Doug Lipinski

A ridge tracking algorithm and error estimate for efficient computation of Lagrangian coherent structures

A ridge tracking algorithm for the computation and extraction of Lagrangian coherent structures (LCS) is developed. This algorithm takes advantage of the spatial coherence of LCS by tracking the ridges which form LCS to avoid unnecessary computations away from the ridges. We also make use of the temporal coherence of LCS by approximating the time dependent motion of the LCS with passive tracer particles. To justify this approximation, we provide an estimate of the difference between the motion of the LCS and that of tracer particles which begin on the LCS. In addition to the speedup in computational time, the ridge tracking algorithm uses less memory and results in smaller output files than the standard LCS algorithm. Finally, we apply our ridge tracking algorithm to two test cases, an analytically defined double gyre as well as the more complicated example of the numerical simulation of a swimming jellyfish. In our test cases, we find up to a 35 times speedup when compared with the standard LCS algorithm.

Flow structures and fluid transport for the hydromedusae Sarsia tubulosa and Aequorea victoria.

SUMMARY The flow structures produced by the hydromedusae Sarsia tubulosa and Aequorea victoria are examined using direct numerical simulation and Lagrangian coherent structures (LCS). Body motion of each hydromedusa is digitized and input to a CFD program. Sarsia tubulosa uses a jetting type of propulsion, emitting a single, strong, fast-moving vortex ring during each swimming cycle while a secondary vortex of opposite rotation remains trapped within the subumbrellar region. The ejected vortex is highly energetic and moves away from the hydromedusa very rapidly. Conversely, A. victoria, a paddling type hydromedusa, is found to draw fluid from the upper bell surface and eject this fluid in pairs of counter-rotating, slow-moving vortices near the bell margins. Unlike S. tubulosa, both vortices are ejected during the swimming cycle of A. victoria and linger in the tentacle region. In fact, we find that A. victoria and S. tubulosa swim with Strouhal numbers of 1.1 and 0.1, respectively. This means that vortices produced by A. victoria remain in the tentacle region roughly 10 times as long as those produced by S. tubulosa, which presents an excellent feeding opportunity during swimming for A. victoria. Finally, we examine the pressure on the interior bell surface of both hydromedusae and the velocity profile in the wake. We find that S. tubulosa produces very uniform pressure on the interior of the bell as well as a very uniform jet velocity across the velar opening. This type of swimming can be well approximated by a slug model, but A. victoria creates more complicated pressure and velocity profiles. We are also able to estimate the power output of S. tubulosa and find good agreement with other hydromedusan power outputs. All results are based on numerical simulations of the swimming jellyfish.

A Lagrangian analysis of a two-dimensional airfoil with vortex shedding

Using invariant material manifolds and flow topology, the flow behavior and structure of flow around a two-dimensional Eppler 387 airfoil is examined with an emphasis on vortex shedding and the time-dependent reattachment profile. The examination focuses on low Reynolds number (Re = 60 000) flow at several angles of attack. Using specialized software, we identify invariant manifolds in the flow and use these structures to illuminate the process of vortex formation and the periodic behavior of the reattachment profile. Our analysis concludes with a topological view of the flow, including fixed points and a discussion of phase plots and the frequency spectrum of several key points in the flow. The behavior of invariant manifolds directly relates to the flow topology and illuminates some aspects seen in phase space during vortex shedding. Furthermore, it highlights the reattachment behavior in ways not seen before.

Dynamic Data Driven Application System for Plume Estimation Using UAVs

In this article, a full dynamic data-driven application system (DDDAS) is proposed for dynamically estimating a concentration plume and planning optimal paths for unmanned aerial vehicles (UAVs) equipped with environmental sensors. The proposed DDDAS dynamically incorporates measured data from UAVs into an environmental simulation while simultaneously steering measurement processes. In order to assimilate incomplete and noisy state observations into this system in real-time, the proper orthogonal decomposition (POD) is used to estimate the plume concentration by matching partial observations with pre-computed dominant modes in a least-square sense. In order to maximize the information gain, UAVs are dynamically driven to hot spots chosen based on the POD modes. Smoothed particle hydrodynamics (SPH) techniques are used for UAV guidance with collision and obstacle avoidance. We demonstrate the efficacy of the data assimilation and control strategies in numerical simulations. Especially, a single UAV outperforms the ten static sensors in this scenario in terms of the mean square error over the full time interval. Additionally, the multi-vehicle data collection scenarios outperform the single vehicle scenarios for both static sensors at optimal positions and UAVs controlled by SPH.

A master-slave fluid cooperative control algorithm for optimal trajectory planning

A control algorithm based on Smoothed Particle Hydrodynamics (SPH) is used to guide a simulated swarm of unmanned vehicles along a pre-computed optimal trajectory. By using a fluid based control method, collision avoidance is automatically incorporated into the control. Given an initial position and goal location, it is computationally impractical to compute the optimal trajectories for a large swarm of vehicles. To overcome this, the optimal trajectory is computed for a single vehicle and the swarm is guided along this trajectory using fluid based control, in this case SPH. Importantly, this method avoids computing a potential field to guide the swarm and is easily adaptable to changing environments. Additionally, this method is intended to be used in the presence of a background flow through which the vehicles must travel. This control algorithm is found to be quite robust in the test case examined here and adding additional vehicles to the swarm has only a small impact on fuel consumption per vehicle.

