Using global interpolation to evaluate the Biot-Savart integral for deformable elliptical Gaussian vortex elements

This paper introduces a new method for approximating the Biot-Savart integral for elliptical Gaussian functions using high-order interpolation and compares it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coefficients by interpolating precomputed values from look-up tables over a wide range of aspect ratios. When implemented in a full nonlinear vortex method, we find that the new technique is almost three times faster and unlike the asymptotic method, provides uniform accuracy over the full range of aspect ratios. As a proof-of-concept for large scale computations, we use the new technique to calculate inviscid axisymmetrization and filamentation of a two-dimensional elliptical fluid vortex. We compare our results with those from a pseudo-spectral computation and from electron vortex experiments, and find good agreement between the three approaches

Dynamics of a class of vortex rings

The contour dynamics method is extended to vortex rings with vorticity varying linearly from the symmetry axis. An elliptic core model is also developed to explain some of the basic physics. Passage and collisions of two identical rings are studied focusing on core deformation, sound generation and stirring of fluid elements. With respect to core deformation, not only the strain rate but how rapidly it varies is important and accounts for greater susceptibility to vortex tearing than in two dimensions. For slow strain, as a passage interaction is completed and the strain relaxes, the cores return to their original shape while permanent deformations remain for rapidly varying strain. For collisions, if the strain changes slowly the core shapes migrate through a known family of two-dimensional steady vortex pairs up to the limiting member of the family. Thereafter energy conservation does not allow the cores to maintain a constant shape. For rapidly varying strain, core deformation is severe and a head-tail structure in good agreement with experiments is formed. With respect to sound generation, good agreement with the measured acoustic signal for colliding rings is obtained and a feature previously thought to be due to viscous effects is shown to be an effect of inviscid core deformation alone. For passage interactions, a component of high frequency is present. Evidence for the importance of this noise source in jet noise spectra is provided. Finally, processes of fluid engulfment and rejection for an unsteady vortex ring are studied using the stable and unstable manifolds. The unstable manifold shows excellent agreement with flow visualization experiments for leapfrogging rings suggesting that it may be a good tool for numerical flow visualization in other time periodic flows

Modeling of Complex Large-Scale Flow Phenomena

Flows at large scales are capable of unmatched complexity. At large spatial scales, they can exhibit phenomena like waves, tornadoes, and a screaming concert audience; at high densities, they can create shockwaves, and can cause stampedes. Though strides have been made in simulating flows like fluids and crowds, extending these algorithms with scale poses challenges in ensuring accuracy while maintaining computational efficiency. In this dissertation, I present novel techniques to simulate large-scale flows using coupled Eulerian-Lagrangian models that employ a combination of discretized grids and dynamic particle-based representations. I demonstrate how such models can efficiently simulate flows at large-scales, while maintaining fine-scale features. In fluid simulation, a long-standing problem has been the simulation of large-scale scenes without compromising fine-scale features. Though approximate multi-scale models exist, accurate simulation of large-scale fluid flow has remained constrained by memory and computational limits of current generation PCs. I propose a hybrid domain-decomposition model that, by coupling Lagrangian vortex-based methods with Eulerian velocity-based methods, reduces memory requirements and improves performance on parallel architectures. The resulting technique can efficiently simulate scenes significantly larger than those possible with either model alone. The motion of crowds is another class of flows that exhibits novel complexities with increasing scale. Navigation of crowds in virtual worlds is traditionally guided by a static global planner, combined with dynamic local collision avoidance. However, such models cannot capture long-range crowd interactions commonly observed in pedestrians. This discrepancy can cause sharp changes in agent trajectories, and sub-optimal navigation. I present a technique to add long-range vision to virtual crowds by performing collision avoidance at multiple spatial and temporal scales for both Eulerian and Lagrangian crowd navigation models, and a novel technique to blend both approaches in order to obtain collision-free velocities efficiently. The resulting simulated crowds show better correspondence with real-world pedestrians in both qualitative and quantitative metrics, while adding a minimal computational overhead. Another aspect of real-world crowds missing from virtual agents is their behavior at high densities. Crowds at such scales can often exhibit chaotic behavior commonly known as emph{crowd turbulence}; this phenomenon has the potential to cause mishaps leading to loss of life. I propose modeling inter-personal stress in dense crowds using an Eulerian model, coupled with a physically-based Lagrangian agent-based model to simulate crowd turbulence. I demonstrate how such a hybrid model can create virtual crowds whose trajectories show visual and quantifiable similarities to turbulent crowds in the real world. The techniques proposed in this thesis demonstrate that hybrid Eulerian-Lagrangian modeling presents a versatile approach for modeling large-scale flows, such as fluids and crowds, efficiently on current generation PCs.Doctor of Philosoph

Dynamics of Quantized Vortices and Electron Bubbles in the Gross-Pitaevskii Model of a Superfluid

