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NASA NTRS2000

A Tool for Automatic Data Distribution for CFD Applications on Structured Grids

Development of HPF versions of NPB and ARC3D has shown that HPF provides an efficient, concise way to express parallelism and to organize data traffic. The use of HPF, as noted in the papers, requires an intimate knowledge of the applications and a detailed analysis of data affinity, data movement, and data granularity. To simplify and accelerate the task of developing HPF versions of existing CFD applications we have designed and implemented ADAPT (Automatic Data Alignment and Placement Tool). ADAPT analyzes a CFD application working on a single structured grid and generates HPF TEMPLATE, (RE)DISTRIBUTION, ALIGNMENT, and INDEPENDENT directives. The directives can be generated on the nest level, subroutine level, application level, or on the application interface level. ADAPT annotates an existing CFD FORTRAN application, performing computations on single or multiple grids. On each grid the application is considered as a sequence of operators, each applied to a set of variables defined in a particular grid domain. ADAPT automatically detects implicit operators (i.e., having data dependences) and explicit operators (without data dependences). For parallelization of an explicit operator ADAPT creates a template for the operator domain, aligns arrays used in the operator with the template, distributes the template, and declares the loops over the distributed dimensions as INDEPENDENT. For parallelization of an implicit operator, the distribution of the operator's domain should be consistent with the operator's dependences. Any dependence between sections distributed on different processors would preclude parallelization if the compiler does not have an ability to pipeline computations. If a data distribution is "orthogonal" to the dependences of an implicit operator, then the loop which implements the operator can be declared as INDEPENDENT. ADAPT starts with an analysis of array index expressions of the loop nests. For each pair of arrays referenced in an assignment statement, it generates an arc in the alignment graph and annotates it with an affinity relation. The template, alignment, and distribution directives for a particular loop nest are then derived from a transitive closure of the affinity relation. A compromise of data distributions in different nests and subroutines is achieved by merging annotated alignment graphs for adjacent nests/stibroutine calls in the nest/call graph of the application in the process called distribution lifting. ADAPT has been implemented as a C++ program running in conjunction with a parallelization tool called CAPTools. ADAPT uses the parse tree, interprocedural analysis and application database generated by CAPTools. It also uses the Directed Graph class, initially implemented in p2d2 (parallel debugger oi distributed programs), and some other classes supporting symbolic computations. ADAPT uses data distribution techniques described. ADAPT was tested with ARC3D and the FT benchmark and has demonstrated a code performance within a factor of 1.5 of handwritten versions.

Frumkin, Michael↗

NASA NTRS1994

Automated Performance Prediction of Message Passing Parallel Programs

As the trend toward massively parallel processing continues, the need for tools that can predict scalability trends becomes greater. While high level languages Eke HPF have come into greater use, explicit message-passing programs proliferate, and will probably do so for some time, thanks to the onslaught of standards such as MPI. Much work has been done to create simple models that represent important characteristics of parallel programs, such as latency, network contention, and communication volume. But many of these methods still require a substantial manual effort to represent an application in the model's format. The YAPP ("Yet Another Performance Predictor") tool is an attempt to automate the formation of first-order expressions for completion time, with a minimum of programmer assistance. The content of this paper is as follows: First, we explore the implementation details of YAPP, and illustrate with examples some of the reasons that automatic prediction is difficult. In the following sections, we present the results of four applications, using execution traces on the Intel i860, analyze the error in YAPP's predictions, explain the limitations of our implementation, and mention possible future additions. In particular, we illustrate techniques used to identify pipeline communication patterns, and demonstrate how compiler analysis and regression are combined to automate the prediction process.

Block, Robert J.↗

NASA NTRS2009

A Study on Advanced Lithium-Based Battery Cell Chemistries to Enhance Lunar Exploration Missions

