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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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

Multiple point least squares equalization in a room

Equalization filters designed to minimize the mean square error between a delayed version of the original electrical signal and the equalized response at a point in a room have previously been investigated. In general, such a strategy degrades the response at positions in a room away from the equalization point. A method is presented for designing an equalization filter by adjusting the filter coefficients to minimize the sum of the squares of the errors between the equalized responses at multiple points in the room and delayed versions of the original, electrical signal. Such an equalization filter can give a more uniform frequency response over a greater volume of the enclosure than can the single point equalizer above. Computer simulation results are presented of equalizing the frequency responses from a loudspeaker to various typical ear positions, in a room with dimensions and acoustic damping typical of a car interior, using the two approaches outlined above. Adaptive filter algorithms, which can automatically adjust the coefficients of a digital equalization filter to achieve this minimization, will also be discussed.

Elliott, S. J.↗
NASA NTRS1990

Asymptotic modal analysis and statistical energy analysis

The sound field of a structural-acoustic enclosure was subject to experimental analysis and theoretical description in order to develop an efficient and accurate method for predicting sound pressure levels in enclosures such as aircraft fuselages. Asymptotic Modal Analysis (AMA) is the method under investigation. AMA is derived from classical modal analysis (CMA) by considering the asymptotic limit of the sound pressure level as the number of acoustic and/or structural modes approaches infinity. Using AMA, results identical to those of Statistical Energy Analysis (SEA) were obtained for the spatially-averaged sound pressure levels in the interior. AMA is systematically derived from CMA and therefore the degree of generality of the end result can be adjusted through the choice of appropriate simplifying assumptions. For example, AMA can be used to obtain local sound pressure levels at particular points inside the enclosure, or to include the effects of varying the size and/or location of the sound source. AMA theoretical results were compared with CMA theory and also with experiment for the case where the structural-acoustic enclosure is a rectangular cavity with part of one wall flexible and vibrating, while the rest of the cavity is rigid.

Dowell, Earl H.↗
NASA NTRS2018

How Do You Go From a Concept Idea to a NASA Selected Mission? Formulating the Psyche Discovery Mission with JPL's Concurrent Engineering Teams

JPL’s Office of Formulation provides continuity of support and access to domain subject matter experts, as Principal Investigators mature their mission concepts from “cocktail napkin” ideas to Preliminary Design Reviews [1]. Using NASA’s Psyche mission as a case study, we describe JPL’s concurrent engineering A-Team and Team X support to the Psyche competed concept study team in the areas of 1) Initial Feasibility, 2) Trade Space Exploration, 3) Spacecraft Point Design and Cost Estimate, 4) Science, Technical, Management, and Cost Review, and 5) Strategy and Communication Development. NASA’s Psyche Discovery-class mission started as a grassroots idea from Principal Investigator L.T. ElkinsTanton. Is there a compelling Discovery mission to visit the interior of a body for the first time, by sending a mission to an iron metal asteroid? In less than five years the Psyche concept was selected as a mission under NASA’s Discovery Program. While Psyche had a dedicated concept development team [2], they utilized JPL’s concurrent engineering teams, methods, analysis tools, and subject matter experts throughout their mission concept formulation lifecycle

Ziemer, John↗
NASA NTRS1991

Application of two-point implicit central-difference methods to hyperbolic systems

This paper presents a general solution algorithm for the set of difference equations that arise when two-point central differences are used to approximate the flux difference terms in systems of hyperbolic differential equations. The general algorithm eliminates the weak points associated with the nonstandard algorithm reported by Wornom and Hafez (1986). The disadvantages of their algorithm relate to its implementation. It consists of separate algorithms for subsonic, supersonic, sonic and shock cells, applied individually, which presents a major bookkeeping problem when multiple sonic and shock cells are present. The general algorithm eliminates this problem and introduces an improved shock treatment which produces shocks with at most one interior shock point.

