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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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At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Auger Spectroscopy of Hydrogenated Diamond Surfaces

An energy shift and a change of the line shape of the carbon core-valence-valence Auger spectra are observed for diamond surfaces after their exposure to an electron beam, or annealing at temperatures higher then 950 C. The effect is studied for both natural diamond crystals and chemical-vapor-deposited diamond films. A theoretical model is proposed for Auger spectra of hydrogenated diamond surfaces. The observed changes of the carbon Auger line shape are shown to be related to the redistribution of the valence-band local density of states caused by the hydrogen desorption from the surface. One-electron calculation of Auger spectra of diamond surfaces with various hydrogen coverages are presented. They are based on self-consistent wave functions and matrix elements calculated in the framework of the local-density approximation and the self-consistent linear muffin-tin orbital method with static core-hole effects taken into account. The major features of experimental spectra are explained.

Krainsky, I. L.↗
DOE OSTI2025

Self-consistent modeling of tokamak edge plasma transport with lithium sources

Magnetic confinement fusion devices require effective heat and particle exhaust solutions on the divertor plates to operate sustainably, especially under reactor-relevant conditions. Liquid lithium divertors have been proposed to address two major challenges: control of excessive heat flux to plasma-facing components through vapor shielding and minimization of core plasma contamination from impurities. The National Spherical Torus Experiment-Upgrade (NSTX-U) will explore lithium as a divertor material due to its potential to meet both objectives. We present a self-consistent coupling framework between the plasma boundary transport code UEDGE and the lithium wall transport code Wall–Li to evaluate the feasibility and operational limits of lithium-based divertors. The model aims to optimize lithium sourcing levels to prevent core plasma contamination via fuel dilution while ensuring divertor protection through vapor shielding. This integrated framework, applicable to any tokamak with lithium sources, dynamically adjusts lithium sourcing based on local plasma conditions and surface temperature. The coupled model is tested using NSTX-like geometry and plasma conditions to assess its performance and reliability. Wall–Li calculates lithium fluxes from plasma-facing components, incorporating physical sputtering, thermally enhanced sputtering, and evaporation driven by surface temperature and ion flux. These fluxes are reintroduced into UEDGE as neutral lithium atoms, enabling simulation of their transport and distribution within the plasma. UEDGE computes plasma and neutral transport, surface heat flux, and iteratively feeds this information back to Wall–Li. A small time step is employed to ensure numerical stability and convergence, enabling accurate simulations over typical tokamak discharge durations. This integrated modeling approach provides a robust tool for identifying operational regimes that balance effective lithium sourcing with minimal core plasma contamination, offering critical insights for optimizing lithium-based divertor systems in current and future fusion devices.

Magnetic confinement fusion↗
NASA NTRS1993

A Regional Analysis of Cloudy Mean Spherical Albedo over the Marine Stratocumulus Region and the Tropical Atlantic Ocean

Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. This study examines the relationships between cloud properties and cloud fraction in order to supplement grid scale parameterizations. The satellite data used in this study is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.50 x 2.50 latitude-longitude grid. Mean cloud spherical albedo, the mean optical depth distribution and cloud fraction are examined and compared off the coast of California and the mid-tropical Atlantic for July 1987 and 1988. Individual grid boxes and spatial averages over several grid boxes are correlated to Coakleys (1991) theory of reflection for uniform and broken layered cloud and to Kedem, et al.(1990) findings that rainfall volume and fractional area of rain in convective systems is linear. Kedem's hypothesis can be expressed in terms of cloud properties. That is, the total volume of liquid in a box is a linear function of cloud fraction. Results for the marine stratocumulus regime indicate that albedo is often invariant for cloud fractions of 20% to 80%. Coakley's satellite model of small and large clouds with cores (1 km) and edges (100 in) is consistent with this observation. The cores maintain high liquid water concentrations and large droplets while the edges contain low liquid water concentrations and small droplets. Large clouds are just a collection of cores. The mean optical depth (TAU) distributions support the above observation with TAU values of 3.55 to 9.38 favored across all cloud fractions. From these results, a method based upon Kedem, et al. theory is proposed to separate the cloud fraction and liquid water path (LWP) calculations in a general circulation model (GCM). In terms of spatial averaging, a linear relationship between albedo and cloud fraction is observed. For tropical locations outside the Intertropical Convergence Zone (ITCZ), results of cloud fraction and albedo spatial averaging followed that of the stratus boxes containing few overcast scenes. Both the ideas of Coakley and Kedem, et al. apply. Within the ITCZ, the grid boxes tended to have the same statistical properties as stratus boxes containing many overcast scenes. Because different dynamical forcing mechanisms are present, it is difficult to devise a method for determining subgrid scale variations. Neither of the theories proposed by Kedem, et al. or Coakley works well for the boxes with numerous overcast scenes.

