Vortex Methods

This paper poses the question, how does winglet length effect lift? The purpose of this investigation was to determine the enhanced lift that could be achieved through varying winglet length thereby increasing efficiency. To further investigate the outcomes, the lift data was compared to theoretically determined lift with identical wingspan variation. This assessed the appropriateness of winglet use in the future development of larger yet spatially suitable aircraft.

A constructed NACA 0015 aerofoil was placed within a homemade wind tunnel, which operated at a tunnel velocity of 5.05 m s-1 and Reynold’s number of around 32477. The aerofoil had a chord length of 100 mm and was analysed with, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10 centimetre winglet attachments. A constant angle of attack of 8° was controlled.

It was determined that lift was increased with an increase in winglet length. The initial relationship was linear with some reduction in lift at greater winglet lengths. When comparing lift due to winglet length variance in comparison to wingspan variance it is clear that winglets are at their most effective in increasing effective wingspan at lower winglet lengths. The study concludes that the use of winglets can increase effective wingspan making winglet length an important design factor for large aircraft that brink airport wingspan regulation.

In the present paper the study of the two-dimensional flow field past a circular cylinder for Reynolds number up to 5 · 10 5 is addressed. A Lagrangian particle method approach has been exploited and the simulations have been performed with high spatial resolutions in order to resolve all the main vortical scales. Long simulation time evolutions have been performed in order to get the vortex shedding dynamics as well as the Fourier analysis of the loads. The adopted numerical method allows to discuss both local (boundary layer and near wake dynamics) and global (far wake dynamics) aspects of the problem. The fundamental aspects related to the different identified flow states as well as the drag crisis mechanism are investigated.

We present the coupling of a hybrid particle-mesh vortex method with immersed lifting lines. The method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticity-velocity formulation. Advection is handled by the particles while the mesh allows the evaluation of the differential operators and the use of fast Poisson solvers. We use a Fourier-based fast Poisson solver which simultaneously allows unbounded directions and inlet/outlet boundaries.
A lifting line approach models the vorticity sources in the flow. Its immersed treatment efficiently captures the development of vorticity from thin sheets into a three-dimensional field. We apply this approach to the simulation of a wind turbine wake at very high Reynolds number. The combined use of particles and multiscale subgrid models allows the capture of wake dynamics with minimal spurious diffusion and dispersion.

This article presents numerical simulation of planar potential flow around an airfoil with possibility of changing its shape. Two-dimensional unsteady flow model with scalar velocity potential, which allows us to calculate pressure distribution along an airfoil from Cauchy-Lagrange integral, is used. For this purpose, an airfoil contour is approximated by a complex cubic spline with possibility of displacement its vertices. This algorithm has been used in the context of fluid-structure interaction and has been applied successfully to determination of stability of an elastic airfoil segment interacting with a flow stream, so-called panel flutter problem. Calculation of external flow is carried out by vortex panel method with Kutta-Joukowski trailing edge condition, which makes mathematical solution unique. Using this method of approximation of an airfoil in combination with the method of discrete vortices provides a semi-analytical solution for complex potential for whole computational domain of air flow. This solution significantly accelerates process of numerical computation of time-averaged aerodynamic force as well as the dynamic stability problem for aeroelastic wing design and temporal evolution of its natural disturbances.

We present the coupling of a vortex particle-mesh method with immersed lifting lines. The method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticityvelocity formulation. Advection is handled by the particles while the mesh allows the evaluation of the differential operators and the use of fast Poisson solvers. We use a Fourier-based fast Poisson solver which simultaneously allows unbounded directions and inlet/outlet boundaries.

We compare different models to simulate two-dimensional vortex wakes behind oscillating plates. In particular, we compare solutions using a vortex sheet model and the simpler Brown–Michael model to solutions of the full Navier–Stokes equations obtained using a penalization method. The goal is to determine whether simpler models can be used to obtain good approximations to the form of the wake and the induced forces on the body.

We present the coupling of a vortex particle-mesh method with immersed lifting lines. The method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticityvelocity formulation. Advection is handled by the particles while the mesh allows the evaluation of the differential operators and the use of fast Poisson solvers. We use a Fourier-based fast Poisson solver which simultaneously allows unbounded directions and inlet/outlet boundaries.

We present the coupling of a vortex particle-mesh method with immersed lifting lines. The method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticityvelocity formulation. Advection is handled by the particles while the mesh allows the evaluation of the differential operators and the use of fast Poisson solvers. We use a Fourier-based fast Poisson solver which simultaneously allows unbounded directions and inlet/outlet boundaries.

