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NASA NTRS2011

COMPASS Final Report: Enceladus Solar Electric Propulsion Stage

The results of the NASA Glenn Research Center (GRC) COllaborative Modeling and Parametric Assessment of Space Systems (COMPASS) internal Solar Electric Propulsion (SEP) stage design are documented in this report (Figure 1.1). The SEP Stage was designed to deliver a science probe to Saturn (the probe design was performed separately by the NASA Goddard Space Flight Center s (GSFC) Integrated Mission Design Center (IMDC)). The SEP Stage delivers the 2444 kg probe on a Saturn trajectory with a hyperbolic arrival velocity of 5.4 km/s. The design carried 30 percent mass, 10 percent power, and 6 percent propellant margins. The SEP Stage relies on the probe for substantial guidance, navigation and control (GN&C), command and data handling (C&DH), and Communications functions. The stage is configured to carry the probe and to minimize the packaging interference between the probe and the stage. The propulsion system consisted of a 1+1 (one active, one spare) configuration of gimbaled 7 kW NASA Evolutionary Xenon Thruster (NEXT) ion propulsion thrusters with a throughput of 309 kg Xe propellant. Two 9350 W GaAs triple junction (at 1 Astronomical Unit (AU), includes 10 percent margin) ultra-flex solar arrays provided power to the stage, with Li-ion batteries for launch and contingency operations power. The base structure was an Al-Li hexagonal skin-stringer frame built to withstand launch loads. A passive thermal control system consisted of heat pipes to north and south radiator panels, multilayer insulation (MLI) and heaters for the Xe tank. All systems except tanks and solar arrays were designed to be single fault tolerant.

Oleson, Steven R.↗

NASA NTRS1974

Loran-C expansion: Impact on precise time/time interval

On 16 May 1974, it was announced that Loran-C was chosen as the navigation system to serve the U. S. Coastal Confluence Zone. At the present time, reliable CONUS Loran-C groundwave timing coverage extends westward only about as far as Boulder, CO. The groundwave hyperbolic and timing coverage which will result from the planned CONUS expansion are illustrated. Time frames are provided. A status report on the planned reduction in Loran-C PTTI tolerances is presented.

Roeber, J. F., Jr.↗

NASA NTRS1984

An incompressible Navier-Stokes flow solver in three-dimensional curvilinear coordinate systems using primitive variables

An implicit, finite-difference computer code has been developed to solve the incompressible Navier-Stokes equations in a three-dimensional, curvilinear coordinate system. The pressure-field solution is based on the pseudo compressibility approach in which the time derivative pressure term is introduced into the mass conservation equation to form a set of hyperbolic equations. The solution procedure employs an implicit, approximate factorization scheme. The Reynolds stresses, that are uncoupled from the implicit scheme, are lagged by one time-step to facilitate implementing various levels of the turbulence model. Test problems for external and internal flows are computed, and the results are compared with existing experimental data. The application of this technique for general three-dimensional problems is then demonstrated.

Kwak, D.↗

NASA NTRS1993

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

The problem of recognizing and positioning of objects in three-dimensional space is important for robotics and navigation applications. In recent years, digital range data, also referred to as range images or depth maps, have been available for the analysis of three-dimensional objects owing to the development of several active range finding techniques. The distinct advantage of range images is the explicitness of the surface information available. Many industrial and navigational robotics tasks will be more easily accomplished if such explicit information can be efficiently interpreted. In this research, a new technique based on analytic geometry for the recognition and description of three-dimensional quadric surfaces from range images is presented. Beginning with the explicit representation of quadrics, a set of ten coefficients are determined for various three-dimensional surfaces. For each quadric surface, a unique set of two-dimensional curves which serve as a feature set is obtained from the various angles at which the object is intersected with a plane. Based on a discriminant method, each of the curves is classified as a parabola, circle, ellipse, hyperbola, or a line. Each quadric surface is shown to be uniquely characterized by a set of these two-dimensional curves, thus allowing discrimination from the others. Before the recognition process can be implemented, the range data have to undergo a set of pre-processing operations, thereby making it more presentable to classification algorithms. One such pre-processing step is to study the effect of median filtering on raw range images. Utilizing a variety of surface curvature techniques, reliable sets of image data that approximate the shape of a quadric surface are determined. Since the initial orientation of the surfaces is unknown, a new technique is developed wherein all the rotation parameters are determined and subsequently eliminated. This approach enables us to position the quadric surfaces in a desired coordinate system. Experiments were conducted on raw range images of spheres, cylinders, and cones. Experiments were also performed on simulated data for surfaces such as hyperboloids of one and two sheets, elliptical and hyperbolic paraboloids, elliptical and hyperbolic cylinders, ellipsoids and the quadric cones. Both the real and simulated data yielded excellent results. Our approach is found to be more accurate and computationally inexpensive as compared to traditional approaches, such as the three-dimensional discriminant approach which involves evaluation of the rank of a matrix. Finally, we have proposed one other new approach, which involves the formulation of a mapping between the explicit and implicit forms of representing quadric surfaces. This approach, when fully realized, will yield a three-dimensional discriminant, which will recognize quadric surfaces based upon their component surfaces patches. This approach is faster than prior approaches and at the same time is invariant to pose and orientation of the surfaces in three-dimensional space.

