Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Mathematical methods”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 829 records · Page 46
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

Interactive flutter analysis and parametric study for conceptual wing design

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed on MathCad (trademark) platform for Macintosh, with integrated documentation, graphics, database and symbolic mathematics. The analysis method was based on nondimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The plots were compiled in a Vaught Corporation report from a vast database of past experiments and wind tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended Wing Body concept, proposed by McDonnell Douglas Corporation. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗
NASA NTRS1996

An Interactive Software for Conceptual Wing Flutter Analysis and Parametric Study

An interactive computer program was developed for wing flutter analysis in the conceptual design stage. The objective was to estimate the flutter instability boundary of a flexible cantilever wing, when well-defined structural and aerodynamic data are not available, and then study the effect of change in Mach number, dynamic pressure, torsional frequency, sweep, mass ratio, aspect ratio, taper ratio, center of gravity, and pitch inertia, to guide the development of the concept. The software was developed for Macintosh or IBM compatible personal computers, on MathCad application software with integrated documentation, graphics, data base and symbolic mathematics. The analysis method was based on non-dimensional parametric plots of two primary flutter parameters, namely Regier number and Flutter number, with normalization factors based on torsional stiffness, sweep, mass ratio, taper ratio, aspect ratio, center of gravity location and pitch inertia radius of gyration. The parametric plots were compiled in a Vought Corporation report from a vast data base of past experiments and wind-tunnel tests. The computer program was utilized for flutter analysis of the outer wing of a Blended-Wing-Body concept, proposed by McDonnell Douglas Corp. Using a set of assumed data, preliminary flutter boundary and flutter dynamic pressure variation with altitude, Mach number and torsional stiffness were determined.

Mukhopadhyay, Vivek↗
NASA NTRS1999

Integrated Aeroservoelastic Optimization: Status and Direction

The interactions of lightweight flexible airframe structures, steady and unsteady aerodynamics, and wide-bandwidth active controls on modern airplanes lead to considerable multidisciplinary design challenges. More than 25 years of mathematical and numerical methods' development, numerous basic research studies, simulations and wind-tunnel tests of simple models, wind-tunnel tests of complex models of real airplanes, as well as flight tests of actively controlled airplanes, have all contributed to the accumulation of a substantial body of knowledge in the area of aeroservoelasticity. A number of analysis codes, with the capabilities to model real airplane systems under the assumptions of linearity, have been developed. Many tests have been conducted, and results were correlated with analytical predictions. A selective sample of references covering aeroservoelastic testing programs from the 1960s to the early 1980s, as well as more recent wind-tunnel test programs of real or realistic configurations, are included in the References section of this paper. An examination of references 20-29 will reveal that in the course of development (or later modification), of almost every modern airplane with a high authority active control system, there arose a need to face aeroservoelastic problems and aeroservoelastic design challenges.

Livne, Eli↗
NASA NTRS1997

Chaotic Time Series Analysis Method Developed for Stall Precursor Identification in High-Speed Compressors

A new technique for rotating stall precursor identification in high-speed compressors has been developed at the NASA Lewis Research Center. This pseudo correlation integral method uses a mathematical algorithm based on chaos theory to identify nonlinear dynamic changes in the compressor. Through a study of four various configurations of a high-speed compressor stage, a multistage compressor rig, and an axi-centrifugal engine test, this algorithm, using only a single pressure sensor, has consistently predicted the onset of rotating stall.

Source record↗
NASA NTRS1998

Some Formal Aspects of Human-Machine Interaction

While automated control systems such as autopilots and medical devices are introduced at a rapid pace, it is widely recognized that user interaction with these machines is problematic (Abbott, Slotte, & Stimson, 1996). One factor commonly cited in the literature is the discrepancy between the machine's behavior and the user's expectations. Design guidelines to reduce this discrepancy focus on two elements: (1) improvement of the "feedback" about what the automation is actually doing, and (2) improvement of the user's "mental model" of the automation (Norman, 1990; Sarter and Woods, 1995). This presentation describes a methodology for investigating these two elements via a formal (Le., mathematical) approach. The method involves two representations: (1) a finite state model of the machine's behavior (2) a finite state model of the user's knowledge and expectations about the machine's behavior. In the analysis phase we compare these two models and identify discrepancies. Such discrepancies can be compensated by augmenting the display and/or the user's model. A taxonomy of these discrepancies will be discussed using examples from automated Eight control systems of modern "glass cockpit" jetliners.