Ginger, Kathryn M.↗
NASA NTRS1979

Semiconvection and period changes in RR Lyrae stars

The possibility is considered that convective mixing inherently associated with composition redistribution inward through a semiconvective zone (SCZ) and into the convective core by the end of the horizontal-branch (HB) phase may be primarily responsible for the observed period changes in RR Lyrae stars. Specifically, it is proposed that the period changes in RR Lyrae stars are caused mainly by small random mixing events within the SCZ and at the edge of the convective core. Tests of several HB models that include semiconvection are presented which demonstrate that stellar evolution cannot satisfactorily account for the observed period changes but that mixing events involving only a very small part of the SCZ or a very small extension of the convective core are sufficient to change the pulsation period of an RR Lyrae star by the amount typically observed. The frequency of the period changes is predicted theoretically and found to be in good agreement with the observed value within the substantial uncertainties involved. A procedure is outlined for future period-change testing of HB models.

Sweigart, A. V.↗
NASA NTRS1979

Development of a severe local storm prediction system: A 60-day test of a mesoscale primitive equation model

The progress and problems associated with the dynamical forecast system which was developed to predict severe storms are examined. The meteorological problem of severe convective storm forecasting is reviewed. The cascade hypothesis which forms the theoretical core of the nested grid dynamical numerical modelling system is described. The dynamical and numerical structure of the model used during the 1978 test period is presented and a preliminary description of a proposed multigrid system for future experiments and tests is provided. Six cases from the spring of 1978 are discussed to illustrate the model's performance and its problems. Potential solutions to the problems are examined.

Paine, D. A.↗
NASA NTRS1993

A regional analysis of cloudy mean spherical albedo over the marine stratocumulus region and the tropical Atlantic Ocean

Since clouds are the largest variable in Earth's radiation budget, it is critical to determine both the spatial and temporal characteristics of their radiative properties. The relationships between cloud properties and cloud fraction are studied in order to supplement grid scale parameterizations. The satellite data used is from three hourly ISCCP (International Satellite Cloud Climatology Project) and monthly ERBE (Earth Radiation Budget Experiment) data on a 2.5 deg x 2.5 deg latitude-longitude grid. Mean cloud spherical albedo, the mean optical depth distribution, and cloud fraction are examined and compared off the coast of California and the mid-tropical Atlantic for July 1987 and 1988. Individual grid boxes and spatial averages over several grid boxes are correlated to Coakley's theory of reflection for uniform and broken layered cloud and to Kedem, et al.'s findings that rainfall volume and fractional area of rain in convective systems is linear. Kedem's hypothesis can be expressed in terms of cloud properties. That is, the total volume of liquid in a box is a linear function of cloud fraction. Results for the marine stratocumulus regime indicate that albedo is often invariant for cloud fractions of 20% to 80%. Coakley's satellite model of small and large clouds with cores (1 km) and edges (100 m) is consistent with this observation. The cores maintain high liquid water concentrations and large droplets while the edges contain low liquid water concentrations and small droplets. Large clouds are just a collection of cores. The mean optical depth (TAU) distributions support the above observation with TAU values of 3.55 to 9.38 favored across all cloud fractions. From these results, a method based upon Kedem, et al's theory is proposed to separate the cloud fraction and liquid water path (LWP) calculations in a general circulation model (GCM). In terms of spatial averaging, a linear relationship between albedo and cloud fraction is observed. For tropical locations outside the Intertropical Convergence Zone (ITCZ), results of cloud fraction and albedo spatial averaging followed that of the stratus boxes containing few overcast scenes. Both the ideas of Coakley and Kedem, et al. apply. Within the ITCZ, the grid boxes tended to have the same statistical properties as stratus boxes containing many overcast scenes. Because different dynamical forcing mechanisms are present, it is difficult to devise a method for determining subgrid scale variations. Neither of the theories proposed by Kedem, et al. or Coakley works well for the boxes with numerous overcast scenes.

