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The FORTRAN static source code analyzer program (SAP) user's guide, revision 1

The FORTRAN Static Source Code Analyzer Program (SAP) User's Guide (Revision 1) is presented. SAP is a software tool designed to assist Software Engineering Laboratory (SEL) personnel in conducting studies of FORTRAN programs. SAP scans FORTRAN source code and produces reports that present statistics and measures of statements and structures that make up a module. This document is a revision of the previous SAP user's guide, Computer Sciences Corporation document CSC/TM-78/6045. SAP Revision 1 is the result of program modifications to provide several new reports, additional complexity analysis, and recognition of all statements described in the FORTRAN 77 standard. This document provides instructions for operating SAP and contains information useful in interpreting SAP output.

Decker, W.↗

The 3-D Navier-Stokes analysis of crossing, glancing shocks/turbulent boundary layer interactions

Three dimensional viscous flow analysis is performed for a configuration where two crossing and glancing shocks interact with a turbulent boundary layer. A time marching 3-D full Navier-Stokes code, called PARC3D, is used to compute the flow field, and the solution is compared to the experimental data obtained at the NASA Lewis Research Center's 1 x 1 ft supersonic wind tunnel facility. The study is carried out as part of the continuing code assessment program in support of the generic hypersonic research at NASA Lewis. Detailed comparisons of static pressure fields and oil flow patterns are made with the corresponding solution on the wall containing the shock/boundary layer interaction in an effort to validate the code for hypersonic inlet applications.

Reddy, D. R.↗

3-D Navier-Stokes analysis of crossing, glancing shocks/turbulent boundary layer interactions

Three dimensional viscous flow analysis is performed for a configuration where two crossing and glancing shocks interact with a turbulent boundary layer. A time marching 3-D full Navier-Stokes code, called PARC3D, is used to compute the flow field, and the solution is compared to the experimental data obtained at the NASA Lewis Research Center's 1 x 1 ft supersonic wind tunnel facility. The study is carried out as part of the continuing code assessment program in support of the generic hypersonic research at NASA Lewis. Detailed comparisons of static pressure fields and oil flow patterns are made with the corresponding solution on the wall containing the shock/boundary layer interaction in an effort to validate the code for hypersonic inlet applications.

Reddy, D. R.↗

Dynamic analysis of spur gears using computer program DANST

DANST is a computer program for static and dynamic analysis of spur gear systems. The program can be used for parametric studies to predict the effect on dynamic load and tooth bending stress of spur gears due to operating speed, torque, stiffness, damping, inertia, and tooth profile. DANST performs geometric modeling and dynamic analysis for low- or high-contact-ratio spur gears. DANST can simulate gear systems with contact ratio ranging from one to three. It was designed to be easy to use, and it is extensively documented by comments in the source code. This report describes the installation and use of DANST. It covers input data requirements and presents examples. The report also compares DANST predictions for gear tooth loads and bending stress to experimental and finite element results.

Oswald, Fred B.↗

Dynamic analysis of spur gears using computer program DANST

DANST is a computer program for static and dynamic analysis of spur gear systems. The program can be used for parametric studies to predict the effect on dynamic load and tooth bending stress of spur gears due to operating speed, torque, stiffness, damping, inertia, and tooth profile. DANST performs geometric modeling and dynamic analysis for low- or high-contact-ratio spur gears. DANST can simulate gear systems with contact ratio ranging from one to three. It was designed to be easy to use, and it is extensively documented by comments in the source code. This report describes the installation and use of DANST. It covers input data requirements and presents examples. The report also compares DANST predictions for gear tooth loads and bending stress to experimental and finite element results.

Oswald, Fred B.↗

Optimization of Car Body under Constraints of Noise, Vibration, and Harshness (NVH), and Crash

