Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical Model”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 937 records · Page 52

Electronic excitation energy transfer and nonstationary processes in KH{sub 2}PO{sub 4}:Tl crystals

We report the results of our experimental study and numerical simulation of the electronic excitation energy transfer to impurity centers under conditions where nonstationary processes take place in the hydrogen sublattice of potassium dihydrogen phosphate (KH{sub 2}PO{sub 4}) single crystals doped with mercury-like Tl{sup +} ions (KDP:Tl). We present the experimental results of our investigation of the decay kinetics of the transient optical absorption (100 ns–50 s) of intrinsic defects in the hydrogen sublattice of KDP:Tl obtained by pulsed absorption spectroscopy and the results of our study of the dynamics of the change in steady-state luminescence intensity with irradiation time (1–5000 s). To explain the transfer of the energy being released during electron recombination involving intrinsic KDP:Tl lattice defects, we formulate a mathematical model for the transfer of this energy to impurity Tl{sup +} luminescence centers. Within the model being developed, we present the systems of differential balance equations describing the nonstationary processes in the electron subsystem and the hydrogen sublattice; provide a technique for calculating the pair correlation functions Y(r, t) of dissimilar defects based on the solution of the Smoluchowski equation for the system of mobile hydrogen sublattice defects; calculate the time-dependent reaction rate constants K(t) for various experimental conditions; and outline the peculiarities and results of the model parametrization based on our experimental data. Based on our investigation, the dramatic and significant effect of a gradual inertial increase by a factor of 50–100 in steady-state luminescence intensity in the 4.5-eV band in KDP:Tl crystals due to the luminescence of mercury-like Tl{sup +} ions has been explained qualitatively and quantitatively.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Model of Tool Wear in Deep Drilling

Parameter identification of the mathematical model of spiral-drill wear in deep drilling is considered. Wear is simulated by piecewise-linear approximation of the growth of drag torque in drilling. The diagnostic index selected is the constant component of the drag torque after the onset of drilling. The significance of the diagnostic index in determining the wear is demonstrated.

42 ENGINEERING↗

Optimal Strategies for Hybrid Battery‐Storage Systems Design

As stationary hybrid energy‐storage systems (HESS) for power systems applications have recently drawn interest due to their enhanced performance and decreasing cost, developing systematic approaches for HESS design while considering controls is gaining traction. Herein, a method is presented to optimally design hybrid battery storage by proposing a mathematical modeling framework, formulated as a mixed integer linear programming model. The optimization is capable of handling multiple subsystems of batteries, considering their economic and technological performance. Decisions involve sizing of the batteries, optimal temporal and strategic dispatch to end uses, and energy sources for charging each battery. The applicability of the model is tested on four case studies for three battery chemistries representing distinct objectives: high‐power, high‐energy, and second life. Compared to traditionally designed battery storage with a homogeneous battery, optimally designed hybrid systems can save 12%–26% of system costs, depending on the nature of the dispatch profile. Findings point to design preference toward the second life battery supplemented with some high‐power or high‐energy battery capacity, or both. With the utilized electricity price structure, customers can experience approximately 10%–35% reduction in their bills.

Koleva, Mariya↗

Prediction of Ablation Rates from Solid Surfaces Exposed to High Temperature Gas Flow

