Optimal Reconstruction of Inviscid Vortices

We address the question of constructing simple inviscid vortex models which optimally approximate realistic flows as solutions of an inverse problem. Assuming the model to be incompressible, inviscid and stationary in the frame of reference moving with the vortex, the "structure" of the vortex is uniquely characterized by the functional relation between the streamfunction and vorticity. It is demonstrated how the inverse problem of reconstructing this functional relation from data can be framed as an optimization problem which can be efficiently solved using variational techniques. In contrast to earlier studies, the vorticity function defining the streamfunction-vorticity relation is reconstructed in the continuous setting subject to a minimum number of assumptions. To focus attention, we consider flows in 3D axisymmetric geometry with vortex rings. To validate our approach, a test case involving Hill's vortex is presented in which a very good reconstruction is obtained. In the second example we construct an optimal inviscid vortex model for a realistic flow in which a more accurate vorticity function is obtained than produced through an empirical fit. When compared to available theoretical vortex-ring models, our approach has the advantage of offering a good representation of both the vortex structure and its integral characteristics.Comment: 33 pages, 10 figure

Formation number of confined vortex rings

This paper investigates the formation number of vortex rings generated by a piston-cylinder mechanism in a confined tube. We use Direct Numerical Simulations (DNS) of axisymmetric confined vortex rings to study the influence of different parameters on the separation (or pinch-off) of the vortex ring from the trailing jet. It is shown that the structure of the vortex ring at pinch-off depends on the type of injection program (pulse dominated by either positive or negative acceleration ramps) and the confinement ratio D w /D , where D w is the inner diameter of the tube and D the diameter of the cylinder). For low confinement ratios ( D w /D ≤ 2), a vortex of opposite sign generated at the lateral wall strongly interacts with the vortex ring and the pinch-off is not clearly observed. The pinch-off is observed and analysed for confinement ratios D w /D ≥ 2 . 5. DNS data are used to estimate the value of the formation time, which is the time necessary for the vortex generator to inject the same amount of circulation as carried by the detached vortex ring. The confined vortex ring at pinch-off is described by the model suggested by Danaila, Kaplanski and Sazhin [A model for confined vortex rings with elliptical core vorticity distribution, Journal of Fluid Mechanics, 811 :67-94, 2017]. This model allows us to take into account the influence of the lateral wall and the elliptical shape of the vortex core. The value of the formation time is predicted using this model and the slug-flow model

Optimal manoeuvres and aeroservoelastic co-design of very flexible wings

The single shooting method is applied to the optimal control of very flexible aeroelastic wings and the combined structural and control design (co-design) of geometrically nonlinear beam models in vacuum. As large deflections occur, the dynamical properties of these systems can undergo substantial changes. Efficient actuation strategies require characterising, and possibly exploiting, these phenomena. With this purpose, geometrically-nonlinear models are built using composite beams and an unsteady vortex-lattice aerodynamics description. Optimal control is employed to identify actuations time-histories. Numerical solutions are obtained via single-shooting and sequential quadratic programming upon parametrisation of the control input. The approach is also extended to assess the feasibility of an integrated design strategy for active geometrically-nonlinear structures. Numerical studies are first presented for a very flexible actuated pendulum with large rigid-body motion. The impact of local (B-splines) and global (discrete sines) basis functions is investigated for increasing levels of actuation authority, underlining the importance of the time-frequency resolution of the parametrisation on the convergence properties and outcome quality of the process. Locking between control and structural vibrations around specific design points is found, thus highlighting the limitations of a sequential design approach. Simultaneous designing of control law and structure is seen, instead, to explore more efficiently larger portions of the design space. The lateral manoeuvring of very flexible partially-supported wings is then considered. A flight-dynamics model based on elastified stability derivatives is shown to capture the relevant dynamics either under slow actuation or for stiff wings, and it is hence used as a reference. Embedding the full aeroelastic description into the optimisation framework expands the space of achievable manoeuvres, allowing for quick wing response with low structural vibrations or large lateral forces with minimal lift losses.Open Acces

Validation of morphine wing methodologies on an unmanned aerial system and a wind tunnel technology demonstrator