Ginger, Kathryn M.↗
NASA NTRSDate not supplied

Constraints on the Origin of Mercury’s Large Core from Core-Mantle Differentiation Models

Mercury’s core is notoriously large when compared to other planets of our solar system. The origin of this large core is still uncertain. Available data on the surface composition and internal structure of Mercury from the past MESSENGER mission and future data collected by BepiColombo will continue to provide clues to Mercury’s formation. Here, we present results combining experimental data on elemental distribution between core and mantle with spacecraft data, to estimate bulk Mercury composition. We applied this strategy to major elements (Fe, Si, Mg, Al and O), as well as minor elements (Cr and Ti), and compared derived compositions to chondritic data and the chemical compositions of the other terrestrial planets. Our results show that Mercury has a chemical composition significantly different from all known materials of the solar system. In addition, numerous scenarios were proposed to explain Mercury’s structure, including “chaotic models” such as giant impacts and “orderly models” such as aerodynamic sorting. Here, we tested whether Mercury’s composition can be explained by mantle stripping by impacts. We will show how such a scenario reconciles several features of Mercury’s geochemistry with chondritic data. We will also discuss the outlook of additional constraints from supplementary data potentially collected by BepiColombo.

Mercury↗
DOE OSTI2024

Picasso: Memory-Efficient Graph Coloring Using Palettes With Applications in Quantum Computing

A coloring of a graph is an assignment of colors to vertices such that no two neighboring vertices have the same color. The need for memory-efficient coloring algorithms is motivated by their application in computing clique partitions of graphs arising in quantum computations where the objective is to map a large set of Pauli strings into a compact set of unitaries. We present Picasso, a randomized memory-efficient iterative parallel graph coloring algorithm with theoretical sublinear space guarantees under practical assumptions. The parameters of our algorithm provide a trade-off between coloring quality and resource consumption. To assist the user, we also propose a machine learning model to predict the coloring algorithm’s parameters considering these trade-offs. We provide a sequential and a parallel implementation of the proposed algorithm. We perform an experimental evaluation on a 64-core AMD CPU equipped with 512 GB of memory and an Nvidia A100 GPU with 40GB of memory. For a small dataset where existing coloring algorithms can be executed within the 512 GB memory budget, we show up to 68× memory savings. On massive datasets we demonstrate that GPU-accelerated Picasso can process inputs with 49.5× more Pauli strings (vertex set in our graph) and 2,478× more edges than state-of-the-art parallel approaches.

artificial intelligence, quantum computing↗
NASA NTRS2008

Experimental Plans for Subsystems of a Shock Wave Driven Gas Core Reactor

This Contractor Report proposes a number of plans for experiments on subsystems of a shock wave driven pulsed magnetic induction gas core reactor (PMI-GCR, or PMD-GCR pulsed magnet driven gas core reactor). Computer models of shock generation and collision in a large-scale PMI-GCR shock tube have been performed. Based upon the simulation results a number of issues arose that can only be addressed adequately by capturing experimental data on high pressure (approx.1 atmosphere or greater) partial plasma shock wave effects in large bore shock tubes ( 10 cm radius). There are three main subsystems that are of immediate interest (for appraisal of the concept viability). These are (1) the shock generation in a high pressure gas using either a plasma thruster or pulsed high magnetic field, (2) collision of MHD or gas dynamic shocks, their interaction time, and collision pile-up region thickness, and (3) magnetic flux compression power generation (not included here).

