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At least 343 records · Page 19

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NASA NTRS1973

Analysis of embedded shock waves calculated by relaxation methods.

The requirements for uniqueness of the calculated jump conditions across embedded shock waves are investigated for type-dependent difference systems used in transonic flow studies. A mathematical analysis shows that sufficient conditions are (1) the equations should be differenced in conservative form and (2) a special difference operator should be used when switching from a hyperbolic to an elliptic operator. The latter results in a consistency condition on the integral equations, rather than the differential, at these points. Calculated jump conditions for several embedded and detached shock waves are analyzed in the physical and hodograph planes. Comparisons are made with previous results, a time-dependent calculation, and data.

Murman, E. M.↗

NASA NTRS1978

Finite element concepts in computational aerodynamics

Finite element theory was employed to establish an implicit numerical solution algorithm for the time averaged unsteady Navier-Stokes equations. Both the multidimensional and a time-split form of the algorithm were considered, the latter of particular interest for problem specification on a regular mesh. A Newton matrix iteration procedure is outlined for solving the resultant nonlinear algebraic equation systems. Multidimensional discretization procedures are discussed with emphasis on automated generation of specific nonuniform solution grids and accounting of curved surfaces. The time-split algorithm was evaluated with regards to accuracy and convergence properties for hyperbolic equations on rectangular coordinates. An overall assessment of the viability of the finite element concept for computational aerodynamics is made.

Baker, A. J.↗

NASA NTRS1992

A new method for recognizing quadric surfaces from range data and its application to telerobotics and automation

Pose and orientation of an object is one of the central issues in 3-D recognition problems. Most of today's available techniques require considerable pre-processing such as detecting edges or joints, fitting curves or surfaces to segment images, and trying to extract higher order features from the input images. We present a method based on analytical geometry, whereby all the rotation parameters of any quadric surface are determined and subsequently eliminated. This procedure is iterative in nature and was found to converge to the desired results in as few as three iterations. The approach enables us to position the quadric surface in a desired coordinate system, and then to utilize the presented shape information to explicitly represent and recognize the 3-D surface. Experiments were conducted with simulated data for objects such as hyperboloid of one and two sheets, elliptic and hyperbolic paraboloid, elliptic and hyperbolic cylinders, ellipsoids, and quadric cones. Real data of quadric cones and cylinders were also utilized. Both of these sets yielded excellent results.

Alvertos, Nicolas↗

NASA NTRS1993

Tsien's method for generating non-Keplerian trajectories. Part 2: The question of thrust to orbit a sphere and the restricted three-body problem

Tsien's method is extended to treat the orbital motion of a body undergoing accelerations and decelerations. A generalized solution is discussed for the generalized case where a body undergoes azimuthal and radial thrust and the problem is further simplified for azimuthal thrust alone. Judicious selection of thrust could generate either an elliptic or hyperbolic trajectory. This is unexpected especially when the body has only enough energy for a lower state trajectory. The methodology is extended treating the problem of vehicle thrust for orbiting a sphere and vehicle thrust within the classical restricted three-body problem. Results for the latter situation can produce hyperbolic trajectories through eigen value decomposition. Since eigen values for no-thrust can be imaginary, thrust can generate real eigen values to describe hyperbolic trajectories. Keplerian dynamics appears to represent but a small subset of a much larger non-Keplerian domain especially when thrust effects are considered. The need for high thrust long duration space-based propulsion systems for changing a trajectory's canonical form is clearly demonstrated.

