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Modeling Enhancements and Demonstration of Shift Capabilities for PBRs and MSRs

This technical report documents the modeling enhancements and demonstrations with the Shift Monte Carlo (MC) code targeted at pebble-bed reactors (PBRs) and molten salt reactors (MSRs) under the US Department of Energy (DOE) Nuclear Energy Advanced Modeling and Simulation (NEAMS) program in fiscal year (FY) 2023. The work performed included several enhancements, such as improvements for multigroup cross section generation, a new eigenvalue mode considering only prompt fission neutrons, and enhancements to the Titan frontend for Shift to allow for new geometry types and tally functionality. Additionally, new PBR equilibrium core search reference calculations were generated with Shift and compared to Serpent calculations provided by Idaho National Laboratory (INL). These enhancements provide a robust foundation for applying Shift for both reference and two-step neutronics analysis for advanced reactor simulation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Ablation of ATJ Graphite at High Temperatures

Results of an extensive experimental program on the ablation of ATJ graphite in air at surface pressures of 0.3 to 4.4 atm and surface temperatures of 2570 to 4030 K are presented. The measured mass-loss rates are correlated with surface temperature, pressure, and effective nose radius. The results are compared with several equilibrium thermochemical ablation theories which differ basically in the chemical species that are considered and in the thermodynamic properties assigned to these species. All the theories predict about the same mass-loss rate in the diffusion-controlled oxidation regime and are in good agreement with the experimental results. At higher temperatures, however, the experimental and theoretical results do not agree. At temperatures above 3700 K, the experimental mass-loss rate becomes independent of pressure and an exponential function of temperature. A comparison of the high-temperature results with the theories indicates that all the theories, except the one based on the thermodynamic properties from the JANAF tables, are invalid because they overpredict the mass-loss rate. On the other hand, the theory based on the JANAF properties underpredicts the measured mass-loss rate by a factor of three at 4000 K. At least a portion of this difference between experiment and theory is attributed to particulate mass loss which is visually observed.

Thermochemical ablation↗

Alloy Design Workbench-Surface Modeling Package Developed

NASA Glenn Research Center's Computational Materials Group has integrated a graphical user interface with in-house-developed surface modeling capabilities, with the goal of using computationally efficient atomistic simulations to aid the development of advanced aerospace materials, through the modeling of alloy surfaces, surface alloys, and segregation. The software is also ideal for modeling nanomaterials, since surface and interfacial effects can dominate material behavior and properties at this level. Through the combination of an accurate atomistic surface modeling methodology and an efficient computational engine, it is now possible to directly model these types of surface phenomenon and metallic nanostructures without a supercomputer. Fulfilling a High Operating Temperature Propulsion Components (HOTPC) project level-I milestone, a graphical user interface was created for a suite of quantum approximate atomistic materials modeling Fortran programs developed at Glenn. The resulting "Alloy Design Workbench-Surface Modeling Package" (ADW-SMP) is the combination of proven quantum approximate Bozzolo-Ferrante-Smith (BFS) algorithms (refs. 1 and 2) with a productivity-enhancing graphical front end. Written in the portable, platform independent Java programming language, the graphical user interface calls on extensively tested Fortran programs running in the background for the detailed computational tasks. Designed to run on desktop computers, the package has been deployed on PC, Mac, and SGI computer systems. The graphical user interface integrates two modes of computational materials exploration. One mode uses Monte Carlo simulations to determine lowest energy equilibrium configurations. The second approach is an interactive "what if" comparison of atomic configuration energies, designed to provide real-time insight into the underlying drivers of alloying processes.

Abel, Phillip B.↗

Precise Control of Dissipative Self-assembly by Light and Electricity

Nature-inspired synthetic dissipative self-assemblies have attracted much attention recently. However, it remains a major challenge to achieve precise control over dissipative supramolecular assembly structures and functions of self-contained systems. Here we combine light and electricity as two clean, and spatiotemporally addressable fuels to provide precise control over the morphology for dissipative self-assembly of a perylene bisimide glycine (PBIg) building block in a self-contained solution. In this design, electrochemical oxidation provides the positive fuel to activate PBIg self-assembly while photoreduction supplies the negative fuel to deactivate the system for disassembly. Further, through programming the two counteracting fuels, we demonstrated the control of PBIg self-assembly into a variety of assembly morphologies in a self-contained system. In addition, by exerting light and electrical dual fuels simultaneously, we could create an active homeostasis exhibiting dynamic instability, leading to morphological change to asymmetric assemblies with curvatures. Such precise control over self-assembly of self-contained systems may find future applications in programming complex active materials as well as formulating pharmaceutical reagents with desired morphologies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