We investigate numerically the Navier-Stokes dynamics of reconnecting vortex rings at small Reynolds number for a variety of configurations. We find that reconnections are dissipative due to the smoothing of vorticity gradients at reconnection kinks and to the formation of secondary structures of stretched antiparallel vorticity which transfer kinetic energy to small scales where it is subsequently dissipated efficiently. In addition, the relaxation of the reconnection kinks excites Kelvin waves which due to strong damping are of low wave number and affect directly only large scale properties of the flow.

Simulation of vehicle aerodynamics using a vortex element method Goeric Daeninck1. Philippe Chatelain2, Michael Rubel2, Gregoire Winckelmans1, and Anthony Leonard2 1 Mechanical Engineering Dept. Universite catholique de Louvain Place du Levant 2. ...

In particle methods, an accuracy degradation can occur because of the distortion of the element positions. A solution consists in the periodic re-initialization of the particles onto regular locations, at the nodes of a lattice. This so-called redistribution works by the interpolation of particle quantities. The present work considers the design of redistribution schemes on general lattices and in particular on lattices with a higher level of symmetry than the usual cubic lattice. Such lattices allow schemes which are more compact and more isotropic. We test our schemes in the context of three-dimensional vortex methods.

We present the Direct Numerical Simulations of high Reynolds numbers aircraft wakes employing vortex particle methods. The simulations involve a highly efficient implementation of vortex methods on massively parallel computers, enabling unprecedented simulations using billions of particles. The method relies on the Lagrangian discretization of the Navier-Stokes equations in vorticity-velocity form and relies on remeshing of the particles in order to ensure the convergence of the method. The remeshed particle locations are utilized for the computation of the field quantities, the discretization of the differential operators for diffusion and vortex stretching, and the solution of the Poisson equation for the advection velocity field. The method exhibits excellent scalability up to 16k BG/L nodes. The results include unprecedented Direct Numerical Simulations of the onset and the evolution of multiple wavelength instabilities induced by ambient noise in aircraft vortex wakes at Re = 6000.

We present a vortex particle-mesh method for fluid-structure
interaction problems. The proposed methodology combines implicit
interface capturing, Brinkmann penalization techniques, and the
self-consistent computation of momentum transfer between the
fluid and the structure. In addition, our scheme is able to
handle immersed bodies characterized by non-solenoidal
deformations, allowing the study of arbitrary deforming geometries.

This attractively simple algorithm is shown to accurately
reproduce reference simulations for rigid and deforming
structures. Its suitability for biological locomotion problems is
then demonstrated with the simulation of self-propelled
anguilliform swimmers.

We present a computationally efficient, adaptive solver for the solution of the Poisson and Helmholtz equation used in flow simulations in domains with combinations of unbounded and periodic directions. The method relies on using FFTs on an extended domain and it is based on the method proposed by Hockney and Eastwood for plasma simulations. The method is well-suited to problems with dynamically growing domains and in particular flow simulations using vortex particle methods. The efficiency of the method is demonstrated in simulations of trailing vortices.

Particle methods are a robust and versatile computational tool for the simulation of continuous and discrete physical systems ranging from Fluid Mechanics to Biology and Social Sciences. In advection dominated problems particle methods can be considered as the method of choice due to their inherent robustness, stability and Lagrangian adaptivity. At the same time however, smooth particle methods encounter major difficulties in simulating the equations they set out to discretize when their computational elements fail to overlap, a condition necessary for their convergence. A number of ad-hoc parameters and artificial dissipation techniques are often introduced in techniques such as Smoothed Particle Hydrodynamics (SPH) in order to remedy these difficulties. In the present paper we demonstrate that the convergence of smooth particle methods can be ensured by a periodic remeshing of the particles using high-order interpolation kernels. This procedure retains the Lagrangian character and stability of particle methods and enables the control of their accuracy while introducing numerical dissipation at levels well below those introduced by temporal discretizations. In addition, remeshing enables two major improvements over grid-free particle methods: First by exploiting the regularity of the remeshed particles, it reduces by at least an order of magnitude their computational cost and facilitates their massively parallel implementation. Second, remeshing enables the development of consistent multiresolution techniques such as wavelet-particle methods. This approach has been implemented efficiently in massively parallel computer architectures allowing for unprecedented vortex dynamics simulations using billions of particles.