Kazeminezhad, F.↗
NASA NTRS2012

Gravity, Topography, and Magnetic Field of Mercury from Messenger

On 18 March 2011, the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft was inserted into a 12-hour, near-polar orbit around Mercury, with an initial periapsis altitude of 200 km, initial periapse latitude of 60 deg N, and apoapsis at approximately 15,200 km altitude in the southern hemisphere. This orbit has permitted the mapping of regional gravitational structure in the northern hemisphere, and laser altimetry from the MESSENGER spacecraft has yielded a geodetically controlled elevation model for the same hemisphere. The shape of a planet combined with gravity provides fundamental information regarding its internal structure and geologic and thermal evolution. Elevations in the northern hemisphere exhibit a unimodal distribution with a dynamic range of 9.63 km, less than that of the Moon (19.9 km), but consistent with Mercury's higher surface gravitational acceleration. After one Earth-year in orbit, refined models of gravity and topography have revealed several large positive gravity anomalies that coincide with major impact basins. These candidate mascons have anomalies that exceed 100 mGal and indicate substantial crustal thinning and superisostatic uplift of underlying mantle. An additional uncompensated 1000-km-diameter gravity and topographic high at 68 deg N, 33 deg E lies within Mercury's northern volcanic plains. Mercury's northern hemisphere crust is generally thicker at low latitudes than in the polar region. The low-degree gravity field, combined with planetary spin parameters, yields the moment of inertia C/MR2 = 0.353 +/- 0.017, where M=3.30 x 10(exp 23) kg and R=2440 km are Mercury's mass and radius, and a ratio of the moment of inertia of Mercury's solid outer shell to that of the planet of Cm/C = 0.452 +/- 0.035. One proposed model for Mercury's radial density distribution consistent with these results includes silicate crust and mantle layers overlying a dense solid (possibly Fe-S) layer, a liquid Fe-rich outer core of radius 2030 +/- 37 km, and an assumed solid inner core. Magnetic field measurements indicate a northward offset of Mercury's axial magnetic dipole from the geographic equator by 479 +/-3 km and provide evidence for a regional-scale magnetic field approximately collocated with the northern volcanic plains of possible crustal origin. These results from MESSENGER indicate a complex and asymmetric evolution of internal structure and dynamics in this end-member inner planet.

Neumann, Gregory A.↗
NASA NTRS1997

Structure of an anti-HIV-1 hammerhead ribozyme complex with a 17-mer DNA substrate analog of HIV-1 gag RNA and a mechanism for the cleavage reaction: 750 MHz NMR and computer experiments