CONTIN XPCS : software for inverse transform analysis of X-ray photon correlation spectroscopy dynamics

X-ray photon correlation spectroscopy (XPCS) and dynamic light scattering (DLS) reveal materials dynamics using coherent scattering, with XPCS permitting the investigation of dynamics in a more diverse array of materials than DLS. Heterogeneous dynamics occur in many material systems. The authors' recent work has shown how classic tools employed in the DLS analysis of heterogeneous dynamics can be extended to XPCS, revealing additional information that conventional Kohlrausch exponential fitting obscures. The present work describes the software implementation of inverse transform analysis of XPCS data. This software, called CONTIN XPCS , is an extension of traditional CONTIN analysis and accommodates the various dynamics encountered in equilibrium XPCS measurements.

36 MATERIALS SCIENCE↗

Porous media matric potential and water content measurements during parabolic flight

Control of water and air in the root zone of plants remains a challenge in the microgravity environment of space. Due to limited flight opportunities, research aimed at resolving microgravity porous media fluid dynamics must often be conducted on Earth. The NASA KC-135 reduced gravity flight program offers an opportunity for Earth-based researchers to study physical processes in a variable gravity environment. The objectives of this study were to obtain measurements of water content and matric potential during the parabolic profile flown by the KC-135 aircraft. The flight profile provided 20-25 s of microgravity at the top of the parabola, while pulling 1.8 g at the bottom. The soil moisture sensors (Temperature and Moisture Acquisition System: Orbital Technologies, Madison, WI) used a heat-pulse method to indirectly estimate water content from heat dissipation. Tensiometers were constructed using a stainless steel porous cup with a pressure transducer and were used to measure the matric potential of the medium. The two types of sensors were placed at different depths in a substrate compartment filled with 1-2 mm Turface (calcined clay). The ability of the heat-pulse sensors to monitor overall changes in water content in the substrate compartment decreased with water content. Differences in measured water content data recorded at 0, 1, and 1.8 g were not significant. Tensiometer readings tracked pressure differences due to the hydrostatic force changes with variable gravity. The readings may have been affected by changes in cabin air pressure that occurred during each parabola. Tensiometer porous membrane conductivity (function of pore size) and fluid volume both influence response time. Porous media sample height and water content influence time-to-equilibrium, where shorter samples and higher water content achieve faster equilibrium. Further testing is needed to develop these sensors for space flight applications.

Parabolic Flight↗

Design of Multi-Stage Solvent Extraction Process for Separation of Rare Earth Elements

Flowsheet design and stage determination for the separation of rare earth elements (REEs) using solvent extraction (SX) is a challenging task because of the chemical similarity of the REEs. Low separation factors between the elements and complex equilibrium chemistry provide unique challenges to designing an efficient flowsheet for the separation of elements. The multi-stage nature of the SX process adds further complexity, making the assessment of products for a proposed design and stage combination difficult. Therefore, to develop a SX flowsheet, it is essential to quantify the performance for various design and separation conditions. This paper attempts to address the challenge by utilizing an equilibrium and process modeling approach. Results from a bench-scale study performed on a 10 g/L rare earth salt mixture were used in studying the extraction/stripping behavior and developing equilibrium models. DEHPA with TBP as a phase modifier was used as an extractant, while hydrochloric acid was utilized as a stripping agent. The results obtained were used in developing extraction/stripping models, which were integrated into a process framework of a SX train in a Matlab/Simulink environment. The models were programmed as a function block routine and used for developing a flowsheet, which was simulated for differing separation and design conditions. To identify optimum stage combinations, a particle swarm optimization (PSO) routine was developed and implemented for each SX train. Recovery and purity of elements of interest were used as objective function criteria. The stage combination leading to the minimization of the objective function was used to identify the optimum stage combination for a series of SX trains to attempt a balance of purity and recovery. The models and optimization method were implemented to separate a feed mixture containing REEs, which indicated that 99.52 and 85.41 percent purity is achievable for Yttrium and Lanthanum separation using 8-12-3 and 10-3-5 stage combination for loading, scrubbing, and striping. The model also indicated difficult separability between neodymium, praseodymium, and cerium.

