User's manual for the GNAT computer program - Numerical analysis of stratification in supercritical oxygen
Description of computer program for detailed stratification model of Apollo supercritical oxygen storage tank
Heinmiller, P. J.↗
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Krylov Subspace Methods for Complex Non-Hermitian Linear Systems
We consider Krylov subspace methods for the solution of large sparse linear systems Ax = b with complex non-Hermitian coefficient matrices. Such linear systems arise in important applications, such as inverse scattering, numerical solution of time-dependent Schrodinger equations, underwater acoustics, eddy current computations, numerical computations in quantum chromodynamics, and numerical conformal mapping. Typically, the resulting coefficient matrices A exhibit special structures, such as complex symmetry, or they are shifted Hermitian matrices. In this paper, we first describe a Krylov subspace approach with iterates defined by a quasi-minimal residual property, the QMR method, for solving general complex non-Hermitian linear systems. Then, we study special Krylov subspace methods designed for the two families of complex symmetric respectively shifted Hermitian linear systems. We also include some results concerning the obvious approach to general complex linear systems by solving equivalent real linear systems for the real and imaginary parts of x. Finally, numerical experiments for linear systems arising from the complex Helmholtz equation are reported.
Freund, Roland W.↗
Science Support for Space-Based Droplet Combustion: Drop Tower Experiments and Detailed Numerical Modeling
This program supports the engineering design, data analysis, and data interpretation requirements for the study of initially single component, spherically symmetric, isolated droplet combustion studies. Experimental emphasis is on the study of simple alcohols (methanol, ethanol) and alkanes (n-heptane, n-decane) as fuels with time dependent measurements of drop size, flame-stand-off, liquid-phase composition, and finally, extinction. Experiments have included bench-scale studies at Princeton, studies in the 2.2 and 5.18 drop towers at NASA-LeRC, and both the Fiber Supported Droplet Combustion (FSDC-1, FSDC-2) and the free Droplet Combustion Experiment (DCE) studies aboard the shuttle. Test matrix and data interpretation are performed through spherically-symmetric, time-dependent numerical computations which embody detailed sub-models for physical and chemical processes. The computed burning rate, flame stand-off, and extinction diameter are compared with the respective measurements for each individual experiment. In particular, the data from FSDC-1 and subsequent space-based experiments provide the opportunity to compare all three types of data simultaneously with the computed parameters. Recent numerical efforts are extending the computational tools to consider time dependent, axisymmetric 2-dimensional reactive flow situations.
Marchese, Anthony J.↗
Re-Computation of Numerical Results Contained in NACA Report No. 496
An extensive examination of NACA Report No. 496 (NACA 496), "General Theory of Aerodynamic Instability and the Mechanism of Flutter," by Theodore Theodorsen, is described. The examination included checking equations and solution methods and re‐computing interim quantities and all numerical examples in NACA 496. The checks revealed that NACA 496 contains computational shortcuts (time‐ and effort‐saving devices for engineers of the time) and clever artifices (employed in its solution methods), but, unfortunately, also contains numerous tripping points (aspects of NACA 496 that have the potential to cause confusion) and some errors. The re‐computations were performed employing the methods and procedures described in NACA 496, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in fair‐to‐very‐good agreement with the re‐computed results. The exceptions included what are speculated to be computational errors in the original in some instances and transcription errors in the original in others. Independent flutter calculations were performed and, in all cases, including those where the original and re‐computed results differed significantly, were in excellent agreement with the re‐computed results. Appendix A contains NACA 496; Appendix B contains a Matlab(Reistered) program that performs the re‐computation of results; Appendix C presents three alternate solution methods, with examples, for the two‐degree‐of-freedom solution method of NACA 496; Appendix D contains the three‐degree‐of‐freedom solution method (outlined in NACA 496 but never implemented), with examples.
Perry, Boyd, III↗
3-D Flow Field Diagnostics and Validation Studies using Stereoscopic Tracking Velocimetry
The measurement of 3-D three-component velocity fields is of great importance in both ground and space experiments for understanding materials processing and fluid physics. Here, we present the investigation results of stereoscopic tracking velocimetry (STV) for measuring 3-D velocity fields. The effort includes diagnostic technology development, experimental velocity measurement, and comparison with analytical and numerical computation. The advantages of STV stems from the system simplicity for building compact hardware and in software efficiency for continual near-real-time process monitoring. It also has illumination flexibility for observing volumetric flow fields from arbitrary directions. STV is based on stereoscopic CCD observations of particles seeded in a flow. Neural networks are used for data analysis. The developed diagnostic tool is tested with a simple directional solidification apparatus using Succinonitrile. The 3-D velocity field in the liquid phase is measured and compared with results from detailed numerical computations. Our theoretical, numerical, and experimental effort has shown STV to be a viable candidate for reliably quantifying the 3-D flow field in materials processing and fluids experiments.