Alvertos, Nicolas↗

NASA NTRS1987

A Taylor weak-statement algorithm for hyperbolic conservation laws

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Baker, A. J.↗

NASA NTRS1976

On the mathematical conditions for the existence of periodic fluctuations in non-uniform media

The assumption that periodic excitations result in periodic responses for the case of waves propagating through nonuniform media is examined by investigating the periodic solutions of linear hyperbolic differential equations whose coefficients vary with position and whose solution must satisfy periodic boundary or source data. It is shown that the nature of the coefficients of undifferentiated terms of the differential system is crucial in determining whether the solution is periodic. Particular attention is paid to the propagation of infinitesimal pressure waves through the nonuniform steady flow of a lossless fluid.

Gunzburger, M. D.↗

NASA NTRS1986

Comparison of mission design options for manned Mars missions

A number of manned Mars mission types, propulsion systems, and operational techniques are compared. Conjunction and opposition class missions for cryogenic, hybrid (cryo/storable), and NERVA propulsion concepts are addressed. In addition, both Earth and Mars orbit aerobraking, direct entry of landers, hyperbolic rendezvous, and electric propulsion cases are examined. A common payload to Mars was used for all cases. The basic figure of merit used was weight in low Earth orbit (LEO) at mission initiation. This is roughly proportional to launch costs.

Gus R Babb↗

NASA NTRS1988

Optimization of motion control laws for tether crawler or elevator systems

Based on the proposal of a motion control law by Lorenzini (1987), a method is developed for optimizing motion control laws for tether crawler or elevator systems in terms of the performance measures of travel time, the smoothness of acceleration and deceleration, and the maximum values of velocity and acceleration. The Lorenzini motion control law, based on powers of the hyperbolic tangent function, is modified by the addition of a constant-velocity section, and this modified function is then optimized by parameter selections to minimize the peak acceleration value for a selected travel time or to minimize travel time for the selected peak values of velocity and acceleration. It is shown that the addition of a constant-velocity segment permits further optimization of the motion control law performance.

Swenson, Frank R.↗

NASA NTRS2021

A Study into Validating a Coupled Method of Characteristics and Direct Simulation Monte Carlo Method Against Empirical Data

The following will outline the methodology and results of validating a coupled Method of Characteristics (MOC) and Direct Simulation Monte Carlo (DSMC) method. This research focused specifically on modeling plume impingement, induced by Reaction Control System (RCS) thrusters that flew on the National Aeronautics and Space Administration’s (NASA’s) space shuttle Discovery. For each simulation, the continuum portion of the RCS thruster was simulated using MOC for solving hyperbolic Partial Differential Equations (PDEs) and computed with the NASA code, Reacting and Multi-phase Program (RAMP). The solution was then implemented as a starting condition into the NASA DSMC code, Direct Simulation and Monte Carlo Analysis Code (DAC). Typically, DSMC models rely on code-to-code validation for fidelity. The significance of this research is in its ability to validate its models against empirical data. Prior to computing solutions for these simulations, the mesh size and structure were optimized and many variants of DSMC input parameters were iterated on in order to acquire a reliable, mesh-independent, fully optimized numerical solution. This research will discuss the mathematical formulation of MOC for nozzle flow and DSMC for rarefied gases. Additionally, it will provide an explanation of how to implement these mathematical concepts into the two solvers: RAMP and DAC. Ultimately, this research will demonstrate that the overall process illustrated produces results in good agreement with empirical data. As a consequence, the methodology presented is granted an increased level of confidence and will greatly contribute to the aerospace industry and its effort in understanding and predicting rarefied flow fields.