Srivastava, Vaibhav (ORCID:0000000212645987)↗

Numerical methods for the calculation of three-dimensional nozzle exhaust flow fields

Numerical codes developed for the calculation of three-dimensional nozzle exhaust flow fields associated with hypersonic airbreathing aircraft are described. Both codes employ reference plane grid networks with respect to three coordinate systems. Program CHAR3D is a characteristic code utilizing a new wave preserving network within the reference planes, while program BIGMAC is a finite difference code utilizing conservation variables and a one-sided difference algorithm. Secondary waves are numerically captured by both codes, while the underexpansion shock and plume boundary are treated discretely. The exhaust gas properties consist of hydrogen-air combustion product mixtures in local chemical equilibrium. Nozzle contours are treated by a newly developed geometry package based on dual cubic splines. Results are presented for simple configurations demonstrating two- and three-dimensional multiple wave interactions.

Dash, S. M.↗

Large Solar-Rejection Filter

NASA utilized Image Intensified Video Cameras for ATV data acquisition from a jet flying at 12.8 km. Afterwards the video was digitized and then analyzed with a modified commercial software package, Image Systems Trackeye. Astrometric results were limited by saturation, plate scale, and imposed linear plate solution based on field reference stars. Time-dependent fragment angular trajectories, velocities, accelerations, and luminosities were derived in each video segment. It was evident that individual fragments behave differently. Photometric accuracy was insufficient to confidently assess correlations between luminosity and fragment spatial behavior (velocity, deceleration). Use of high resolution digital video cameras in future should remedy this shortcoming. A scenically accurate description of matter interpreted as a substance made up of corpuscular constituents was established during the course of the 19th century. In this description, atoms--the building blocks of the matter--form molecules. The properties of the molecules were described by chemistry or thermodynamics depending on what characteristics of the matter were investigated. In both theories, the molecules can dissociate to atoms when the kinetic energies of the atoms exceed the strength of the chemical bonds. The number of atoms is always preserved in a closed system. This is not true, however, when the matter takes up much higher energies at relativistic scales. New particles can be produced at the expense of the kinetic energy. The number of particles is no longer preserved. There are other conserved quantities, however, these quantities, the charge, baryon number, lepton number, are associated with particles that are considered elementary today. The properties and behavior of these elementary particles is the subject of Particle Physics or High Energy Physics. Practice Page: A crewmember touching a positively charged surface was thought to be galvanically isolated from the vehicle ground analogous to a bird on a high voltage power wire. Recent analysis confirms that positive floating potentials, ionospheric currents to the EVA suit, can be hazardous. The analysis is wrong in that the ionospheric plasma itself can close the circuit. Parametric analysis of very low voltage exposures (2 to 15 volts) could cause pain and/or involuntary muscle tetani or spinal cord shock. NASA worked with the Naval Health Research Center Detachment Directed Energy Bioeffects Laboratory to examine the affects electrical hazards could have on extravehicular activity using two models. The results of the two computational models were combined to predict areas of the body in which neurons of different diameters would be excited. They predicted that physiologically active current could be conducted across the crew member causing catastrophic hazards. Future work to analyze additional current paths was proposed. The FUSE spectrum of BB Dor, observed in a high state, is modeled with an accretion disk with a very low inclination (possibly lower than 10 degrees). Assuming an average WD mass of 0.8 solar mass leads to a distance of the order of approximately 650pc, consistent with the extremely low galactic reddening in its direction, and a mass accretion rate of 10 (exp -9) solar mass a year. The spectrum presents some broad and deep silicon and sulfur absorption lines, indicating that these elements are over-abundant: silicon is 3 times solar, and sulfur is 20 times solar. The FUSE spectrum of BB Dor, observed in a high state, is modeled with an accretion disk with a very low inclination (possibly lower than 10 degrees). Assuming an average WD mass of 0.8 solar mass leads to a distance of the order of approximately 650pc, consistent with the extremely low galactic reddening in its direction, and a mass accretion rate of 10 (exp -9) solar mass a year. The spectrum presents some broad and deep silicon and sulfur absorption lines, indicating that these elements are over-abundant: silicon is times solar, and sulfur is 20 times solar. From its previously observed optical emission lines, P831-57 (WD 0334 6400 or Ret 1 in A Catalog and Atlas of Cataclysmic Variables: Living Edition) has been suspected to contain an accretion disk associated with a companion star in orbit around a subdwarf star with a temperature T is greater than 21,000K. P831-57 has therefore been classified as a nova-like. However, our present observations show it to be a DA + dMe binary. The analysis of its Far Ultraviolet Spectroscopic Explorer (FUSE) spectrum (continuum and lines) reveal an average mass white dwarf (Log(g) approximately equals 7.8 plus or minus 0.1)with a temperature T approximately equals 37,000 plus or minus 500K, an extremely low projected rotational velocity, and a distance of about 115 plus or minus 5pc. The photosphere contains C, N, Si, and S (at about 1% of solar abundances). The dMe star is seen as a flux excess in near-infrared photometry and appears to show occasional flaring of about one magnitude as seen in the Harvard plates. There is no evidence of periodic variability in the spectroscopic or photometric data. We find no evidence of a an accretion disk, instead we find evidence of wind accretion as the stellar carbon abundance (N(C)/N(H) = 2.5 x 10 (exp -6) is about ten times larger than predicted by radiative levitation for such a gravity and temperature. The power needs and solutions for the space exploration and lunar mobility program are discussed. Long term missions in space and on the lunar surface require high energy batteries. Rechargeable batteries for mobility systems and portable utility pallet are needed for successful exploration missions. Nanomaterial usage increases the energy density of the cells apart from increasing the power density. The symptoms and threats from acute mountain sickness (AMS) are discussed. The underlying assumptions concerning spacecraft atmosphere mean there is a potential risk to astronauts. The baseline worst case scenario is about 25% based on direct ascent to 8.0 psia with 32% O2. The practical mitigation approach is a staged depressurization scheme. Due to the uncertainty about potential AMS risk the flight surgeon should prepare, focused research should proceed, and current analytical efforts should continue. This slide presentation reviews the threat astronauts face from acute mountain sickness (AMS). The incidence of AMS is highly variable and the risk to astronauts is unclear. However, the potential risk is higher than current EAAs suggest and precautions should be implemented. Due to the uncertain nature of the risk flight surgeons should prepare, and focused research should proceed. Quasiparticle tunneling can be understood at low temperatures using a non-equilibrium kinetic theory. Low-temperature tunneling can be suppressed using existing techniques: island-lead gap engineering, lead cooling with SIN junctions, and quasiparticle traps. The slide presentation reviews the science goals and mission planning for the proposed Jupiter System Observer (JSO). The spacecraft would accommodate 9 instruments making the instrument payload more capable than any previously flown to Jupiter. The would-be mission includes study programs for Jupiter's satellites, interior, magnetosphere and atmosphere. The power needs and solutions for the space exploration and lunar mobility program are discussed. Long term missions in space and on the lunar surface require high energy batteries. Rechargeable batteries for mobility systems and portable utility pallet are needed for successful exploration missions. Nanomaterial usage increases the energy density of the cells apart from increasing the power density. This slide presentation reviews the power requirements for the space exploration and the lunar surface mobility programs. It includes information about the specifications for high energy batteries and the power requirements for lunar rovers,