A mathematical model and a solution algorithm is developed to study the physics of high temperature heat transfer and material ablation and identify the problems associated with the flow of hydrogen gas at very high temperatures and velocities through pipes and various components of Nuclear Thermal Rocket (NTR) motors. Ablation and melting can be experienced when the inner solid surface of the cooling channels and the diverging-converging nozzle of a Nuclear Thermal Rocket (NTR) motor is exposed to hydrogen gas flow at temperatures around 2500 degrees Kelvin and pressures around 3.4 MPa. In the experiments conducted on typical NTR motors developed in 1960s, degradation of the cooling channel material (cracking in the nuclear fuel element cladding) and in some instances melting of the core was observed. This paper presents the results of a preliminary study based on two types of physics based mathematical models that were developed to simulate the thermal-hydrodynamic conditions that lead to ablation of the solid surface of a stainless steel pipe exposed to high temperature hydrogen gas near sonic velocities. One of the proposed models is one-dimensional and assumes the gas flow to be unsteady, compressible and viscous. An in-house computer code was developed to solve the conservations equations of this model using a second-order accurate finite-difference technique. The second model assumes the flow to be three-dimensional, unsteady, compressible and viscous. A commercial CFD code (Fluent) was used to solve the later model equations. Both models assume the thermodynamic and transport properties of the hydrogen gas to be temperature dependent. In the solution algorithm developed for this study, the unsteady temperature of the pipe is determined from the heat equation for the solid. The solid-gas interface temperature is determined from an energy balance at the interface which includes heat transfer from or to the interface by conduction, convection, radiation, and ablation. Two different ablation models are proposed to determine the heat loss from the solid surface due to the ablation of the solid material. Both of them are physics based. Various numerical simulations were carried out using both models to predict the temperature distribution in the solid and in the gas flow, and then predict the ablation rates at a typical NTR motor hydrogen gas temperature and pressure. Solid mass loss rate per foot of a pipe was also calculated from these predictions. The results are presented for fully developed turbulent flow conditions in a sample SS pipe with a 6 inch diameter.

Akyuzlu, Kazim M.↗

Conditions for translation and scaling invariance of the neutron diffusion equation

Lie group methods are applied to the time-dependent, monoenergetic neutron diffusion equation in materials with spatial and time dependence. To accomplish this objective, the underlying 2nd order partial differential equation (PDE) is recast as an exterior differential system so as to leverage the isovector symmetry analysis approach. Some of the advantages of this method as compared to traditional symmetry analysis approaches are revealed through its use in the context of a 2nd order PDE. In this context, various material properties appearing in the mathematical model (e.g., a diffusion coefficient and macroscopic cross section data) are left as arbitrary functions of space and time. The symmetry analysis that follows is restricted to a search for translation and scaling symmetries; consequently the Lie derivative yields specific material conditions that must be satisfied in order to maintain the presence of these important similarity transformations. The principal outcome of this work is thus the determination of analytic material property functions that enable the presence of various translation and scaling symmetries within the time-dependent, monoenergetic neutron diffusion equation. The results of this exercise encapsulate and generalize many existing results already appearing in the literature. While the results contained in this work are primarily useful as phenomenological guides pertaining to the symmetry behavior of the neutron diffusion equation under certain assumptions, they may eventually be useful in the construction of exact solutions to the underlying mathematical model. Furthermore, the results of this work are also useful as a starting point or framework for future symmetry analysis studies pertaining to the neutron transport equation and its many surrogates.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

High performance real-time flight simulation at NASA Langley

In order to meet the stringent time-critical requirements for real-time man-in-the-loop flight simulation, computer processing operations must be deterministic and be completed in as short a time as possible. This includes simulation mathematical model computational and data input/output to the simulators. In 1986, in response to increased demands for flight simulation performance, personnel at NASA's Langley Research Center (LaRC), working with the contractor, developed extensions to a standard input/output system to provide for high bandwidth, low latency data acquisition and distribution. The Computer Automated Measurement and Control technology (IEEE standard 595) was extended to meet the performance requirements for real-time simulation. This technology extension increased the effective bandwidth by a factor of ten and increased the performance of modules necessary for simulator communications. This technology is being used by more than 80 leading technological developers in the United States, Canada, and Europe. Included among the commercial applications of this technology are nuclear process control, power grid analysis, process monitoring, real-time simulation, and radar data acquisition. Personnel at LaRC have completed the development of the use of supercomputers for simulation mathematical model computational to support real-time flight simulation. This includes the development of a real-time operating system and the development of specialized software and hardware for the CAMAC simulator network. This work, coupled with the use of an open systems software architecture, has advanced the state of the art in real time flight simulation. The data acquisition technology innovation and experience with recent developments in this technology are described.