Direct Simulation Monte Carlo Analysis Code↗

NASA NTRS2021

A Study into Validating A Coupled Method of Characteristics And Direct Simulation Monte Carlo Method Against Empirical Data

DAC↗

NASA NTRS1996

4-Dimensional Special Orthonormal Frames for Vacuum Gravity

By adopting Nester's 4-dimensional special orthonormal frames, the tetrad equations for vacum gravity are put into explicitly causal and symmetric hyperbolic form, independent of any time slicing or other gauge or coordinate specialization.

differential systems vacuum vacuum gravity vacuum ↗

NASA NTRS2018

The Laser Enhanced Arc-Jet Facility (LEAF-Lite): Simulating Convective and Radiative Heating with Arc-Jets and Multiple 50-KW CW Lasers

LEAF-Lite (Laser Enhanced Arc-Jet Facility) is a radiative laser heating facility that has been added to the 60 MW Interaction Heating Facility (IHF) convective plasma arc-jet located at NASA Ames Research Center. Together, these two systems can simulate both convective and radiative heating at heat fluxes reaching 551 W/cm2 by simultaneously combining a highest measured heat flux of 160 W/cm2 convective and 391 W/cm2 radiative heating on a 152-mm x 152-mm wedge model configuration. Adding radiant heating to an existing convective facility better simulates Earth atmospheric entry from hyperbolic lunarreturn speeds. The radiative heat is provided by multiple 50-kW CW IR lasers, which is nearly uniform across the illuminated surface with a total variation less than 6%, while the convective heat is provided by a high enthalpy plasma arc-jet. In a later phase, the facility will expand to test panel test articles of 432-mm x 432-mm and provide 100 W/cm2 of radiative heating in a plasma convective flow environment. The paper describes this new combined heating capability, its current testing conditions, and the unique application of the laser system with respect to the Orion test flight lunar orbits.

Cushman, Geoff↗

NASA NTRS1983

Second-order explicit finite-difference methods for transient-flow analysis

Three second-order accurate numerical methods - MacCormack's method, Lambda scheme and Gabutti scheme - are introduced to solve the quasi-linear, hyperbolic partial differential equations describing transient flows in closed conduits. The details of these methods and the treatment of boundary conditions are presented and the results computed by using these methods for a typical piping system are compared. It is shown that for the same accuracy, second-order methods require considerably lesser number of computational nodes and computer time as compared to those required by the first-order methods.

Chaudhry, M. H.↗

NASA NTRS1992

GridMan: A grid manipulation system

GridMan is an interactive grid manipulation system. It operates on grids to produce new grids which conform to user demands. The input grids are not constrained to come from any particular source. They may be generated by algebraic methods, elliptic methods, hyperbolic methods, parabolic methods, or some combination of methods. The methods are included in the various available structured grid generation codes. These codes perform the basic assembly function for the various elements of the initial grid. For block structured grids, the assembly can be quite complex due to a large number of clock corners, edges, and faces for which various connections and orientations must be properly identified. The grid generation codes are distinguished among themselves by their balance between interactive and automatic actions and by their modest variations in control. The basic form of GridMan provides a much more substantial level of grid control and will take its input from any of the structured grid generation codes. The communication link to the outside codes is a data file which contains the grid or section of grid.

Eiseman, Peter R.↗

NASA NTRS1992

Three-dimensional boundary layer calculation by a characteristic method

A numerical method for solving the three-dimensional boundary layer equations for bodies of arbitrary shape is presented. In laminar flows, the application domain extends from incompressible to hypersonic flows with the assumption of chemical equilibrium. For turbulent boundary layers, the application domain is limited by the validity of the mixing length model used. In order to respect the hyperbolic nature of the equations reduced to first order partial derivative terms, the momentum equations are discretized along the local streamlines using of the osculator tangent plane at each node of the body fitted coordinate system. With this original approach, it is possible to overcome the use of the generalized coordinates, and therefore, it is not necessary to impose an extra hypothesis about the regularity of the mesh in which the boundary conditions are given. By doing so, it is possible to limit, and sometimes to suppress, the pre-treatment of the data coming from an inviscid calculation. Although the proposed scheme is only semi-implicit, the method remains numerically very efficient.

Houdeville, R.↗

NASA NTRS1994

TIGGERC: Turbomachinery Interactive Grid Generator for 2-D Grid Applications and Users Guide

A two-dimensional multi-block grid generator has been developed for a new design and analysis system for studying multiple blade-row turbomachinery problems. TIGGERC is a mouse driven, interactive grid generation program which can be used to modify boundary coordinates and grid packing and generates surface grids using a hyperbolic tangent or algebraic distribution of grid points on the block boundaries. The interior points of each block grid are distributed using a transfinite interpolation approach. TIGGERC can generate a blocked axisymmetric H-grid, C-grid, I-grid or O-grid for studying turbomachinery flow problems. TIGGERC was developed for operation on Silicon Graphics workstations. Detailed discussion of the grid generation methodology, menu options, operational features and sample grid geometries are presented.

