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NASA NTRS2006

The NASA Constellation University Institutes Project: Thrust Chamber Assembly Virtual Institute

This paper documents key aspects of the Constellation University Institutes Project (CUIP) Thrust Chamber Assembly (TCA) Virtual Institute (VI). Specifically, the paper details the TCA VI organizational and functional aspects relative to providing support for Constellation Systems. The TCA VI vision is put forth and discussed in detail. The vision provides the objective and approach for improving thrust chamber assembly design methodologies by replacing the current empirical tools with verified and validated CFD codes. The vision also sets out ignition, performance, thermal environments and combustion stability as focus areas where application of these improved tools is required. Flow physics and a study of the Space Shuttle Main Engine development program are used to conclude that the injector is the key to robust TCA design. Requirements are set out in terms of fidelity, robustness and demonstrated accuracy of the design tool. Lack of demonstrated accuracy is noted as the most significant obstacle to realizing the potential of CFD to be widely used as an injector design tool. A hierarchical decomposition process is outlined to facilitate the validation process. A simulation readiness level tool used to gauge progress toward the goal is described. Finally, there is a description of the current efforts in each focus area. The background of each focus area is discussed. The state of the art in each focus area is noted along with the TCA VI research focus in the area. Brief highlights of work in the area are also included.

Tucker, P. Kevin↗

NASA NTRS1994

Design of 3-D Nacelle near Flat-Plate Wing Using Multiblock Sensitivity Analysis (ADOS)

One of the major design tasks involved in reducing aircraft drag is the integration of the engine nacelles and airframe. With this impetus, nacelle shapes with and without the presence of a flat-plate wing nearby were optimized. This also served as a demonstration of the 3-D version of the recently developed aerodynamic design optimization methodology using sensitivity analysis, ADOS. The required flow analyses were obtained by solving the three-dimensional, compressible, thin-layer Navier-Stokes equations using an implicit, upwind-biased, finite volume scheme. The sensitivity analyses were performed using the preconditioned version of the SADD scheme (sensitivity analysis on domain decomposition). In addition to demonstrating the present method's capability for automatic optimization, the results offered some insight into two important issues related to optimizing the shapes of multicomponent configurations in close proximity. First, inclusion of the mutual interference between the components resulted in a different shape as opposed to shaping an isolated component. Secondly, exclusion of the viscous effects compromised not only the flow physics but also the optimized shapes even for isolated components.

Eleshaky, Mohamed E.↗

NASA NTRS2018

Exploring Li-Air Batteries for High Specific Energy and High Power Applications: A Simulation Study

Commercialization of lithium-air batteries face many challenges, such as electrolyte decomposition, short cycle life, low energy efficiency, low power density, etc. However, commercialization of Li-air batteries for mass sensitive applications such as electric vehicles, portable power source, and drones is more challenging due to additional constraints of safety, electrolyte evaporation, high specific energy requirements, and reliable discharge times. In this presentation, we will present our finite element simulation results comparing Li-O2 and Li-air batteries using power density, energy density, specific power, and discharge times as metrics to evaluate different electrolytes and electrode geometry to reduce total mass and maximize discharge current. We use a finite element model and a discharge product model developed in which is based on porous electrode and concentrated electrolyte theories and the discharge product is modeled using quantum tunneling; for reaction kinetics and oxygen diffusion, an improved model was used. The electrolyte properties such as ion conductivity and ion diffusion were obtained from Molecular Dynamics (MD) simulations while the other parameters for the finite element model were calibrated to match experiments at high discharge current densities (>1.5 mA/cm2). The mass densities of different electrolytes were computed using MD simulations as well. For this presentation, we examine the practical electrochemical mass of a system at different current ratings, the sensitivity of mass to the use of ambient air as compared to pure oxygen as well as the electrolyte, which affects maximum current density and the total mass associated with the electrolyte (which includes the mass of additional components), and, the optimization of battery geometry for total discharge time, average discharge voltage, maximum discharge current, and minimum electrochemical mass.