NASA's Exploration Technology Development Program (ETDP) Energy Storage Project conducted an advanced lithium-based battery chemistry feasibility study to determine the best advanced chemistry to develop for the Altair lunar lander and the Extravehicular Activities (EVA) advanced lunar surface spacesuit. These customers require safe, reliable energy storage systems with extremely high specific energy as compared to today's state-of-the-art batteries. Based on customer requirements, the specific energy goals for the development project are 220 watt-hours per kilogram (Wh/kg) delivered at the battery level at 0 degrees Celsius (degrees Celcius) at a C/10 discharge rate. Continuous discharge rates between C/5 and C/2, operation over 0 to 30 degrees C, and 200 cycles are targeted. The team, consisting of members from NASA Glenn Research Center, Johnson Space Center, and Jet Propulsion laboratory, surveyed the literature, compiled information on recent materials developments, and consulted with other battery experts in the community to identify advanced battery materials that might be capable of achieving the desired results with further development. A variety of electrode materials were considered, including layered metal oxides, spinel oxides, and olivine-type cathode materials, and lithium metal, lithium alloy, and silicon-based composite anode materials. lithium-sulfur systems were also considered. Hypothetical cell constructs that combined compatible anode and cathode materials with suitable electrolytes, separators, current collectors, headers, and cell enclosures were modeled. While some of these advanced materials are projected to obtain the desired electrical performance, there are risks that also factored into the decision making process. The risks include uncertainties due to issues such as safety of a system containing some of these materials, ease of scaling-up of large batches of raw materials, adaptability of the materials to processing using established or reasonable cost manufacturing techniques, manufacturability of the materials in dimensions required for integration into battery cells of practical capacities, low Technology Readiness levels (TRl), and the ability to achieve the desired performance by the customer need dates. The advanced cell chemistry options were evaluated with respect to multiple quantitative and qualitative attributes while considering their projected performance at the end of the available development timeframe. Following a rigorous ranking process, a chemistry that combines a lithiated nickel manganese cobalt oxide (lithium NMC) cathode with a silicon-based composite anode was selected as the technology that can offer the best combination of safety, specific energy, energy density, and likelihood of success. Tasks over the next three years will focus on development of electrode materials, compatible electrolytes, and separator materials, and integration of promising components to assess their combined performance in working cells. Cells of the chosen chemistry will be developed to TRl 6 by 2014 and will then be transferred to the customers for infusion into their mission paths.

Reid, Concha↗

NASA NTRS2002

Determining Greenland Ice Sheet Accumulation Rates from Radar Remote Sensing

An important component of NASA's Program for Arctic Regional Climate Assessment (PARCA) is a mass balance investigation of the Greenland Ice Sheet. The mass balance is calculated by taking the difference between the areally Integrated snow accumulation and the net ice discharge of the ice sheet. Uncertainties in this calculation Include the snow accumulation rate, which has traditionally been determined by interpolating data from ice core samples taken from isolated spots across the ice sheet. The sparse data associated with ice cores juxtaposed against the high spatial and temporal resolution provided by remote sensing , has motivated scientists to investigate relationships between accumulation rate and microwave observations as an option for obtaining spatially contiguous estimates. The objective of this PARCA continuation proposal was to complete an estimate of surface accumulation rate on the Greenland Ice Sheet derived from C-band radar backscatter data compiled in the ERS-1 SAR mosaic of data acquired during, September-November, 1992. An empirical equation, based on elevation and latitude, is used to determine the mean annual temperature. We examine the influence of accumulation rate, and mean annual temperature on C-band radar backscatter using a forward model, which incorporates snow metamorphosis and radar backscatter components. Our model is run over a range of accumulation and temperature conditions. Based on the model results, we generate a look-up table, which uniquely maps the measured radar backscatter, and mean annual temperature to accumulation rate. Our results compare favorably with in situ accumulation rate measurements falling within our study area.

Jezek, Kenneth C.↗

NASA NTRS2014

Development and Implementation of Dynamic Scripts to Support Local Model Verification at National Weather Service Weather Forecast Offices

Local modeling with a customized configuration is conducted at National Weather Service (NWS) Weather Forecast Offices (WFOs) to produce high-resolution numerical forecasts that can better simulate local weather phenomena and complement larger scale global and regional models. The advent of the Environmental Modeling System (EMS), which provides a pre-compiled version of the Weather Research and Forecasting (WRF) model and wrapper Perl scripts, has enabled forecasters to easily configure and execute the WRF model on local workstations. NWS WFOs often use EMS output to help in forecasting highly localized, mesoscale features such as convective initiation, the timing and inland extent of lake effect snow bands, lake and sea breezes, and topographically-modified winds. However, quantitatively evaluating model performance to determine errors and biases still proves to be one of the challenges in running a local model. Developed at the National Center for Atmospheric Research (NCAR), the Model Evaluation Tools (MET) verification software makes performing these types of quantitative analyses easier, but operational forecasters do not generally have time to familiarize themselves with navigating the sometimes complex configurations associated with the MET tools. To assist forecasters in running a subset of MET programs and capabilities, the Short-term Prediction Research and Transition (SPoRT) Center has developed and transitioned a set of dynamic, easily configurable Perl scripts to collaborating NWS WFOs. The objective of these scripts is to provide SPoRT collaborating partners in the NWS with the ability to evaluate the skill of their local EMS model runs in near real time with little prior knowledge of the MET package. The ultimate goal is to make these verification scripts available to the broader NWS community in a future version of the EMS software. This paper provides an overview of the SPoRT MET scripts, instructions for how the scripts are run, and example use cases.