To increase the aerodynamic efficiency of aircraft, in order to reduce the fuel consumption, a novel morphing wing concept has been developed. It consists in replacing a part of the wing upper and lower surfaces with a flexible skin whose shape can be modified using an actuation system placed inside the wing structure. Numerical studies in two and three dimensions were performed in order to determine the gains the morphing system achieves for the case of an Unmanned Aerial System and for a morphing technology demonstrator based on the wing tip of a transport aircraft. To obtain the optimal wing skin shapes in function of the flight condition, different global optimization algorithms were implemented, such as the Genetic Algorithm and the Artificial Bee Colony Algorithm. To reduce calculation times, a hybrid method was created by coupling the population-based algorithm with a fast, gradient-based local search method. Validations were performed with commercial state-of-the-art optimization tools and demonstrated the efficiency of the proposed methods. For accurately determining the aerodynamic characteristics of the morphing wing, two new methods were developed, a nonlinear lifting line method and a nonlinear vortex lattice method. Both use strip analysis of the span-wise wing section to account for the airfoil shape modifications induced by the flexible skin, and can provide accurate results for the wing drag coefficient. The methods do not require the generation of a complex mesh around the wing and are suitable for coupling with optimization algorithms due to the computational time several orders of magnitude smaller than traditional three-dimensional Computational Fluid Dynamics methods. Two-dimensional and three-dimensional optimizations of the Unmanned Aerial System wing equipped with the morphing skin were performed, with the objective of improving its performances for an extended range of flight conditions. The chordwise positions of the internal actuators, the spanwise number of actuation stations as well as the displacement limits were established. The performance improvements obtained and the limitations of the morphing wing concept were studied. To verify the optimization results, high-fidelity Computational Fluid Dynamics simulations were also performed, giving very accurate indications of the obtained gains. For the morphing model based on an aircraft wing tip, the skin shapes were optimized in order to control laminar flow on the upper surface. An automated structured mesh generation procedure was developed and implemented. To accurately capture the shape of the skin, a precision scanning procedure was done and its results were included in the numerical model. High-fidelity simulations were performed to determine the upper surface transition region and the numerical results were validated using experimental wind tunnel data

A model for confined vortex rings with elliptical-core vorticity distribution

We present a new model for an axisymmetric vortex ring confined in a tube. The model takes into account the elliptical (elongated) shape of the vortex ring core and thus extends our previous model [Danaila, Kaplanski and Sazhin, J. of Fluid Mechanics, 774, 2015] derived for vortex rings with quasi-circular cores. The new model offers a more accurate description of the deformation of the vortex ring core, induced by the lateral wall, and a better approximation of the translational velocity of the vortex ring, compared with the previous model. The main ingredients of the model are the following: the description of the vorticity distribution in the vortex ring is based on the previous model of unconfined elliptical-core vortex rings [Kaplanski, Fukumoto and Rudi, Physics of Fluids, 24, 2012]; Brasseur's approach [Brasseur, PhD Thesis, 1979] is then applied to derive a wall-induced correction for the Stokes stream function of the confined vortex ring flow. We derive closed formulae for the flow stream function and vorticity distribution. An asymptotic expression for the long time evolution of the drift velocity of the vortex ring as a function of the ellipticity parameter is also derived. The predictions of the model are shown to be in agreement with direct numerical simulations of confined vortex rings generated by a piston-cylinder mechanism. The predictions of the model support the recently suggested heuristic relation [Krieg andMohseni, J. Fluid Engineering, 135, 2013] between the energy and circulation of vortex rings with converging radial velocity. A new procedure for fitting experimental and numerical data with the predictions of the model is described. This opens the way for applying the model to realistic confined vortex rings in various applications including those in internal combustion engines

Numerical and experimental investigations on unsteady aerodynamics of flapping wings

The development of a dynamic unstructured grid high-order accurate spectral difference (SD) method for the three dimensional compressible Navier-Stokes (N-S) equations and its applications in flapping-wing aerodynamics are carried out in this work. Grid deformation is achieved via an algebraic blending strategy to save computational cost. The Geometric Conservation Law (GCL) is imposed to ensure that grid deformation will not contaminate the flow physics. A low Mach number preconditioning procedure is conducted in the developed solver to handle the bio-inspired flow. The capability of the low Mach number preconditioned SD solver is demonstrated by a series of two dimensional (2D) and three dimensional (3D) simulations of the unsteady vortex dominated flow. Several topics in the flapping wing aerodynamics are numerically and experimentally investigated in this work. These topics cover some of the cutting-edge issues in flapping wing aerodynamics, including the wake structure analysis, airfoil thickness and kinematics effects on the aerodynamic performances, vortex structure analysis around 3D flapping wings and the kinematics optimization. Wake structures behind a sinusoidally pitching NACA0012 airfoil are studied with both experimental and numerical approaches. The experiments are carried out with Particle Image Velocimetry (PIV) and two types of wake transition processes, namely the transition from a drag-indicative wake to a thrust-indicative wake and that from the symmetric wake to the asymmetric wake are distinguished. The numerical results from the developed SD solver agree well with the experimental results. It is numerically found that the deflective direction of the asymmetric wake is determined by the initial conditions, e.g. initial phase angle. As most insects use thin wings (i. e., wing thickness is only a few percent of the chord length) in flapping flight, the effects of airfoil thickness on thrust generation are numerically investigated by simulating the flow fields around a series of plunging NACA symmetric airfoils with thickness ratio ranging from 4.0% to 20.0% of the airfoil chord length. The contribution of viscous force to flapping propulsion is accessed and it is found that viscous force becomes thrust producing, instead of drag producing, and plays a non-negligible role in thrust generation for thin airfoils. This is closely related to the variations of the dynamics of the unsteady vortex structures around the plunging airfoils. As nature flyers use complex wing kinematics in flapping flight, kinematics effects on the aerodynamic performance with different airfoil thicknesses are numerically studied by using a series of NACA symmetric airfoils. It is found that the combined plunging and pitching motion can outperform the pure plunging or pitching motion by sophisticatedly adjusting the airfoil gestures during the oscillation stroke. The thin airfoil better manipulates leading edge vortices (LEVs) than the thick airfoil (NACA0030) does in studied cases, and there exists an optimal thickness for large thrust generation with reasonable propulsive efficiency. With the present kinematics and dynamic parameters, relatively low reduced frequency is conducive for thrust production and propulsive efficiency for all tested airfoil thicknesses. In order to obtain the optimal kinematics parameters of flapping flight, a kinematics optimization is then performed. A gradient-based optimization algorithm is coupled with a second-order SD Navier-Stokes solver to search for the optimal kinematics of a certain airfoil undergoing a combined plunging and pitching motion. Then a high-order SD scheme is used to verify the optimization results and reveal the detailed vortex structures associated with the optimal kinematics of the flapping flight. It is found that for the case with maximum propulsive efficiency, there exists no leading edge separation during most of the oscillation cycle. In order to provide constructive suggestions to the design of micro-air-vehicles (MAVs), 3D simulations of the flapping wings are carried out in this work. Both the rectangular and bio-inspired wings with different kinematics are investigated. The formation process of two-jet-like wake patterns behind the finite-span flapping wing is found to be closely related to the interaction between trailing edge vortices and tip vortices. Then the effects of the wing planforms on the aerodynamics performance of the finite-span flapping wings are elucidated in terms of the evolution and dynamic interaction of unsteady vortex structures

