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At least 55 records · Page 3

Approaching Moons from Resonance via Invariant Manifolds

In this work, the approach phase from the final resonance of the endgame scenario in a tour design is examined within the context of invariant manifolds. Previous analyses have typically solved this problem either by using numerical techniques or by computing a catalog of suitable trajectories. The invariant manifolds of a selected set of libration orbits and unstable resonant orbits are computed here to serve as guides for desirable approach trajectories. The analysis focuses on designing an approach phase that may be tied into the final resonance in the endgame sequence while also targeting desired conditions at the moon.

endgame

Comparison of Low-Energy Lunar Transfer Trajectories to Invariant Manifolds

In this study, transfer trajectories from the Earth to the Moon that encounter the Moon at various flight path angles are examined, and lunar approach trajectories are compared to the invariant manifolds of selected unstable orbits in the circular restricted three-body problem. Previous work focused on lunar impact and landing trajectories encountering the Moon normal to the surface, and this research extends the problem with different flight path angles in three dimensions. The lunar landing geometry for a range of Jacobi constants are computed, and approaches to the Moon via invariant manifolds from unstable orbits are analyzed for different energy levels.

inveriant manifolds

Generalized fiducial inference on differentiable manifolds

We introduce a novel approach to inference on parameters that take values in a Riemannian manifold embedded in a Euclidean space. Parameter spaces of this form are ubiquitous across many fields, including chemistry, physics, computer graphics, and geology. Here, this new approach uses generalized fiducial inference (GFI) to obtain a posterior-like distribution on the manifold, without needing to know local parameterizations that map to the constrained space from an unconstrained Euclidean space. Using mathematical tools from Riemannian geometry, we construct a constrained generalized fiducial distribution (CGFD). A Bernstein-von Mises-type result for the CGFD, which provides intuition for how the desirable asymptotic qualities of the unconstrained generalized fiducial distribution are inherited by the CGFD, is provided. To illustrate the practical use of the CGFD, we provide a proof-of-concept example in the context of a linear logspline density estimation problem, and demonstrate that CGFD-based confidence sets exhibit desirable coverage properties via simulation. As an application, we fit a CGFD to COVID-19 case count data from North Carolina, USA.

97 MATHEMATICS AND COMPUTING

A Design for Remanufacturing Framework Incorporating Identification, Evaluation, and Validation: A Case Study of Hydraulic Manifold

In recent years, academic researchers and engineers in the industry have widely recognized the necessity of integrating remanufacturing considerations into product design iterations to advance sustainability objectives. Acknowledging the importance of design for remanufacturing (DfRem), efforts were made to develop tools and guidelines that could be implemented in practice. However, such methods largely rely upon experiential insights and qualitative assessments, leaving a gap in the ability to quantitatively assess the economic and environmental impacts of design choices. To bridge this gap, we investigate existing efforts and present a framework for DfRem that integrates established design and remanufacturing practices into a cohesive workflow with quantitative assessments. To demonstrate its efficacy for making practical design changes for remanufacturing, we apply the framework to a hydraulic manifold in a transmission system for heavy-duty tractors. Through this industry-relevant case study, we focus on showcasing the practical utility of our framework. Based on the identified design modifications from remanufacturability analysis, we estimate the reductions in life cycle costs, energy consumption, and emissions. Afterward, the modifications are tested using physical experiments with plans for integration into future iterations of the hydraulic manifold design and production. Here, we anticipate this framework can illustrate the process of remanufacturing that ensures improvements in sustainability while maintaining performance and reliability standards.

design for X

Collimated beam manifold with the number of output beams variable at a given output angle

An optical manifold is described which transforms a collimated beam, such as a laser beam, into a plurality of parallel beams having uniform intensity or having a desired intensity ratio. The manifold comprises an optical substrate coated on its rear surface with a fully reflective layer and on its front surface with a partially reflecting layer having a reflectivity gradient. An input collimated beam entering the rear surface and impinging on the front surface is reflected, multiply between the front and rear surfaces producing a plurality of parallel beams that emerge from the front surface. The intensities of the emerging beams have a relationship that depends on the reflectivity of the front surface at the points where the beams emerge. By properly selecting the reflectivity gradient, the emerging beams have uniform intensity or a desired intensity ratio.

Campbell, C. W.