Mehta, M.↗

NASA NTRS2003

Mechanical Testing of PMCs under Simulated Rapid Heat-Up Propulsion Environments: In-Plane Compressive Behavior - II

Carbon fiber thermoset polymer matrix composites (PMC) with high temperature polyimide based in-situ polymerized monomer reactant (PMR) resin has been used for some time in applications which can see temperatures up to 550 F. Currently, graphite fiber PMR based composites are used in several aircraft engine components including the outer bypass duct for the GE F-404, exit flaps for the P&W F-100-229, and the core cowl for the GE/Snecma CF6-80A3. Newer formulations, including PMR-II-50 are being investigated as potential weight reduction replacements of various metallic components in next generation high performance propulsion rocket engines that can see temperatures which exceed 550 F. Extensive FEM thermal modeling indicates that these components are exposed to rapid heat-up rates (up to -200 F/sec) and to a maximum temperature of around 600 F. Even though the predicted maximum part temperatures were within the capability of PW-II-50, the rapid heat-up causes significant through-thickness thermal gradients in the composite part and even more unstable states when combined with moisture. Designing composite parts for such extreme service environments will require accurate measurement of intrinsic and transient mechanical properties and the hygrothermal performance of these materials under more realistic use conditions. The mechanical properties of polymers degrade when exposed to elevated temperatures even in the absence of gaseous oxygen. Accurate mechanical characterization of the material is necessary in order to reduce system weight while providing sufficient factors of safety. Historically, the testing of PMCs at elevated temperatures has been plagued by the antagonism between two factors. First, moisture has been shown to profoundly affect the mechanical response of these materials at temperatures above their glass transition temperature while concurrently lowering the material's Tg. Moisture phenomena is due to one or a combination of three effects, i.e., plastization of polymeric material by water, the internal pressure generated by the volatilization of water at elevated temperatures, and hydrolytic chemical decomposition. However, moisture is lost from the material at increasing rates as temperature increases. Second, because PMCs are good thermal insulators, when they are externally heated at even mild rates large thermal gradients can develop within the material. At temperatures where a material property changes rapidly with temperature the presence of a large thermal gradient is unacceptable for intrinsic property characterization purposes. Therefore, long hold times are required to establish isothermal conditions. However, in the service environments high-heating-rates, high temperatures, high-loading rates are simultaneous present along with residual moisture. In order to capture the effects of moisture on the material, holding at- temperature until isothermal conditions are reached is unacceptable particularly in materials with small physical dimensions. Thus, the effects due to moisture on the composite's mechanical characteristics, ie., their so-called analog response, may be instructive. One approach employed in this program was rapid heat-up (approx. 200 F/sec.) and loading of both dry and wet in-plane compressive specimens to examine the effects of moisture on this resin dominated mechanical property of the material.

Stokes, Eric H.↗

NASA NTRS1990

Army-NASA aircrew/aircraft integration program (A3I) software detailed design document, phase 3

The capabilities and design approach of the MIDAS (Man-machine Integration Design and Analysis System) computer-aided engineering (CAE) workstation under development by the Army-NASA Aircrew/Aircraft Integration Program is detailed. This workstation uses graphic, symbolic, and numeric prototyping tools and human performance models as part of an integrated design/analysis environment for crewstation human engineering. Developed incrementally, the requirements and design for Phase 3 (Dec. 1987 to Jun. 1989) are described. Software tools/models developed or significantly modified during this phase included: an interactive 3-D graphic cockpit design editor; multiple-perspective graphic views to observe simulation scenarios; symbolic methods to model the mission decomposition, equipment functions, pilot tasking and loading, as well as control the simulation; a 3-D dynamic anthropometric model; an intermachine communications package; and a training assessment component. These components were successfully used during Phase 3 to demonstrate the complex interactions and human engineering findings involved with a proposed cockpit communications design change in a simulated AH-64A Apache helicopter/mission that maps to empirical data from a similar study and AH-1 Cobra flight test.