Wornom, Stephen F.↗
DOE OSTI2014

Harmonic analysis for the characterization and correction of geometric distortion in MRI

Purpose: Magnetic resonance imaging (MRI) is gaining widespread use in radiation therapy planning, patient setup verification, and real-time guidance of radiation delivery. Successful implementation of these technologies relies on the development of simple and efficient methods to characterize and monitor the geometric distortions arising due to system imperfections and gradient nonlinearities. To this end, the authors present the theory and validation of a novel harmonic approach to the quantification of system-related distortions in MRI. Methods: The theory of spatial encoding in MRI is applied to demonstrate that the 3D distortion vector field (DVF) is given by the solution of a second-order boundary value problem (BVP). This BVP is comprised of Laplace’s equation and a limited measurement of the distortion on the boundary of a specified region of interest (ROI). An analytical series expansion solving this BVP within a spherical ROI is obtained, and a statistical uncertainty analysis is performed to determine how random errors in the boundary measurements propagate to the ROI interior. This series expansion is then evaluated to obtain volumetric DVF mappings that are compared to reference data obtained on a 3 T full-body scanner. This validation is performed within two spheres of 20 cm diameter (one centered at the scanner origin and the other offset +3 cm along each of the transverse directions). Initially, a high-order mapping requiring measurements at 5810 boundary points is used. Then, after exploring the impact of the boundary sampling density and the effect of series truncation, a reduced-order mapping requiring measurements at 302 boundary points is evaluated. Results: The volumetric DVF mappings obtained from the harmonic analysis are in good agreement with the reference data. Following distortion correction using the high-order mapping, the authors estimate a reduction in the mean distortion magnitude from 0.86 to 0.42 mm and from 0.93 to 0.39 mm within the central and offset ROIs, respectively. In addition, the fraction of points with a distortion magnitude greater than 1 mm is reduced from 35.6% to 2.8% and from 40.4% to 1.5%, respectively. Similarly, following correction using the reduced-order mapping, the mean distortion magnitude reduces to 0.45–0.42 mm within the central and offset ROIs, and the fraction of points with a distortion magnitude greater than 1 mm is reduced to 2.8% and 1.5%, respectively. Conclusions: A novel harmonic approach to the characterization of system-related distortions in MRI is presented. This method permits a complete and accurate mapping of the DVF within a specified ROI using a limited measurement of the distortion on the ROI boundary. This technique eliminates the requirement to exhaustively sample the DVF at a dense 3D array of points, thereby permitting the design of simple, inexpensive phantoms that may incorporate additional modules for auxiliary quality assurance objectives.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
NASA NTRS1987

Space station interior noise analysis program

Documentation is provided for a microcomputer program which was developed to evaluate the effect of the vibroacoustic environment on speech communication inside a space station. The program, entitled Space Station Interior Noise Analysis Program (SSINAP), combines a Statistical Energy Analysis (SEA) prediction of sound and vibration levels within the space station with a speech intelligibility model based on the Modulation Transfer Function and the Speech Transmission Index (MTF/STI). The SEA model provides an effective analysis tool for predicting the acoustic environment based on proposed space station design. The MTF/STI model provides a method for evaluating speech communication in the relatively reverberant and potentially noisy environments that are likely to occur in space stations. The combinations of these two models provides a powerful analysis tool for optimizing the acoustic design of space stations from the point of view of speech communications. The mathematical algorithms used in SSINAP are presented to implement the SEA and MTF/STI models. An appendix provides an explanation of the operation of the program along with details of the program structure and code.