To be competitive on the today's market, cars have to be as light as possible while meeting the Noise, Vibration, and Harshness (NVH) requirements and conforming to Government-man dated crash survival regulations. The latter are difficult to meet because they involve very compute-intensive, nonlinear analysis, e.g., the code RADIOSS capable of simulation of the dynamics, and the geometrical and material nonlinearities of a thin-walled car structure in crash, would require over 12 days of elapsed time for a single design of a 390K elastic degrees of freedom model, if executed on a single processor of the state-of-the-art SGI Origin2000 computer. Of course, in optimization that crash analysis would have to be invoked many times. Needless to say, that has rendered such optimization intractable until now. The car finite element model is shown. The advent of computers that comprise large numbers of concurrently operating processors has created a new environment wherein the above optimization, and other engineering problems heretofore regarded as intractable may be solved. The procedure, shown, is a piecewise approximation based method and involves using a sensitivity based Taylor series approximation model for NVH and a polynomial response surface model for Crash. In that method the NVH constraints are evaluated using a finite element code (MSC/NASTRAN) that yields the constraint values and their derivatives with respect to design variables. The crash constraints are evaluated using the explicit code RADIOSS on the Origin 2000 operating on 256 processors simultaneously to generate data for a polynomial response surface in the design variable domain. The NVH constraints and their derivatives combined with the response surface for the crash constraints form an approximation to the system analysis (surrogate analysis) that enables a cycle of multidisciplinary optimization within move limits. In the inner loop, the NVH sensitivities are recomputed to update the NVH approximation model while keeping the Crash response surface constant. In every outer loop, the Crash response surface approximation is updated, including a gradual increase in the order of the response surface and the response surface extension in the direction of the search. In this optimization task, the NVH discipline has 30 design variables while the crash discipline has 20 design variables. A subset of these design variables (10) are common to both the NVH and crash disciplines. In order to construct a linear response surface for the Crash discipline constraints, a minimum of 21 design points would have to be analyzed using the RADIOSS code. On a single processor in Origin 2000 that amount of computing would require over 9 months! In this work, these runs were carried out concurrently on the Origin 2000 using multiple processors, ranging from 8 to 16, for each crash (RADIOSS) analysis. Another figure shows the wall time required for a single RADIOSS analysis using varying number of processors, as well as provides a comparison of 2 different common data placement procedures within the allotted memories for each analysis. The initial design is an infeasible design with NVH discipline Static Torsion constraint violations of over 10%. The final optimized design is a feasible design with a weight reduction of 15 kg compared to the initial design. This work demonstrates how advanced methodology for optimization combined with the technology of concurrent processing enables applications that until now were out of reach because of very long time-to-solution.

Kodiyalam, Srinivas↗

Updated Chemical Kinetics and Sensitivity Analysis Code

An updated version of the General Chemical Kinetics and Sensitivity Analysis (LSENS) computer code has become available. A prior version of LSENS was described in "Program Helps to Determine Chemical-Reaction Mechanisms" (LEW-15758), NASA Tech Briefs, Vol. 19, No. 5 (May 1995), page 66. To recapitulate: LSENS solves complex, homogeneous, gas-phase, chemical-kinetics problems (e.g., combustion of fuels) that are represented by sets of many coupled, nonlinear, first-order ordinary differential equations. LSENS has been designed for flexibility, convenience, and computational efficiency. The present version of LSENS incorporates mathematical models for (1) a static system; (2) steady, one-dimensional inviscid flow; (3) reaction behind an incident shock wave, including boundary layer correction; (4) a perfectly stirred reactor; and (5) a perfectly stirred reactor followed by a plug-flow reactor. In addition, LSENS can compute equilibrium properties for the following assigned states: enthalpy and pressure, temperature and pressure, internal energy and volume, and temperature and volume. For static and one-dimensional-flow problems, including those behind an incident shock wave and following a perfectly stirred reactor calculation, LSENS can compute sensitivity coefficients of dependent variables and their derivatives, with respect to the initial values of dependent variables and/or the rate-coefficient parameters of the chemical reactions.

Radhakrishnan, Krishnan↗

Static Controls Performance Tool for Lunar Landers

This document presents a static analysis tool used to evaluate the controllability of Lunar landers. This was created as part of the NASA Lunar Cargo Transportation and Landing by Soft Touchdown (Lunar CATALYST) program. This tool is capable of accepting typical design information such as location and direction of thrusters, maximum thruster forces, gravity vectors, and center of mass locations. The tool evaluates how far the center of gravity can move from its starting position while still maintaining control. This type of analysis is intended to support results produced by time domain simulations. The code created for this project was implemented in Python, and it was designed to be integrated into systems level optimization tools to yield first-cut results on optimal thruster placement.