Zavordsky, Bradley↗

NASA NTRS2014

Development and Implementation of Dynamic Scripts to Support Local Model Verification at National Weather Service Weather Forecast Offices

Zavodsky, Bradley↗

NASA NTRS1992

Fiberoptic characteristics for extreme operating environments

Fiberoptics could offer several major benefits for cryogenic liquid-fueled rocket engines, including lightning immunity, weight reduction, and the possibility of implementing a number of new measurements for engine condition monitoring. The technical feasibility of using fiberoptics in the severe environments posed by cryogenic liquid-fueled rocket engines was determined. The issues of importance and subsequent requirements for this use of fiberoptics were compiled. These included temperature ranges, moisture embrittlement succeptability, and the ability to withstand extreme shock and vibration levels. Different types of optical fibers were evaluated and several types of optical fibers' ability to withstand use in cryogenic liquid-fueled rocket engines was demonstrated through environmental testing of samples. This testing included: cold-bend testing, moisture embrittlement testing, temperature cycling, temperature extremes testing, vibration testing, and shock testing. Three of five fiber samples withstood the tests to a level proving feasibility, and two of these remained intact in all six of the tests. A fiberoptic bundle was also tested, and completed testing without breakage. Preliminary cabling and harnessing for fiber protection was also demonstrated. According to cable manufacturers, the successful -300 F cold bend, vibration, and shock tests are the first instance of any major fiberoptic cable testing below roughly -55 F. This program has demonstrated the basic technical feasibility of implementing optical fibers on cryogenic liquid-fueled rocket engines, and a development plan is included highlighting requirements and issues for such an implementation.

Delcher, R. C.↗

NASA NTRS1996

GRASP/Ada 95: Reverse Engineering Tools for Ada

The GRASP/Ada project (Graphical Representations of Algorithms, Structures, and Processes for Ada) has successfully created and prototyped an algorithmic level graphical representation for Ada software, the Control Structure Diagram (CSD), and a new visualization for a fine-grained complexity metric called the Complexity Profile Graph (CPG). By synchronizing the CSD and the CPG, the CSD view of control structure, nesting, and source code is directly linked to the corresponding visualization of statement level complexity in the CPG. GRASP has been integrated with GNAT, the GNU Ada 95 Translator to provide a comprehensive graphical user interface and development environment for Ada 95. The user may view, edit, print, and compile source code as a CSD with no discernible addition to storage or computational overhead. The primary impetus for creation of the CSD was to improve the comprehension efficiency of Ada software and, as a result, improve reliability and reduce costs. The emphasis has been on the automatic generation of the CSD from Ada 95 source code to support reverse engineering and maintenance. The CSD has the potential to replace traditional prettyprinted Ada source code. The current update has focused on the design and implementation of a new Motif compliant user interface, and a new CSD generator consisting of a tagger and renderer. The Complexity Profile Graph (CPG) is based on a set of functions that describes the context, content, and the scaling for complexity on a statement by statement basis. When combined graphicafly, the result is a composite profile of complexity for the program unit. Ongoing research includes the development and refinement of the associated functions, and the development of the CPG generator prototype. The current Version 5.0 prototype provides the capability for the user to generate CSDs and CPGs from Ada 95 source code in a reverse engineering as well as forward engineering mode with a level of flexibility suitable for practical application. This report provides an overview of the GRASP/Ada project with an emphasis on the current update.

