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At least 559 records · Page 31

Parahydrogen Properties Version 05 Database Release for Nuclear Thermal Propulsion Applications

Consistent modeling assumptions across any large project are crucial to minimize errors between different approaches. Use of consistent material and fluid properties across a large project supports consistent interpretation and application within modeling and simulation results as well as their relevancy to operational systems. NASA’s Space Nuclear Propulsion program dedicates extensive resources towards establishing consistent and, to the extent possible, accurate property databases for its internal staff and all external partners. This work highlights the extensive research performed to modernize the fluid property database of hydrogen which is the leading propellant option for in-space nuclear propelled spacecraft. Specifically, the parahydrogen spin state is of interest since the propellant is stored in a near normal boiling point liquid state which results in it consisting almost entirely of the parahydrogen spin isomer. This database tool has taken recent NASA work and modernized it into a python-based package for easy usage across all modeling entities. The package allows users to provide temperature and pressure pairs along with their desired output properties to yield results accounting for both real-gas and equilibrium dissociation effects while also sharing the default thermodynamic reference state provided by the National Institute of Standards and Technology (NIST) Standard Database 23. The suite also includes advanced capabilities to increase usability, such as on-the-fly interpolation and multidimensional plotting.

Nuclear Thermal Propulsion↗

Parahydrogen Properties Version 05 Database Release for NTP Applications

Consistent modeling assumptions across any large project are crucial to minimize errors between different approaches. Use of consistent material and fluid properties across a large project supports consistent interpretation and application within modeling and simulation results as well as their relevancy to operational systems. NASA’s Space Nuclear Propulsion program dedicates extensive resources towards establishing consistent and, to the extent possible, accurate property databases for its internal staff and all external partners. This work highlights the extensive research performed to modernize the fluid property database of hydrogen which is the leading propellant option for in-space nuclear propelled spacecraft. Specifically, the parahydrogen spin state is of interest since the propellant is stored in a near normal boiling point liquid state which results in it consisting almost entirely of the parahydrogen spin isomer. This database tool has taken recent NASA work and modernized it into a python-based package for easy usage across all modeling entities. The package allows users to provide temperature and pressure pairs along with their desired output properties to yield results accounting for both real-gas and equilibrium dissociation effects while also sharing the default thermodynamic reference state provided by the National Institute of Standards and Technology (NIST) Standard Database 23. The suite also includes advanced capabilities to increase usability, such as on-the-fly interpolation and multidimensional plotting.

Nuclear Thermal Propulsion↗

Turbulence modeling for separated flow

Two projects are described in this report. The first involves assessing turbulence models in separated flow. The second addresses the anomalous behavior of certain turbulence models in stagnation point flow. The primary motivation for developing turbulent transport models is to provide tools for computing non-equilibrium, or complex, turbulent flows. Simple flows can be analyzed using data correlations or algebraic eddy viscosities, but in more complicated flows such as a massively separated boundary layer, a more elaborate level of modeling is required. It is widely believed that at least a two-equation transport model is required in such cases. The transport equations determine the evolution of suitable velocity and time-scales of the turbulence. The present study included assessment of second-moment closures in several separated flows, including sharp edge separation; smooth wall, pressure driven separation; and unsteady vortex shedding. Flows with mean swirl are of interest for their role in enhancing mixing both by turbulent and mean motion. The swirl can have a stabilizing effect on the turbulence. An axi-symmetric extension to the INS-2D computer program was written adding the capability of computing swirling flow. High swirl can produce vortex breakdown on the centerline of the jet and it occurs in various combustors.

Durbin, Paul A.↗

Thermal Electron Heat Fluxes Associated with Precipitated Auroral Electrons During the Saint Patrick's Days 2013 and 2015 Geomagnetic Storms

The Rice Convection Model-Equilibrium (RCM-E) and SuperThermal Electron Transport (STET) are combined to investigate electron heat flux formation in the region of the diffuse aurora for the geomagnetic storms of 17 March 2013 and 17 March 2015. The primary electron precipitation into the atmosphere resulting from wave particle scattering in the magnetosphere are simulated by the magnetically and electrically RCM-E during these two geomagnetic storms. The primary precipitating electron fluxes are modified by the STET model by taking into account atmospheric backscatter processes. The modified electron energy fluxes and their mean energies are coupled to the STET code to calculate electron thermal fluxes associated with diffuse aurora on a global scale. We use the simulated heat flux to estimate electron temperatures at the upper ionospheric altitudes and compare them with corresponding observations from the Defense Meteorological Satellite Program satellite.