Aretskin-Hariton, Eliot D.↗

Large Angle Transient Dynamics (LATDYN) demonstration problem manual

LATDYN is a computer code for modeling the Large Angle Transient Dynamics of structures. The objective in developing the code was to investigate new techniques for analyzing flexible deformation and control/structure interaction problems associated with large angular motions of spacecraft. Such motions may consist of pointing the entire spacecraft or articulation of individual components, events which occur frequently during construction, operation, and maintenance of large spacecraft. This type of analysis is beyond the routine capability of conventional analytical tools without simplifying assumptions. In some instances, the motion may be sufficiently slow and the spacecraft (or component) sufficiently rigid to simplify the analysis of dynamics and controls by making pseudo-static and/or rigid body assumptions. LATDYN introduces a new approach to the problem by combining finite element structural analysis, multi-body dynamics, and control system analysis in a single tool. It includes a new type of finite element that can deform and rotate through large angles at the same time, and which can be connected to other finite elements either rigidly or through mechanical joints. LATDYN also provides symbolic capabilities for modeling control systems which are interfaced directly with the finite element structural model. Thus, the nonlinear equations representing the structural model are integrated along with the equations representing sensors, processing, and controls as a coupled system.

Wu, Shih-Chin↗

Experimental Evaluation of Verification and Validation Tools on Martian Rover Software

We report on a study to determine the maturity of different verification and validation technologies (V&V) on a representative example of NASA flight software. The study consisted of a controlled experiment where three technologies (static analysis, runtime analysis and model checking) were compared to traditional testing with respect to their ability to find seeded errors in a prototype Mars Rover. What makes this study unique is that it is the first (to the best of our knowledge) to do a controlled experiment to compare formal methods based tools to testing on a realistic industrial-size example where the emphasis was on collecting as much data on the performance of the tools and the participants as possible. The paper includes a description of the Rover code that was analyzed, the tools used as well as a detailed description of the experimental setup and the results. Due to the complexity of setting up the experiment, our results can not be generalized, but we believe it can still serve as a valuable point of reference for future studies of this kind. It did confirm the belief we had that advanced tools can outperform testing when trying to locate concurrency errors. Furthermore the results of the experiment inspired a novel framework for testing the next generation of the Rover.

Brat, Guillaume↗

Support for Systematic Code Reviews with the SCRUB Tool

SCRUB is a code review tool that supports both large, team-based software development efforts (e.g., for mission software) as well as individual tasks. The tool was developed at JPL to support a new, streamlined code review process that combines human-generated review reports with program-generated review reports from a customizable range of state-of-the-art source code analyzers. The leading commercial tools include Codesonar, Coverity, and Klocwork, each of which can achieve a reasonably low rate of false-positives in the warnings that they generate. The time required to analyze code with these tools can vary greatly. In each case, however, the tools produce results that would be difficult to realize with human code inspections alone. There is little overlap in the results produced by the different analyzers, and each analyzer used generally increases the effectiveness of the overall effort. The SCRUB tool allows all reports to be accessed through a single, uniform interface (see figure) that facilitates brows ing code and reports. Improvements over existing software include significant simplification, and leveraging of a range of commercial, static source code analyzers in a single, uniform framework. The tool runs as a small stand-alone application, avoiding the security problems related to tools based on Web browsers. A developer or reviewer, for instance, must have already obtained access rights to a code base before that code can be browsed and reviewed with the SCRUB tool. The tool cannot open any files or folders to which the user does not already have access. This means that the tool does not need to enforce or administer any additional security policies. The analysis results presented through the SCRUB tool s user interface are always computed off-line, given that, especially for larger projects, this computation can take longer than appropriate for interactive tool use. The recommended code review process that is supported by the SCRUB tool consists of three phases: Code Review, Developer Response, and Closeout Resolution. In the Code Review phase, all tool-based analysis reports are generated, and specific comments from expert code reviewers are entered into the SCRUB tool. In the second phase, Developer Response, the developer is asked to respond to each comment and tool-report that was produced, either agreeing or disagreeing to provide a fix that addresses the issue that was raised. In the third phase, Closeout Resolution, all disagreements are discussed in a meeting of all parties involved, and a resolution is made for all disagreements. The first two phases generally take one week each, and the third phase is concluded in a single closeout meeting.