Stusnick, E.↗
DOE OSTI2014

Network Algorithms for Detection of Radiation Sources

In support of national defense, Domestic Nuclear Detection Office’s (DNDO) Intelligent Radiation Sensor Systems (IRSS) program supported the development of networks of radiation counters for detecting, localizing and identifying low-level, hazardous radiation sources. Industry teams developed the first generation of such networks with tens of counters, and demonstrated several of their capabilities in indoor and outdoor characterization tests. Subsequently, these test measurements have been used in algorithm replays using various sub-networks of counters. Test measurements combined with algorithm outputs are used to extract Key Measurements and Benchmark (KMB) datasets. We present two selective analyses of these datasets: (a) a notional border monitoring scenario that highlights the benefits of a network of counters compared to individual detectors, and (b) new insights into the Sequential Probability Ratio Test (SPRT) detection method, which lead to its adaptations for improved detection. Using KMB datasets from an outdoor test, we construct a notional border monitoring scenario, wherein twelve 2”*2” NaI detectors are deployed on the periphery of 21*21meter square region. A Cs-137 (175 uCi) source is moved across this region, starting several meters from outside and finally moving away. The measurements from individual counters and the network were processed using replays of a particle filter algorithm developed under IRSS program. The algorithm outputs from KMB datasets clearly illustrate the benefits of combining measurements from all networked counters: the source was detected before it entered the region, during its trajectory inside, and until it moved several meters away. When individual counters are used for detection, the source was detected for much shorter durations, and sometimes was missed in the interior region. The application of SPRT for detecting radiation sources requires choosing the detection threshold, which in turn requires a source strength estimate, typically specified as a multiplier of the background radiation level. A judicious selection of this source multiplier is essential to achieve optimal detection probability at a specified false alarm rate. Typically, this threshold is chosen from the Receiver Operating Characteristic (ROC) by varying the source multiplier estimate. ROC is expected to have a monotonically increasing profile between the detection probability and false alarm rate. We derived ROCs for multiple indoor tests using KMB datasets, which revealed an unexpected loop shape: as the multiplier increases, detection probability and false alarm rate both increase until a limit, and then both contract. Consequently, two detection probabilities correspond to the same false alarm rate, and the higher is achieved at a lower multiplier, which is the desired operating point. Using the Chebyshev’s inequality we analytically confirm this shape. Then, we present two improved network-SPRT methods by (a) using the threshold off-set as a weighting factor for the binary decisions from individual detectors in a weighted majority voting fusion rule, and (b) applying a composite SPRT derived using measurements from all counters.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2021

In-situ synchrotron X-ray micro-diffraction investigation of ultra-low-strain deformation microstructure in laminated Ti-Al composites

An ultra-low-strain deformation microstructure was revealed for the first time non-destructively in the bulk interior of an annealed laminated Ti-Al composite-in the "fully recrystallized" Al layer-by a synchrotron-based micro-diffraction technique, namely differential aperture X-ray microscopy (DAXM), through real space mapping with a very high angular resolution (0.01 degrees). This ultra-low-strain deformation microstructure was found to result from the thermal stress, induced during cooling after annealing, due to the different coefficients of thermal expansion for the Ti and Al layers. The annealed sample was further tensile deformed to a strain of 1.66% and followed by in situ DAXM and analyzed by various misorientation mapping methods. The results pointed to the important effects of the initial microstructure and the interface constraint, as well as the grain size and crystal orientation, on the plastic deformation. A gradient in dislocation density from the layer interface to the center was found in the Al layer of the annealed sample, and this gradient increased slightly during tensile deformation. The variation of the dislocation density was further discussed based on the activation and interaction of dislocations in grains of different sizes and orientations during plastic deformation. The findings of this study provided valuable insights in understanding the constraint effect of the laminated metal composite and the design of novel composite materials. (c) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Crystallographic orientation↗
NASA NTRS1987

Vibrations and structureborne noise in space station

Analytical models were developed to predict vibrations and structureborne noise generation of cylindrical and rectangular acoustic enclosures. These models are then used to determine structural vibration levels and interior noise to random point input forces. The guidelines developed could provide preliminary information on acoustical and vibrational environments in space station habitability modules under orbital operations. The structural models include single wall monocoque shell, double wall shell, stiffened orthotropic shell, descretely stiffened flat panels, and a coupled system composed of a cantilever beam structure and a stiffened sidewall. Aluminum and fiber reinforced composite materials are considered for single and double wall shells. The end caps of the cylindrical enclosures are modeled either as single or double wall circular plates. Sound generation in the interior space is calculated by coupling the structural vibrations to the acoustic field in the enclosure. Modal methods and transfer matrix techniques are used to obtain structural vibrations. Parametric studies are performed to determine the sensitivity of interior noise environment to changes in input, geometric and structural conditions.