Banda, Carolyn↗

NASA NTRS1992

Intelligent robots for planetary exploration and construction

Robots capable of practical applications in planetary exploration and construction will require realtime sensory-interactive goal-directed control systems. A reference model architecture based on the NIST Real-time Control System (RCS) for real-time intelligent control systems is suggested. RCS partitions the control problem into four basic elements: behavior generation (or task decomposition), world modeling, sensory processing, and value judgment. It clusters these elements into computational nodes that have responsibility for specific subsystems, and arranges these nodes in hierarchical layers such that each layer has characteristic functionality and timing. Planetary exploration robots should have mobility systems that can safely maneuver over rough surfaces at high speeds. Walking machines and wheeled vehicles with dynamic suspensions are candidates. The technology of sensing and sensory processing has progressed to the point where real-time autonomous path planning and obstacle avoidance behavior is feasible. Map-based navigation systems will support long-range mobility goals and plans. Planetary construction robots must have high strength-to-weight ratios for lifting and positioning tools and materials in six degrees-of-freedom over large working volumes. A new generation of cable-suspended Stewart platform devices and inflatable structures are suggested for lifting and positioning materials and structures, as well as for excavation, grading, and manipulating a variety of tools and construction machinery.

Albus, James S.↗

NASA NTRS1992

Turbulent fluid motion IV-averages, Reynolds decomposition, and the closure problem

Ensemble, time, and space averages as applied to turbulent quantities are discussed, and pertinent properties of the averages are obtained. Those properties, together with Reynolds decomposition, are used to derive the averaged equations of motion and the one- and two-point moment or correlation equations. The terms in the various equations are interpreted. The closure problem of the averaged equations is discussed, and possible closure schemes are considered. Those schemes usually require an input of supplemental information unless the averaged equations are closed by calculating their terms by a numerical solution of the original unaveraged equations. The law of the wall for velocities and temperatures, the velocity- and temperature-defect laws, and the logarithmic laws for velocities and temperatures are derived. Various notions of randomness and their relation to turbulence are considered in light of ergodic theory.

Deissler, Robert G.↗

NASA NTRS1992

Implementation of non-hierarchic decomposition for multidisciplinary system optimization

Modular prototype software has been designed to implement the method of non-hierarchic decomposition for optimization of coupled, multidisciplinary systems. The modules are intended to be run concurrently on separate processors and to automate all aspects of the method except for the objective function and subspace analysis subroutines, which are inherently problem-dependent. Minimal analysis of problem structure is required, since the software is designed to handle arbitrary system coupling with full generality. The basic feasibility of the approach has been confirmed using six example problems, with varying degrees of lateral coupling among the subspace constraints and dependent variables. Results are given for two of the test problems.

Eason, Ernest D.↗

NASA NTRSDate not supplied

Identification and Study of Validation Level Test Cases for Computational Modeling of Non-Charring Ablators

Computational modeling of Thermal Protection System (TPS) materials, used for aerospace applications, provides numerous advantages in preliminary selection and design of a heatshield material and shape for atmospheric entry vehicles. However, to serve as a reliable tool for prediction of material thermal and ablative behavior, the modeling approach needs to be validated against real experimental and flight data, preferably at a range of applied conditions. The validation study is typically very complex as it requires reliable measured data not only for the material thermal response and surface recession, but also well characterized environmental conditions. The validation problem becomes even more complex when the material thermal response is dictated by multi-physics effects such as solid conduction, in-depth thermal decomposition, pyrolysis gas flow and chemical reactions. The multi-physics effects complicate not only the modeling effort, but also the experimental measurement for validation of various aspects of the highly coupled problem. In this study, an attempt is made to identify suitable experimental data that could serve as a source for validation of material thermal response modeling tools. To reduce the computational complexity, this study focuses only on non-charring ablators, where the material thermal response could be modeled with a single governing equation for solid conduction and the ablation is limited only to the surface of the material. With a well characterized and publicly available experimental data being sparse, the study is limited in presenting test cases for only three materials: camphor, graphite and FiberForm® in the sequence of increased modeling complexity. Graphite is a commonly used TPS material for aerospace applications, both for leading edges of high-speed vehicles and internal insulation of solid rocket motors. FiberForm® is a porous carbon pre-form used in preparation of the well known PICA material Tran et al. [1996]. Inclusion of camphor into the list is conditioned with the relative simplicity in modeling the material thermal and chemical response and the low-enthalpy flow environment. In addition, camphor has been used as a simple test material for study of flow transition behavior by Stock and Ginoux [1973] and assessment of a heatshield shape change at flight relevant conditions by Rotondi et al. [2022]. In this work, the identified experimental data was extracted from the public literature and test cases that yet have been published. As it was found from the review, not a single test case contains an exhaustive set of data that would validate every aspect of the material physics. However, in the data collected, various aspects of the material behavior can be still validated, such as surface and in-depth temperature, amount of recession and a shape change. The identified experimental data for each case is accompanied with a characterized flow environment and simulated boundary conditions predicted by a Data-Parallel Line Relaxation (DPLR) code Wright et al. [1998]. In addition, material thermal response numerical simulations in each test case are performed with Kentucky Aerothermodynamics and Thermal Response System (KATS-MR) Zibitsker et al. [2022] providing a comparative study and a sanity check for the proposed validation data. Sample results from the performed numerical study are shown below. Figure 1 shows distribution of surface heat flux and pressure values on a hemi-cylinder model made of FiberForm® and tested in HyMETS arc-jet facility. The results are shown for the high pressure condition among the two tests. Flow simulation was performed with DPLR code on a quarter of original geometry. In the figure, the quarter shape was mirrored across zx and xy planes to show the complete distribution. Figure 2 shows the material response results for the high pressure case (7500 Pa), simulated with KATS-MR and a comparison to the experimental data for the surface temperature and shape shape. The simulation was performed on a 2-D slice, extracted in the xy plane at the middle of the sample. Figure 3 shows the material response simulation for the low pressure case (3500 Pa) and a comparison to the experimental data for surface temperature and shape change.