Holzmann, Gerald J.↗

A Collaborative Analysis Tool for Integrated Hypersonic Aerodynamics, Thermal Protection Systems, and RBCC Engine Performance for Single Stage to Orbit Vehicles

Presented is a computer-based tool that connects several disciplines that are needed in the complex and integrated design of high performance reusable single stage to orbit (SSTO) vehicles. Every system is linked to every other system, as is the case of SSTO vehicles with air breathing propulsion, which is currently being studied by NASA. An RBCC propulsion system integrates airbreathing and rocket propulsion into a single engine assembly enclosed within a cowl or duct. A typical RBCC propulsion system operates as a ducted rocket up to approximately Mach 3. Then there is a transition to a ramjet mode for supersonic-to-hypersonic acceleration. Around Mach 8 the engine transitions to a scramjet mode. During the ramjet and scramjet modes, the integral rockets operate as fuel injectors. Around Mach 10-12 (the actual value depends on vehicle and mission requirements), the inlet is physically closed and the engine transitions to an integral rocket mode for orbit insertion. A common feature of RBCC propelled vehicles is the high degree of integration between the propulsion system and airframe. At high speeds the vehicle forebody is fundamentally part of the engine inlet, providing a compression surface for air flowing into the engine. The compressed air is mixed with fuel and burned. The combusted mixture must be expanded to an area larger than the incoming stream to provide thrust. Since a conventional nozzle would be too large, the entire lower after body of the vehicle is used as an expansion surface. Because of the high external temperatures seen during atmospheric flight, the design of an airbreathing SSTO vehicle requires delicate tradeoffs between engine design, vehicle shape, and thermal protection system (TPS) sizing in order to produce an optimum system in terms of weight (and cost) and maximum performance. To adequately determine the performance of the engine/vehicle, the Hypersonic Flight Inlet Model (HYFIM) module was designed to interface with the RBCC engine model. HYFIM performs the aerodynamic analysis of forebodies and inlet characteristics of RBCC powered SSTO launch vehicles. HYFIM is applicable to the analysis of the ramjet/scramjet engine operations modes (Mach 3-12), and provides estimates of parameters such as air capture area, shock-on-lip Mach number, design Mach number, compression ratio, etc., based on a basic geometry routine for modeling axisymmetric cones, 2-D wedge geometries. HYFIM also estimates the variation of shock layer properties normal to the forebody surface. The thermal protection system (TPS) is directly linked to determination of the vehicle moldline and the shaping of the trajectory. Thermal protection systems to maintain the structural integrity of the vehicle must be able to mitigate the heat transfer to the structure and be lightweight. Herein lies the interdependency, in that as the vehicle's speed increases, the TPS requirements are increased. And as TPS masses increase the effect on the propulsion system and all other systems is compounded. The need to analyze vehicle forebody and engine inlet is critical to be able to design the RBCC vehicle. To adequately determine insulation masses for an RBCC vehicle, the hypersonic aerodynamic environment and aeroheating loads must be calculated and the TPS thicknesses must be calculated for the entire vehicle. To accomplish this an ascent or reentry trajectory is obtained using the computer code Program to Optimize Simulated Trajectories (POST). The trajectory is then used to calculate the convective heat rates on several locations on the vehicles using the Miniature Version of the JA70 Aerodynamic Heating Computer Program (MINIVER). Once the heat rates are defined for each body point on the vehicle, then insulation thicknesses that are required to maintain the vehicle within structural limits are calculated using Systems Improved Numerical Differencing Analyzer (SINDA) models. If the TPS masses are too heavy for the performance of the vehicle the process may be repeated altering the trajectory or some other input to reduce the TPS mass. E-PSURBCC is an "engine performance" model and requires the specification of inlet air static temperature and pressure as well as Mach number (which it pulls from the HYFIM and POST trajectory files), and calculates the corresponding stagnation properties. The engine air flow path geometry includes inlet, a constant area section where the rocket is positioned, a subsonic diffuser, a constant area afterburner, and either a converging nozzle or a converging-diverging nozzle. The current capabilities of E-PSURBCC ejector and ramjet mode treatment indicated that various complex flow phenomena including multiple choking and internal shocks can occur for combinations of geometry/flow conditions. For a given input deck defining geometry/flow conditions, the program first goes through a series of checks to establish whether the input parameters are sound in terms of a solution path. If the vehicle/engine performance fails mission goals, the engineer is able to collaboratively alter the vehicle moldline to change aerodynamics, or trajectory, or some other input to achieve orbit. The problem described is an example of the need for collaborative design and analysis. RECIPE is a cross-platform application capable of hosting a number of engineers and designers across the Internet for distributed and collaborative engineering environments. Such integrated system design environments allow for collaborative team design analysis for performing individual or reduced team studies. To facilitate the larger number of potential runs that may need to be made, RECIPE connects the computer codes that calculate the trajectory data, aerodynamic data based on vehicle geometry, heat rate data, TPS masses, and vehicle and engine performance, so that the output from each tool is easily transferred to the model input files that need it.

