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Results for “leapfrog energy”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1995

Building a better leapfrog

In stellar dynamical computer simulations, as well as other types of simulations using particles, time step size is often held constant in order to guarantee a high degree of energy conservation. In many applications, allowing the time step size to change in time can offer a great saving in computational cost, but variable-size time steps usually imply a substantial degradation in energy conservation. We present a meta-algorithm' for choosing time steps in such a way as to guarantee time symmetry in any integration scheme, thus allowing vastly improved energy conservation for orbital calculations with variable time steps. We apply the algorithm to the familiar leapfrog scheme, and generalize to higher order integration schemes, showing how the stability properties of the fixed-step leapfrog scheme can be extended to higher order, variable-step integrators such as the Hermite method. We illustrate the remarkable properties of these time-symmetric integrators for the case of a highly eccentric elliptical Kepler orbit and discuss applications to more complex problems.

Hut, Piet↗
NASA NTRS1990

Satellite sweeping of electrons at Neptune and Uranus

Knowledge of satellite sweeping parameters at Neptune and Uranus, and of their functional dependences on particle energy and pitch angle, can be critical in the proper identification of parent absorbers for observed absorption signatures in regions where OTD (offset, tilted dipole) models are valid representations of the measured magnetic fields. In this paper, critical electron energies are calculated for longitudinal drift resonance, snowplow (i.e., strong) absorption, leapfrog, and corkscrew effects, using a reduced version of OTD that neglects nonaxial dipole offsets. Earlier analytic work on sweeping rates is extended to give the radial dependence of these rates within the minimum-L region and to set limits on diffusion of electrons with the simplifying approximation that leapfrog effects are ignored.

Cooper, John F.↗
NASA NTRS1979

Explicit large time-step schemes for the shallow water equations

Modifications to explicit finite difference schemes for solving the shallow water equations for meteorological applications by increasing the time step for the fast gravity waves are analyzed. Terms associated with the gravity waves in the shallow water equations are treated on a coarser grid than those associated with the slow Rossby waves, which contain much more of the available energy and must be treated with higher accuracy, enabling a several-fold increase in time step without degrading the accuracy of the solution. The method is presented in Cartesian and spherical coordinates for a rotating earth, using generalized leapfrog, frozen coefficient, and Fourier filtering finite difference schemes. Computational results verify the numerical stability of the approach.

Turkel, E.↗
NASA NTRS2004

Two-Fluid Models and Interfacial Area Transport in Microgravity Condition

The objective of the present study is to develop a two-fluid model formulation with interfacial area transport equation applicable for microgravity conditions. The new model is expected to make a leapfrog improvement by furnishing the constitutive relations for the interfacial interaction terms with the interfacial area transport equation, which can dynamically model the changes of the interfacial structures. In the first year of this three-year project supported by the U.S. NASA, Office of Biological and Physics Research, the primary focus is to design and construct a ground-based, microgravity two-phase flow simulation facility, in which two immiscible fluids with close density will be used. In predicting the two-phase flow behaviors in any two-phase flow system, the interfacial transfer terms are among the most essential factors in the modeling. These interfacial transfer terms in a two-fluid model specify the rate of phase change, momentum exchange, and energy transfer at the interface between the two phases. For the two-phase flow under the microgravity condition, the stability of the fluid particle interface and the interfacial structures are quite different from those under normal gravity condition. The flow structure may not reach an equilibrium condition and the two fluids may be loosely coupled such that the inertia terms of each fluid should be considered separately by use of the two-fluid model. Previous studies indicated that, unless phase-interaction terms are accurately modeled in the two-fluid model, the complex modeling does not necessarily warrant an accurate solution.

Ishii, Mamoru↗
NASA NTRS1989

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.

Shariff, Karim↗
NASA NTRS2013

High Speed Mobility Through On-Demand Aviation

Game changing advances come about by the introduction of new technologies at a time when societal needs create the opportunity for new market solutions. A unique opportunity exists for NASA to bring about such a mobility revolution in General Aviation, extendable to other aviation markets, to maintain leadership in aviation by the United States. This report outlines the research carried out so far under NASA's leadership towards developing a new mobility choice, called Zip Aviation1,2,3. The feasibility, technology and system gaps that need to be addressed, and pathways for successful implementation have been investigated to guide future investment. The past decade indicates exciting trends in transportation technologies, which are quickly evolving. Automobiles are embracing automation to ease driver tasks as well as to completely control the vehicle with added safety (Figure 1). Electric propulsion is providing zero tail-pipe emission vehicles with dramatically lower energy and maintenance costs. These technologies have not yet been applied to aviation, yet offer compelling potential benefits across all aviation markets, and in particular to General Aviation (GA) as an early adopter market. The benefits of such an adoption are applicable in the following areas: 􀁸 Safety: The GA market experiences accident rates that are substantially higher than automobiles or commercial airlines, with 7.5 fatal accidents per 100 million vehicle miles compared to 1.3 for automobiles and.068 for airlines. Approximately 80% of these accidents are caused by some form of pilot error, with another 13% caused by single point propulsion system failure. 􀁸 Emissions: Environmental constraints are pushing for the elimination of 100Low Lead (LL) fuel used in most GA aircraft, with aviation fuel the #1 source of lead emissions into the environment. Aircraft also have no emission control systems (i.e. no catalytic converters etc.), so they are gross hydrocarbon polluters compared to automobiles. 􀁸 Community Noise: Hub and smaller GA airports are facing increasing noise restrictions, and while commercial airliners have dramatically decreased their community noise footprint over the past 30 years, GA aircraft noise has essentially remained same, and moreover, is located in closer proximity to neighborhoods and businesses. 􀁸 Operating Costs: GA operating costs have risen dramatically due to average fuel costs of over $6 per gallon, which has constrained the market over the past decade and resulted in more than 50% lower sales and 35% less yearly operations. Infusion of autonomy and electric propulsion technologies can accomplish not only a transformation of the GA market, but also provide a technology enablement bridge for both larger aircraft and the emerging civil Unmanned Aerial Systems (UAS) markets. The NASA Advanced General Aviation Transport Experiments (AGATE) project successfully used a similar approach to enable the introduction of primary composite structures and flat panel displays in the 1990s, establishing both the technology and certification standardization to permit quick adoption through partnerships with industry, academia, and the Federal Aviation Administration (FAA). Regional and airliner markets are experiencing constant pressure to achieve decreasing levels of community emissions and noise, while lowering operating costs and improving safety. But to what degree can these new technology frontiers impact aircraft safety, the environment, operations, cost, and performance? Are the benefits transformational enough to fundamentally alter aircraft competiveness and productivity to permit much greater aviation use for high speed and On-Demand Mobility (ODM)? These questions were asked in a Zip aviation system study named after the Zip Car, an emerging car-sharing business model. Zip Aviation investigates the potential to enable new emergent markets for aviation that offer "more flexibility than the existing transportation solutions." These studies indicate that autonomy and electric propulsion technology infusions offer a unique opportunity to provide breakthrough capabilities for new high speed, on-demand travel alternatives that can leapfrog the need for future expensive ground-based infrastructure investment. At the same time, such investments offer a method of laying the foundation for these technologies to be incubated for commercial aviation at lower cost, and with lower initial certification thresholds due to the relatively poor capabilities of GA aircraft to permit early adoption and private market capitalization by rapid technology accelerations, as depicted in Figure 2.

Moore, Mark D.↗