The structure of an anti-HIV-1 ribozyme-DNA abortive substrate complex was investigated by 750 MHz NMR and computer modeling experiments. The ribozyme was a chimeric molecule with 30 residues-18 DNA nucleotides, and 12 RNA residues in the conserved core. The DNA substrate analog had 17 residues. The chimeric ribozyme and the DNA substrate formed a shortened ribozyme-abortive substrate complex of 47 nucleotides with two DNA stems (stems I and III) and a loop consisting of the conserved core residues. Circular dichroism spectra showed that the DNA stems assume A-family conformation at the NMR concentration and a temperature of 15 degrees C, contrary to the conventional wisdom that DNA duplexes in aqueous solution populate entirely in the B-form. It is proposed that the A-family RNA residues at the core expand the A-family initiated at the core into the DNA stems because of the large free energy requirement for the formation of A/B junctions. Assignments of the base H8/H6 protons and H1' of the 47 residues were made by a NOESY walk. In addition to the methyl groups of all T's, the imino resonances of stems I and III and AH2's were assigned from appropriate NOESY walks. The extracted NMR data along with available crystallographic data, were used to derive a structural model of the complex. Stems I and III of the final model displayed a remarkable similarity to the A form of DNA; in stem III, a GC base pair was found to be moving into the floor of the minor groove defined by flanking AT pairs; data suggest the formation of a buckled rhombic structure with the adjacent pair; in addition, the base pair at the interface of stem III and the loop region displayed deformed geometry. The loop with the catalytic core, and the immediate region of the stems displayed conformational multiplicity within the NMR time scale. A catalytic mechanism for ribozyme action based on the derived structure, and consistent with biochemical data in the literature, is proposed. The complex between the anti HIV-1 gag ribozyme and its abortive DNA substrate manifests in the detection of a continuous track of A.T base pairs; this suggests that the interaction between the ribozyme and its DNA substrate is stronger than the one observed in the case of the free ribozyme where the bases in stem I and stem III regions interact strongly with the ribozyme core region (Sarma, R. H., et al. FEBS Letters 375, 317-23, 1995). The complex formation provides certain guidelines in the design of suitable therapeutic ribozymes. If the residues in the ribozyme stem regions interact with the conserved core, it may either prevent or interfere with the formation of a catalytically active tertiary structure.

NASA Discipline Exobiology↗
NASA NTRSDate not supplied

Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗
NASA NTRS1996

Stability of Wavy Films in Gas-Liquid Two-Phase Flows at Normal and Microgravity Conditions

For flow rates of technological interest, most gas-liquid flows in pipes are in the annular flow regime, in which, the liquid moves along the pipe wall in a thin, wavy film and the gas flows in the core region. The waves appearing on the liquid film have a profound influence on the transfer rates, and hence on the design of these systems. We have recently proposed and analyzed two boundary layer models that describe the characteristics of laminar wavy films at high Reynolds numbers (300-1200). Comparison of model predictions to 1-g experimental data showed good agreement. The goal of our present work is to understand through a combined program of experimental and modeling studies the characteristics of wavy films in annular two-phase gas-liquid flows under normal as well as microgravity conditions in the developed and entry regions.

Balakotaiah, V.↗
NASA NTRSDate not supplied

TriTruss Packaging and Deployment Trade Study

An architecture and feasibility study of next generation In-Space Assembled Telescopes (iSAT) concluded that robotic in-space assembly of modular components is necessary to enable large (>15-meter diameter) primary apertures. The iSAT study recommended that the foundational structure be assembled from modular TriTruss modules that are packaged for launch, deployed on-orbit and robotically assembled into the final configuration. This paper will describe and summarize the results of a trade study that investigated viable concept of operations (ConOps) for the packaging and deployment (P&D) of individual planar TriTruss modules that could be assembled to form a large aperture iSAT. The ideal TriTruss P&D concept is defined as one that: allows for efficient packaging; has sufficient geometric versatility to be launch vehicle independent; provides a stiff and lightweight structure; has low mechanical complexity; and has component modularity. The P&D concept should allow for prelaunch subsystem or utility integration if required. The concept would be kinematically simple and be robotically deployed using a minimum number of specialized tools. In this first phase of an ongoing more comprehensive trade study, concepts were proposed and then evaluated based on initial metrics representing features of an ideal P&D concept. The P&D concepts evaluated are categorized as: core collapse, face collapse, and erectable structures. Sub-scale models were constructed to help understand the kinematics and mechanical complexity required to enable P&D. Based on a weighting scale, the most promising candidate P&D concepts have selected and will undergo more rigorous structural design, analysis, and testing in the study’s next phase. The ultimate goal of the comprehensive trade study will be to recommend a single TriTruss design and associated P&D concept that will be built and evaluated at NASA Langley Research Center’s In-Space Assembly Laboratory.