Cleveland, Jeff I., II↗

The Effects of Partial Mechanical Loading and Ibandronate on Skeletal Tissues in the Adult Rat Hindquarter Suspension Model for Microgravity

We report initial data from a suspended rat model that quantitatively relates chronic partial weightbearing to bone loss. Chronic partial weightbearing is our simulation of the effect of limited artificial gravity aboard spacecraft or reduced planetary gravity. Preliminary analysis of bone by PQCT, histomorphometry, mechanical testing and biochemistry suggest that chronic exposure to half of Earth gravity is insufficient to prevent severe bone loss. The effect of episodic full weightbearing activity (Earth Gravity) on rats otherwise at 50% weightbearing was also explored. This has similarity to treatment by an Earth G-rated centrifuge on a spacecraft that normally maintained artificial gravity at half of Earth G. Our preliminary evidence, using the above techniques to analyze bone, indicate that 2 hours daily of full weightbearing was insufficient to prevent the bone loss observed in 50% weightbearing animals. The effectiveness of partial weightbearing and episodic full weightbearing as potential countermeasures to bone loss in spaceflight was compared with treatment by ibandronate. Ibandronate, a long-acting potent bisphosphonate proved more effective in preventing bone loss and associated functionality based upon structure than our first efforts at mechanical countermeasures. The effectiveness of ibandronate was notable by each of the testing methods we used to study bone from gross structure and strength to tissue and biochemistry. These results appear to be independent of generalized systemic stress imposed by the suspension paradigm. Preliminary evidence does not suggest that blood levels of vitamin D were affected by our countermeasures. Despite the modest theraputic benefit of mechanical countermeasures of partial weightbearing and episodic full weightbearing, we know that some appropriate mechanical signal maintains bone mass in Earth gravity. Moreover, the only mechanism that correctly assigns bone mass and strength to oppose regionally specific force applied to bone is mechanical, a process based upon bone strain. Substantial evidence indicates that the specifics of dynamic loading i.e. time-varying forces are critical. Bone strain history is a predictor of the effect that mechanical conditions have on bone structure mass and strength. Using servo-controlled force plates on suspended rats with implanted strain gauges we manipulated impact forces of ambulation in the frequency (Fourier) domain. Our results indicate that high frequency components of impact forces are particularly potent in producing bone strain independent of the magnitude of the peak force or peak energy applied to the leg. Because a servo-system responds to forces produced by the rat's own muscle activity during ambulation, the direction of ground-reaction loads act on bone through the rat's own musculature. This is in distinction to passive vibration of the floor where forces reach bone through the natural filters of soft tissue and joints. Passive vibration may also be effective, but it may or may not increase bone in the appropriate architectural pattern to oppose the forces of normal ambulatory activity. Effectiveness of high frequency mechanical stimulation in producing regional (muscle directed) bone response will be limited by 1. the sensitivity of bone to a particular range of frequencies and 2. the inertia of the muscles, limiting their response to external forces by increasing tension along insertions. We have begun mathematical modeling of normal ambulatory activity. Effectiveness of high frequency mechanical stimulation in producing regional (muscle directed) bone response will be limited by 1. the sensitivity of bone to a particular range of frequencies and 2. the inertia of the muscles, limiting their response to external forces by increasing tension along insertions. We have begun mathematical modeling of the rat forelimb as a transfer function between impact force and bone strain to predict optimal dynamic loading conditions for this system. We plan additional studies of mechanical counter-measures that incorporate improved dynamic loading, features relevant to anticipated evaluation of artificial gravity, exercise regimens and exposure to Martian gravity, The combination of mechanical countermeasures with ibandronate will also be investigated for signs of synergy.