Cha, Soyoung Stephen↗
Viscosity Measurement of Highly Viscous Liquids Using Drop Coalescence in Low Gravity
The method of drop coalescence is being investigated for use as a method for determining the viscosity of highly viscous undercooled liquids. Low gravity environment is necessary in this case to minimize the undesirable effects of body forces and liquid motion in levitated drops. Also, the low gravity environment will allow for investigating large liquid volumes which can lead to much higher accuracy for the viscosity calculations than possible under 1 - g conditions. The drop coalescence method is preferred over the drop oscillation technique since the latter method can only be applied for liquids with vanishingly small viscosities. The technique developed relies on both the highly accurate solution of the Navier-Stokes equations as well as on data from experiments conducted in near zero gravity environment. In the analytical aspect of the method two liquid volumes are brought into contact which will coalesce under the action of surface tension alone. The free surface geometry development as well as its velocity during coalescence which are obtained from numerical computations are compared with an analogous experimental model. The viscosity in the numerical computations is then adjusted to bring into agreement of the experimental results with the calculations. The true liquid viscosity is the one which brings the experiment closest to the calculations. Results are presented for method validation experiments performed recently on board the NASA/KC-135 aircraft. The numerical solution for this validation case was produced using the Boundary Element Method. In these tests the viscosity of a highly viscous liquid, in this case glycerine at room temperature, was determined to high degree of accuracy using the liquid coalescence method. These experiments gave very encouraging results which will be discussed together with plans for implementing the method in a shuttle flight experiment.
Antar, Basil N.↗
Three-Dimensional Stereoscopic Tracking Velocimetry and Experimental/Numerical Comparison of Directional Solidification
Measurement of three-dimensional (3-D) three-component velocity fields is of great importance in both ground and space experiments for understanding materials processing and fluid physics. The experiments in these fields most likely inhibit the application of conventional planar probes for observing 3-D phenomena. Here, we present the investigation results of stereoscopic tracking velocimetry (STV) for measuring 3-D velocity fields, which include diagnostic technology development, experimental velocity measurement, and comparison with analytical and numerical computation. STV is advantageous in system simplicity for building compact hardware and in software efficiency for continual near-real-time monitoring. It has great freedom in illuminating and observing volumetric fields from arbitrary directions. STV is based on stereoscopic observation of particles-Seeded in a flow by CCD sensors. In the approach, part of the individual particle images that provide data points is likely to be lost or cause errors when their images overlap and crisscross each other especially under a high particle density. In order to maximize the valid recovery of data points, neural networks are implemented for these two important processes. For the step of particle overlap decomposition, the back propagation neural network is utilized because of its ability in pattern recognition with pertinent particle image feature parameters. For the step of particle tracking, the Hopfield neural network is employed to find appropriate particle tracks based on global optimization. Our investigation indicates that the neural networks are very efficient and useful for stereoscopically tracking particles. As an initial assessment of the diagnostic technology performance, laminar water jets with and without pulsation are measured. The jet tip velocity profiles are in good agreement with analytical predictions. Finally, for testing in material processing applications, a simple directional solidification apparatus is built for experimenting with a metal analog of succinonitrile. Its 3-D velocity field at the liquid phase is then measured to be compared with those from numerical computation. Our theoretical, numerical, and experimental investigations have proven STV to be a viable candidate for reliably measuring 3-D flow velocities. With current activities are focused on further improving the processing efficiency, overall accuracy, and automation, the eventual efforts of broad experimental applications and concurrent numerical modeling validation will be vital to many areas in fluid flow and materials processing.
Lee, David↗
Application of high-performance computing to numerical simulation of human movement
We have examined the feasibility of using massively-parallel and vector-processing supercomputers to solve large-scale optimization problems for human movement. Specifically, we compared the computational expense of determining the optimal controls for the single support phase of gait using a conventional serial machine (SGI Iris 4D25), a MIMD parallel machine (Intel iPSC/860), and a parallel-vector-processing machine (Cray Y-MP 8/864). With the human body modeled as a 14 degree-of-freedom linkage actuated by 46 musculotendinous units, computation of the optimal controls for gait could take up to 3 months of CPU time on the Iris. Both the Cray and the Intel are able to reduce this time to practical levels. The optimal solution for gait can be found with about 77 hours of CPU on the Cray and with about 88 hours of CPU on the Intel. Although the overall speeds of the Cray and the Intel were found to be similar, the unique capabilities of each machine are better suited to different portions of the computational algorithm used. The Intel was best suited to computing the derivatives of the performance criterion and the constraints whereas the Cray was best suited to parameter optimization of the controls. These results suggest that the ideal computer architecture for solving very large-scale optimal control problems is a hybrid system in which a vector-processing machine is integrated into the communication network of a MIMD parallel machine.
