynamics: mass density ratio between wing and fluid, spring elastic constant and distance between the wing center of mass and the spring anchor point on the wing. We found relationships between these parameters which rule the transition between stable equilibrium and fluttering. The shape…
Turbulent flow separation induced by a protuberance on one of the walls of an otherwise planar channel is investigated using Direct Numerical Simulations. Different bulge geometries and Reynolds numbers - with the highest friction Reynolds number simulation reaching a peak of Reτ = 900 - are addressed to understand the effect of the wall curvature and of the Reynolds number on the dynamics of the recirculating bubble behind the bump. Most of the drag is due to the form contribution, whilst the friction contribution does not change appreciably with respect to an equivalent planar channel flow. …
This work introduces a novel data-driven framework to formulate explicit algebraic Reynolds-averaged Navier-Stokes (RANS) turbulence closures. Recent years have witnessed a blossom in applying machine learning (ML) methods to revolutionize the paradigm of turbulence modeling. However, due to the black-box essence of most ML methods, it is currently hard to extract interpretable information and knowledge from data-driven models. To address this critical limitation, this work leverages deep learning with symbolic regression methods to discover hidden governing equations of Reynolds stress models…
The vorticity confinement (VC) method was used with total variation diminishing (TVD) schemes to reduce possible over-confinement and applied to tip vortices shed by edges of wings in order to predict induced drag using far-field integration. The optimal VC parameter was determined first by application to 2-D vortices and then to tip vortices shed by a 3-D wing. The 3-D inviscid simulations were post-processed using the wake-integral technique to determine lift-induced drag force. Dependence of the VC parameter on the flight Mach number and the angle of attack was evaluated. Grid convergence s…
This study reports on the vortex-induced lift production mechanisms in low Reynolds number flows over low aspect-ratio rectangular wings. We use a rigorous force partitioning method which allows for the estimation of the pressure-induced aerodynamic loads due to distinct flow features or vortex structures in the flow around the wing. The specific focus of this work is on distinguishing the effect of spanwise and cross-span oriented vortex structures on pressure-induced lift production. We quantify the lift induced on the wing by these different vortices, and also estimate their influence withi…
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 …
Unsteady Lifting-Line Theory (ULLT) is a low order method capable of modeling interacting unsteady and finite wing effects at low computational cost. Most formulations of the method assume inviscid flow and small amplitudes. Whilst these assumptions might be suitable for small-amplitude aeroelastic problems at high Reynolds numbers, modern engineering applications increasingly involve lower Reynolds numbers, large amplitude kinematics and vortex structures that lead to aerodynamic non-linearities. This paper establishes that ULLT still provides a good solution for low Reynolds number, large-am…
Compared with fixed-wing flight, flapping flight can generate a higher lift and is also more maneuverable, largely resulting from the benefits of wing rotation. By analyzing the real wing kinematics of fruit flies, we found that the wing rotation is smart modulated and can be simplified into the advanced $Φ>0$, symmetrical $Φ=0$, and delayed $Φ<0$ modes, where $Φ$ is the phase between stroke reversal and wing rotation. Thus, an experiment of a Robotic fly at Reynolds number of 240 was designed to address how insects control the flow patterns to modulate the flight forces by the smart wing rota…
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of high-fidelity data and the convergence and stability problem in the coupling process of turbulence models and the RANS solvers. In this paper, we propose an improved ensemble kalman inversion method as a unified approach of data assimilation and turbulence modeling for separated flows at high Reynolds numbers. The trainable parameters of the DNN are optimize…
Aeroelastic structures, from insect wings to wind turbine blades, experience transient unsteady aerodynamic loads that are coupled to their motion. Effective real-time control of flexible structures relies on accurate and efficient predictions of both the unsteady aeroelastic forces and airfoil deformation. For rigid wings, classical unsteady aerodynamic models have recently been reformulated in state-space for control and extended to include viscous effects. Here we further extend this modeling framework to include the deformation of a flexible wing in addition to the quasi-steady, added mass…
A variational technique is used to derive analytical expressions for the sensitivity of recirculation length to steady forcing in separated flows. Linear sensitivity analysis is applied to the two-dimensional steady flow past a circular cylinder for Reynolds numbers $40 \leq Re \leq 120$, both in the subcritical and supercritical regimes. Regions which are the most sensitive to volume forcing and wall blowing/suction are identified. Control configurations which reduce the recirculation length are designed based on the sensitivity information, in particular small cylinders used as control devic…
High-lift Wing Separation Control via Bayesian Optimization and Deep Reinforcement Learning
TUAREG, Universitat Politècnica de Catalunya (UPC)（TUAREG，西班牙巴塞罗那理工大学）；Mechanical Engineering, Delft University of Technology (TU Delft)（代尔夫特理工大学机械工程系）；CASE, Barcelona Supercomputing Center (BSC)（巴塞罗那超级计算中心）
Dragonfly beats its wings independently, resulting in its superior maneuverability. Depending on the magnitude of phase difference between the fore- and hind-wings of dragonfly, the vortical structures and their interaction with wings become significantly changed, and so does the aerodynamic performance. In this study, we consider hovering flights of modelled dragonfly with three different phase differences (phi=-90, 90, 180 degrees). The three-dimensional wing shape is based on that of Aeschna juncea (Norberg, 1972), and the Reynolds number is 1,000 based on the maximum translational velocity…
Information-theoretic machine learning for time-varying mode decomposition of separated aerodynamic flows
Department of Aerospace Engineering, Tohoku University（东京东京大学航空工程系）；Department of Mechanical and Aerospace Engineering, Tokyo University of Science（东京科学大学机械与航空航天工程系）
The results of a DNS of the flow around a wing section represented by a NACA4412 profile, with Rec = 400, 000 and 5 degree angle of attack, are presented in this study. The high-order spectral element code Nek5000 was used for the computations. The Clauser pressure-gradient parameter ? ranges from 0 and 85 on the suction side, and the maximum Re_theta and Re_tau values are around 2,800 and 373, respectively. Comparisons between the suction side with ZPG TBL data show a more prominent wake, a steeper logarithmic region and lower velocities in the buffer region. The APG also leads to a progressi…