Schultheis, Lester W.↗

Diffusioosmotic flow reversals due to ion–ion electrostatic correlations

Existing theories of diffusioosmosis have neglected ion–ion electrostatic correlations, which are important in concentrated electrolytes. Here, we develop a mathematical model to numerically compute the diffusioosmotic mobilities of binary symmetric electrolytes across low to high concentrations in a charged parallel-plate channel. We use the modified Poisson equation to model the ion–ion electrostatic correlations and the Bikerman model to account for the finite size of ions. We report two key findings. First, ion–ion electrostatic correlations can cause a unique reversal in the direction of diffusioosmosis. Such a reversal is not captured by existing theories, occurs at ≈ 0.4 M for a monovalent electrolyte, and at a much lower concentration of ≈ 0.003 M for a divalent electrolyte in a channel with the same surface charge. This highlights that diffusioosmosis of a concentrated electrolyte can be qualitatively different from that of a dilute electrolyte, not just in its magnitude but also its direction. Second, we predict a separate diffusioosmotic flow reversal, which is not due to electrostatic correlations but the competition between the underlying chemiosmosis and electroosmosis. This reversal can be achieved by varying the magnitude of the channel surface charge without changing its sign. However, electrostatic correlations can radically change how this flow reversal depends on the channel surface charge and ion diffusivity between a concentrated and a dilute electrolyte. Furthermore, the mathematical model developed here can be used to design diffusioosmosis of dilute and concentrated electrolytes, which is central to applications such as species mixing and separation, enhanced oil recovery, and reverse electrodialysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

An Analysis of the Impact of Particle Growth on Transport Losses in Polymer-Electrolyte Fuel Cells

Voltage cycling causes catalyst nanoparticles in polymer-electrolyte fuel cells to grow. The concomitant loss of interfacial area results in larger kinetic, transport, and possibly ohmic overpotentials. This paper uses recently published experimental data and mathematical models to investigate the evolutions of transport and ohmic resistances to platinum nanoparticles located on the surface and inside the micropores of carbon black supports. Resistance to oxygen transport rises as surface area declines primarily because the flux to each remaining larger platinum particle increases. The path lengths governing oxygen diffusion to surface and buried platinum sites also increase as nanoparticles grow. Platinum nanoparticles on the surface become relatively less favorable as voltage cycling proceeds because they grow faster than platinum in micropores. Because voltage cycling causes total interfacial area to decline, and the fraction located inside micropores to increase, nanoscale ohmic losses increase as a catalyst layer decays. The practical importance of this effect is difficult to discern because proton conductivity in carbon micropores is not well characterized.

07 ISOTOPE AND RADIATION SOURCES↗

Actively Controlled Shaft Seals for Aerospace Applications

This study experimentally investigates an actively controlled mechanical seal for aerospace applications. The seal of interest is a gas seal, which is considerably more compact than previous actively controlled mechanical seals that were developed for industrial use. In a mechanical seal, the radial convergence of the seal interface has a primary effect on the film thickness. Active control of the film thickness is established by controlling the radial convergence of the seal interface with a piezoelectric actuator. An actively controlled mechanical seal was initially designed and evaluated using a mathematical model. Based on these results, a seal was fabricated and tested under laboratory conditions. The seal was tested with both helium and air, at rotational speeds up to 3770 rad/sec, and at sealed pressures as high as 1.48 x 10(exp 6) Pa. The seal was operated with both manual control and with a closed-loop control system that used either the leakage rate or face temperature as the feedback. The output of the controller was the voltage applied to the piezoelectric actuator. The seal operated successfully for both short term tests (less than one hour) and for longer term tests (four hours) with a closed-loop control system. The leakage rates were typically 5-15 slm (standard liters per minute), and the face temperatures were generally maintained below 100C. When leakage rate was used as the feedback signal, the setpoint leakage rate was typically maintained within 1 slm. However, larger deviations occurred during sudden changes in sealed pressure. When face temperature was used as the feedback signal, the setpoint face temperature was generally maintained within 3 C, with larger deviations occurring when the sealed pressure changes suddenly. the experimental results were compared to the predictions from the mathematical model. The model was successful in predicting the trends in leakage rate that occurred as the balance ratio and sealed pressure changed, although the leakage rates were not quantitatively predicted with a high degree of accuracy. This model could be useful in providing valuable design information for future actively controlled mechanical seals.

