Vortex Dynamics

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. (c) 2007 Elsevier B.V. All rights reserved.

The hydrodynamics of anguilliform swimming motions was investigated using three-dimensional simulations of the fluid flow past a self-propelled body. The motion of the body is not specified a priori, but is instead obtained through an evolutionary algorithm used to optimize the swimming efficiency and the burst swimming speed. The results of the present simulations support the hypothesis that anguilliform swimmers modify their kinematics according to different objectives and provide a quantitative analysis of the swimming motion and the forces experienced by the body. The kinematics of burst swimming is characterized by the large amplitude of the tail undulations while the anterior part of the body remains straight. In contrast, during efficient swimming behavior significant lateral undulation occurs along the entire length of the body. In turn, during burst swimming, the majority of the thrust is generated at the tail, whereas in the efficient swimming mode, in addition to the tail, the middle of the body contributes significantly to the thrust. The burst swimming velocity is 42% higher and the propulsive efficiency is 15% lower than the respective values during efficient swimming. The wake, for both swimming modes, consists largely of a double row of vortex rings with an axis aligned with the swimming direction. The vortex rings are responsible for producing lateral jets of fluid, which has been documented in prior experimental studies. We note that the primary wake vortices are qualitatively similar in both swimming modes except that the wake vortex rings are stronger and relatively more elongated in the fast swimming mode. The present results provide quantitative information of three-dimensional fluid-body interactions that may complement related experimental studies. In addition they enable a detailed quantitative analysis, which may be difficult to obtain experimentally, of the different swimming modes linking the kinematics of the motion with the forces acting on the self-propelled body. Finally, the optimization procedure helps to identify, in a systematic fashion, links between swimming motion and biological function.

We investigate the optimal morphologies for fast and efficient anguilliform swimmers at intermediate Reynolds numbers, by combining an evolution strategy with three-dimensional viscous vortex methods. We show that anguilliform swimmer shapes enable the trapping and subsequent acceleration of regions of fluid transported along the entire body by the midline travelling wave. A sensitivity analysis of the optimal morphological traits identifies that the width thickness in the anterior of the body and the height of the caudal fin are critical factors for both speed and efficiency. The fastest swimmer without a caudal fin, however, still retains 80 % of its speed, showing that the entire body is used to generate thrust. The optimal shapes share several features with naturally occurring morphologies, but their overall appearances differ. This demonstrates that engineered swimmers can outperform biomimetic swimmers for the criteria considered here.

We investigate the C-start escape response of larval fish by combining flow simulations using remeshed vortex methods with an evolutionary optimization. We test the hypothesis of the optimality of C-start of larval fish by simulations of larval-shaped, two- and three-dimensional self-propelled swimmers. We optimize for the distance travelled by the swimmer during its initial bout, bounding the shape deformation based on the larval mid-line curvature values observed experimentally. The best motions identified within these bounds are in good agreement with in vivo experiments and show that C-starts do indeed maximize escape distances. Furthermore we found that motions with curvatures beyond the ones experimentally observed for larval fish may result in even larger escape distances. We analyse the flow field and find that the effectiveness of the C-start escape relies on the ability of pronounced C-bent body configurations to trap and accelerate large volumes of fluid, which in turn correlates with large accelerations of the swimmer.

We present a vortex particle method coupled with a penalization technique to simulate single and multiple swimmers in an incompressible, viscous flow in two and three dimensions. The proposed algorithm can handle arbitrarily deforming bodies and their corresponding non-divergence free deformation velocity fields. The method is validated on a number of benchmark problems with stationary and moving boundaries. Results include flows of tumbling objects and single and multiple self-propelled swimmers.

We investigate schemes to accelerate the decay of aircraft trailing vortices. These structures are susceptible to several instabilities that lead to their eventual destruction. We employ an Evolution Strategy to design a lift distribution and a lift perturbation scheme that minimize the wake hazard as proposed in [6]. The performance of a scheme is mea- sured as the reduction of the mean rolling moment that would be induced on a following aircraft; it is computed by means of a Direct Numerical Simulation using a parallel vortex particle code. We find a configuration and a perturbation scheme characterized by an intermediate wavelength {λ} {\sim} 4.64, necessary to trigger medium wavelength instabilities between tail and flap vortices and subsequently amplify long wavelength modes.

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. (c) 2007 Elsevier B.V. All rights reserved.

Direct numerical simulation (DNS) of the channel {fl}ow with an anisotropic compliant surface is performed in order to investigate its drag reduction effect in a fully developed turbulent {fl}ow. The computational domain is set to be 3{δ} {\texttimes} 2{δ} {\texttimes} 3{δ} , where {δ} is the channel half-width. The surface is passively driven by the pressure and wall-shear stress {fl}uctuations, and the surface velocity provides a boundary condition for the {fl}uid velocity {fi}eld. An evolutionary optimization method (CMA-ES) is used to optimize the parameters of the anisotropic compliant surface. The optimization identi{fi}es several sets of parameters that result in a reduction of the friction drag with a maximum reduction rate of 8%. The primary mechanism for drag reduction is attributed to the decrease of the Reynolds shear stress (RSS) near the wall induced by the kinematics of the surface. The resultant wall motion is a uniform wave traveling downstream. The compliant wall, with the parameters found in the optimization study, is also tested in a computational domain that is doubled in the streamwise direction. The drag, however, is found to increase in the larger computational domain due to excessively large wall-normal velocity {fl}uctuations.

We present direct numerical simulations of the turbulent decay of vortex rings with Re-Gamma = 7500. We analyse the vortex dynamics during the nonlinear stage of the instability along with the structure of the vortex wake during the turbulent stage. These simulations enable the quantification of vorticity dynamics and their correlation with structures from dye visualization and the observations of circulation decay that have been reported in related experimental works. Movies are available with the online version of the paper.

The hydrodynamics of anguilliform swimming motions was investigated using three-dimensional simulations of the fluid flow past a self-propelled body. The motion of the body is not specified a priori, but is instead obtained through an evolutionary algorithm used to optimize the swimming efficiency and the burst swimming speed. The results of the present simulations support the hypothesis that anguilliform swimmers modify their kinematics according to different objectives and provide a quantitative analysis of the swimming motion and the forces experienced by the body. The kinematics of burst swimming is characterized by the large amplitude of the tail undulations while the anterior part of the body remains straight. In contrast, during efficient swimming behavior significant lateral undulation occurs along the entire length of the body. In turn, during burst swimming, the majority of the thrust is generated at the tail, whereas in the efficient swimming mode, in addition to the tail, the middle of the body contributes significantly to the thrust. The burst swimming velocity is 42% higher and the propulsive efficiency is 15% lower than the respective values during efficient swimming. The wake, for both swimming modes, consists largely of a double row of vortex rings with an axis aligned with the swimming direction. The vortex rings are responsible for producing lateral jets of fluid, which has been documented in prior experimental studies. We note that the primary wake vortices are qualitatively similar in both swimming modes except that the wake vortex rings are stronger and relatively more elongated in the fast swimming mode. The present results provide quantitative information of three-dimensional fluid-body interactions that may complement related experimental studies. In addition they enable a detailed quantitative analysis, which may be difficult to obtain experimentally, of the different swimming modes linking the kinematics of the motion with the forces acting on the self-propelled body. Finally, the optimization procedure helps to identify, in a systematic fashion, links between swimming motion and biological function.