Roberts, William↗

Bond Selective Photochemistry at Metal Nanoparticle Surfaces: CO Desorption from Pt and Pd

The use of visible photon fluxes to influence catalytic reactions on metal nanoparticle surfaces has attracted attention based on observations of reaction mechanisms and selectivity not observed under equilibrium heating. These observations suggest that photon fluxes can selectively impact the rates of certain elementary steps, creating nonequilibrium energy distributions among various reaction pathways. However, quantitative studies validating these hypotheses on metal nanoparticle surfaces are lacking. Here, we examine the influence of continuous wave visible photon fluxes on the CO desorption rates from 1 to 2 nm diameter Pt and Pd nanoparticle surfaces supported on γ-Al 2 O 3 . Temperature-programmed desorption measurements quantified via diffuse reflectance infrared Fourier transform spectroscopy demonstrate that visible photon fluxes significantly enhanced the rate of CO desorption from Pt nanoparticles in a wavelength-dependent manner. 440 nm photons most efficiently promoted CO desorption from Pt nanoparticle surfaces, aligning with the excitation energy for the interfacial electronic transition within the Pt–CO bond. Conversely, visible photon fluxes had no measurable influence on CO desorption rates from Pd nanoparticle surfaces after accounting for photon-induced heating. Density functional theory calculations demonstrate that the Pt–CO bond exhibits a narrower LUMO resonance, stronger coupling between the photoexcitation and forces induced on the metal–C bond, and vibrational energy dissipation that more effectively couples to desorption as compared to Pd–CO. These results demonstrate the specificity photons provide in facilitating chemical reactions on metal nanoparticle surfaces and substantiate the idea that photon fluxes can steer processes and outcomes of catalytic reactions in ways not achievable by equilibrium heating.