Cross, James H., II↗

NASA NTRS2006

A Concept for Run-Time Support of the Chapel Language

A document presents a concept for run-time implementation of other concepts embodied in the Chapel programming language. (Now undergoing development, Chapel is intended to become a standard language for parallel computing that would surpass older such languages in both computational performance in the efficiency with which pre-existing code can be reused and new code written.) The aforementioned other concepts are those of distributions, domains, allocations, and access, as defined in a separate document called "A Semantic Framework for Domains and Distributions in Chapel" and linked to a language specification defined in another separate document called "Chapel Specification 0.3." The concept presented in the instant report is recognition that a data domain that was invented for Chapel offers a novel approach to distributing and processing data in a massively parallel environment. The concept is offered as a starting point for development of working descriptions of functions and data structures that would be necessary to implement interfaces to a compiler for transforming the aforementioned other concepts from their representations in Chapel source code to their run-time implementations.

James, Mark↗

NASA NTRS1986

Active Control Evaluation for Spacecraft (ACES)

The Air Force goal is to develop vibration control techniques for large flexible spacecraft by addressing sensor, actuator, and control hardware and dynamic testing. The Active Control Evaluation for Spacecraft (ACES) program will address the Air Force goal by looking at two leading control techniques and implementing them on a structural model of a flexible spacecraft under laboratory testing. The first phase in the ACES program is to review and to assess the High Authority Control/Low Authority Control (HAC/LAC) and Filter accomodated Model Error Sensitivity Suppression (FAMESS) control techniques for testing on the modified VCOSS structure. Appropriate sensors and actuators will be available for use with both techniques; locations will be the same for both techniques. The control actuators will be positioned at the midpoint and free end of the structure. The laser source for the optical sensor is mounted on the feed mast. The beam will be reflected from a mirror on the offset antenna onto the detectors mounted above the shaker table bay. The next phase is to develop an analysis simulation with the control algorithms implemented for dynamics verification. The third phase is to convert the control laws into high level computer language and test them in the NASA-MSFC facility. The final phase is to compile all analytical and test results for performance comparisons.

Pearson, J.↗

NASA NTRS1973

Magnetic materials selection for static inverter and converter transformers

A program to study magnetic materials is described for use in spacecraft transformers used in static inverters, converters, and transformer-rectifier supplies. Different magnetic alloys best suited for high-frequency and high-efficiency applications were comparatively investigated together with an investigation of each alloy's inherent characteristics. The materials evaluated were the magnetic alloys: (1) 50% Ni, 50% Fe; (2) 79% Ni, 17% Fe, 4% Mo; (3) 48% Ni, 52% Fe; (4) 78% Ni, 17% Fe, 5% Mo; and (5) 3% Si, 97% Fe. Investigations led to the design of a transformer with a very low residual flux. Tests were performed to determine the dc and ac magnetic properties at 2400 Hz using square-wave excitation. These tests were performed on uncut cores, which were then cut for comparison of the gapped and ungapped magnetic properties. When the data of many transformers in many configurations were compiled the optimum transformer was found to be that with the lowest residual flux and a small amount of air gap in the magnetic material. The data obtained from these tests are described, and the potential uses for the materials are discussed.

Mclyman, W. T.↗

NASA NTRS1988

SMM X-ray polychromator

The range of observing and analysis programs accomplished with the X-Ray Polychromator (XRP) instruments during the decline of solar cycle 21 and the rise of the solar cycle 22 is summarized. Section 2 describes XRP operations and current status. This is meant as a guide on how the instrument is used to obtain data and what its capabilities are for potential users. The science section contains a series of representative abstracts from recently published papers on major XRP science topics. It is not meant to be a complete list but illustrates the type of science that can come from the analysis of the XRP data. There then follows a series of appendixes that summarize the major data bases that are available. Appendix A is a complete bibliography of papers and presentations produced using XRP data. Appendix B lists all the spectroscopic data accumulated by the Flat Crystal Spectrometer (FCS). Appendix C is a compilation of the XRP flare catalogue for events equivalent to a GOES C-level flare or greater. It lists the start, peak and end times as well as the peak Ca XIX flux.