NASA Discipline Musculoskeletal↗
Programmer's guide for the GNAT computer program (numerical analysis of stratification in supercritical oxygen)
This document is the programmer's guide for the GNAT computer program developed under MSC/TRW Task 705-2, Apollo cryogenic storage system analysis, subtask 2, is reported. Detailed logic flow charts and compiled program listings are provided for all program elements.
Heinmiller, J. P.↗
A method of obtaining signal components of residual carrier signal with their power content and computer simulation
A novel algorithm to obtain all signal components of a residual carrier signal with any number of channels is presented. The phase modulation type may be NRZ-L or split phase (Manchester). The algorithm also provides a simple way to obtain the power contents of the signal components. Steps to recognize the signal components that influence the carrier tracking loop and the data tracking loop at the receiver are given. A computer program for numerical computation is also provided.
Kantak, Anil V.↗
Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems
This publication contains the proceedings of the Fourth Computational Aeroacoustics (CAA) Workshop on Benchmark Problems. In this workshop, as in previous workshops, the problems were devised to gauge the technological advancement of computational techniques to calculate all aspects of sound generation and propagation in air directly from the fundamental governing equations. A variety of benchmark problems have been previously solved ranging from simple geometries with idealized acoustic conditions to test the accuracy and effectiveness of computational algorithms and numerical boundary conditions; to sound radiation from a duct; to gust interaction with a cascade of airfoils; to the sound generated by a separating, turbulent viscous flow. By solving these and similar problems, workshop participants have shown the technical progress from the basic challenges to accurate CAA calculations to the solution of CAA problems of increasing complexity and difficulty. The fourth CAA workshop emphasized the application of CAA methods to the solution of realistic problems. The workshop was held at the Ohio Aerospace Institute in Cleveland, Ohio, on October 20 to 22, 2003. At that time, workshop participants presented their solutions to problems in one or more of five categories. Their solutions are presented in this proceedings along with the comparisons of their solutions to the benchmark solutions or experimental data. The five categories for the benchmark problems were as follows: Category 1:Basic Methods. The numerical computation of sound is affected by, among other issues, the choice of grid used and by the boundary conditions. Category 2:Complex Geometry. The ability to compute the sound in the presence of complex geometric surfaces is important in practical applications of CAA. Category 3:Sound Generation by Interacting With a Gust. The practical application of CAA for computing noise generated by turbomachinery involves the modeling of the noise source mechanism as a vortical gust interacting with an airfoil. Category 4:Sound Transmission and Radiation. Category 5:Sound Generation in Viscous Problems. Sound is generated under certain conditions by a viscous flow as the flow passes an object or a cavity.
Dahl, Milo D.↗
Verification of Numerical Programs: From Real Numbers to Floating Point Numbers
Numerical algorithms lie at the heart of many safety-critical aerospace systems. The complexity and hybrid nature of these systems often requires the use of interactive theorem provers to verify that these algorithms are logically correct. Usually, proofs involving numerical computations are conducted in the infinitely precise realm of the field of real numbers. However, numerical computations in these algorithms are often implemented using floating point numbers. The use of a finite representation of real numbers introduces uncertainties as to whether the properties veri ed in the theoretical setting hold in practice. This short paper describes work in progress aimed at addressing these concerns. Given a formally proven algorithm, written in the Program Verification System (PVS), the Frama-C suite of tools is used to identify sufficient conditions and verify that under such conditions the rounding errors arising in a C implementation of the algorithm do not affect its correctness. The technique is illustrated using an algorithm for detecting loss of separation among aircraft.
Goodloe, Alwyn E.↗
Computational and numerical analysis of hypersonic nozzle flows with comparisons to wind tunnel calibration data
Navier-Stokes (NS), parabolized NS codes, and classical method of characteristics prediction techniques are employed to compute hypersonic nozzle flowfields for the 15 in Mach 6 High Temperature Tunnel and the 16 in Mach 17 Nitrogen Tunnel, which are part of the Langley Research Center. The study focuses on defining the accuracy of these techniques by comparing the computational results to wind tunnel pitot pressure measurements conducted in the newly designed nozzle of the Mach 6 tunnel and in the original nozzle of the Mach 17 tunnel. The comparisons between predicted results and test section pitot surveys for the Mach 6 nozzle are in good agreement and show highly uniform flow over a range of reservoir pressures and temperatures.
