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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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At least 109 records · Page 6

On the Convergence of Inexact Predictor-Corrector Methods for Linear Programming

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear system of equations at each iteration. In common applications of linear programming, particularly in machine learning and scientific computing, the size of this linear system can become prohibitively large, requiring the use of iterative solvers, which provide an approximate solution to the linear system. However, approximately solving the linear system at each iteration of an IPM invalidates the theoretical guarantees of common IPM analyses. To remedy this, we theoretically and empirically analyze (slightly modified) predictor-corrector IPMs when using approximate linear solvers: our approach guarantees that, when certain conditions are satisfied, the number of IPM iterations does not increase and that the final solution remains feasible. We also provide practical instantiations of approximate linear solvers that satisfy these conditions for special classes of constraint matrices using randomized linear algebra.

Dexter, Gregory↗

Riemannian Optimization Applied to AC Optimal Power Flow

The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. This is done by using the Julia programming language and the Julia packages PowerModels.jl and Manopt.jl.

AC optimal power flow↗

A new measurement method for separating airborne and structureborne aircraft interior noise

It is pointed out that interior noise levels of propeller driven aircraft are substantially higher than levels measured for other types of CTOL aircraft. Reduction of interior noise of such aircraft requires a knowledge of the relative importance of the acoustic and structural noise transmission paths. Noise entering the aircraft interior via an acoustic path is the noise radiated by an external noise source (propellers, exhaust noise), which propagates through the acoustic medium (air) and is then transmitted through the aircraft fuselage. This type of incoming noise is referred to as airborne noise. Noise entering the aircraft interior via a structural path is the noise which has its source in the vibrational energy which has been transmitted through the structure from a remote vibrational energy source (engines, wind flutter). This type of incoming noise is referred to as structureborne noise. A new method for separating airborne and structureborne noise is presented. It is based on two-microphone cross spectral acoustic intensity measurements.

Mcgary, M. C.↗

Mission design for a halo orbiter of the earth

The International Sun-Earth Explorer (ISEE) scientific satellite to be stationed in 1978 in the vicinity of the sun-earth interior libration point to continuously monitor the space between the sun and the earth, including the distant geomagnetic tail is described. Orbit selection considerations for the ISEE-C are discussed along with stationkeeping requirements and fuel-optimal trajectories. Due to the alignment of the interior libration point with the sun as viewed from the earth, it will be necessary to place the satellite into a 'halo orbit' around the libration point, in order to eliminate solar interference with down-link telemetry. Parametric data for transfer trajectories between an earth parking orbit (altitude about 185 km) and a libration-point orbit are presented. It is shown that the insertion magnitude required for placing a satellite into an acceptable halo orbit is rather modest.

Farquhar, R. W.↗

A station-keeping method for libration point trajectories

Three-dimensional orbits in the vicinity of the interior libration point of the sun-earth/moon barycenter system are currently being considered for use with a number of missions planned for the 1990s. Since such libration-point trajectories are generally unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. The primary goal of this effort is the development of a stationkeeping strategy applicable to such trajectories. A method is presented that uses maneuvers executed impulsively at discrete time intervals. The analysis includes some investigation of a number of the problem parameters that affect the overall maneuver costs. Simulations are designed to provide representative stationkeeping costs for a spacecraft moving in a libration-point trajectory, and preliminary results are summarized.

Howell, K. C.↗

Algebraic grid generation about wing-fuselage bodies

An algebraic procedure for generating boundary-fitted grids about wing-fuselage configurations is presented. A wing-fuselage configuration consists of two aircraft components specified by cross sections and mathematically represented by Coons' patches. Several grid blocks are constructed to cover the entire region surrounding the configuration, and each grid block maps into a computational cube. Grid points are first determined on the six boundary surfaces of a block and then in the interior. Grid points on the surface of the configuration are derived from the intersection of planes with the Coons' patch definition. Approximate arc length distributions along the resulting grid curves concentrate and disperse grid points. The two-boundary technique and transfinite interpolation are used to determine grid points on the remaining boundary surfaces and block interiors.