In this thesis we present an extensive study on quantised vortex dynamics using the Gross-Pitaevskii model of a superfluid in the limit of zero temperature. We make use of an accurate and robust numerical method that we developed to detect topological defects present in the scalar order parameter characterising the superfluid. We begin by focusing on the scattering of vortex rings by a superfluid line vortex. Thereafter, we focus on the development and decay of a turbulent vortex tangle, measuring the Vinen’s decay law for the total vortex length. Moreover, the temporal evolution of the Kelvin wave spectrum is obtained providing evidence of the development of a weak-wave turbulence cascade. The study of superfluid vortex reconnections is also carried out in order to identify what aspects of the reconnection process are universal. Aside from the investigation on quantised vortex dynamics, in this thesis we also present a study on the motion of an electron bubble in a superfluid. The electron bubble dynamics is studied in the adiabatic approximation using the Gross-Pitaevskii equation to model the superfluid wavefunction and a Schro¨dinger equation to model the electron wavefunction. This model allows us to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. We determine the vortex-nucleation limited mobility of the ion to recover values in reasonable agreement with measured data. Moreover, considering the scenario of an ion trapped on the core of a vortex line, we investigate how small and large amplitude Kelvin waves and solitary waves affect the drift velocity of the ion. In particular, we have identified that Hasimoto soliton-bubble complexes propagating along the vortex can arise

Propeller Effects on Very Flexible Aircraft

High Altitude Long Endurance aircraft are unmanned air vehicles with the capability of performing long-duration flights and can be used in many applications, such as communication and data relay, Earth observation, etc. To achieve their higher aerodynamic performance, HALE aircraft are typically high-aspect-ratio configurations, resulting in a very flexible structure. Moreover, the typical low cruise speeds often require a propeller-engine combination for propulsion. Although many studies have been done in propeller-wing interaction, propeller effects on very flexible aircraft (VFA) have not received any attention. State-of-the-art nonlinear aeroelastic frameworks lack complete propeller modeling and, instead, use concentrated forces to model its thrust. This work aims to fill this gap by incorporating propeller aerodynamics and inertial effects into a coupled nonlinear aeroelastic-flight dynamics framework. For that, the University of Michigan's Nonlinear Aeroelastic Simulation Toolbox (UM/NAST) is enhanced with an Unsteady Vortex Lattice for the lifting surfaces and a Lifting Line and Viscous Vortex Particle (LL/VVPM) methods to model the propeller aerodynamics. Furthermore, inertia effects associated with the rotating rigid blades are also incorporated. Verification tests are performed for each of the new components added to the enhanced framework. Results for static and dynamic aeroelastic analysis with the coupled UM/NAST and Vortex Lattice model, isolated propeller, propeller-wing interaction, and the gyroscopic loads calculation are compared with results from other codes or published numerical and experimental data available in the literature. Additionally, an approach based on system identification and proper orthogonal decomposition is introduced and verified for the stability analysis of VFA with propellers based on a time-series signal. The method is successfully verified against UM/NAST modal analysis for a purely structural case. Based on the new developments, investigation of propeller effects on the aeroelastic response and stability of a VFA is presented and discussed. The results showed that the presence of propellers can influence the aeroelastic static and dynamic response of a VFA, as well as modify the aeroelastic modes and affect the flutter onset. Therefore, the additional propeller effects (besides just the incorporation of thrust) should be included in aeroelastic simulations. Although focused on very flexible aircraft applications, it should be noted that the new enhanced framework can also be used to analyze new propeller-driven aircraft concepts such as the ones being proposed for Urban Air Mobility and distributed propulsion configurations.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/153439/1/pct_1.pd

Rotary Wing Aerodynamics

This book contains state-of-the-art experimental and numerical studies showing the most recent advancements in the field of rotary wing aerodynamics and aeroelasticity, with particular application to the rotorcraft and wind energy research fields

Experimental Investigation into the Boundary Layer of a Robotic Anguilliform Propulsor

Boundary layer information local to three longitudinal positions has been characterized for a 130 cm long biomimetic self-propulsor known as NEELBOT-1.1 that swims with undulatory anguilliform-like motions, via analysis of stereo particle image velocimetry (PIV) measurements for key moments in the undulation cycle and for numerous combinations of swimming conditions and motion parameters, ideal and non-ideal. No obvious turbulent flow structures or indications of boundary layer separation were observed at nonzero advance speeds, and skin friction coefficients were subsequently estimated for magnitude relative to the dynamic pressure associated with operation at the design swimming speed of Uo = 0.25 m/s. Estimates were correlated with measurements made for an oscillating and non-oscillating cylindrical test article that were benchmarked by initial mono PIV investigations of steady laminar flow over a flat plate at zero incidence which was tested while stationary and oscillating in its own plane. Behavior of boundary layer profiles pertaining to the robot, apparently significantly influenced by the traveling flexion waves characteristic of the anguilliform motions, is clearly distinguished from local oscillatory flow structures related to the other two test articles. Approximately 10–15% increases in local skin friction are observed for the robot over similar conditions for the cylinder, and downstream vortex shedding is readily observed for the oscillating cylinder. The results of this thesis will be used in validation of numerical analyses performed in parallel with this research for the purpose of calculating the time-mean frictional drag experienced by the robot and to determine whether it can produce enough thrust to overcome its drag without simultaneously increasing it beyond realizable thrust generation capabilities. Theoretical hydrodynamic descriptions of the wake velocity field agreed well with previous PIV measurements, but the theory does not treat viscous effects. Furthermore, the preliminary semi-empirical, quasi-static attempts to estimate frictional drag were shown to under-predict the actual drag by net force measurements taken while towing the robot at its design speed which was undulating for that expected swimming speed, hence the necessity of this thesis as further investigation