George V. Khazanov↗

Quantifying the Impact of Metal Population Distribution in MFI-Supported Mo Catalysts for Methane Dehydroaromatization

Precise evaluation of intrinsic kinetic behavior in Mo/MFI catalysts for methane dehydroaromatization (MDA) is confounded by variations in Mo dispersion and speciation, which are influenced by metal loading and zeolite acidity. This work advances the utility of H 2 -temperature programmed reduction (H 2 -TPR) for characterizing Mo/MFI catalysts by enabling quantitative comparison of MoO x populations distinguished by reduction behavior and linked to initial catalytic performance. A comprehensive H 2 reduction pathway is established through systematic H 2 - TPR studies varying catalyst composition (1–10 wt % Mo, Si/Al = 15, 40, ∞), supplemented by UV-Raman spectroscopy, X-ray powder diffraction, N 2 physisorption, NH 3 -TPD, and advanced spectroscopic analysis (in situ XAS with principal component analysis/multivariate curve resolution—alternating least squares). Two low-temperature H 2 -TPR regions capture distinct Mo populations undergoing initial Mo(VI)→Mo(IV) reduction: a lower-temperature population (Mo-RI) associated primarily with highly dispersed, anchored MoO x species expected to predominantly reside within MFI channels, and a higher-temperature population (Mo-RII) corresponding to a broader set of MoO x species that becomes increasingly bulk-like/extrazeolitic at higher Mo loading. Quantification of these populations provides practical, kinetically relevant descriptors for comparing initial MDA rates across catalysts with varying Mo loading, Si/Al ratio, and MoO x heterogeneity. Application of lower-temperature Mo-RI estimates to kinetic measurements reveals a minimum threshold of ∼0.12 × 10 –3 mol Mo-RI/g cat , above which initial forward benzene rates normalized to this population converge despite differences in metal loading and zeolite Brønsted acidity. This threshold coincides with a transition toward a common C 2 -mediated benzene-forming regime, as indicated by approach-to-equilibrium analysis of methane-to-ethane, ethane-to-ethylene, and ethylene-to-benzene reaction steps. Above this threshold, normalized initial benzene rates are nearly invariant with increasing Mo-RII/Mo-RI population ratio, indicating that excess Mo-RII populations, including bulk-like/extrazeolitic MoO x domains present at higher loading, do not measurably suppress benzene formation associated with anchored and mostly channel-confined Mo population under the initial-rate conditions examined.

Mo/MFI↗

Development of Low Density Titanium Alloys for Structural Applications

In this report the results of a program designed to reduce the density of titanium by adding magnesium are presented. Because these two elements are immiscible under conventional ingot metallurgy techniques, two specialized powder metallurgy methods namely, mechanical alloying (MA) and physical vapor deposition (PVD) were implemented. The mechanical alloying experiments were done both at the University of Idaho and at the Defense Research Agency in UK. Since titanium is reactive with interstitial elements, a secondary goal of this research was to correlate solubility extensions with interstitial contamination content, especially oxygen and nitrogen. MA was carried out in SPEX 8000 shaker mils and different milling containers were utilized to control the level of contamination. Results showed that solubilities of Mg in Ti were obtained up to 28 at.% (16.4 wt. %) Mg in Ti for Ti-39.6 at. % (25 wt. %) Mg alloys, which greatly exceed those obtained under equilibrium conditions. This reflects a density reduction of approximately 26 %. Contamination of oxygen and nitrogen seemed to increase the solubility of magnesium in titanium in some cases; however, we were not able to make a clear correlation between contamination levels with solubilities. Work at the DRA has emphasized optimization of present PVD equipment, specifically composition and temperature control. Preliminary PVD data has shown Ti-Mg deposits have successfully been made up to 2 mm thick and that solubility extensions were achieved. The potential for density reduction of titanium by alloying with magnesium has been demonstrated; however, this work has only scratched the surface of the development of such low density alloys. Much research is needed before such alloys could be implemented into industry. Further funding is required in order to optimize the MA/PVD processes including contamination control, determination of optimal alloy compositions, microstructure development, and mechanical property determination.