Strong, Keith T.↗

NASA NTRS2000

Test Cases for a Rectangular Supercritical Wing Undergoing Pitching Oscillations

Steady and unsteady measured pressures for a Rectangular Supercritical Wing (RSW) undergoing pitching oscillations have been presented. From the several hundred compiled data points, 27 static and 36 pitching oscillation cases have been proposed for computational Test Cases to illustrate the trends with Mach number, reduced frequency, and angle of attack. The wing was designed to be a simple configuration for Computational Fluid Dynamics (CFD) comparisons. The wing had an unswept rectangular planform plus a tip of revolution, a panel aspect ratio of 2.0, a twelve per cent thick supercritical airfoil section, and no twist. The model was tested over a wide range of Mach numbers, from 0.27 to 0.90, corresponding to low subsonic flows up to strong transonic flows. The higher Mach numbers are well beyond the design Mach number such as might be required for flutter verification beyond cruise conditions. The pitching oscillations covered a broad range of reduced frequencies. Some early calculations for this wing are given for lifting pressure as calculated from a linear lifting surface program and from a transonic small perturbation program. The unsteady results were given primarily for a mild transonic condition at M = 0.70. For these cases the agreement with the data was only fair, possibly resulting from the omission of viscous effects. Supercritical airfoil sections are known to be sensitive to viscous effects (for example, one case cited). Calculations using a higher level code with the full potential equations have been presented for one of the same cases, and with the Euler equations. The agreement around the leading edge was improved, but overall the agreement was not completely satisfactory. Typically for low-aspect-ratio rectangular wings, transonic shock waves on the wing tend to sweep forward from root to tip such that there are strong three-dimensional effects. It might also be noted that for most of the test, the model was tested with free transition, but a few points were taken with an added transition strip for comparison. Some unpublished results of a rigid wing of the same airfoil and planform that was tested on the pitch and plunge apparatus mount system (PAPA) showed effects of the lower surface transition Strip on flutter at the lower subsonic Mach numbers. Significant effects of a transition strip were also obtained on a wing with a thicker supercritical section on the PAPA mount system. Both of these flutter tests on the PAPA resulted in very low reduced frequencies that may be a factor in this influence of the transition strip. However, these results indicate that correlation studies for RSW may require some attention to the estimation of transition location to accurately treat viscous effects. In this report several Test Cases are selected to illustrate trends for a variety of different conditions with emphasis on transonic flow effects. An overview of the model and tests is given and the standard formulary for these data is listed. Sample data points are presented in both tabular and graphical form. A complete tabulation and plotting of all the Test Cases is given. Only the static pressures and the real and imaginary parts of the first harmonic of the unsteady pressures are available. All the data for the test are available in electronic file form. The Test Cases are also available as separate electronic files.

Bennett, Robert M.↗

NASA NTRS2002

Laboratory Astrophysics Needs of the Herschel Space Observatory

The science teams of the Herschel Space Observatory have identified a number of areas where laboratory study is required for proper interpretation of Herschel observational data. The most critical is the collection and compilation of laboratory data on spectral line frequencies, transition probabilities and energy levels for the known astrophysical atomic and molecular species in 670 to 57 micron wavelength range of Herschel. The second most critical need is the compilation of collisional excitation cross sections for the species known to dominate the energy balance in the ISM and the temperature dependent chemical reaction rates. On the theoretical front, chemical and radiative transfer models need to be prepared in advance to assess calibration and identify instrument anomalies. In the next few years there will be a need to incorporate spectroscopists and theoretical chemists into teams of astronomers so that the spectroscopic surveys planned can he properly calibrated and rapidly interpreted once the data becomes available. The science teams have also noted that the enormous prospects for molecular discovery will be greatly handicapped by the nearly complete lack of spectroscopic data for anything not already well known in the ISM. As a minimum, molecular species predicted to exist by chemical models should be subjected to detailed laboratory study to ensure conclusive detections. This has the greatest impact on any astrobiology program that might be proposed for Herschel. Without a significant amount of laboratory work in the very near future Herschel will not be prepared for many planned observations, much less addressing the open questions in molecular astrophysics.

Pearson, J. C.↗

NASA NTRS1990

The onset of galactic winds in early-type galaxies

Researchers report on a program using Einstein x ray observations of the x ray spectra and surface brightness profiles (or extents) of a large sample of early-type (elliptical and SO) galaxies for which the goal is to determine the critical optical luminosity for which galactic winds are important. For galaxies in which the x ray emission is dominated by hydrostatic coronae, the x ray spectra will be relatively soft (characterized by a temperature of approx. 10 to the 7th power K), while for galaxies with a galactic wind, the emission will be dominated by the spectrally harder discrete sources (since the x ray emission from the wind is essentially negligible). In this new sample of 180 galaxies, there are 28 early type galaxies with sufficient counts to obtain a spectrum with the Einstein Image Proportional Counter (IPC). This sample more than doubles the total number of early-type galaxies in earlier compilations (Forman, Jones, and Tucker 1985; Canizares et al. 1987). The new spectral observations will help determine the critical optical luminosity for the onset of galactic winds which is important for understanding the chemical evolution of galaxies and of the intergalactic medium. The implications of galactic winds for the heavy element enrichment and energy content of the intracluster medium are discussed.