ablation↗

NASA NTRS2000

A Bridge Health Monitoring Method Using the Hilbert-Huang Transform: A Case Study

We have developed a new method for nondestructive instrument method to monitor the health of a bridge. This new method is based on a transient test load and simple data collection. The nuclear of the method is the new invented nonstationary and nonlinear time series analysis method, the Empirical Mode Decomposition and Hilbert Spectral Analysis. The final decision on the health of the bridge structure is based on the nonlinear characteristic of the data, and on the comparison between the free and the forced vibration frequencies. Thus this alternative method enjoys many advantages: (1) no a priori data required, (2) simple data collection, and (3) minimum traffic disruption. Results from a case study of the Shing-Nan Bridge in Hou-Wei will be reported.

Huang, Norden E.↗

NASA NTRS2008

A Data Type for Efficient Representation of Other Data Types

A self-organizing, monomorphic data type denoted a sequence has been conceived to address certain concerns that arise in programming parallel computers. A sequence in the present sense can be regarded abstractly as a vector, set, bag, queue, or other construct. Heretofore, in programming a parallel computer, it has been necessary for the programmer to state explicitly, at the outset, what parts of the program and the underlying data structures must be represented in parallel form. Not only is this requirement not optimal from the perspective of implementation; it entails an additional requirement that the programmer have intimate understanding of the underlying parallel structure. The present sequence data type overcomes both the implementation and parallel structure obstacles. In so doing, the sequence data type provides unified means by which the programmer can represent a data structure for natural and automatic decomposition to a parallel computing architecture. Sequences exhibit the behavioral and structural characteristics of vectors, but the underlying representations are automatically synthesized from combinations of programmers advice and execution use metrics. Sequences can vary bidirectionally between sparseness and density, making them excellent choices for many kinds of algorithms. The novelty and benefit of this behavior lies in the fact that it can relieve programmers of the details of implementations. The creation of a sequence enables decoupling of a conceptual representation from an implementation. The underlying representation of a sequence is a hybrid of representations composed of vectors, linked lists, connected blocks, and hash tables. The internal structure of a sequence can automatically change from time to time on the basis of how it is being used. Those portions of a sequence where elements have not been added or removed can be as efficient as vectors. As elements are inserted and removed in a given portion, then different methods are utilized to provide both an access and memory strategy that is optimized for that portion and the use to which it is put.

