Results for “chaotic motion” — Page 7

NASA NTRS2019

SPARROW: A Steam Propelled Autonomous Retrieval Robot for Ocean Worlds

This paper presents the results of a NIAC Phase I study into the use of a propulsively hopping robot for the exploration of Europa’s rugged, icy surface. Named the“Steam Propelled Retrieval Robot for Ocean Worlds,” SPARROW is a multi-thruster robot passively gimballed within a protective, spherical shell, which enables it to freely rotate, self-right, and tumble over chaotic terrains. SPARROW is envisioned as a soccerball-sized payload to a primary lander mission. Europa’s abundant surface ice would be harvested as an in situ propellant source. The principal objective of SPARROW would be to increase the science return of a Europa landed asset by enabling access to distal, spatially distributed geologic units. The design of mobility systems for Europa is challenging, due in part to its almost entirely unconstrained surface topography and strength. Images returned by Voyager and Galileo yielded resolutions on the order of hundreds of meters per pixel, with localized regions reaching 6 meters per pixel—still far larger than a typical rover. A key beneﬁt of SPARROW’s hopping, impact-tolerant design, is that it eliminates the need for a piori information on the terrain topography and surface strength; no surface reaction forces are required for motion. In this context, SPARROW is entirely terrain agnostic. In this paper we detail the results of three study objectives: i) to quantify the energy required to collect surface ice, change its phase, and maintain propellant temperature, ii) to identify control and estimation strategies that enable SPARROW to successfully reach, and return from, regions of scientiﬁc interest, and iii) to characterize the impact of SPARROW’s range on likely science return. Five water-based propellant architectures are presented alongside their mass, power, and volume requirements. Monte Carlo simulations of SPARROW hopping and tumbling over 1 km of glacial ice are summarized, characterizing SPARROW’s sensitivity to uncertainty in: initial conditions, thrust control, and cage-terrain interaction. Finally, a science traceability matrix is presented, which details the effect of sortie range on three science goals: constraining Europa’s evolutionary morphology, assessing sub-surface ocean habitability, and searching for life and/or biosignatures.

Phillips, Cynthia↗

NASA NTRS2002

Transient Mixing Driven by Buoyancy Flows

Mixing driven by buoyancy-induced flows is of particular interest to microgravity processes, as the body force that governs the intensity of flow fields can be directly controlled. We consider a model experimental system to explore the dynamics of mixing which employs two miscible liquids inside a cavity separated initially by a divider. The two liquids are oriented vertically inside a rectangular cavity with constant width and height, and varying depths to span the range of a Hele-Shaw cell to a 3-[) configuration. The two miscible liquids can be sufficiently diluted and died, for example water and deuterium oxide, such that a distinct interface exists across the divider. The transient mixing characteristic of the two fluids is addressed by following the Lagrangian history of the interface for various aspect ratios in the z-plane (depth variation) as well as a range of pulling velocities of the divider. The mixing characteristics of the two fluids are quantified from measurement of the length stretch of the interface and its flow field using respectively image processing techniques and Particle Imaging Velocimetry. Scaling analysis shows that the length stretch depends on four governing parameters, namely the Grashof number (Gr), Schmidt number (Sc), aspect ratio (Ar), and Reynolds number (Re). Variation of the Schmidt number is taken into account through thermophysical property variation. Thus our problem reduces to a codimension three bifurcation in parametric space for Gr, Ar, and Re. Our experimental results show that for Gr on the order of 106 and a nominal cavity aspect ratio Ar = 0.2, the net effect of removal of the divider and the overwhelming buoyancy force causes an overturning motion which stretches and folds the interface to produce ml internal breakwave. The structure of the breakwave is similar to the ubiquitous Rayleigh-Taylor instability morphology. The breakwave is dissipated either through internal or wall collision depending on the impulsive velocity of the divider as prescribed by the Reynolds number. The decay of the collision event occurs through sloshing oscillations over a short time scale. The two fluids then become stably stratified with a diffusive band at the interface indicating local mass transport. The local bifurcation of the internal breakwave is investigated as a function of aspect ratio. Results show that for narrow cavities on the order of 2mm (Ar = 0.04) folding does not occur, the interface only stretches. As the cavity size increases folding occurs through a supercritical bifurcation. Insight into the mechanism of folding is obtained from measurement of the flow field which shows that in the neighborhood of the folding event, there exists hyperbolic points caused by multiple vortex interactions. The global length stretch of the interface as a function of time is nearly Gaussian; calculations of finite-time Liapunov exponents as well as construction of horseshoe maps indicate the likelihood of a chaotic transient.

W.M.B. Duval↗