Smith, R.E.↗

Melting Curve and Phase Relations of Fe-Ni Alloys: Implications for the Earth's Core Composition

We discuss that nickel is the second most abundant element in the Earth's core. However, the properties of Fe-Ni alloys are still poorly constrained under planetary cores conditions, in particular concerning the effect of Ni on the melting curve of Fe. Here we show that Ni alloying up to 36 wt% does not affect the melting curve of Fe up to 100 GPa. However, Ni strongly modifies the hexagonal-closed-packed/face-centered-cubic (hcp/fcc) phase boundary, pushing the hcp/fcc/liquid triple point of Fe-20wt%Ni to higher pressures and temperatures. Our results allow constraining the triple point for Fe-10wt%Ni, a composition relevant for the Earth interior, and point out a decrease of the melting temperature at core-mantle boundary by 400 K with respect to pure Fe. A lower amount of light elements than previously predicted is thus required to reduce the crystallization temperature of core materials below that of a peridotitic lower mantle, in better agreement with geochemical observations.

36 MATERIALS SCIENCE↗

Sun-earth libration point trajectories that avoid the solar exclusion zone

Three-dimensional orbits in the restricted three-body problem have been the subject of a number of recent studies. One type of three-dimensional, quasi-periodic orbit that emanates from the general vicinity of the collinear libration points is known as a 'Lissajous' trajectory. Future mission plans include trajectories near the interior libration point. (L1) in the sun-earth system and may consider Lissajous orbits as part of the trajectory design. Such orbits may be constrained, however, to remain beyond the region of the solar disk as viewed from earth. This effort involves the numerical determination of Lissajous trajectories of arbitrary, but predetermined, length that never violate such a constraint as a result of maneuvers directed, in general, perpendicular to the ecliptic plane.

Howell, K. C.↗

Grid evolution in time asymptotic problems

A technique for generating systems of coordinates for solving time asymptotic problems is described which provides a simple way of moving the mesh points in physical space and reduces the error in the solution relative to that obtained using a fixed mesh. First order partial differential equations are formulated for the grid point velocity in transient problems. Local flow information and boundary motion are used to determine the interior grid point motion.

Rai, M. M.↗

Applying Dynamical Systems Theory to Optimize Libration Point Orbit Stationkeeping Maneuvers for WIND

NASA's WIND mission has been operating in a large amplitude Lissajous orbit in the vicinity of the interior libration point of the Sun-Earth/Moon system since 2004. Regular stationkeeping maneuvers are required to maintain the orbit due to the instability around the collinear libration points. Historically these stationkeeping maneuvers have been performed by applying an incremental change in velocity, or (delta)v along the spacecraft-Sun vector as projected into the ecliptic plane. Previous studies have shown that the magnitude of libration point stationkeeping maneuvers can be minimized by applying the (delta)v in the direction of the local stable manifold found using dynamical systems theory. This paper presents the analysis of this new maneuver strategy which shows that the magnitude of stationkeeping maneuvers can be decreased by 5 to 25 percent, depending on the location in the orbit where the maneuver is performed. The implementation of the optimized maneuver method into operations is discussed and results are presented for the first two optimized stationkeeping maneuvers executed by WIND.

WIND↗

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Roberts, Craig E.↗

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions - the Solar Heliospheric Observatory (SOHO), the Advanced Composition Explorer (ACE), and the Global Geoscience WIND - have been orbiting the Sun-Earth interior libration point L1 continuously since 1996, 1997, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center Flight Dynamics Facility. While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND prior to 2004 flew a remarkable 10-year deep-space trajectory that featured 38 targeted lunar flybys. The L1 orbits and the mission histories of the three spacecraft are briefly reviewed, and the station-keeping techniques and orbit maneuver experience are discussed.