Froes, F. H.↗

GRO: Black hole models for gamma-ray bursts

The Burst and Transient Source Experiment (BATSE) on board the Compton Gamma Ray Observatory (CGRO) has established that the distribution of gamma-ray bursts (GRB's) is isotropic but is bound radially. This finding suggests that the bursts are either cosmological or they originate from an extended Galactic halo. The implied luminosities and the observed variability of the GRB's on time scales as short as one millisecond suggest that they originate from compact objects. We are presently studying black hole models for GRB's. Any such model must produce a non-thermal photon spectrum to agree with the observed properties. For a wide range of burst parameters the assumed bursting source consists of a non-thermal electron-positron-photon plasma of very high density. It seems possible to produce such a plasma in accretion onto black holes. In our on-going work, we are developing the kinetic theory for a non-equilibrium pair plasma. The main new features of our work are as follows: (1) We do not assume the presence of a thermal electron bath. (2) Non-thermal, high-energy pairs are allowed to have an arbitrary concentration and energy distribution. (3) There is no soft photon source in our model; initially all the photons in the plasma are either energetic X-rays or gamma-rays. (4) The initial energy distribution of the pairs as well as photons is arbitrary. (5) We collect the analytical expressions for the kinetic kernels for all relevant processes. And (6) we present a different approach to finding the time-evolution of pair and photon spectra, which is a combination of the kinetic-theory and the non-linear Monte-Carlo schemes. We have developed many Monte-Carlo programs to model various process, to take into account the time evolution, and to incorporate various physical effects which are unique to non-thermal plasmas. The hydrodynamics of fireballs in GRB's was studied before. Applying results from kinetic theory will improve our understanding of these systems.

Ruderman, Malvin↗

High Pressure, Earth-storable Rocket Technology

The effect of elevated chamber pressure on combustion efficiency and heat transfer has been determined at the 100 lbf (445 N) thrust level for nitrogen tetroxide propellants. Measurements were made up to 500 psia (3.45 Mpa) with testbed hardware; tests at 100 psia (0.690 MPa) and 250 psia (1.72 MPa) were made with radiation-cooled rhenium chambers. The first task of the program served to determine desirable thruster applications and operating conditions: high total impulse, i.e. communication satellite or spacecraft bus axial engines, at chamber pressures up to 250 psia (1.72 MPa) pressure-fed, or up to 500 psia (3.45 MPa) pump-fed. The hardware modifications and testing required to obtain the data were determined in Task 2, which included design-support hot fire tests; supplemental hardware, including a 250 psia (1.72 MPa) Pc rhenium chamber and a 20% fuel-film cooled platelet injector was fabricated in Task 3. Testing showed that satisfactory operation of Ir-Re radiation chambers is assured at pressures up to 250 psia and may be possible up to 500. The heat transfer data obtained show good correlation with throat Reynolds number and are generally under values given by the simplified Bartz equation; chambers equilibrium temperatures match predicted values. Preliminary optimization of trip configuration and mixture ratio were made; Isp performance from thrust measurements was within 1% of predicted values. Stability, compatibility, and front-end thermal management were determined to be satisfactory.

Jassowski, D. M.↗

High Pressure, Earth-storable Rocket Technology

The effect of elevated chamber pressure on combustion efficiency and heat transfer has been determined at the 100 lbf (445 N) thrust level for nitrogen tetroxide propellants. Measurements were made up to 500 psia (3.45 MPa) with testbed hardware; tests at 100 psia (0.690 MPa) and 250 psia (1.72 MPa) were made with radiation-cooled rhenium chambers. The first task of the program served to determine desirable thruster applications and operating conditions: high total impulse, i.e., communication satellite or spacecraft bus axial engines, at chamber pressures up to 250 psia (1.72 MPa) pressure-fed, or up to 500 psia (3.45 MPa) pump-fed. The hardware modifications and testing required to obtain the data were determined in Task 2, which included design-support hot fire tests; supplemental hardware, including a 250 psia (1.72 MPa) Pc rhenium chamber and a 20% fuel-film cooled platelet injector was fabricated in Task 3. Testing showed that satisfactory operation of Ir-Re radiation chambers is assured at pressures up to 250 psia and may be possible up to 500. The heat transfer data obtained show good correlation with throat Reynolds number and are generally under values given by the simplified Bartz equation; chambers equilibrium temperatures match predicted values. Preliminary optimization of trip configuration and mixture ratio were made; Isp performance from thrust measurements was within 1% of predicted values. Stability, compatibility, and front-end thermal management were determined to be satisfactory.