Miller, David P.↗

NASA NTRSDate not supplied

Next Generation Thermal Protection System for Outer Planet Probes and Orbiter

Saturn Probe and Ice Giant Orbiter along with in-situ Probe Missions continue to be very high priority mis-sions. A result of the advocacy by OPAG and other Analysis Groups, the 3D Woven, Dual-Layer HEEET thermal protection system, mature at TRL 6, has closed the TPS gap for extreme environment missions. A mid density follow on to DL HEEET, developed to meet earth entry requirements, is a Single Layer vari-ant of the 3D woven TPS, which provides a mass effi-cient single layer 3D Mid-Density TPS (3MDCP) that has been baselined as the heatshield for MSR EEV. Continued development of 3MDCP will elevate it to TRL 6 by 2025. Conformal-PICA (C-PICA) devel-opment was pursued to establish a more efficient and robust alternate to PICA, and it is at TRL 4+. Our rationale for the next generation of TPS de-velopment is based on the on the missions needs of the next decade Outer Planet missions that are unique and more demanding than any other destinations. Taking advantage of the recent planned development of sev-eral materials, the next generation of TPS offers a much more mass efficient option for small, medium, and large class Outer Planet missions. Saturn Probes: While mission designers are gen-erally interested in shallow entry to maintain the g-load during entry around 50g, the heat-load for shallow entry can range between (100 kJ/cm2 – 300 kJ/cm2), two orders of magnitude higher than Venus or Sample Return missions. TPS must not only offer protection but must be mass efficient to perform reasonable sci-ence. TPS mass can quickly become 50% or more of the mass of the entire entry system. Recent analysis performed shows Saturn Probe missions could signifi-cantly benefit from the single layer HEEET (SL-HEEET/3MDCP). A DL-HEEET based heatshield mass could be ~ (40% -50%), SL-HEEET can provide additional (30% - 50%) mass savings. At the same time, C-PICA can provide (30% - 50%) mass savings on the backshell. The combined mass savings can be significant enough to carry an additional probe, if de-sired. Ice Giant Aerocapture Missions: Aerocapture mission architectures can provide significant ad-vantage over traditional propulsive insertion missions in multiple ways. 1) Reduced trip time ~ (4- 6) years (30% -40%), 2) Enables placing the orbiter, probe, and lander, all together and 3) Allows for greater science mass (probes and landers) due to mass efficiency. The delivery of a probe from orbit makes it easier and eliminates mission design constraints by HEEET for direct entry [4] of probes and allows for more targeted in-situ science once the Orbiter is able to collect data. In the past 20 years, progress made in GN&C for lift-guided entry missions (MSL, Orion EFT1, Mars 2020) and the expertise in blunt body aerodynamics at large scale (~ 5m) has led the EDL community to conclude that aerocapture is a “go do” engineering activity. An aerocapture mission that will deplete the excess energy of a fast arrival mission will require a mass efficient TPS that can handle extreme heat-load, ~ (100 kJ/cm2 – 500 kJ/cm2). Hence TPS, feasibility as well as mass efficiency requires assessment. Utilizing the recent developments, a comprehensive, bounding analysis was done to establish the potential for SOA (HEEET) system as well as emerging new TPS such as SL-HEEET and C-PICA. In this proposed poster, we will outline the process by which we establish bounding aerocapture trajecto-ries for hyperbolic excess velocities ranging from 27 km/s to 35 km/s, for low L/D (~ 0.4) configurations and determine conservative/bounding estimate of aer-othermal environment by using a combination of CFD simulations and stagnation point heating estimates [7]. This engineering approach allows us to assess the TPS need vs. TPS capability and determine the applicability of existing TPS. Once an applicable suite of TPS is determined, the TPS thickness and mass are comput-ed. We show that the TPS mass fraction can be as low as 5% to as high as 20%, depending on the use of ad-vanced TPS, while HEEET is sufficient but will require 50% of the entry mass.

E Venkatapathy↗

NASA NTRS1972

The entropy rate admissibility criterion for solution of hyperbolic conservation laws

The entropy rate admissibility criterion for solutions of hyperbolic conservation laws is numerically analyzed. The following admissibility criterion for solutions of hyperbolic conservation laws is proposed: a weak solution is admissible if the total entropy decays with the highest possible rate. The equivalence of this criterion and viscosity criterion is established for the single equation and the system of equations of one dimensional nonlinear elasticity.

Dafermos, C. M.↗