Murad, P. A.↗

NASA NTRSDate not supplied

Electric Sail Design Sensitivities

Electric Sails (E-Sails) are a promising propulsion technology that seek to enable high characteristic propellentless acceleration for spacecraft to reach distant and/or difficult to reach orbits such as rapid transit to heliopause. The E-Sail system exchanges momentum by using positively charged electrostatic tethers to repel solar wind photons to push it through space. This concept was first theorized by Pekka Janhunen in 2004 with further developments occurring including a NASA Innovative Advanced Concepts Phase 1 and Phase 2 hosted out of NASA’s Marshall Space Flight Center (MSFC). These developments led to further maturation of the overall system, and this paper is designed to help identify different design sensitivities of an integrated Electric Sail system. To approach this, a small team at MSFC took an in-house developed three degrees of freedom (3DoF) simulation tool and a trajectory modelling tool to look at different design parameters and to determine a potential ideal E-Sail configuration. An E-Sail system has different design architectures including a barbell design, hub and spoke design, and a potential hybrid solution. The barbell design features two equally massed satellites that spin around a central point in the tether system. The hub and spoke design features a large central spacecraft with small end spacecraft to aid in formation control of the overall E-Sail system. Leveraging elements from both the hub and spoke, and barbell design, a hybrid option exists where one could have a larger central mass and one or two tethers extended to a smaller end mass [2]. In summary, the hub and spoke design is the ideal configuration for E-Sail with tethers spanning kilometers to achieve the designed design characteristic acceleration of at least one mm/s2 with this architecture being the focus of this study. Different key design parameters were varied as part of this study. These parameters include the total number of tethers, the length of the tethers, spin rate, relative spacecraft mass, tether voltage, inertia per tether, and impact of slew rate changes. These results started from an internal MSFC technology demonstration mission design and then the parameters were varied with engineering judgement to ensure that the results were consistent with expected results. These were varied in the MSFC 3DoF tool and compared to baseline results to generate a candidate ideal E-Sail design system. These results were then used to help inform the mission analysis design for the system. The 3DoF trajectory optimization was performed in the Astrodynamics and Space Science Enabling Toolbox (ASSET) and utilized collocation optimization of control vector pointing with the objective function being transfer duration. A representative model of the E-Sail force was derived as a function of the Sun-pointing vector direction. This model was initialized with a zero Sun Incidence Angle (SIA) trajectory for the initial guess generation, then with a portion of the mission optimized SIA time history for fast outbound transfers. After the trajectory is hyperbolic relative to a heliocentric frame, the SIA is maintained at 0 degrees except for any needed trajectory correction maneuvers. This trajectory optimization looked at different characteristic acceleration values to analyze the impact it had on mission performance. As a result of this study, the team can best inform mission designers and technology development efforts to mature the E-Sail system. This study will allow mission designers to have defined rules-of-thumb to design an E-Sail system to meet desired mission needs as well as providing several sample mission profiles. These design drivers will inform maturation efforts on which design requirements to consider for an integrated E-Sail design.

E-Sail↗

NASA NTRS1987

Conservative finite volume solutions of a linear hyperbolic transport equation in two and three dimensions using multiple grids

The feasibility of the multiple grid technique is investigated by solving linear hyperbolic equations for simple two- and three-dimensional cases. The results are compared with exact solutions and those obtained from the single grid calculations. It is demonstrated that the technique works reasonably well when two grid systems contain grid cells of comparative sizes. The study indicates that use of the multiple grid does not introduce any significant error and that it can be used to attack more complex problems.

Tiwari, Surendra N.↗

NASA NTRS1996

GENIE(++): A Multi-Block Structured Grid System

The computer code GENIE++ is a continuously evolving grid system containing a multitude of proven geometry/grid techniques. The generation process in GENIE++ is based on an earlier version. The process uses several techniques either separately or in combination to quickly and economically generate sculptured geometry descriptions and grids for arbitrary geometries. The computational mesh is formed by using an appropriate algebraic method. Grid clustering is accomplished with either exponential or hyperbolic tangent routines which allow the user to specify a desired point distribution. Grid smoothing can be accomplished by using an elliptic solver with proper forcing functions. B-spline and Non-Uniform Rational B-splines (NURBS) algorithms are used for surface definition and redistribution. The built in sculptured geometry definition with desired distribution of points, automatic Bezier curve/surface generation for interior boundaries/surfaces, and surface redistribution is based on NURBS. Weighted Lagrance/Hermite transfinite interpolation methods, interactive geometry/grid manipulation modules, and on-line graphical visualization of the generation process are salient features of this system which result in a significant time savings for a given geometry/grid application.

Williams, Tonya↗

NASA NTRS1985

Design, performance investigation and delivery of a miniaturized Cassegrainian concentrator solar array

A miniaturized Cassegrainian concentrator (MCC) solar array concept is being developed with the objective of significantly reducing the recurring cost of multikilowatt solar arrays. The desired cost reduction is obtained as a result of using very small high efficiency solar cells in conjunction with low-cost optics. In the MCC single element concept and panel concept, incident solar radiation is reflected from a primary parabolic reflector to a secondary hyperbolic reflector and finally to a 4-millimetr diameter solar cell. A light catcher cone is used to improve off-axis performance. An element is approximately 13-millimeters thick which permits efficient launch stowage of the concentrator system panels without complex optical component deployments or retractions. The MCC elements are packed in bays within graphite epoxy frames and are electrically connected into appropriate series-parallel circuits. A MCC single element with a 21 sq cm entrance aperture and a 20 percent efficient, 0.25 sq cm gallium arsenide solar cell has the same power output as 30-sq cm of 11-percent efficiency (at 68 C) silicon solar cells. The MCC concept provides the potential for a significant reduction in array cost due to a 99 percent reduction in required cell area and a 30 percent reduction in array area relative to planar array of equivalent power.