Forman, W.↗

NASA NTRS1998

Flammability, Odor, Offgassing, and Compatibility Requirements and Test Procedures for Materials in Environments that Support Combustion

This handbook establishes NASA program requirements for evaluation, testing, and selection of materials to preclude unsafe conditions related to flammability, odor, offgassing, and fluid compatibility. Materials intended for use in space vehicles, specified test facilities, and specified ground support equipment (GSE) must meet the requirements of this document. Additional materials performance requirements may be specified in other program or NASA center specific documentation. Responsible NASA centers materials organizations must include applicable requirements of this document in their materials control programs. Materials used in habitable areas of spacecraft, including the materials of the spacecraft, stowed equipment, and experiments, must be evaluated for flammability, odor, and offgassing characteristics. All materials used in other areas must be evaluated for flammability characteristics. In addition, materials that are exposed to liquid oxygen (LOX), gaseous oxygen (GOX), and other reactive fluids' must be evaluated for compatibility with the fluid in their use application. Materials exposed to pressurized breathing gases also must be evaluated for odor and offgassing characteristics. The worst-case anticipated use environment (most hazardous pressure, temperature, material thickness, and fluid exposure conditions) must be used in the evaluation process. Materials that have been shown to meet the criteria of the required tests are acceptable for further consideration in design. Whenever possible, materials should be selected that have already been shown to meet the test criteria in the use environment. Existing test data are compiled in the NASA Marshall Space Flight Center (MSFC) Materials and Processes Technical Information System (MAPTIS) and published periodically as the latest revision of a joint document with Johnson Space Center (JSC), MSFC-HDBK-527/JSC 09604. MAPTIS can be accessed by computer datalink. Systems containing materials that have not been tested or do not meet the criteria of the required tests must be verified to be acceptable in the use configuration by analysis or testing. This verification rationale must be documented and submitted to the responsible NASA center materials organization for approval.

Source record↗

NASA NTRS1991

A kill curve for Phanerozoic marine species

A kill curve for Phanerozoic species is developed from an analysis of the stratigraphic ranges of 17,621 genera, as compiled by Sepkoski. The kill curve shows that a typical species' risk of extinction varies greatly, with most time intervals being characterized by very low risk. The mean extinction rate of 0.25/m.y. is thus a mixture of long periods of negligible extinction and occasional pulses of much higher rate. Because the kill curve is merely a description of the fossil record, it does not speak directly to the causes of extinction. The kill curve may be useful, however, to li inverted question markmit choices of extinction mechanisms.

NASA Discipline Number 52-40↗

NASA NTRS1994

Turbine design and application volumes 1, 2, and 3

NASA has an interest in turbines related primarily to aeronautics and space applications. Airbreathing turbine engines provide jet and turboshaft propulsion, as well as auxiliary power for aircraft. Propellant-driven turbines provide rocket propulsion and auxiliary power for spacecraft. Closed-cycle turbine engines using inert gases, organic fluids, and metal fluids have been studied for providing long-duration electric power for spacecraft. Other applications of interest for turbine engines include land-vehicle (cars, trucks, buses, trains, etc.) propulsion power and ground-based electrical power. In view of the turbine-system interest and efforts at Lewis Research Center, a course entitled 'Turbine Design and Application' was presented during 1968-69 as part of the In-house Graduate Study Program. The course was somewhat revised and again presented in 1972-73. Various aspects of turbine technology were covered including thermodynamic and fluid-dynamic concepts, fundamental turbine concepts, velocity diagrams, losses, blade aerodynamic design, blade cooling, mechanical design, operation, and performance. The notes written and used for the course have been revised and edited for publication. Such a publication can serve as a foundation for an introductory turbine course, a means for self-study, or a reference for selected topics. Any consistent set of units will satisfy the equations presented. Two commonly used consistent sets of units and constant values are given after the symbol definitions. These are the SI units and the U.S. customary units. A single set of equations covers both sets of units by including all constants required for the U.S. customary units and defining as unity those not required for the SI units. Three volumes are compiled into one.

Engine design↗