Salant, Richard F.↗

Foaming during Nuclear Waste Melter Feeds Conversion to Glass: Application of Evolved Gas Analysis

During the final stages of batch-to-glass conversion in a waste-glass melter, gases evolving in the cold cap produce primary foam, the formation and collapse of which control the glass production rate via its effect on heat transfer to the reacting batch. We performed quantitative evolved gas analysis (EGA) for several HLW melter feeds with temperatures ranging from 100 °C to 1150 °C, the whole temperature span in a cold cap. EGA results were supplemented with visual observation of batch-to-glass transition using the feed expansion tests. Upon heating, most of the gases—mainly H2O, CO2, NO, NO2, N2 and O2—evolve at temperatures below 700 °C and escape directly to the atmosphere through open porosity. However, as open porosity closes when enough glass-forming melt appears at 720 °C, the residual gas evolution leads to the formation of primary foam. We found that primary foaming is mostly caused by the decomposition of residual carbonates, though oxygen evolution from iron-redox reaction can also play a role. We also show that the gas evolution shifts to a higher temperature when the heating rate increases. The implications for the mathematical modeling of foam layer in the cold cap are presented.

Hujova, Miroslava↗

Cold-cap formation from a slurry feed during nuclear waste vitrification

The time-temperature history of waste slurry feed during melting strongly affects various kinetic processes, such as reaction or dissolution rates, and, consequently, the melting rate. To analyze the time-temperature history of the feed in a cold-cap during nuclear waste vitrification, this work focuses on understanding how the main coldcap body forms, how the aqueous feed slurry interacts with the cold-cap, and estimating the cold-cap heat conductivity. To simulate the conditions during cold-cap formation, samples were prepared by rapid water evaporation from slurry feed. After water evaporated from the sample, a fresh slurry with tracer was poured onto the dry sample. X-ray fluorescence was then used to investigate the degree of penetration and/or mixing between the incoming slurry and the original sample. We show that the slurry does not interact or mix with the previously dry cold-cap crust, but that water-soluble components concentrate at the bottom of the boiling pools, where most of the water evaporates. Further, using the rate of water evaporation, the heat conductivity of the cold-cap was calculated from the measured temperature profile. The resulting conductivity is significantly higher than the values obtained in previous studies. We discuss the implications of the results for the cold-cap formation in the melter and for the development of the cold-cap mathematical model.

Hujova, Miroslava↗

How Germinal Centers Evolve Broadly Neutralizing Antibodies: the Breadth of the Follicular Helper T Cell Response

Many HIV-1-infected patients evolve broadly neutralizing antibodies (bnAbs). This evolutionary process typically takes several years and is poorly understood as selection taking place in germinal centers occurs on the basis of antibody affinity. B cells with the highest-affinity receptors tend to acquire the most antigen from the follicular dendritic cell (FDC) network and present the highest density of cognate peptides to follicular helper T (Tfh) cells, which provide survival signals to the B cell. bnAbs are therefore expected to evolve only when the B cell lineage evolving breadth is consistently capturing and presenting more peptides to Tfh cells than other lineages of more specific B cells. Here we develop mathematical models of Tfh cells in germinal centers to explicitly define the mechanisms of selection in this complex evolutionary process. Our results suggest that broadly reactive B cells presenting a high density of peptides bound to major histocompatibility complex class II molecules (pMHC) are readily outcompeted by B cells responding to lineages of HIV-1 that transiently dominate the within host viral population. Conversely, if broadly reactive B cells acquire a large variety of several HIV-1 proteins from the FDC network and present a high diversity of several pMHC, they can be rescued by a large fraction of the Tfh cell repertoire in the germinal center. Under such circumstances the evolution of bnAbs is much more consistent. Increasing either the magnitude of the Tfh cell response or the breadth of the Tfh cell repertoire markedly facilitates the evolution of bnAbs. Because both the magnitude and breadth can be increased by vaccination with several HIV-1 proteins, this calls for experimental testing. Many HIV-infected patients slowly evolve antibodies that can neutralize a large variety of viruses. Such broadly neutralizing antibodies (bnAbs) could in the future become therapeutic agents. bnAbs appear very late, and patients are typically not protected by them. At the moment, we fail to understand why this takes so long and how the immune system selects for broadly neutralizing capacity. Typically, antibodies are selected based on affinity and not on breadth. We developed mathematical models to study two different mechanisms by which the immune system can select for broadly neutralizing capacity. One of these is based upon the repertoire of different follicular helper T (Tfh) cells in germinal centers. In conclusion, we suggest that broadly reactive B cells may interact with a larger fraction of this repertoire and demonstrate that this would select for bnAbs. Intriguingly, this suggests that broadening the Tfh cell repertoire by vaccination may speed up the evolution of bnAbs.