Vaicaitis, R.↗
NASA NTRS2018

Impact-Seismic Investigations of the InSight Mission

Impact investigations will be an important aspect of the InSight mission. One of the scientific goals of the mission is a measurement of the current impact rate at Mars. Impacts will additionally inform the major goal of investigating the interior structure of Mars. In this paper, we review the current state of knowledge about seismic signals from impacts on the Earth, Moon, and laboratory experiments. We describe the generalized physical models that can be used to explain these signals. A discussion of the appropriate source time function for impacts is presented, along with spectral characteristics including the cutoff frequency and its dependence on impact momentum. Estimates of the seismic efficiency (ratio between seismic and impact energies) vary widely. Our preferred value for the seismic efficiency at Mars is 5 × 10−4, which we recommend using until we can measure it during the InSight mission, when seismic moments are not used directly. Effects of the material properties at the impact point and at the seismometer location are considered. We also discuss the processes by which airbursts and acoustic waves emanate from bolides, and the feasibility of detecting such signals. We then consider the case of impacts on Mars. A review is given of the current knowledge of present-day cratering on Mars: the current impact rate, characteristics of those impactors such as velocity and directions, and the morphologies of the craters those impactors create. Several methods of scaling crater size to impact energy are presented. The Martian atmosphere, although thin, will cause fragmentation of impactors, with implications for the resulting seismic signals. We also benchmark several different seismic modeling codes to be used in analysis of impact detections, and those codes are used to explore the seismic amplitude of impactinduced signals as a function of distance from the impact site. We predict a measurement of the current impact flux will be possible within the timeframe of the prime mission (one Mars year) with the detection of ∼ a few to several tens of impacts. However, the error bars on these predictions are large. Specific to the InSight mission, we list discriminators of seismic signals from impacts that will be used to distinguish them from marsquakes. We describe the role of the InSight Impacts Science Theme Group during mission operations, including a plan for possible night-time meteor imaging. The impacts detected by these methods during the InSight mission will be used to improve interior structure models, measure the seismic efficiency, and calculate the size frequency distribution of current impacts.

Ingrid Daubar↗
DOE OSTI2019

Thermal Analysis Of Saltstone Disposal Units

SRR requested that SRNL develop a two-dimensional computer simulation model to be capable of predicting grout temperatures attained in Saltstone Disposal Units (SDUs) during the transient addition of saltstone grout and its subsequent storage period. A simulation model was developed to calculate the transient grout temperatures of the SDU facility by taking an axisymmetric and two-dimensional Computational Fluid Dynamics (CFD) approach. The final performance calculations were based on the conduction and radiation model without a convection cooling mechanism for conservative estimate of the grout temperatures and computational efficiency. While convection within the SDU is disabled in the current calculations, the simulation model has the capability of turning convection back on if desired by the user. Hence, the thermal model in its current configuration is best characterized as a finite-volume heat transfer model. However, given that the model can account for convection if desired by the user, it will be referred to as a CFD model. The grout material contains a transient heat source due to the exothermic hydration reactions of the cementitious material mixed with salt solution. The model can predict the transient temperatures at point locations within the poured grout and the overlying vapor space, and at the interior and exterior surfaces of the structure. The thermal model has been developed for two SDUs at the Savannah River Site (SRS); namely, SDU 2A and SDU 6. SDU 2A is a cylindrical unit measuring 150 feet (ft) in diameter, 22 ft tall, and holds approximately three million gallons of grout. SDU 6 is 375 ft in diameter and 43 ft high with a capacity of over thirty million gallons. Prior to performing the thermal calculations for the SDU 6 facility, the benchmarking test for the smaller SDU 2A unit was performed to establish the solution method and to verify the computational results using existing thermocouple data. Based on the Lagrangian discrete method and boundary conditions established by the SDU 2A benchmarking test, the CFD calculations were performed to predict the transient temperatures at local positions of the poured grout and air spaces within the SDU 6 structure.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2016

SU-F-T-336: A Quick Auto-Planning (QAP) Method for Patient Intensity Modulated Radiotherapy (IMRT)

Purpose: The aim of this study is to develop a quick auto-planning system that permits fast patient IMRT planning with conformal dose to the target without manual field alignment and time-consuming dose distribution optimization. Methods: The planning target volume (PTV) of the source and the target patient were projected to the iso-center plane in certain beameye- view directions to derive the 2D projected shapes. Assuming the target interior was isotropic for each beam direction boundary analysis under polar coordinate was performed to map the source shape boundary to the target shape boundary to derive the source-to-target shape mapping function. The derived shape mapping function was used to morph the source beam aperture to the target beam aperture over all segments in each beam direction. The target beam weights were re-calculated to deliver the same dose to the reference point (iso-center) as the source beam did in the source plan. The approach was tested on two rectum patients (one source patient and one target patient). Results: The IMRT planning time by QAP was 5 seconds on a laptop computer. The dose volume histograms and the dose distribution showed the target patient had the similar PTV dose coverage and OAR dose sparing with the source patient. Conclusion: The QAP system can instantly and automatically finish the IMRT planning without dose optimization.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1981