Hackett, Charles M.↗
Application of Acoustical Holography for Projecting Near-Field Data to the Far Field
In this report, the application of the acoustical holography (AH) technique for projecting near-field acoustic data to the far field is discussed. Test problems will be used to showcase the accuracy and utility of this technique and to demonstrate its superiority over the more common technique of spherical spreading projection. Three versions of the technique will be presented: planar, cylindrical, and spherical. Depending on the nature of the acoustic field, one or more of these versions may be useful and practical to use. Since the cylindrical and spherical versions depend on the accurate numerical computations of certain special functions, such as the Hankel functions and the associated Legendre polynomials, the implementation of the high-precision numerical computation of the required special functions on a computer are included in the appendixes at the end of the report. In some cases, the material presented in these appendixes represents a substantial extension of the results previously published in the open literature. As appropriate, special considerations associated with the use of the AH technique in practical situations are discussed.
Holography↗
Re-Computation of Numerical Results Contained in NACA Report No. 685
In an engineering note published in the Journal of Aircraft in the year 2000, Thomas A. Zeiler made generally known that some of the early works on aeroelastic flutter by Theodore Theodorsen and I.E. Garrick (NACA Report Nos. 496, 685, and 741) contained numerical errors in some of their numerical examples. Some of the plots containing numerical errors were later reproduced in two classic aeroelasticity texts (BAH and BA). Because these foundational papers and texts are often used in graduate courses on aeroelasticity, Zeiler recommended that an effort be undertaken to employ the computational resources available today (digital computers) to recompute the example problems in these early works and to publish the results to provide a complete and error-free set of numerical examples. This paper presents recomputed theoretical results contained in NACA Report No. 685 (NACA 685), “Mechanism of Flutter, A Theoretical and Experimental Investigation of the Flutter Problem,” by Theodore Theodorsen and I.E. Garrick. The recomputations were performed employing the solution method described in NACA 685, but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in good-to-excellent agreement with the recomputed results, a surprising but gratifying result considering that the NACA 685 results were computed “by hand” using pencil, paper, slide rules, and mechanical calculators called comptometers. Checks on the recomputations (about 25% were checked) were performed using the so-called 𝑝𝑝-method of flutter solution. In all cases, including those where the original and recomputed results differed significantly, the checks were in excellent agreement with the recomputed results.
Boyd Perry, III↗
Library Of Subprograms In FORTRAN 77
MATH77, Release 3.17, is library of 412 FORTRAN 77 subprograms for use in numerical computation. Subprograms providing machine and system characteristic parameters make library operational on any computer system supporting full FORTRAN 77 standard. Portability and high quality of subprograms and user's manual make MATH77 extremely versatile and valuable tool for all numerical computation applications. Written in FORTRAN 77. Program and documentation copyrighted products of California Institute of Technology.
Lawson, Charles L.↗
Re-Computation of Numerical Results Contained in NACA Report No. 741
This paper presents recomputed theoretical results and compares those results with original results contained in NACA Report No. 741 (NACA 741), “Flutter Calculations in Three Degrees of Freedom,” by Theodore Theodorsen and I.E. Garrick. The recomputations were performed employing the solution method described in NACA 741 but using modern computational tools. With some exceptions, the magnitudes and trends of the original results were in good-to-excellent agreement with the recomputed results, a surprising but gratifying result considering that the NACA 741 results were computed “by hand” using pencil, paper, slide rules, and mechanical calculators called comptometers. Checks on the recomputations (about 25% to 30% were checked) were performed using the so-called k-method of flutter solution. In all cases, including those where the original and recomputed results differed significantly, the checks were in excellent agreement with the recomputed results.
Numerical results↗
Combined structures-controls optimization of lattice trusses
The role that distributed parameter model can play in CSI is demonstrated, in particular in combined structures controls optimization problems of importance in preliminary design. Closed form solutions can be obtained for performance criteria such as rms attitude error, making possible analytical solutions of the optimization problem. This is in contrast to the need for numerical computer solution involving the inversion of large matrices in traditional finite element model (FEM) use. Another advantage of the analytic solution is that it can provide much needed insight into phenomena that can otherwise be obscured or difficult to discern from numerical computer results. As a compromise in level of complexity between a toy lab model and a real space structure, the lattice truss used in the EPS (Earth Pointing Satellite) was chosen. The optimization problem chosen is a generic one: of minimizing the structure mass subject to a specified stability margin and to a specified upper bond on the rms attitude error, using a co-located controller and sensors. Standard FEM treating each bar as a truss element is used, while the continuum model is anisotropic Timoshenko beam model. Performance criteria are derived for each model, except that for the distributed parameter model, explicit closed form solutions was obtained. Numerical results obtained by the two model show complete agreement.
Balakrishnan, A. V.↗