Patterson, R. E.↗

NASA NTRS2012

Resin-Impregnated Carbon Ablator: A New Ablative Material for Hyperbolic Entry Speeds

Ablative materials are required to protect a space vehicle from the extreme temperatures encountered during the most demanding (hyperbolic) atmospheric entry velocities, either for probes launched toward other celestial bodies, or coming back to Earth from deep space missions. To that effect, the resin-impregnated carbon ablator (RICA) is a high-temperature carbon/phenolic ablative thermal protection system (TPS) material designed to use modern and commercially viable components in its manufacture. Heritage carbon/phenolic ablators intended for this use rely on materials that are no longer in production (i.e., Galileo, Pioneer Venus); hence the development of alternatives such as RICA is necessary for future NASA planetary entry and Earth re-entry missions. RICA s capabilities were initially measured in air for Earth re-entry applications, where it was exposed to a heat flux of 14 MW/sq m for 22 seconds. Methane tests were also carried out for potential application in Saturn s moon Titan, with a nominal heat flux of 1.4 MW/sq m for up to 478 seconds. Three slightly different material formulations were manufactured and subsequently tested at the Plasma Wind Tunnel of the University of Stuttgart in Germany (PWK1) in the summer and fall of 2010. The TPS integrity was well preserved in most cases, and results show great promise.

Esper, Jaime↗

NASA NTRS1960

An Analysis of the Corridor and Guidance Requirements for Supercircular Entry into Planetary Atmospheres

An analysis is presented of supercircular entry into a planet's atmosphere giving particular attention to the corridor through which spacecraft must be guided in order to accomplish various maneuvers. A dimensionless parameter based on conditions at the conic perigee altitude is introduced for characterizing supercircular entries and conveniently pre-scribing corridor widths associated with elliptic, parabolic, or hyperbolic approach trajectories. The analysis applies to vehicles of arbitrary weight, shape, and size. Illustrative calculations are made for Venus, Earth, Mars, Jupiter, and Titan. For nonlifting vehicles having fixed aerodynamic coefficients, curves are presented of dimensionless parameters from which can be calculated the maximum deceleration, maximum rate of laminar convective heating, and total laminar heat absorbed during single-pass entry at velocities up to twice circular velocity. For lifting vehicles, curves are presented of the maximum deceleration and overshoot boundary of an entry corridor; equations are presented for estimating laminar aerodynamic heating from the maximum deceleration. It is shown that the corridor width is independent of vehicle weight, dimensions, and drag coefficient, provided these are the same at the overshoot boundary as at undershoot. The corridors of certain planets can be broadened markedly by the application of aerodynamic lift; for example, the 10-earth-g corridor width for single- pass, nonlifting, parabolic entry is increased from 0 miles for Jupiter, 7 for Earth, and 8 for Venus, to 52, 51, and 52 miles, respectively, by employing a lift-drag ratio of 1. The use of aerodynamic lift does not increase appreciably the corridors of Mars and Titan. All corridor widths decrease rapidly as the entry velocity is increased. Terminal guidance requirements on accuracy of velocity and flight path angle for successfully entering various corridors are compared with analogous requirements for putting a satellite into orbit, for hitting the moon from the earth, and for achieving ICBM accuracy. Consideration is given to the terminal guidance problem involved in using a planet's atmosphere-rather than rocket fuel-to effect orbital transfers from heliocentric to planetocentric motion, thereby converting a hyperbolic approach trajectory to an elliptic orbit about the target planet. This fuel saving maneuver appears technologically feasible for certain planetary voyages, and implies the possibility of achieving a large reduction in required Earth lift-off weight of chemical propulsion systems.