Detection of the J-10 Manifold of the Pure Rotational Band of Phosphine on Saturn

The detection of the J = 10 manifold of the pure rotational band of PH3 on Saturn is reported. The observations were made from the far-infrared cooled grating spectrometer. The wavelengths and observed brightness temperatures for the full disk plus rings are 89 + or - 3 K at 97.04 micrometer, 77 + or - 3 K at 102.72 micrometer, 77 + or - 3 K at 102.94 micrometer, and 83 + or - 3 K at 105.12 micrometers. The points of 97.04 and 105.12 micrometers establish the continuum level and the two points near 103 micrometers measure the depth of the PH3 manifold. After the flux due to the rings is subtracted, the depth of the feature is 16 + or - 6 K relative to the nearby 102 K continuum. These results are compared to theoretical models which parameterize the PH3 mixing ratio as x = x sub zero (P/P sub zero)(alpha) for P P sub zero and as x = x sub zero for P or = P, where P is the total pressure and alpha = H/h is the ratio of the dynamical scale height (H) and the scale height for decreasing the PH3 mixing ratio (h). The parameters x sub zero, P sub zero, and h were varied, as well as the H/He mixing ratio and the pressure-temperature profile. The data are well fitted using pressure-temperature profiles. The preferred values of h, P sub zero, and x sub zero imply that there is little or no PH3 above the thermal inversion and that the mixing ratio below the inversion is consistent with PH3 being 1 to 4 times overabundant relative to the solar P/H ratio.

Haas, M. R.

Experimental evaluation of an advanced Space Shuttle main engine hot-gas manifold design concept

This study, using an extensively modified, full-scale space shuttle main engine (SSME) hot-gas manifold (HGM), established a detailed aerodynamic data base to support development of an advanced, three-dimensional, fluid-dynamic analysis computer model. In addition, the advanced SSME hot-gas manifold design used in this study demonstrated improved flow environment (uniformity) in the fuel side turbine exit and transfer duct exit regions. Major modifications were incorporated in the full-scale HGM flow test article model using two large transfer ducts on the fuel turbine side of the HGM in place of the three small transfer ducts in the present design. Other model features included an increases in the flow areas downstream of the 180-degree turn and in the fishbowl regions.

Pelaccio, D. G.

Manifold Coal-Slurry Transport System

Feeding several slurry pipes into main pipeline reduces congestion in coal mines. System based on manifold concept: feeder pipelines from each working entry joined to main pipeline that carries coal slurry out of panel and onto surface. Manifold concept makes coal-slurry haulage much simpler than existing slurry systems.

Liddle, S. G.

Computational fluid dynamics as a design tool for the hot gas manifold of the Space Shuttle Main Engine

The paper discusses the application of computational fluid dynamics as a design tool for the Hot Gas Manifold of the Space Shuttle Main Engine. An improved Hot Gas Manifold configuration was arrived at computationally. This configuration was then built and air flow tested. Testing verified this configuration to be a substantial improvement over existing flight designs.

Ziebarth, J. P.

Numerical analysis of flow in the hot gas manifold of the Space Shuttle main engine

This paper presents a numerical model and results of analyses carried out to characterize the flow through the two duct configuration of the Hot Gas Manifold of the Space Shuttle Main Engine. Three dimensional computations have been performed for a half-scale air test model using a nonorthogonal body-fitted coordinate system. The calculation domain is extended from the inlet of the turnaround duct to the exit of the transfer duct. Three test cases, one for laminar flow and two for turbulent flow, have been considered. For turbulent flows, constant eddy viscosity and the k-epsilon model of turbulence were employed. As expected, laminar flow calculation predicts much larger pressure drop than turbulent flow cases. The turbulent flow results are in good agreement with the available flow-visualization data. This study and experimental data indicate that the two-transfer duct design will significantly improve the flow distribution in the Hot Gas Manifold and thereby enhance the overall performance of the SSME.

Owens, S. F.

Numerical simulation of flow path in the oxidizer side hot gas manifold of the Space Shuttle main engine

The purpose of this study is to examine in detail incompressible laminar and turbulent flows inside the oxidizer side Hot Gas Manifold of the Space Shuttle Main Engine. To perform this study, an implicit finite difference code cast in general curvilinear coordinates is further developed. The code is based on the method of pseudo-compressibility and utilize ADI or implicit approximate factorization algorithm to achieve computational efficiency. A multiple-zone method is developed to overcome the complexity of the geometry. In the present study, the laminar and turbulent flows in the oxidizer side Hot Gas Manifold have been computed. The study reveals that: (1) there exists large recirculation zones inside the bowl if no vanes are present; (2) strong secondary flows are observed in the transfer tube; and (3) properly shaped and positioned guide vanes are effective in eliminating flow separation.

Lin, S. J.

Comparative Performance of Engines Using a Carburetor, Manifold Injection, and Cylinder Injection

The comparative performance was determined of engines using three methods of mixing the fuel and the air: the use of a carburetor, manifold injection, and cylinder injection. The tests were made of a single-cylinder engine with a Wright 1820-G air-cooled cylinder. Each method of mixing the fuel and the air was investigated over a range of fuel-air ratios from 0.10 to the limit of stable operation and at engine speeds of 1,500 and 1,900 r.p.m. The comparative performance with a fuel-air ratio of 0.08 was investigated for speeds from 1,300 to 1,900 r.p.m. The results show that the power obtained with each method closely followed the volumetric efficiency; the power was therefore the highest with cylinder injection because this method had less manifold restriction. The values of minimum specific fuel consumption obtained with each method of mixing of fuel and air were the same. For the same engine and cooling conditions, the cylinder temperatures are the same regardless of the method used for mixing the fuel and the air.