The helium abundance of Jupiter from Voyager

The helium abundance in the Jovian atmosphere is derived from Voyager 1 data by two methods. The first method uses only infrared spectra from selected locations on the planet while the second method uses a thermal profile independently derived from radio occultation measurements and infrared spectra recorded near the occultation point. A hydrogen mole fraction of 0.897 plus or minus 0.030 is obtained from the first method, while the second method gives 0.880 plus or minus 0.036, corresponding to helium mass fractions of 0.19 plus or minus 0.05 and 0.21 plus or minus 0.06, respectively. The estimated errors for the first method are primarily due to systematic uncertainties in the H2 and He absorption coefficients, while those for the second method result mainly from errors in the radio occultation profile and are less well known. Random errors in the measured infrared spectra are found to be negligible in both cases. The results are consistent with a uniform mix of hydrogen and helium within Jupiter's interior, but a modest amount of helium depletion (Delta Y equal to or less than 0.05) cannot be excluded.

Gautier, D.↗
DOE OSTI2015

Radiological data consolidation and 3D modeling of a building - 15473

A portion of a building at an industrial facility that conducted monazite sands-processing operations in the 1950's under contract to the Atomic Energy Commission (AEC) became contaminated. Subsequently the U.S. Department of Energy designated the facility for remedial action under the Formerly Used Sites Remedial Action Program (FUSRAP). Remedial investigation, remedial actions and post-remediation surveys have been conducted in portions of the building. Radiological data for the interior of the building were compiled, evaluated and presented in a three dimensional (3-D) model (the model) created by AMEC Foster Wheeler in order to identify areas that meet the Record of Decision (ROD) cleanup criteria, and identity areas that may require remedial action or may require additional investigation due to data gaps. The data from different phases of investigation and remediation cover different portions of the building and in some cases overlap. In addition, the data were collected over a period of more than ten years, for different objectives, and thus the instruments and methods for establishing efficiency were not necessarily consistent. The data consolidation process included determining the relative quality of data points to include in the model and the development of rationale associated with assigning a quality level (i.e. ranking) to each data point. The rationale for ranking data quality included, as the primary determining factors, chronological order of the data (most recent was ranked as more reliable), certainty of the sample locations within the building, and analytical data quality. A 3-D model of the building was created using a laser point cloud scan which was then converted into a 3-D design model. Sample locations were then entered into the model and linked with the analytical database to allow display of the radiological results in the model. The visual model allows both strategic and tactical decisions to be made, depending on the level of detail examined. The evaluation process allowed maximum use of the historical data set, rather than requiring older data to be disregarded, and provided at a minimum a qualitative sense of data quality/confidence in the data. The (authors)process also highlights the importance of collecting high quality data from the very beginning with a consistent locational coordinate system, and the need for a good visualization model in order to assess contaminant locations during remedial action or post-remediation surveys.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2018