Chapman, Dean R.↗

NASA NTRS1984

Transformation of two and three-dimensional regions by elliptic systems

The research during this period continued to expand the class of numerical algorithms that can be accurately and efficiently implemented on overlapping grids. Whereas previous calculations have been used to solve elliptic equations and to find the steady-state solution of parabolic equations, the present work is aimed towards developing time-accurate solution techniques for parabolic and hyperbolic equations. The primary difficulty here is in the correct treatment of the interior boundary nodes that must be updated at each iteration. The implementation of explicit methods is straightforward. However, the common practice of lagging these values when using an implicit methods leads to inconsistencies in the difference equation. One way to avoid this problem is to alternately calculate with an implicit and an explicit method on each subgrid. With this procedure, the explicit method generates boundary values at the next time level which are then used by the implicit step. It can be shown that when a backward implicit method is combined with a forward explicit method, the composite method is second order accurate and unconditionally stable for linear problems. A second area in which progress can be reported is in the distribution of grid points on curves and surfaces.

Mastin, E. W.↗

NASA NTRSDate not supplied

Advances in Automation of Overset Structured Volume Mesh Generation and Domain Connectivity

Automation of overset structured surface mesh generation has recently been accomplished by the creation of face, edge, and node meshes based on Boundary Representation solids as the geometry input. The current work continues the automation effort in overset volume mesh generation and domain connectivity based on the auto-generated surface meshes. All near-body curvilinear volume meshes are automatically generated using hyperbolic methods. Automation of this step is enabled by appropriate surface grid point distribution, and selection of boundary-splay and smoothing parameters based on concave and convex surface features. The off-body domain is covered by two automatically generated grid systems. The first contains a single Cartesian mesh with a uniform core enclosing all near-body volume meshes and stretched layers that extend to the far field, while the second consists of a set of small stretched Cartesian grids covering pockets of off-body orphan points. With high quality mesh overlap mostly guaranteed by the surface meshing scheme, orphan points that need to be covered by the second Cartesian mesh system are located away from the fine grid spacing region near the wall. Using line-segment and ray-pierce tests against the surface grids, hole-cutting is accomplished on both near and off-body volume grids resulting in appropriate clearances from the wall. The complete mesh generation automation process is demonstrated on five test cases where flow solutions are also computed and compared with solutions obtained using other methods.

TTT↗

NASA NTRS2003

Finite Volume Methods: Foundation and Analysis

Finite volume methods are a class of discretization schemes that have proven highly successful in approximating the solution of a wide variety of conservation law systems. They are extensively used in fluid mechanics, porous media flow, meteorology, electromagnetics, models of biological processes, semi-conductor device simulation and many other engineering areas governed by conservative systems that can be written in integral control volume form. This article reviews elements of the foundation and analysis of modern finite volume methods. The primary advantages of these methods are numerical robustness through the obtention of discrete maximum (minimum) principles, applicability on very general unstructured meshes, and the intrinsic local conservation properties of the resulting schemes. Throughout this article, specific attention is given to scalar nonlinear hyperbolic conservation laws and the development of high order accurate schemes for discretizing them. A key tool in the design and analysis of finite volume schemes suitable for non-oscillatory discontinuity capturing is discrete maximum principle analysis. A number of building blocks used in the development of numerical schemes possessing local discrete maximum principles are reviewed in one and several space dimensions, e.g. monotone fluxes, E-fluxes, TVD discretization, non-oscillatory reconstruction, slope limiters, positive coefficient schemes, etc. When available, theoretical results concerning a priori and a posteriori error estimates are given. Further advanced topics are then considered such as high order time integration, discretization of diffusion terms and the extension to systems of nonlinear conservation laws.

Barth, Timothy↗

NASA NTRS1977

Variants and extensions of a fast direct numerical cauchy-riemann solver, with illustrative applications

Revised and extended versions of a fast, direct (noniterative) numerical Cauchy-Riemann solver are presented for solving finite difference approximations of first order systems of partial differential equations. Although the difference operators treated are linear and elliptic, one significant application of these extended direct Cauchy-Riemann solvers is in the fast, semidirect (iterative) solution of fluid dynamic problems governed by the nonlinear mixed elliptic-hyperbolic equations of transonic flow. Different versions of the algorithms are derived and the corresponding FORTRAN computer programs for a simple example problem are described and listed. The algorithms are demonstrated to be efficient and accurate.

Martin, E. D.↗

NASA NTRS1986

On the search for trajectories for a cometary nucleus sample return mission

The steps in the procedure for the generation of single trajectories for a comet nucleus sample return mission described by Stuhlinger et al. (1985) are discussed. The following assumptions are made for such a mission: (1) the spacecraft is equipped with an ion propulsion system supplied by solar cells, and (2) the comet has a low inclination and a period of about six years. The calculation of a specific trajectory incorporates the following main parameters: (1) the spacecraft mass at the beginning of the mission and the hyperbolic excess velocity, (2) the mass as a function of the injection energy, and (3) the available thrust level. The limitation of a supply of solar electric power to the region within 3 AU of the sun and the placement of permanent in-situ experiments at the comet are discussed. It is concluded that single trajectories for a nucleus sample return mission can be generated. A further step would be an integration of single solutions into classes of trajectories.

