Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solution theory”

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 343 records · Page 19
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

A Study in HRT Resolution: Seeking Maximum Sensitivity Among Variations in Sensing Element Material

The EXACT (Experiments Along Coexistence near Tricriticality) project endeavors to perform the most rigorous test to date of Renormalization Group theory. In most cases, the theory gives only approximate solutions, but it offers exact predictions in the case of the He-3-He-4 tricritical point. Currently, the project is focused on maximizing the performance of the low-temperature system's HRT (high resolution thermometer) near the tricritical point. The HRT uses a PdMn sensing element, the qualities of which change based on its Mn concentration and whether or not it is annealed. All sensing element combinations will be catalogued, and through the data, the optimum configuration will be reported.

Morales, Jeremy M.↗
NASA NTRS2007

Mie Scattering of Growing Molecular Contaminants

Molecular contamination of optical surfaces from outgassed material has been shown in many cases to proceed from acclimation centers and to produce many roughly hemispherical "islands" of contamination on the surface. The mathematics of the hemispherical scattering is simplified by introducing a Virtual source below the plane of the optic, in this case a mirror, allowing the use of Mie theory to produce a solution for the resulting sphere .in transmission. Experimentally, a fixed wavelength in the vacuum ultraviolet was used as the illumination source and scattered light from the polished and coated glass mirrors was detected at a fixed angle as the contamination islands grew in time.

Herren, Kenneth A.↗
NASA NTRS2018

Digital Technologies at NASA for Science and Engineering

While scientific and engineering advancements used to rely primarily on theoretical studies and physical experiments, today digital technology enabled by petaflops-scale supercomputers is an equal, if not a greater, contributor to such achievements. In addition, computational modeling and simulation serves as a predictive tool that is not otherwise available. As a result, the use of high performance computing is integral to NASA's work in all mission areas such as space exploration, aeronautics, and scientific discovery. But traditional supercomputing alone is not sufficient for all of the space agency's needs. The success of many NASA missions depends on solving complex computing challenges, some of which are NP-hard (decision theory) if using classical solution methods. Quantum computing promises an unprecedented ability to solve such intractable problems by harnessing quantum mechanical effects such as tunneling, superposition, and entanglement. Another disruptive digital technology is neuromorphic computing that uses brain-inspired lessons to generate new architectures that are much more energy efficient, and capable of massive parallel processing and learning in-situ. Finally, with large amounts of observational and computational data sets, the opportunities of big data and data analytics can be leveraged to enable deep learning and knowledge discovery - it's all a massive digital transformation. This talk will be an overview how NASA utilizes digital technologies for its science and engineering efforts.

Biswas, Rupak↗
NASA NTRSDate not supplied

Validation of Actuator Disk, Actuator Line and Sliding Mesh Methods within the LAVA Solver

In this study the implementation of actuator-disk, actuator-line and sliding-mesh methodologies in the Launch Ascent and Vehicle Aerodynamics (LAVA) solver is described and validated against several test-cases. The different models are validated against available numerical as well as experimental data. Both steady and unsteady Reynolds-Averaged Navier-Stokes (RANS) simulations using the Spallart Allmaras (SA) turbulence model are performed for several different configurations representative of aeroscience applications. The first part of the paper is focused on the verification and validation of the implemented propulsor models. The first validation case is a theoretical rotor in hover, compared with the 1D analytical solution derived from momentum theory. The second validation is the Rotor-Airframe Interaction Model of Georgia Institute of Technology (GIT), representing the application of actuator disks to top-mounted rotorcraft vehicles or unmanned aerial vehicles (UAVs). The third case is a representative configuration for tip-mounted rotor-craft vehicles such as NASA’s X57 airplane. The second part of the paper shows the implemented models applied to realistic engineering configurations such as NASA’s X57 airplane and the R4 Advanced Ducted Propellor (ADT). A modification to the actuator line method in order to represent the blade geometry more closely is proposed and comparisons with simulations modeling the blade utilizing a sliding-mesh approach are made.

ARMD↗
NASA NTRS1981

Solutions of the Helmholtz equation with boundary conditions for force-free magnetic fields

It is shown that the solution, with one ignorable coordinate, for the Taylor minimum energy state (resulting in a force-free magnetic field) in either a straight cylindrical or a toroidal geometry with arbitrary cross section can be reduced to the solution of either an inhomogeneous Helmholtz equation or a Grad-Shafranov equation with simple boundary conditions. Standard Green's function theory is, therefore, applicable. Detailed solutions are presented for the Taylor state in toroidal and cylindrical domains having a rectangular cross section. The focus is on solutions corresponding to the continuous eigenvalue spectra. Singular behavior at 90 deg corners is explored in detail.

Rasband, S. N.↗
NASA NTRS1972

Transient axisymmetric motions of a conical bar.