James, Mark↗

NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗

NASA NTRS1999

Parallelization of the Physical-Space Statistical Analysis System (PSAS)

Atmospheric data assimilation is a method of combining observations with model forecasts to produce a more accurate description of the atmosphere than the observations or forecast alone can provide. Data assimilation plays an increasingly important role in the study of climate and atmospheric chemistry. The NASA Data Assimilation Office (DAO) has developed the Goddard Earth Observing System Data Assimilation System (GEOS DAS) to create assimilated datasets. The core computational components of the GEOS DAS include the GEOS General Circulation Model (GCM) and the Physical-space Statistical Analysis System (PSAS). The need for timely validation of scientific enhancements to the data assimilation system poses computational demands that are best met by distributed parallel software. PSAS is implemented in Fortran 90 using object-based design principles. The analysis portions of the code solve two equations. The first of these is the "innovation" equation, which is solved on the unstructured observation grid using a preconditioned conjugate gradient (CG) method. The "analysis" equation is a transformation from the observation grid back to a structured grid, and is solved by a direct matrix-vector multiplication. Use of a factored-operator formulation reduces the computational complexity of both the CG solver and the matrix-vector multiplication, rendering the matrix-vector multiplications as a successive product of operators on a vector. Sparsity is introduced to these operators by partitioning the observations using an icosahedral decomposition scheme. PSAS builds a large (approx. 128MB) run-time database of parameters used in the calculation of these operators. Implementing a message passing parallel computing paradigm into an existing yet developing computational system as complex as PSAS is nontrivial. One of the technical challenges is balancing the requirements for computational reproducibility with the need for high performance. The problem of computational reproducibility is well known in the parallel computing community. It is a requirement that the parallel code perform calculations in a fashion that will yield identical results on different configurations of processing elements on the same platform. In some cases this problem can be solved by sacrificing performance. Meeting this requirement and still achieving high performance is very difficult. Topics to be discussed include: current PSAS design and parallelization strategy; reproducibility issues; load balance vs. database memory demands, possible solutions to these problems.

Larson, J. W.↗

NASA NTRS2017

Aeroelastic Uncertainty Quantification Studies Using the S4T Wind Tunnel Model

This paper originates from the joint efforts of an aeroelastic study team in the Applied Vehicle Technology Panel from NATO Science and Technology Organization, with the Task Group number AVT-191, titled "Application of Sensitivity Analysis and Uncertainty Quantification to Military Vehicle Design." We present aeroelastic uncertainty quantification studies using the SemiSpan Supersonic Transport wind tunnel model at the NASA Langley Research Center. The aeroelastic study team decided treat both structural and aerodynamic input parameters as uncertain and represent them as samples drawn from statistical distributions, propagating them through aeroelastic analysis frameworks. Uncertainty quantification processes require many function evaluations to asses the impact of variations in numerous parameters on the vehicle characteristics, rapidly increasing the computational time requirement relative to that required to assess a system deterministically. The increased computational time is particularly prohibitive if high-fidelity analyses are employed. As a remedy, the Istanbul Technical University team employed an Euler solver in an aeroelastic analysis framework, and implemented reduced order modeling with Polynomial Chaos Expansion and Proper Orthogonal Decomposition to perform the uncertainty propagation. The NASA team chose to reduce the prohibitive computational time by employing linear solution processes. The NASA team also focused on determining input sample distributions.

Nikbay, Melike↗

NASA NTRS2008

A Review of Radiolysis Concerns for Water Shielding in Fission Surface Power Applications

This paper presents an overview of radiolysis concerns with regard to water shields for fission surface power. A review of the radiolysis process is presented and key parameters and trends are identified. From this understanding of the radiolytic decomposition of water, shield pressurization and corrosion are identified as the primary concerns. Existing experimental and modeling data addressing concerns are summarized. It was found that radiolysis of pure water in a closed volume results in minimal, if any net decomposition, and therefore reduces the potential for shield pressurization and corrosion. With the space program focus m emphasize more on permanent return to the Moon and eventually manned exploration of Mars, there has been a renewed look at fission power to meet the difficult technical & design challenges associated with this effort. This is due to the ability of fission power to provide a power rich environment that is insensitive to solar intensity and related aspects such as duration of night, dusty environments, and distance from the sun, etc. One critical aspect in the utilization of fission power for these applications of manned exploration is shielding. Although not typically considered for space applications, water shields have been identified as one potential option due to benefits in mass savings and reduced development cost and technical risk (Poston, 2006). However, the water shield option requires demonstration of its ability to meet key technical challenges including such things as adequate natural circulation for thermal management and capability for operational periods up to 8 years. Thermal management concerns have begun to be addressed and are not expected to be a problem (Pearson, 2007). One significant concern remaining is the ability to maintain the shield integrity through its operational lifetime. Shield integrity could be compromised through shield pressurization and corrosion resulting from the radiolytic decomposition of water.