Stanley, Thomas Troy↗

Python-Based Scientific Analysis and Visualization of Precipitation Systems at NASA Marshall Space Flight Center

At NASA Marshall Space Flight Center (MSFC), Python is used several different ways to analyze and visualize precipitating weather systems. A number of different Python‐based software packages have been developed, which are available to the larger scientific community. The approach in all these packages is to utilize pre‐existing Python modules as well as to be object‐oriented and scalable. The first package that will be described and demonstrated is the Python Advanced Microwave Precipitation Radiometer (AMPR) Data Toolkit, or PyAMPR for short. PyAMPR reads geolocated brightness temperature data from any flight of the AMPR airborne instrument over its 25‐year history into a common data structure suitable for user‐defined analyses. It features rapid, simplified (i.e., one line of code) production of quick‐look imagery, including Google Earth overlays, swath plots of individual channels, and strip charts showing multiple channels at once. These plotting routines are also capable of significant customization for detailed, publication‐ready figures. Deconvolution of the polarization‐varying channels to static horizontally and vertically polarized scenes is also available. Examples will be given of PyAMPR's contribution toward real‐time AMPR data display during the Integrated Precipitation and Hydrology Experiment (IPHEx), which took place in the Carolinas during May‐June 2014. The second software package is the Marshall Multi‐Radar/Multi‐Sensor (MRMS) Mosaic Python Toolkit, or MMM‐Py for short. MMM‐Py was designed to read, analyze, and display three‐dimensional national mosaicked reflectivity data produced by the NOAA National Severe Storms Laboratory (NSSL). MMM‐Py can read MRMS mosaics from either their unique binary format or their converted NetCDF format. It can also read and properly interpret the current mosaic design (4 regional tiles) as well as mosaics produced prior to late July 2013 (8 tiles). MMM‐Py can easily stitch multiple tiles together to provide a larger regional or national picture of precipitating weather systems. Composites, horizontal and vertical crosssections, and combinations thereof are easily displayed using as little as one line of code. MMM‐Py can also write to the native MRMS binary format, and sub‐sectioning of tiles (or multiple stitched tiles) is anticipated to be in place by the time of this meeting. Thus, MMM‐Py also can be used to power the creation of custom mosaics for targeted regional studies. Overlays of other data (e.g., lightning observations) are easily accomplished. Demonstrations of MMM‐Py, including the creation of animations, will be shown. Finally, Marshall has done significant work to interface Python‐based analysis routines with the U.S. Department of Energy's Py‐ART software package for radar data ingest, processing, and analysis. One example of this is the Python Turbulence Detection Algorithm (PyTDA), an MSFC‐based implementation of the National Center for Atmospheric Research (NCAR) Turbulence Detection Algorithm (NTDA) for the purposes of convective‐scale analysis, situational awareness, and forensic meteorology. PyTDA exploits Py‐ART's radar data ingest routines and data model to rapidly produce aviation‐relevant turbulence estimates from Doppler radar data. Work toward processing speed optimization and better integration within the Py‐ART framework will be highlighted. Python‐based analysis within the Py‐ART framework is also being done for new research related to intercomparison of ground‐based radar data with satellite estimates of ocean winds, as well as research on the electrification of pyrocumulus clouds.

Lang, Timothy J.↗

Development of a C-ELS Specimen-Based Numerical Benchmark for Mode II Delamination and Assessment of Two VCCT-Based Propagation Strategies

A finite element (FE) benchmark example inspired by the calibrated end-loaded split (C-ELS) specimen is developed and used to assess the performance of delamination propagation capabilities based on linear elastic fracture mechanics (LEFM). The C-ELS specimen has the advantage of a longer region of stable delamination propagation compared to the existing mode II benchmark case. The new benchmark example may therefore provide a better assessment tool by enabling more stable crack growth in regions further away from the boundary conditions or load application. First, a benchmark result is created manually using two-dimensional finite element models of the C-ELS specimen with different delamination lengths. Second, the performance of the virtual crack closure technique (VCCT) delamination propagation capabilities in the Abaqus/Standard®1 FE code and the recently developed Progressive Release eXplicit-VCCT (PRX-VCCT) method are assessed by comparing the results to the benchmark case. Two examples with different starter delamination lengths are studied. A shorter starter length is chosen to create a scenario with unstable delamination propagation. A longer delamination encourages stable delamination propagation. Detailed results from three-dimensional analyses with aligned and misaligned meshes and two levels of mesh refinement are provided. In general, good agreement can be achieved between the results obtained from the quasi-static propagation analysis and the benchmark analysis. Numerical artifacts including anomalous unreleased nodes in the crack wake and zig-zag crack fronts occur for propagation analyses using Abaqus/Standard VCCT. In comparison, continuous, smooth, delamination fronts are observed for PRX-VCCT. The use of the benchmark case to assess different VCCT-based propagation strategies illustrates the value of establishing benchmark cases.