Three bar of revolution theories are developed. The most inclusive theory is equivalent to the Mindlin-McNiven theory for circular bars in that it includes radial, axial shear, and longitudinal modes. By removing the axial shear mode in the foregoing, a theory equivalent to the Mindlin-Herrmann theory for circular bars is obtained. Finally, by eliminating all the radial effects in this latter theory, a simple theory incorporating only longitudinal effects is obtained. Each of these three theories is then specialized for a conical geometry and solved by the method of characteristics for the case of a longitudinal impact. The solutions for each of these theories are then compared to published surface meridional strain and internal strain data. In addition, the importance of impact pulse duration in establishing the validity of the approximate bar theories for impact problems is analytically indicated.

Mortimer, R. W.↗
NASA NTRS1974

Theory of discrete vortex noise

A solution is obtained for the noise induced by vortex shedding from the trailing edge of a semiinfinite flat plate. The method of solution for the potential flow is based on a procedure whereby an inner incompressible flow is matched to an outer acoustic field. Acoustic wave fronts are calculated and compared qualitatively with schlieren photographs of similar flows. The acoustic directivity pattern is obtained, and the extreme sensitivity of this parameter to the incompressible flow near the trailing edge of the plate is investigated.

Davis, S. S.↗
NASA NTRS1974

On the theory of large amplitude Alfven waves

Solutions of the MHD equations are derived, which describe the propagation of nonplanar large-amplitude Alfven waves in an infinite homogeneous plasma with no background flow. Some features of interplanetary Alfven waves are discussed, and a typical solution is described qualitatively.

Goldstein, M. L.↗
NASA NTRS1978

A high order accurate finite element algorithm for high Reynolds number flow prediction

A Galerkin-weighted residuals formulation is employed to establish an implicit finite element solution algorithm for generally nonlinear initial-boundary value problems. Solution accuracy, and convergence rate with discretization refinement, are quantized in several error norms, by a systematic study of numerical solutions to several nonlinear parabolic and a hyperbolic partial differential equation characteristic of the equations governing fluid flows. Solutions are generated using selective linear, quadratic and cubic basis functions. Richardson extrapolation is employed to generate a higher-order accurate solution to facilitate isolation of truncation error in all norms. Extension of the mathematical theory underlying accuracy and convergence concepts for linear elliptic equations is predicted for equations characteristic of laminar and turbulent fluid flows at nonmodest Reynolds number. The nondiagonal initial-value matrix structure introduced by the finite element theory is determined intrinsic to improved solution accuracy and convergence. A factored Jacobian iteration algorithm is derived and evaluated to yield a consequential reduction in both computer storage and execution CPU requirements while retaining solution accuracy.

Baker, A. J.↗
NASA NTRS1975

Flutter of laminated plates in supersonic flow

A solution procedure was developed using linear small deflection theory for the flutter of simply supported laminated plates. For such plates, the bending and extensional governing equations are coupled and have cross-stiffness terms which do not appear in classical plate theory. An extended Galerkin method is used to obtain approximate solutions to the governing equations, and the aerodynamic pressure loading used in the analysis is that given by linear piston theory with flow at arbitrary cross-flow angle. A limited parametric study was conducted for typical laminated composite plates. The calculations show that both the bending-extensional coupling and the cross-stiffness terms have a large destabilizing effect on flutter. Since classical plate theory does not consider bending-extensional coupling and cross stiffness terms, it usually gives inaccurate and nonconservative flutter boundaries for laminated plates.

Sawyer, J. W.↗
NASA NTRS1927

Multiplicity of Solutions in Aerodynamics

One of the most striking phenomena which accompany the flow of fluids such as air and water about bodies, is that of changes in character. This phenomena is still very little understood. We will first discuss the nature of these changes and then show that pure theory leads to a multiplicity of characters of flow, among which we will endeavor to indicate those bearing some analogy to experimental results.

AERODYNAMICS↗
NASA NTRS1973

A sequence solution to the Fokker-Planck equation.

In this paper a new approach to nonlinear system analysis based on the Fokker-Planck equation is developed. The development begins as a modification of the parametrix method of partial differential equation theory and provides a sequence solution to the multidimensional time-varying Fokker-Planck equation. This sequence is simplified for the case where only a steady-state solution or a solution for the variance of a particular combination of states is desired. Equations are presented in a form suitable for obtaining numerical results using a digital computer.

Mayfield, W. W.↗
NASA NTRS1995

A Simple Theory of Capillary-Gravity Wave Turbulence

An analytical solution is presented for deriving inertial spectra of capillary-gravity waves. The theory successfully explains dependence of the wave spectrum on wind input and describes the accelerated roll-off of the spectral density function in the narrow sub-range separating scale-invariant regimes of purely gravity and capillary waves.

multi-wave↗
NASA NTRS1995

An outflow boundary condition for aeroacoustic computations

A formulation of boundary condition for flows with small disturbances is presented. The authors test their methodology in an axisymmetric jet flow calculation, using both the Navier-Stokes and Euler equations. Solutions in the far field are assumed to be oscillatory. If the oscillatory disturbances are small, the growth of the solution variables can be predicted by linear theory. Eigenfunctions of the linear theory are used explicitly in the formulation of the boundary conditions. This guarantees correct solutions at the boundary in the limit where the predictions of linear theory are valid.

Hayder, M. Ehtesham↗