Jassowski, D. M.↗

High Pressure, Earth-Storable Rocket Technology: Appendices C and D - Volume 3

The effect of elevated chamber pressure on combustion efficiency and heat transfer has been determined at the 100 lbf (445 N) thrust level for nitrogen tetroxide propellants. Measurements were made up to 500 psia (3.45 MPa) with testbed hardware; tests at 100 psia (0.690 MPa) and 250 psia (1.72 MPa) were made with radiation-cooled rhenium chambers. The first task of the program served to determine desirable thruster applications and operating conditions: high total impulse, i.e. communication satellite or spacecraft bus axial engines, at chamber pressures up to 250 psia (1.72 MPa) pressure-fed, or up to 500 psia (3.45 MPa) pump-fed. The hardware modifications and testing required to obtain the data were determined in Task 2, which included design-support hot fire tests; supplemental hardware, including a 250 psia (1.72 MPa) Pc rhenium chamber and a 20% fuel-film cooled platelet injector was fabricated in Task 3. Testing showed that satisfactory operation of Ir-Re radiation chambers is assured at pressures up to 250 psia and may be possible up to 500. The heat transfer data obtained show good correlation with throat Reynolds number and are generally under values given by the simplified Bartz equation; chambers equilibrium temperatures match predicted values. Preliminary optimization of trip configuration and mixture ratio were made; Isp performance from thrust measurements was within 1% of predicted values. Stability, compatibility, and front-end thermal management were determined to be satisfactory.

Jassowski, D. M.↗

Data from: Ecosystem carbon exchange on conversion of Conservation Reserve Program grasslands to annual and perennial cropping systems

Land use changes into and out of agricultural production may substantially influence ecosystem carbon (C) balance for many years. We examined ecosystem C balances for eight years after the conversion of 22 year-old Conservation Reserve Program (CRP) grasslands and formerly tilled agricultural fields (AGR) to annual (continuous no-till corn) and perennial (switchgrass and restored prairie) cropland. An unconverted CRP field (CRP-Ref) was maintained as a historical reference. Ecosystem C balance was assessed using adjusted net ecosystem carbon exchange (NEEadj) calculated by adding C removed in harvested biomass to NEE measured using eddy covariance method. The cumulative NEEadj of the corn and perennial systems on former CRP fields showed that these systems were a net C source to the atmosphere over the 8-year period while on former AGR fields, the perennial systems were net C sinks and the corn system near-neutral. The CRP-Ref was near neutral until a drought year when it became a net source. The corn system on the CRP field will likely reach a new lower soil C equilibrium at least 14 years after conversion but will never regain the C lost upon conversion under current no-till management with residue partially removed. On the other hand, the perennial systems could fully regain in ~14 years the C lost following conversion. The cumulative NEEadj of the corn systems exhibited a higher C emission than did the perennial systems within the same land use histories, reflecting the dominant role of crop type and management in agricultural ecosystem C balance. Results suggest that converting croplands to grasslands results in immediate C gains whereas converting grasslands to croplands results in permanent (no-till corn with partial residue removal) or temporary (perennial herbaceous crops) net C loss to the atmosphere. This has a significant implications for global climate change mitigation where biomass production from annual and perennial crops is promoted to avoid fossil-fuel C emissions (biofuel) or to remove CO2 from the atmosphere (bioenergy C capture and storage).

54 ENVIRONMENTAL SCIENCES↗

Water uptake by growing cells: an assessment of the controlling roles of wall relaxation, solute uptake, and hydraulic conductance

Growing plant cells increase in volume principally by water uptake into the vacuole. There are only three general mechanisms by which a cell can modulate the process of water uptake: (a) by relaxing wall stress to reduce cell turgor pressure (thereby reducing cell water potential), (b) by modifying the solute content of the cell or its surroundings (likewise affecting water potential), and (c) by changing the hydraulic conductance of the water uptake pathway (this works only for cells remote from water potential equilibrium). Recent studies supporting each of these potential mechanisms are reviewed and critically assessed. The importance of solute uptake and hydraulic conductance is advocated by some recent studies, but the evidence is indirect and conclusions remain controversial. For most growing plant cells with substantial turgor pressure, it appears that reduction in cell turgor pressure, as a consequence of wall relaxation, serves as the major initiator and control point for plant cell enlargement. Two views of wall relaxation as a viscoelastic or a chemorheological process are compared and distinguished.