in-space assembly (ISA)↗
NASA NTRS2012

Structural Analysis and Optimization of a Composite Fan Blade for Future Aircraft Engine

This report addresses the structural analysis and optimization of a composite fan blade sized for a large aircraft engine. An existing baseline solid metallic fan blade was used as a starting point to develop a hybrid honeycomb sandwich construction with a polymer matrix composite face sheet and honeycomb aluminum core replacing the original baseline solid metallic fan model made of titanium. The focus of this work is to design the sandwich composite blade with the optimum number of plies for the face sheet that will withstand the combined pressure and centrifugal loads while the constraints are satisfied and the baseline aerodynamic and geometric parameters are maintained. To satisfy the requirements, a sandwich construction for the blade is proposed with composite face sheets and a weak core made of honeycomb aluminum material. For aerodynamic considerations, the thickness of the core is optimized whereas the overall blade thickness is held fixed so as to not alter the original airfoil geometry. Weight is taken as the objective function to be minimized by varying the core thickness of the blade within specified upper and lower bounds. Constraints are imposed on radial displacement limitations and ply failure strength. From the optimum design, the minimum number of plies, which will not fail, is back-calculated. The ply lay-up of the blade is adjusted from the calculated number of plies and final structural analysis is performed. Analyses were carried out by utilizing the OpenMDAO Framework, developed at NASA Glenn Research Center combining optimization with structural assessment.

Coroneos, Rula M.↗
NASA NTRS2013

Advancements in Spacecraft Brine Water Recovery: Development of a Radial Vaned Capillary Drying Tray

Technology improvements in the recovery of water from brine are critical to establishing closedloop water recovery systems, enabling long duration missions, and achieving a sustained human presence in space. A genre of 'in-place drying' brine water recovery concepts, collectively referred to herein as Brine Residual In-Containment (BRIC), are under development which aim to increase the overall robustness and reliability of the brine recovery process by performing drying inside the container used for final disposal of the solid residual waste. Implementation of in-place drying techniques have been demonstrated for applications where gravity is present and phase separation occurs naturally by buoyancy induced effects. In this work, a microgravity compatible analogue of the gravity-driven phase separation process is considered by exploiting capillarity in the form of surface wetting, surface tension, and container geometry. The proposed design consists of a series of planar radial vanes aligned about a central slotted core. Preliminary testing of the fundamental geometry in a reduced gravity environment has shown the device to spontaneously fill and saturate rapidly creating a free surface from which evaporation and phase separation can occur similar to a 1-g like 'cylindrical pool' of fluid. Mathematical modeling and analysis of the design suggest predictable rates of filling and stability of fluid containment as a function of relevant system dimensions, e.g., number of vanes, vane length, width, and thickness. A description of the proposed capillary design solution is presented along with preliminary results from testing, modeling and analysis of the system.

Callahan, Michael R.↗
NASA NTRS1976

Pressure and velocity in a developing coaxial jet

Determinations of static pressure, mean velocity and turbulence intensity in the developing region of coaxial jets are presented. Detailed profiles were obtained at twelve axial locations (extending from the nozzle exit for a distance of 5 diameters) downstream from a single element of the Bell Aerospace H2/O2 19-element coaxial injector. Measurements of mass-flux per unit area (using a constant temperature anemometer), total pressure and local temperature were used in the determination of local static pressure and velocity. These data show a low pressure region exists near the nozzle exit. Although this pressure reduction is small (0.34 psi), it substantially altered the flow development. Comparison of results shows that velocity near the nozzle exit decreases initially (no central velocity core) as a result of both pressure gradients and viscous mixing. These data are compared with analytical predictions made using available computer codes. Results show the need to consider pressure effects in any proposed mathematical model.

Moon, L. F.↗