desorption↗

The Hubble PanCET Program: A Metal-rich Atmosphere for the Inflated Hot Jupiter HAT-P-41b

We present a comprehensive analysis of the 0.3–5 μm transit spectrum for the inflated hot Jupiter HAT-P-41b. The planet was observed in transit with Hubble STIS and WFC3 as part of the Hubble Panchromatic Comparative Exoplanet Treasury (PanCET) program, and we combine those data with warm Spitzer transit observations. We extract transit depths from each of the data sets, presenting the STIS transit spectrum (0.29–0.93 μm) for the first time. We retrieve the transit spectrum both with a free-chemistry retrieval suite (AURA) and a complementary chemical equilibrium retrieval suite (PLATON) to constrain the atmospheric properties at the day–night terminator. Both methods provide an excellent fit to the observed spectrum. Both AURA and PLATON retrieve a metal-rich atmosphere for almost all model assumptions (most likely O/H ratio of log{sub 10}Z/Z{sub ⊙}=1.46{sub −0.68}{sup +0.53} and log{sub 10}Z/Z{sub ⊙}=2.33{sub −0.25}{sup +0.23}, respectively); this is driven by a 4.9σ detection of H{sub 2}O as well as evidence of gas absorption in the optical (>2.7σ detection) due to Na, AlO, and/or VO/TiO, though no individual species is strongly detected. Both retrievals determine the transit spectrum to be consistent with a clear atmosphere, with no evidence of haze or high-altitude clouds. Interior modeling constraints on the maximum atmospheric metallicity (log{sub 10}Z/Z{sub ⊙}<1.7) favor the AURA results. The inferred elemental oxygen abundance suggests that HAT-P-41b has one of the most metal-rich atmospheres of any hot Jupiters known to date. Overall, the inferred high metallicity and high inflation make HAT-P-41b an interesting test case for planet formation theories.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Implementation of a vibrationally linked chemical reaction model for DSMC

A new procedure closely linking dissociation and exchange reactions in air to the vibrational levels of the diatomic molecules has been implemented in both one- and two-dimensional versions of Direct Simulation Monte Carlo (DSMC) programs. The previous modeling of chemical reactions with DSMC was based on the continuum reaction rates for the various possible reactions. The new method is more closely related to the actual physics of dissociation and is more appropriate to the particle nature of DSMC. Two cases are presented: the relaxation to equilibrium of undissociated air initially at 10,000 K, and the axisymmetric calculation of shuttle forebody heating during reentry at 92.35 km and 7500 m/s. Although reaction rates are not used in determining the dissociations or exchange reactions, the new method produces rates which agree astonishingly well with the published rates derived from experiment. The results for gas properties and surface properties also agree well with the results produced by earlier DSMC models, equilibrium air calculations, and experiment.

Carlson, A. B.↗

Infrared Signature Masking by Air Plasma Radiation

This report describes progress during the second year of our research program on Infrared Signature Masking by Air Plasmas at Stanford University. This program is intended to investigate the masking of infrared signatures by the air plasma formed behind the bow shock of high velocity missiles. Our previous annual report described spectral measurements and modeling of the radiation emitted between 3.2 and 5.5 microns by an atmospheric pressure air plasma in chemical and thermal equilibrium at a temperature of approximately 3100 K. One of our goals was to examine the spectral emission of secondary species such as water vapor or carbon dioxide. The cold air stream injected in the plasma torch contained approximately 330 parts per million Of CO2, which is the natural CO2 concentration in atmospheric air at room temperature, and a small amount of water vapor with an estimated mole fraction of 3.8 x 10(exp -4). As can be seen from Figure 1, it was found that the measured spectrum exhibited intense spectral features due to the fundamental rovibrational bands of NO at 4.9 - 5.5 microns and the V(3) band of CO2 (antisymmetric stretch) at 4.2-4.8 microns. These observations confirmed the well-known fact that infrared signatures between 4.15 - 5.5 microns can be masked by radiative emission in the interceptor's bow-shock. Figure I also suggested that the range 3.2 - 4.15 microns did not contain any significant emission features (lines or continuum) that could mask IR signatures. However, the signal-to-noise level, close to one in that range, precluded definite conclusions. Thus, in an effort to further investigate the spectral emission in the range of interest to signature masking problem, new measurements were made with a higher signal-to-noise ratio and an extended wavelength range.