Degani, Asaf↗
NASA NTRS2017

Early Estimation of Solar Activity Cycle: Potential Capability and Limits

The variable solar magnetic activity known as the 11-year solar cycle has the longest history of solar observations. These cycles dramatically affect conditions in the heliosphere and the Earth's space environment. Our current understanding of the physical processes that make up global solar dynamics and the dynamo that generates the magnetic fields is sketchy, resulting in unrealistic descriptions in theoretical and numerical models of the solar cycles. The absence of long-term observations of solar interior dynamics and photospheric magnetic fields hinders development of accurate dynamo models and their calibration. In such situations, mathematical data assimilation methods provide an optimal approach for combining the available observational data and their uncertainties with theoretical models in order to estimate the state of the solar dynamo and predict future cycles. In this presentation, we will discuss the implementation and performance of an Ensemble Kalman Filter data assimilation method based on the Parker migratory dynamo model, complemented by the equation of magnetic helicity conservation and longterm sunspot data series. This approach has allowed us to reproduce the general properties of solar cycles and has already demonstrated a good predictive capability for the current cycle, 24. We will discuss further development of this approach, which includes a more sophisticated dynamo model, synoptic magnetogram data, and employs the DART Data Assimilation Research Testbed.

Kitiashvili, Irina N.↗
DOE OSTI2017

Storyline Visualization: A Compelling Way to Understand Patterns over Time and Space

Storyline visualization is a compelling way to understand patterns over time and space. Much effort has been spent developing efficient and aesthetically pleasing layout optimization algorithms. But what if those algorithms are optimizing the wrong things? To answer this question, we conducted a design study with different storyline layout algorithms. We found that users with our new design principles for storyline visualization outperform existing methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS2017

Cause and Cure - Deterioration in Accuracy of CFD Simulations with Use of High-Aspect-Ratio Triangular/Tetrahedral Grids

Traditionally high-aspect ratio triangular/tetrahedral meshes are avoided by CFD researchers in the vicinity of a solid wall, as it is known to reduce the accuracy of gradient computations in those regions. Although for certain complex geometries, the use of high-aspect ratio triangular/tetrahedral elements in the vicinity of a solid wall can be replaced by quadrilateral/prismatic elements, ability to use triangular/tetrahedral elements in such regions without any degradation in accuracy can be beneficial from a mesh generation point of view. The benefits also carry over to numerical frameworks such as the space-time conservation element and solution element (CESE), where simplex elements are the mandatory building blocks. With the requirement of the CESE method in mind, a rigorous mathematical framework that clearly identifies the reason behind the difficulties in use of such high-aspect ratio simplex elements is formulated using two different approaches and presented here. Drawing insights from the analysis, a potential solution to avoid that pitfall is also provided as part of this work. Furthermore, through the use of numerical simulations of practical viscous problems involving high-Reynolds number flows, how the gradient evaluation procedures of the CESE framework can be effectively used to produce accurate and stable results on such high-aspect ratio simplex meshes is also showcased.

CESE Method↗
NASA NTRS1976

Geared-elevator flutter study

An experimental and analytical study was made of the transonic flutter characteristics of a supersonic transport tail assembly model having an all-movable, horizontal tail with a geared elevator. Two model configurations, namely, one with a gear-elevator (2.8 to 1.0 gear ratio) and one with locked-elevator (1.0 to 1.0 gear ratio), were flutter tested in the Langley transonic dynamics tunnel with an empennage cantilever-mounted on a sting. The geared-elevator configuration fluttered experimentally at about 20% higher dynamic pressures than the locked-elevator configuration. The experimental flutter dynamic pressure boundaries for both configurations were nearly flat over a Mach number range from 0.9 to 1.1. Flutter calculations (mathematical models) were made for the geared-elevator configuration using three subsonic lifting-surface methods. In one method, the elevator was treated as a discrete surface, and in the other two methods, the stabilizer and elevator were treated as a single warped-surface with the primary difference between these two methods being in the mathematical implementation used. A comparison of the experimental and analytical results shows that the discrete-elevator method predicted best the experimental flutter dynamic pressure level. However, the single warped-surface methods predicts more closely the experimental flutter frequencies and Mach number trends.