Schobert, D.↗

NASA NTRS2020

Optimal Low Thrust Orbit Transfers for Space Telescope Refueling at SEL2

The James Webb Space Telescope (JWST), a ten billion-dollar infrared telescope with a 6.5m primary mirror to be launched in 2021, is designed to operate in a Halo orbit around the second Sun-Earth Lagrange point (SEL2) for five to ten years. At that point fuel for station keeping and attitude maneuvers will run out. Refueling missions to JWST, as well as to similar space telescope missions proposed for SEL2, could greatly enhance the “science-per-dollar” value and promote a more sustainable use of space assets. In this paper, we present a novel approach to designing fuel optimal trajectories that will allow the refueling spacecraft to arrive at the SEL2 Halo orbit with maximum final mass (i.e. fuel payload). The low thrust optimal control problem is formulated using an indirect optimization method, leading to a two-point boundary value problem with a bang-bang control structure. We make use of a hyperbolic tangent smoothing technique for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and, thus, promote convergence. The problem is posed and solved in the circular restricted three-body problem. In this dynamical system, invariant manifolds exist that can be utilized to reduce fuel consumption. The here presented methodology to this challenging and important problem in astrodynamics demonstrates a significant potential for low-cost refueling mission design.

Woollands, Robyn↗

NASA NTRSDate not supplied

Impact of Magnetohydrodynamic (MHD) Induced Drag on High Ballistic Coefficient Aerocapture at Neptune

This paper presents analyses illustrating the benefits of magnetohydrodynamic (MHD) drag force control for a capsule performing aerocapture at Neptune relative to the same capsule utilizing conventional aerodynamic-only control across a range of design and flight conditions. MHD technology utilizes an onboard mag-net to create a magnetic field that interacts with the ionized plasma surrounding the capsule at hypersonic velocities, thus creating an electron current and inducing a Lorentz force used to increase capsule drag. The study assumes a 4.57-meterMars Science Laboratory (MSL) 70-degree sphere-cone capsule aerodynamic shape arrives hyperbolically at Neptune and aerocaptures into a synchronous Tri-ton orbit (3986 km x 430,000 km orbit inclined 157 degrees) that offers repeated flyby opportunities. Hyperbolic arrival velocity and the capsule entry mass (i.e., ballistic coefficient) are varied over a wide range of values to study the impact of these variables on key flight performance and sizing parameters. Results show reduced heat rates, heat loads, and thermal protection system mass for MHD cases at all conditions, with the benefit of MHD relative to conventional aerodynamic-only options increasing as ballistic coefficient increases, suggesting the payoff for MHD is significantly better for high-mass entry system design concepts with high ballistic coefficients.

Entry Descent and Landing↗

NASA NTRS2018

Powered Explicit Guidance Modifications and Enhancements for Space Launch System Block-1 and Block-1B Vehicles

NASA is currently building the Space Launch System (SLS) Block-1 launch vehicle for the Exploration Mission 1 (EM-1) test flight. NASA is also currently designing the next evolution of SLS, the Block-1B. The Block-1 and Block-1B vehicles will use the Powered Explicit Guidance (PEG) algorithm (of Space Shuttle heritage) for closed loop guidance. To accommodate vehicle capabilities and design for future evolutions of SLS, modifications were made to PEG for Block-1 to handle multi-phase burns, provide PEG updated propulsion information, and react to a core stage engine out. In addition, due to the relatively low thrust-to-weight ratio of the Exploration Upper Stage (EUS) and EUS carrying out Lunar Vicinity and Earth Escape missions, certain enhancements to the Block-1 PEG algorithm are needed to perform Block-1B missions to account for long burn arcs and target translunar and hyperbolic orbits. This paper describes the design and implementation of modifications to the Block-1 PEG algorithm as compared to Space Shuttle. Furthermore, this paper illustrates challenges posed by the Block-1B vehicle and the required PEG enhancements. These improvements make PEG capable for use on the SLS Block-1B vehicle as part of the Guidance, Navigation, and Control (GN&C) System.

Von der Porten, Paul↗