NAS technical summaries. Numerical aerodynamic simulation program, March 1992 - February 1993

NASA created the Numerical Aerodynamic Simulation (NAS) Program in 1987 to focus resources on solving critical problems in aeroscience and related disciplines by utilizing the power of the most advanced supercomputers available. The NAS Program provides scientists with the necessary computing power to solve today's most demanding computational fluid dynamics problems and serves as a pathfinder in integrating leading-edge supercomputing technologies, thus benefitting other supercomputer centers in government and industry. The 1992-93 operational year concluded with 399 high-speed processor projects and 91 parallel projects representing NASA, the Department of Defense, other government agencies, private industry, and universities. This document provides a glimpse at some of the significant scientific results for the year

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

Adaptive structures for the control of cellular separation

This work describes the research undertaken on the development of adaptive structures to reduce turbulent boundary layer separation from a wing. Separation control is a safety critical function that is currently filled by the application of static vortex generators to the wings on most modern aircraft. These devices generate vorticity which produces a downstream mixing effect, energising the boundary layer and postponing separation. The mixing of the boundary layer also increases the drag of the aircraft, reducing efficiency. As static devices, the mixing effect is also permanent, regardless of the current likelihood of separation. Adaptive structures allow the development of beneficial geometry from the body’s surface without the use of breaks or mechanisms in the structure surface. This allows geometry modification without sources of parasitic drag or turbulent transition. The first subject of this work is the development of an adaptive surface to provide the desired momentum transfer through the boundary layer when required, and which can be retracted when not needed, reducing drag and increasing efficiency. Adaptive structures inhabit a complex design space due to the coupling between bending and in-plane stretching of the surface. In previous morphing studies, design optimisation has frequently been used to identify the ideal design parameters. Initially, the design methodology is developed on a test case transferring momentum within a zero-pressure gradient boundary layer. The resulting geometry is then tested experimentally and the structural and fluidic response is found to compare well to simulations. Once the design approach is validated, it must be applied to an efficient location on an aerofoil. The second area of research is therefore the complex, three-dimensional, separation from a 2D aerofoil. This is investigated experimentally with both mean and time-dependent data. The naturally occurring, three-dimensional and spanwise periodic topology of the separated flow, termed a `stall cell', is investigated to determine a suitable location for the application of targeted control at a critical point. Fourier analysis and Proper Orthogonal Decomposition are applied to the time-dependent data gathered to extract coherent, periodic, fluctuations in the separated flow field. The variation of the relative strengths of these features, distinct in frequency, is isolated to regions within the stall cell. Knowledge of the flow field gained during this work is applied to stall cell reduction and a single vortex generator is applied to the wing upstream of an identified critical point within the flow field. The separated area is seen to reduce significantly with this actuation. The design methodology developed previously is applied to the initially curved surface of an aerofoil. The final structure is manufactured and tested experimentally and found to be effective in reducing the separation extent. The control is found to be less effective than the static vortex generators. However, unlike the static device, the adaptive version is fully elastic, in both deployment and reaction, and thus shows none of the detrimental effects associated with traditional devices.Open Acces