Schey, Oscar W

On the transition towards slow manifold in shallow-water and 3D Euler equations in a rotating frame

The long-time, asymptotic state of rotating homogeneous shallow-water equations is investigated. Our analysis is based on long-time averaged rotating shallow-water equations describing interactions of large-scale, horizontal, two-dimensional motions with surface inertial-gravity waves field for a shallow, uniformly rotating fluid layer. These equations are obtained in two steps: first by introducing a Poincare/Kelvin linear propagator directly into classical shallow-water equations, then by averaging. The averaged equations describe interaction of wave fields with large-scale motions on time scales long compared to the time scale 1/f(sub o) introduced by rotation (f(sub o)/2-angular velocity of background rotation). The present analysis is similar to the one presented by Waleffe (1991) for 3D Euler equations in a rotating frame. However, since three-wave interactions in rotating shallow-water equations are forbidden, the final equations describing the asymptotic state are simplified considerably. Special emphasis is given to a new conservation law found in the asymptotic state and decoupling of the dynamics of the divergence free part of the velocity field. The possible rising of a decoupled dynamics in the asymptotic state is also investigated for homogeneous turbulence subjected to a background rotation. In our analysis we use long-time expansion, where the velocity field is decomposed into the 'slow manifold' part (the manifold which is unaffected by the linear 'rapid' effects of rotation or the inertial waves) and a formal 3D disturbance. We derive the physical space version of the long-time averaged equations and consider an invariant, basis-free derivation. This formulation can be used to generalize Waleffe's (1991) helical decomposition to viscous inhomogeneous flows (e.g. problems in cylindrical geometry with no-slip boundary conditions on the cylinder surface and homogeneous in the vertical direction).

Mahalov, A.

Manifold For Flushing Tubes With Cleaning Solution

Custom-built manifold mounted on cleaning basket enables simultaneous flushing of 80 tubes with cleaning solution. In original application, tubes components of rocket-engine nozzle under construction. However, basic manifold configuration adapted to other applications (e.g., fabrication of heat exchangers) in which there is need for simultaneous cleaning of many tubes of identical size and shape.

Morgan, Gene E.

Application of Low Dimensional Manifolds in NO(x) Prediction

A new post-processing technique has been developed, based on the Intrinsic Low Dimensional Manifold (ILDM) method of Maas and Pope. The ILDM method is a dynamical systems approach to the simplification of large chemical kinetic mechanisms. By identifying low-dimensional attracting manifolds, the method allows complex full mechanisms to be parameterized by just a few variables: In effect, generating reduced chemical mechanisms by an automatic procedure. These resulting mechanisms however, still retain all the species used in the full mechanism. The NO(x) post-processor takes an ILDM reduced mechanism and attempts to map this mechanism to the results of a CFD calculation. This mapping allows the NO(x) concentrations at each grid node to be obtained from the ILDM reduced mechanism, as well as other trace species of interest. Because a mapping procedure is used, this method is very fast, being able to process one million node calculations in just a few minutes.

Norris, A. T.

Clogging of Manifolds with Evaporatively Frozen Propellants: Analysis - Part 2

The mechanisms of evaporative freezing of leaking propellant and the creation of flow stoppages within injector manifolds is discussed. A quantitative analysis of the conditions, including the existence of minimum and maximum leak rates, for the accumulation of evaporatively frozen propellant is presented. Clogging of the injector manifolds of the Apollo SPS and the Gemini OAMS engines by the freezing of leaking propellant is predicted and the seriousness of the consequences are discussed. Based on the analysis a realistic evaluation of selected techniques to eliminate flow stoppages by frozen propellant is made.

Simmon, J. A.

Lightweight Exhaust Manifold and Exhaust Pipe Ducting for Internal Combustion Engines

An improved exhaust system for an internal combustion gasoline-and/or diesel-fueled engine includes an engine exhaust manifold which has been fabricated from carbon- carbon composite materials in operative association with an exhaust pipe ducting which has been fabricated from carbon-carbon composite materials. When compared to conventional steel. cast iron. or ceramic-lined iron paris. the use of carbon-carbon composite exhaust-gas manifolds and exhaust pipe ducting reduces the overall weight of the engine. which allows for improved acceleration and fuel efficiency: permits operation at higher temperatures without a loss of strength: reduces the "through-the wall" heat loss, which increases engine cycle and turbocharger efficiency and ensures faster "light-off" of catalytic converters: and, with an optional thermal reactor, reduces emission of major pollutants, i.e. hydrocarbons and carbon monoxide.

Northam, G. Burton