Kruger, C. H.↗

Interdisciplinary investigations of comparative planetology

Research supported wholly or in part by NASA's Planetary Programs Office is summarized. Topics covered include: the evaporation of ice in planetary atmospheres: ice-covered rivers on Mars; reducing greenhouses and the temperature history of Earth and Mars; particle motion on Mars inferred from the Viking Lander cameras; the nature and visibility of crater-associated streaks on Mars; the equilibrium figure of Phobos and other small bodies; striations on Phobos; radiation pressure and Poynting-Robertson drag for small spherical particles; direct imaging of extra-solar planets with stationary occultations; the relation between planetology and conventional astrophysics; remote spectral studies and in situ X-ray fluorescence analysis of the Martian surface; small channels on Mars; junction angles of Martian channels; constraints on Aeolian phenomena on Mars; the geology of Mars; and the flow of erosional debris on the Martian terrain.

Sagan, C.↗

Organic synthesis in experimental impact shocks

Laboratory simulations of shocks created with a high-energy laser demonstrate that the efficacy of organic production depends on the molecular, not just the elemental composition of the shocked gas. In a methane-rich mixture that simulates a low-temperature equilibrium mixture of cometary material, hydrogen cyanide and acetylene were produced with yields of 5 x 10(17) molecules per joule. Repeated shocking of the methane-rich mixture produced amine groups, suggesting the possible synthesis of amino acids. No organic molecules were produced in a carbon dioxide-rich mixture, which is at odds with thermodynamic equilibrium approaches to shock chemistry and has implications for the modeling of shock-produced organic molecules on early Earth.

NASA Discipline Exobiology↗

Myths of German Graphite in World War II, with Original Translations

We re-examine the common narrative that a 1941 experimental error by physicists Walther Bothe and Peter Jensen led Germany to abandon graphite as a reactor moderator during World War II. We first detail the history of both German and American graphite experiments, noting that the Americans faced similar setbacks but succeeded only at the end of a costly 18-month graphite purification program. We then use Monte Carlo N-Particle simulations to reconstruct Bothe's 1941 experiment. We find the thermal absorption cross section of Bothe's Siemens electrographite to be 12.2 mb, in contrast to his reported 7.9 mb. This discrepancy arises because the neutrons in Bothe's experiment did not reach thermal equilibrium, leading to an underestimation of neutron absorption. Additionally, despite misconceptions that the Germans were unaware of boron impurities, we share evidence that Wilhelm Hanle accurately measured boron and cadmium impurities in the electrographite. To support our findings, we provide 9 excerpted and 3 complete English translations of classified wartime reports by Heisenberg, Joos, Bothe, Jensen, Höcker, Hanle, and Kremer. Our work aims to illuminate the rational constraints behind Germany's decision to forgo graphite moderation.

Park, Patrick J.↗

Supersonic Flow of Chemically Reacting Gas-Particle Mixtures. Volume 2: RAMP - A Computer Code for Analysis of Chemically Reacting Gas-Particle Flows

A computer program written in conjunction with the numerical solution of the flow of chemically reacting gas-particle mixtures was documented. The solution to the set of governing equations was obtained by utilizing the method of characteristics. The equations cast in characteristic form were shown to be formally the same for ideal, frozen, chemical equilibrium and chemical non-equilibrium reacting gas mixtures. The characteristic directions for the gas-particle system are found to be the conventional gas Mach lines, the gas streamlines and the particle streamlines. The basic mesh construction for the flow solution is along streamlines and normals to the streamlines for axisymmetric or two-dimensional flow. The analysis gives detailed information of the supersonic flow and provides for a continuous solution of the nozzle and exhaust plume flow fields. Boundary conditions for the flow solution are either the nozzle wall or the exhaust plume boundary.

Penny, M. M.↗

Structural Dynamics, Stability, and Control of Helicopters

The dynamic synthesis of gyroscopic structures consisting of point-connected substructures is investigated. The objective is to develop a mathematical model capable of an adequate simulation of the modal characteristics of a helicopter using a minimum number of degrees of freedom. The basic approach is to regard the helicopter structure as an assemblage of flexible substructures. The variational equations for the perturbed motion about certain equilibrium solutions are derived. The discretized variational equations can be conveniently exhibited in matrix form, and a great deal of information about the system modal characteristics can be extracted from the coefficient matrices. The derivation of the variational equations requires a monumental amount of algebraic operations. To automate this task a symbolic manipulation program on a digital computer is developed.

Meirovitch, L.↗