Non-NASA Center↗

Three CLIPS-based expert systems for solving engineering problems

We have written three expert systems, using the CLIPS PC-based expert system shell. These three expert systems are rule based and are relatively small, with the largest containing slightly less than 200 rules. The first expert system is an expert assistant that was written to help users of the ASPEN computer code choose the proper thermodynamic package to use with their particular vapor-liquid equilibrium problem. The second expert system was designed to help petroleum engineers choose the proper enhanced oil recovery method to be used with a given reservoir. The effectiveness of each technique is highly dependent upon the reservoir conditions. The third expert system is a combination consultant and control system. This system was designed specifically for silicon carbide whisker growth. Silicon carbide whiskers are an extremely strong product used to make ceramic and metal composites. The manufacture of whiskers is a very complicated process. which to date. has defied a good mathematical model. The process was run by experts who had gained their expertise by trial and error. A system of rules was devised by these experts both for procedure setup and for the process control. In this paper we discuss the three problem areas of the design, development and evaluation of the CLIPS-based programs.

Parkinson, W. J.↗

A Novel Approach for Modeling Chemical Reaction in Generalized Fluid System Simulation Program

The Generalized Fluid System Simulation Program (GFSSP) is a computer code developed at NASA Marshall Space Flight Center for analyzing steady state and transient flow rates, pressures, temperatures, and concentrations in a complex flow network. The code, which performs system level simulation, can handle compressible and incompressible flows as well as phase change and mixture thermodynamics. Thermodynamic and thermophysical property programs, GASP, WASP and GASPAK provide the necessary data for fluids such as helium, methane, neon, nitrogen, carbon monoxide, oxygen, argon, carbon dioxide, fluorine, hydrogen, water, a hydrogen, isobutane, butane, deuterium, ethane, ethylene, hydrogen sulfide, krypton, propane, xenon, several refrigerants, nitrogen trifluoride and ammonia. The program which was developed out of need for an easy to use system level simulation tool for complex flow networks, has been used for the following purposes to name a few: Space Shuttle Main Engine (SSME) High Pressure Oxidizer Turbopump Secondary Flow Circuits, Axial Thrust Balance of the Fastrac Engine Turbopump, Pressurized Propellant Feed System for the Propulsion Test Article at Stennis Space Center, X-34 Main Propulsion System, X-33 Reaction Control System and Thermal Protection System, and International Space Station Environmental Control and Life Support System design. There has been an increasing demand for implementing a combustion simulation capability into GFSSP in order to increase its system level simulation capability of a liquid rocket propulsion system starting from the propellant tanks up to the thruster nozzle for spacecraft as well as launch vehicles. The present work was undertaken for addressing this need. The chemical equilibrium equations derived from the second law of thermodynamics and the energy conservation equation derived from the first law of thermodynamics are solved simultaneously by a Newton-Raphson method. The numerical scheme was implemented as a User Subroutine in GFSSP.

Sozen, Mehmet↗

Structural Fluctuations and Thermophysical Properties of Molten II-VI Compounds

The objectives of the project are to conduct ground-based experimental and theoretical research on the structural fluctuations and thermophysical properties of molten II-VI compounds to enhance the basic understanding of the existing flight experiments in microgravity materials science programs as well as to study the fundamental heterophase fluctuation phenomena in these melts by: 1) conducting neutron scattering analysis and measuring quantitatively the relevant thermophysical properties of the II-VI melts (such as viscosity, electrical conductivity, thermal diffusivity and density) as well as the relaxation characteristics of these properties to advance the understanding of the structural properties and the relaxation phenomena in these melts and 2) performing theoretical analyses on the melt systems to interpret the experimental results. All the facilities required for the experimental measurements have been procured, installed and tested. Thermal diffusivity of molten tellurium has been measured by a laser flash method in the temperature range of 500 C to 900 C. The measured diffusivity as a function of temperature agrees fairly well with published data. However, a relaxation phenomenon, which shows a slow drift of the measured thermal conductivity toward the equilibrium value after cooling of the melt, was observed for the first time. An apparatus based on the transient torque induced by a rotating magnetic field has been developed to determine the viscosity and electrical conductivity of semiconducting liquids. Viscosity measurements on molten tellurium showed a similar relaxation behavior to the measured diffusivity. The density and volume expansion coefficients for pure Te and HgTe melts were measured as a function of temperature using a pycnometric method. A density maximum was found for both melts but no relaxation behavior was observed. Neutron scattering experiments were performed on the HgTe and HgZnTe melts and the results on pair distribution showed better resolution than previously reported. A simple kinetic theory, which contains the formation reactions of Te polymerization that increases the molecular weight, was proposed to interpret the relaxation behavior of HgZnTe viscosity data.