Composite Materials↗

Investigation of a Macromechanical Approach to Analyzing Triaxially-Braided Polymer Composites

A macro level finite element-based model has been developed to simulate the mechanical and impact response of triaxially-braided polymer matrix composites. In the analytical model, the triaxial braid architecture is simulated by using four parallel shell elements, each of which is modeled as a laminated composite. The commercial transient dynamic finite element code LS-DYNA is used to conduct the simulations, and a continuum damage mechanics model internal to LS-DYNA is used as the material constitutive model. The material stiffness and strength values required for the constitutive model are determined based on coupon level tests on the braided composite. Simulations of quasi-static coupon tests of a representative braided composite are conducted. Varying the strength values that are input to the material model is found to have a significant influence on the effective material response predicted by the finite element analysis, sometimes in ways that at first glance appear non-intuitive. A parametric study involving the input strength parameters provides guidance on how the analysis model can be improved.

Goldberg, Robert K.↗

Structural analysis of wind turbine rotors for NSF-NASA Mod-0 wind power system

Preliminary estimates are presented of vibratory loads and stresses in hingeless and teetering rotors for the proposed NSF-NASA Mod-0 wind power system. Preliminary blade design utilizes a tapered tubular aluminum spar which supports nonstructural aluminum ribs and skin and is joined to the rotor hub by a steel shank tube. Stresses in the shank of the blade are calculated for static, rated, and overload operating conditions. Blade vibrations were limited to the fundamental flapping modes, which were elastic cantilever bending for hingeless rotor blades and rigid-body rotation for teetering rotor blades. The MOSTAB-C computer code was used to calculate aerodynamic and mechanical loads. The teetering rotor has substantial advantages over the hingeless rotor with respect to shank stresses, fatigue life, and tower loading. The hingeless rotor analyzed does not appear to be structurally stable during overloads.

Spera, D. A.↗

Unstructed Navier-Stokes Analysis of Wind-Tunnel Aeroelastic Effects on TCA Model 2

The aim of this work is to demonstrate a simple technique which accounts for aeroelastic deformations experienced by HSR wind-tunnel models within CFD computations. With improved correlations, CFD can become a more effective tool for augmenting the post-test understanding of experimental data. The present technique involves the loose coupling of a low-level structural representation within the ELAPS code, to an unstructured Navier-Stokes flow solver, USM3Dns. The ELAPS model is initially calibrated against bending characteristics of the wind-tunnel model. The strength of this method is that, with a single point calibration of a simple structural representation, the static aeroelastic effects can be accounted for in CFD calculations across a range of test conditions. No prior knowledge of the model deformation during the wind-on test is required. This approach has been successfully applied to the high aspect-ratio planforms of subsonic transports. The current challenge is to adapt the procedure to low aspect-ratio planforms typical of HSR configurations.

Frink, Neal T.↗

LSENS: A General Chemical Kinetics and Sensitivity Analysis Code for homogeneous gas-phase reactions. Part 1: Theory and numerical solution procedures

LSENS, the Lewis General Chemical Kinetics and Sensitivity Analysis Code, has been developed for solving complex, homogeneous, gas-phase chemical kinetics problems and contains sensitivity analysis for a variety of problems, including nonisothermal situations. This report is part 1 of a series of three reference publications that describe LENS, provide a detailed guide to its usage, and present many example problems. Part 1 derives the governing equations and describes the numerical solution procedures for the types of problems that can be solved. The accuracy and efficiency of LSENS are examined by means of various test problems, and comparisons with other methods and codes are presented. LSENS is a flexible, convenient, accurate, and efficient solver for chemical reaction problems such as static system; steady, one-dimensional, inviscid flow; reaction behind incident shock wave, including boundary layer correction; and perfectly stirred (highly backmixed) reactor. In addition, the chemical equilibrium state can be computed for the following assigned states: temperature and pressure, enthalpy and pressure, temperature and volume, and internal energy and volume. For static problems the code computes the sensitivity coefficients of the dependent variables and their temporal derivatives with respect to the initial values of the dependent variables and/or the three rate coefficient parameters of the chemical reactions.

Radhakrishnan, Krishnan↗