Ruhlin, C. L.↗
DOE OSTI2018

Special Issue: Microbial Community Modeling: Prediction of Microbial Interactions and Community Dynamics

Microbial communities are networks of species, the interaction structure of which dynamically reorganizes in a varying environment. Even in a static condition, community dynamics are often difficult to predict due to highly nonlinear interspecies interactions. Understanding fundamental principles of microbial interactions is therefore key for predicting and harnessing community function and properties. As extensively reviewed previously, mathematical models and computational methods that can predictively link interactions to community behaviors are indispensable tools for achieving this goal. This Special Issue of Processes collects eleven papers from lead scientists and researchers active in the area under the topic of “Microbial Community Modeling: Prediction of Microbial Interactions and Community Dynamics.” The collected papers cover various topics of interest: 1) two review/opinion papers discussing recent advances in biofilm modeling and specific issues for successful collaboration between experimentalists and theorists, 2) one paper on the dynamics of complex environmental communities, 3) six papers dealing with fundamental aspects of microbial interactions and stability in model communities, and 4) two papers on the development and utilization of microbial consortia for biotechnology applications.

Song, Hyun-Seob (ORCID:0000000221546358)↗
NASA NTRS1992

A regularization method for extrapolation of solar potential magnetic fields

The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.

Gary, G. A.↗
NASA NTRS1980

The Split Coefficient Matrix method for hyperbolic systems of gasdynamic equations

The Split Coefficient Matrix (SCM) finite difference method for solving hyperbolic systems of equations is presented. This new method is based on the mathematical theory of characteristics. The development of the method from characteristic theory is presented. Boundary point calculation procedures consistent with the SCM method used at interior points are explained. The split coefficient matrices that define the method for steady supersonic and unsteady inviscid flows are given for several examples. The SCM method is used to compute several flow fields to demonstrate its accuracy and versatility. The similarities and differences between the SCM method and the lambda-scheme are discussed.

Chakravarthy, S. R.↗
NASA NTRS2001

On Multifunctional Collaborative Methods in Engineering Science

Multifunctional methodologies and analysis procedures are formulated for interfacing diverse subdomain idealizations including multi-fidelity modeling methods and multi-discipline analysis methods. These methods, based on the method of weighted residuals, ensure accurate compatibility of primary and secondary variables across the subdomain interfaces. Methods are developed using diverse mathematical modeling (i.e., finite difference and finite element methods) and multi-fidelity modeling among the subdomains. Several benchmark scalar-field and vector-field problems in engineering science are presented with extensions to multidisciplinary problems. Results for all problems presented are in overall good agreement with the exact analytical solution or the reference numerical solution. Based on the results, the integrated modeling approach using the finite element method for multi-fidelity discretization among the subdomains is identified as most robust. The multiple method approach is advantageous when interfacing diverse disciplines in which each of the method's strengths are utilized.

Ransom, Jonathan B.↗
DOE OSTI2024

Physics-Informed Learning Machines for Multiscale and Multiphysics Problems (PHILMS) (Technical Report)

The research work at University of California Santa Barbara (UCSB) resulted in several new developments in the areas of scientific machine learning, numerical analysis, and practical methods for data-driven modeling, prediction, reductions, and simulation. Many of the projects were carried out in collaboration with members of the national laboratories at Sandia National Laboratories (SNL), Pacific Northwestern National Laboratories (PNNL), and other institutions. Results included developing new scientific machine learning methods, related theory and mathematical frameworks for analysis and training, data-driven numerical solvers, and related tools and software for scientific computation. During the support period, over 16+ papers were submitted for publication, and 4 open-source software packages were developed and released (available at http://atzberger.org/). In addition, 7+ students and 2 post-docs were mentored in collaboration with the laboratory staff for future careers in academia, government labs, and industry.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1987

Design sensitivity analysis of rotorcraft airframe structures for vibration reduction

Optimization of rotorcraft structures for vibration reduction was studied. The objective of this study is to develop practical computational procedures for structural optimization of airframes subject to steady-state vibration response constraints. One of the key elements of any such computational procedure is design sensitivity analysis. A method for design sensitivity analysis of airframes under vibration response constraints is presented. The mathematical formulation of the method and its implementation as a new solution sequence in MSC/NASTRAN are described. The results of the application of the method to a simple finite element stick model of the AH-1G helicopter airframe are presented and discussed. Selection of design variables that are most likely to bring about changes in the response at specified locations in the airframe is based on consideration of forced response strain energy. Sensitivity coefficients are determined for the selected design variable set. Constraints on the natural frequencies are also included in addition to the constraints on the steady-state response. Sensitivity coefficients for these constraints are determined. Results of the analysis and insights gained in applying the method to the airframe model are discussed. The general nature of future work to be conducted is described.

Murthy, T. Sreekanta↗
NASA NTRS1989

Finite element analysis in fluids; Proceedings of the Seventh International Conference on Finite Element Methods in Flow Problems, University of Alabama, Huntsville, Apr. 3-7, 1989

Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.

Chung, T. J.↗