Cooperative Control of a Team of Unmanned Vehicles Using Smoothed Particle Hydrodynamics

A procedure is outlined for trajectory planning based on Lagrangian coherent structures (LCS) and using a fluid cooperative control algorithm. Smoothed particle hydrodynamics (SPH) was used to obtain a reduced model of the fluid cooperation. LCS provide insight in flow transport and allow for plausible trajectory planning while fluid based control provides a simple and uniform control mechanism with built in collision avoidance. The resulting near optimal trajectories are compared to truely optimal trajectories that are found by numerically solving an optimal control problem given a cost function which combines fuel and time costs. The LCS based trajectories with fluid control provide good results, but fail to reproduce the optimal trajectories in terms of pure fuel savings or pure speed. Finally, a hybrid approach is proposed. This approach solves the optimal control problem for a single vehicle and then uses SPH control to allow a swarm of vehicles to follow this single trajectory while maintaining spacing and avoiding collisions.

Cooperative control using data-driven feedback for mobile sensors

This article describes and validates a data-driven cooperative feedback control system for mobile sensors. The system can be used to guide resource constrained mobile sensors through a dynamically changing environment in order to obtain a path that results in data collection at important locations in the domain. A simulated chemical puff is used as a test application where small, resource constrained aerial vehicles provide mobile sensing capabilities. A fluid-based control scheme is used to guide the mobile sensors through the domain to collect data on the puff. The data is then used to update and improve a model of the puff concentration. Simulations are provided, demonstrating the decrease in error between the simulated and actual puffs over time. Additionally, the effect of using different numbers of mobile sensors as well as different schemes for guiding the mobile sensors is investigated. The feasibility of the technique using real sensors is demonstrated experimentally using a single UAV tracking a simulated puff.

Nearly fuel-optimal trajectories for vehicle swarms in open domains with strong background flows

Using a multi-vehicle control scheme based on smoothed particle hydrodynamics, a simulated swarm of unmanned underwater vehicles is guided along a pre-computed optimal trajectory between two points in an open domain under the influence of a strong background flow. The pre-computed trajectory is optimal in terms of fuel usage for a single vehicle. If the gradient of the velocity field is small compared to the total swarm radius, guiding a swarm of vehicles along this trajectory gives nearly optimal trajectories for all vehicles in the swarm without requiring additional costly optimization computations. We provide a bound on the maximum energy cost for vehicles in the swarm and also provide a more realistic estimate of the maximum energy cost. We also determine that the energy cost scales as N3/2 for swarms with large numbers of vehicles, N. The algorithm and fuel cost bounds are verified in simulations of unmanned underwater vehicles moving across a double gyre system on the scale of a small ocean basin.

Flow Structures and Fluid Transport for the Hydromedusa Sarsia Tubulosa

The flow structures produced by the hydromedusa Sarsia tubulosa are examined using direct numerical simulation Lagrangian coherent structures (LCS). Sarsia tubulosa uses a jetting type of propulsion, emitting a single strong, fast moving vortex ring during each swimming cycle while a secondary vortex of opposite rotation remains trapped within the subumbrellar region. This secondary vortex has not been observed prior to this study. The ejected vortex is highly energetic and moves away from the hydromedusa very rapidly. We find that Sarsia tubulosa swims with a Strouhal number of 0.1. This means that vortices produced by Sarsia tubulosa move away from the hydromedusa at a rate of about 10 diameters per swimming cycle. This presents very little feeding opportunity during swimming for the hydromedusa. Finally, we examine the pressure on the interior bell surface and the velocity profile in the wake of Sarsia tubulosa. We find that the swimming closely resembles a slug of fluid being shot from the velar opening and might be closely approximated by a slug model. All results are based on numerical simulations of the swimming hydromedusa. This paper has been prepared for submission to the 19th AIAA Computational Fluid Dynamics conference in the catagory of Lagrangian and vortex methods

Identifying and modeling motion primitives for the hydromedusae Sarsia tubulosa and Aequorea victoria

The movements of organisms can be thought of as aggregations of motion primitives: motion segments containing one or more significant actions. Here, we present a means to identify and characterize motion primitives from recorded movement data. We address these problems by assuming that the motion sequences can be characterized as a series of dynamical-system-based pattern generators. By adopting a nonparametric, Bayesian formalism for learning and simplifying these pattern generators, we arrive at a purely data-driven model to automatically identify breakpoints in the movement sequences. We apply this model to swimming sequences from two hydromedusa. The first hydromedusa is the prolate Sarsia tubulosa, for which we obtain five motion primitives that correspond to bell cavity pressurization, jet formation, jetting, cavity fluid refill, and coasting. The second hydromedusa is the oblate Aequorea victoria, for which we obtain five motion primitives that correspond to bell compression, vortex separation, cavity fluid refill, vortex formation, and coasting. Our experimental results indicate that the breakpoints between primitives are correlated with transitions in the bell geometry, vortex formation and shedding, and changes in derived dynamical quantities. These dynamics quantities include terms like pressure, power, drag, and thrust. Such findings suggest that dynamics information is inherently present in the observed motions.