59 BASIC BIOLOGICAL SCIENCES↗

Melting rate correlation with batch properties and melter operating conditions during conversion of nuclear waste melter feeds to glasses

The rate of conversion of nuclear waste melter feed to glass is affected by the selection of melter feed materials and by melter design and operation. The melting rate correlation (MRC) is an equation that relates the glass production rate with two types of variables: (1) feed and melt properties: conversion heat, cold-cap bottom temperature, and glass melt viscosity; and (2) melter design and operation parameters: melter geometry, melter operating temperature, and gas bubbling rate. The MRC shows good agreement for an extended melting-rate data set of high-level waste (HLW) melter feeds and a data set generated for low-activity waste (LAW) melter feeds. Laboratory observation of heated melter feed samples is often used to assess the cold-cap bottom temperature of HLW melter feeds (moderately foaming feeds), but this technique appears inadequate for LAW melter feeds (vigorously foaming feeds). For LAW feeds, an adequate assessment of the cold-cap bottom temperature was achieved using evolved gas analysis, which allows identification of the collapse of primary foam for oxidized feeds. This assessment shows that the cold-cap bottom temperature for vigorously foaming LAW feeds is higher than that for moderately foaming HLW feeds. When the results of MRC are compared, LAW feeds are generally less sensitive to the bubbling rate and melt viscosity, and more sensitive to the cold-cap bottom temperature than HLW feeds. The MRC qualifies as a promising tool to support the selection of melter feed materials and melter operating conditions, which is determined from expensive independent scaled melter experiments, and sophisticated mathematical models.

Lee, Seung Min↗

Modification of the MTS model for high strain-rate behavior of TI-6AL-4V

The Mechanical Threshold Stress (MTS) model provides excellent predictive capabilities for the material constitutive response for a wide range of temperatures and strain rates. However, the MTS model fails to capture the rapidly increasing yield stress at high strain rate behavior as the deformation controlling mechanism transitions from thermal activation to drag mechanisms, only capturing the linear behavior. Further, the model typically over predicts the flow stress behavior at yield and post yield due to its use of a constant work hardening rate parameter derived from the stress–strain response at constant saturation stress. An alternative approach to fitting portions of the MTS model is investigated and mathematical models are developed to address these issues. The results show that with appropriate experimental data, the mechanical threshold stress and work hardening rate parameters within the MTS model can quite easily and accurately be modified to extend applicability to high strain rate behavior and more accurately model the initial flow stress behavior at early work hardening rates without modification of the functions core to the MTS model itself.

36 MATERIALS SCIENCE↗

A mathematical simulation model of the CH-47B helicopter, volume 1

A nonlinear simulation model of the CH-47B helicopter was adapted for use in the NASA Ames Research Center (ARC) simulation facility. The model represents the specific configuration of the ARC variable stability CH-47B helicopter and will be used in ground simulation research and to expedite and verify flight experiment design. Modeling of the helicopter uses a total force approach in six rigid body degrees of freedom. Rotor dynamics are simulated using the Wheatlely-Bailey equations including steady-state flapping dynamics. Also included in the model is the option for simulation of external suspension, slung-load equations of motion.

Weber, J. M.↗

Evaluation of Mathematical Turbulence Models

Simplified models for internal flow described, and their predictions compared with experimental results. Report presents account of various models used in computation of turbulent flows. Applications of these models to internal flows evaluated by analysis of predictions of various turbulence models in some important flow configurations.

Nallasamy, M.↗