Schoenfeld, Michael P.↗

NASA NTRS1994

Preconditioned domain decomposition scheme for three-dimensional aerodynamic sensitivity analysis

A discrete sensitivity analysis algorithm had previously been developed and applied to two-dimensional aerodynamic optimization problems, where the computational domains were discretized by using single grids. The sparse, unsymmetric systems of linear equations resulting from this algorithm were solved by a direct matrix inversion matrix. However, for large two-dimensional problems and, practically, all three-dimensional problems, direct inversion methods become inapplicable, primarily due to the prohibitive computer storage needed. In an attempt to alleviate such hindrances, the sensitivity analysis with domain decomposition (SADD) scheme was developed. This scheme divides the computational domain into smaller and nonoverlapping subdomains (multiblock grids) that are solved separately. Then, the final solution is constructed from the subdomain solutions. As the number of grid points in the interface boundaries of the subdomains becomes large, the computer memory required to store the effective coefficient matrix of these interface points starts to increase. Presented in this Technical Note is a preconditioned iterative procedure to overcome this particular problem.

Eleshaky, Mohamed E.↗

NASA NTRS2001

Flame Synthesis of Single- and Multi-Walled Carbon Nanotubes and Nanofibers

Metal-catalyzed carbon nanotubes are highly sought for a diverse range of applications that include nanoelectronics, battery electrode material, catalysis, hydrogen storage media and reinforcing agents in polymer composites. These latter applications will require vast quantities of nanotubes at competitive prices to be economically feasible. Moreover, reinforcing applications may not require ultrahigh purity nanotubes. Indeed, functionalization of nanotubes to facilitate interfacial bonding within composites will naturally introduce defects into the tube walls, lessening their tensile strength. Current methods of aerosol synthesis of carbon nanotubes include laser ablation of composite targets of carbon and catalyst metal within high temperature furnaces and decomposition of a organometallics in hydrocarbons mixtures within a tube furnace. Common to each approach is the generation of particles in the presence of the reactive hydrocarbon species at elevated temperatures. In the laser-ablation approach, the situation is even more dynamic in that particles and nanotubes are borne during the transient cooling phase of the laser-induced plasma for which the temperature far exceeds that of the surrounding hot gases within the furnace process tube. A shared limitation is that more efficient methods of nanoparticle synthesis are not readily incorporated into these approaches. In contrast, combustion can quite naturally create nanomaterials such as carbon black. Flame synthesis is well known for its commercial scalability and energy efficiency. However, flames do present a complex chemical environment with steep gradients in temperature and species concentrations. Moreover, reaction times are limited within buoyant driven flows to tens of milliseconds. Therein microgravity can greatly lessen temperature and spatial gradients while allowing independent control of flame residence times. In preparation for defining the microgravity experiments, the work presented here focuses on the effect of catalyst particle size and reactant gas in 1g.

VanderWal, R. L.↗

NASA NTRS2007

Quaternion Averaging

Many applications require an algorithm that averages quaternions in an optimal manner. For example, when combining the quaternion outputs of multiple star trackers having this output capability, it is desirable to properly average the quaternions without recomputing the attitude from the the raw star tracker data. Other applications requiring some sort of optimal quaternion averaging include particle filtering and multiple-model adaptive estimation, where weighted quaternions are used to determine the quaternion estimate. For spacecraft attitude estimation applications, derives an optimal averaging scheme to compute the average of a set of weighted attitude matrices using the singular value decomposition method. Focusing on a 4-dimensional quaternion Gaussian distribution on the unit hypersphere, provides an approach to computing the average quaternion by minimizing a quaternion cost function that is equivalent to the attitude matrix cost function Motivated by and extending its results, this Note derives an algorithm that deterniines an optimal average quaternion from a set of scalar- or matrix-weighted quaternions. Rirthermore, a sufficient condition for the uniqueness of the average quaternion, and the equivalence of the mininiization problem, stated herein, to maximum likelihood estimation, are shown.

Markley, F. Landis↗