Su, Ching-Hua↗

Energetic Metastable Oxygen and Nitrogen Atoms in the Terrestrial Atmosphere

This report summarizes our research performed under NASA Grant NAG5-11857. The three-year grant have been supported by the Geospace Sciences SR&T program. We have investigated the energetic metastable oxygen and nitrogen atoms in the terrestrial stratosphere, mesosphere and thermosphere. Hot atoms in the atmosphere are produced by solar radiation, the solar wind and various ionic reactions. Nascent hot atoms arise in ground and excited electronic states, and their translational energies are larger by two - three orders of magnitude than the thermal energies of the ambient gas. The relaxation kinetics of hot atoms determines the rate of atmospheric heating, the intensities of aeronomic reactions, and the rate of atom escape from the planet. Modeling of the non-Maxwellian energy distributions of metastable oxygen and nitrogen atoms have been focused on the determination of their impact on the energetics and chemistry of the terrestrial atmosphere between 25 and 250 km . At this altitudes, we have calculated the energy distribution functions of metastable O and N atoms and computed non-equilibrium rates of important aeronomic reactions, such as destruction of the water molecules by O(1D) atoms and production of highly excited nitric oxide molecules. In the upper atmosphere, the metastable O(lD) and N(2D) play important role in formation of the upward atomic fluxes. We have computed the upward fluxes of the metastable and ground state oxygen atoms in the upper atmosphere above 250 km. The accurate distributions of the metastable atoms have been evaluated for the day and night-time conditions.

Kharchenko, Vasili↗

Community Based Data of Uranium Adsorption onto Quartz

This data upload includes a compilation of experiments for quantifying uranium adsorption onto quartz. The provided .csv file has been compiled from the literature in a findable, accessible, interoperable, reusable (FAIR) data format. This was accomplished using the Lawrence Livermore National Laboratory Surface Complexation Database Converter (SCDC) code written in the R programming language (free licensing available at https://ipo.llnl.gov/technologies/software/llnl-surface-complexation-database-converter-scdc). This constitutes all current data compiled on uranium-quartz interactions in the L-SCIE (LLNL Surface Complexation/Ion Exchange) database (as of 02/28/2022). This data was used to develop surface complexation models that fit the global community dataset (https://doi.org/10.1021/acs.est.1c07109). The FAIR-formatted dataset also enables the implementation of alternative machine-learning approaches that can be explored in the future.

54 ENVIRONMENTAL SCIENCES↗

Users manual for updated computer code for axial-flow compressor conceptual design

An existing computer code that determines the flow path for an axial-flow compressor either for a given number of stages or for a given overall pressure ratio was modified for use in air-breathing engine conceptual design studies. This code uses a rapid approximate design methodology that is based on isentropic simple radial equilibrium. Calculations are performed at constant-span-fraction locations from tip to hub. Energy addition per stage is controlled by specifying the maximum allowable values for several aerodynamic design parameters. New modeling was introduced to the code to overcome perceived limitations. Specific changes included variable rather than constant tip radius, flow path inclination added to the continuity equation, input of mass flow rate directly rather than indirectly as inlet axial velocity, solution for the exact value of overall pressure ratio rather than for any value that met or exceeded it, and internal computation of efficiency rather than the use of input values. The modified code was shown to be capable of computing efficiencies that are compatible with those of five multistage compressors and one fan that were tested experimentally. This report serves as a users manual for the revised code, Compressor Spanline Analysis (CSPAN). The modeling modifications, including two internal loss correlations, are presented. Program input and output are described. A sample case for a multistage compressor is included.

Glassman, Arthur J.↗