Roberts, Craig E.↗

Direct control of the grid point distribution in meshes generated by elliptic equations

The generation of computational grids suitable for obtaining accurate numerical solutions to the three-dimensional Navier-Stokes equations is the subject of intensive research. For a wide class of nozzle configurations, a three-dimensional grid can be constructed by a sequence of two-dimensional grids in successive cross-sectional planes. The present paper is concerned with numerical generation of two-dimensional grids. An effective method of interior grid control is presented based on a modified elliptic system containing free parameters. For a simply connected region, the free parameters are computed from the Dirichlet boundary values. The resulting interior grid point distribution is controlled entirely by a priori selection of the grid point distribution along the boundaries of the section.

Middlecoff, J. F.↗

Application of two-point implicit central-difference methods to hyperbolic systems

This paper presents a general solution algorithm for the set of difference equations that arise when two-point central differences are used to approximate the flux difference terms in systems of hyperbolic differential equations. The general algorithm eliminates the weak points associated with the nonstandard algorithm reported by Wornom and Hafez (1986). The disadvantages of their algorithm relate to its implementation. It consists of separate algorithms for subsonic, supersonic, sonic and shock cells, applied individually, which presents a major bookkeeping problem when multiple sonic and shock cells are present. The general algorithm eliminates this problem and introduces an improved shock treatment which produces shocks with at most one interior shock point.

Wornom, Stephen F.↗

Gradient-Informed Design Optimization of Select Nuclear Systems

In this work, we present a gradient-informed design optimization of nuclear reactor core components based on neutronics objectives with both continuous and discrete materials. The main argument in favor of using gradient-informed design optimization is that it scales well with increasing dimensionality of the design space. First, a challenge problem with 121 free parameters is solved with a gradient-informed method and then with a genetic algorithm. Then, a challenge problem to optimize the flux profile of a simplified assembly with eight axial zones is solved. Both challenge problems are solved using directly calculated derivatives from Tools for Sensitivity and Uncertainty Analysis Methodology Implementation (TSUNAMI) in the SCALE package. Furthermore, we demonstrate how a discrete optimization problem—selection of materials for 121 voxels—can be lifted into a continuous problem with mixed materials. In the continuous space, adjoint-based gradients are well-defined, and gradient descent is applicable. Then, a forcing function is introduced that with the selection of an appropriately sized hyperparameter can be used to guide the optimized continuous solution back into a discrete solution. This paper presents an account of the challenges that were faced when applying a gradient-informed optimization algorithm using a Monte Carlo calculation to estimate the gradient information and compares a gradient descent optimization method to a genetic algorithm optimization of the same geometry. Overall, this work demonstrates the potential use of adjoint-based gradient calculations in design optimization of nuclear systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Mass diffusion in a self-confined rotating flow

The effectiveness of fluid containment near an interior stagnation point and within a self-confined stagnation region is determined by numerically solving the species conservation equation for a bi-component mixture. The flow geometry is that of a swirling fluid stream containing a stationary eddy on the axis of rotation. The base flow is axisymmetric, and the Reynolds number is equal to 50. Schmidt numbers range from 0.1 to 10.

Torrance, K. E.↗

The computation of steady nozzle flow by a time-dependent method

The steady flow in two-dimensional and axisymmetric nozzles was computed using a time-dependent method. In this method the interior mesh points were computed using the MacCormack finite-difference scheme, while a characteristic scheme was used to calculate the boundary mesh points. No explicit artificial viscosity term was included. The fluid was assumed to be a perfect gas. This method was used to compute the flow in a 45 deg - 15 deg conical, converging-diverging nozzle, a 15 deg conical, converging nozzle, and a 10 deg conical, plug nozzle. Good agreement between the numerical solution and experimental data was found. In contrast to previous time-dependent methods, the computational times were less than one minute on a CDC 6600 computer.

Cline, M. C.↗