The Physics and Chemistry of Cluster-based Catalyst Systems

In this project we used first principles calculations to investigate the physical and chemical properties of atomic clusters, small clumps of matter containing up to a few hundred atoms. The calculations are based on density functional theory, the most efficient and accurate method available for computing and thereby predicting the properties of molecules, clusters, and solids. An initial focus of our work involved studying the reactivity of small Pd clusters. We demonstrated that H2 molecules readily dissociate on Pd clusters and that multiple dissociations can occur on clusters larger than a few Pd atoms. For example, up to eight H2 molecules will dissociate on Pd13 at room temperature. A second focus of the project was to study the evolution of the electrical behavior of clusters, in particular, the evolution of metallic behavior in clusters of metal atoms. We developed a technique for using the electric dipole polarizability of the clusters – the response of the cluster to an applied electric field -- as a probe of this behavior. By decomposing the polarizability into so-called charge transfer (or metallic) and local (or insulating) contributions, we obtained the remarkable result that the per atom charge transfer contributions in sodium clusters attain the same value as occurs in bulk sodium metal for clusters containing as few as 10 atoms. Our calculated total polarizabilities matched experimentally measured trends essentially perfectly, validating the reliability of the calculations and supporting our conclusion that tiny clusters already display bulk-like metallic character. Similar results were obtained for other metal atom clusters, including potassium, aluminum, and zinc. We discovered that the evolution toward bulk metallic behavior for each of these cluster species is essentially identical, when judged using these polarizability-based descriptors. This suggests a universality in the approach of metal clusters to bulk-like metallicity. This discovery is a major outcome of our project. We also used our polarizability-based metrics to investigate the evolution of the properties of Si and NaCl clusters. These systems are non-metallic in the bulk limit. For Si, we find the behavior of small clusters to be metal-like and we attribute this to bonding arrangements in the clusters that are very different from the open structure of crystalline silicon. As the clusters get larger, the bonding in the cluster interior becomes more and more like that of the bulk material. We expect a transition from metal-like to insulator-like behavior to accompany this change is structure. Our results point to a transition at sizes beyond 146 atoms, the largest size treated in our study. We hope to study this transition further in the future. A third thrust of our project involved work on a new approach to eliminating unphysical electron self-interaction from density functional theory calculations. Two electrons exert repulsive forces on each other, but a single electron should not interact with itself. Because of approximations made in density functional theory, individual electrons effectively interact with themselves. The effect of this self-interaction is often small, especially when atoms are near their equilibrium positions in molecules. But the effects can be pronounced when bonds are stretched and also in some situations involving transition metals even when the atoms are near equilibrium. Our research involved the further development of a method for removing self-interaction called the Fermi-Löwdin orbital self-interaction correction or FLO-SIC. We conducted the first systematic FLO-SIC calculations for the individual atoms ranging from Li – Kr. We also carried out a critical comparison of the results of FLO-SIC with an older method known as the Perdew-Zunger self-interaction correction (PZ-SIC). FLO-SIC can be thought of as a modified approach to PZ-SIC that is expected to be computationally more efficient. We demonstrated that the two methods are distinct, but give essentially the same results for quantities such as molecular binding energies or electron removal energies. We are continuing to develop the FLO-SIC methodology with a goal of creating a computationally efficient method that is free of self-interaction effects.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1984

Solar Seismology from Space. a Conference at Snowmass, Colorado

The quality of the ground based observing environment suffers from several degrading factors: diurnal interruptions and thermal variations, atmospheric seeing and transparency fluctuations and adverse weather interruptions are among the chief difficulties. The limited fraction of the solar surface observable from only one vantage point is also a potential limitation to the quality of the data available without going to space. Primary conference goals were to discuss in depth the scientific return from current observations and analyses of solar oscillations, to discuss the instrumental and site requirements for realizing the full potential of the seismic analysis method, and to help bring new workers into the field by collecting and summarizing the key background theory. At the conclusion of the conference there was a clear consensus that ground based observation would not be able to provide data of the quality required to permit a substantial analysis of the solar convection zone dynamics or to permit a full deduction of the solar interior structure.

Ulrich, R. K.↗
NASA NTRS1973

Matrix operator theory of radiative transfer. I - Rayleigh scattering.

An entirely rigorous method for the solution of the equations for radiative transfer based on the matrix operator theory is reviewed. The advantages of the present method are: (1) all orders of the reflection and transmission matrices are calculated at once; (2) layers of any thickness may be combined, so that a realistic model of the atmosphere can be developed from any arbitrary number of layers, each with different properties and thicknesses; (3) calculations can readily be made for large optical depths and with highly anisotropic phase functions; (4) results are obtained for any desired value of the surface albedo including the value unity and for a large number of polar and azimuthal angles; (5) all fundamental equations can be interpreted immediately in terms of the physical interactions appropriate to the problem; and (6) both upward and downward radiance can be calculated at interior points from relatively simple expressions.

Plass, G. N.↗
NASA NTRS1975

Analysis of liquid-metal-jet impingement cooling in a corner region and for a row of jets

A conformal mapping method was used to analyze liquid-metal-jet impingement heat transfer. The jet flow region and energy equation are transformed to correspond to uniform flow in a parallel plate channel with nonuniform heat addition along a portion of one wall. The exact solution for the wall-temperature distribution was obtained in the transformed channel, and the results are mapped back into the physical plane. Two geometries are analyzed. One is for a single slot jet directed either into an interior corner formed by two flat plates, or over the external sides of the corner; the flat plates are uniformly heated, and the corner can have various included angles. The heat-transfer coefficient at the stagnation point at the apex of the plates is obtained as a function of the corner angle, and temperature distributions are calculated along the heated walls. The second geometry is an infinite row of uniformly spaced parallel slot jets impinging normally against a uniformly heated plate. The heat-transfer behavior is obtained as a function of the spacing between the jets. Results are given for several jet Peclet numbers from 5 to 50.

Siegel, R.↗