Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “rational approximations”

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 127 records · Page 7

Study of Lubricant Jet Flow Phenomena in Spur Gears: Out of Mesh Condition

Oil jet lubrication on the disengaging side of a gear mesh was analyzed. Results of the analysis were computerized and used to determine the oil jet impingement depth for several gear ratios and oil jet to pitch line velocity ratios. A gear test rig using high speed photography was used to experimentally determine the oil jet impingement depth on the disengaging side of mesh. Impingement depth reached a maximum at gear ratio near 1.5 where chopping by the leading gear tooth limited impingement depth. The pinion impingement depth is zero above a gear ratio of 1.172 for a jet velocity to pitch time velocity ration of 1.0 and is similar for other velocity ratios. The impingement depth for gear and pinion are equal and approximately one half the maximum at a gear ration of 7.0.

Townsend, D. P.↗

Surface temperatures and glassy state investigations in tribology, part 1

The research in this report is divided into two categories: (1) lubricant rheological behavior, and (2) thermal behavior of a simulated elastohydrodynamic contact. The studies of the lubricant rheological behavior consists of high pressure, low shear rate viscosity measurements, viscoelastic transition measurements, by volume dilatometry, dielectric transitions at atmospheric pressure and light scattering transitions. Lubricant shear stress-strain behavior in the amorphous glassy state was measured on several fluids. It appears clear from these investigations that many lubricants undergo viscoplastic transitions in typical EHD contacts and that the lubricant has a limiting maximum shear stress it can support which in turn will determine the traction in the contact except in cases of very low slide-roll ratio. Surface temperature measurements were made for a naphthenic mineral oil and a polyphenyl ether. The maximum surface temperature in these experiments was approximately symmetrical about the zero slide-roll ration except for absolute values of slide-roll ratio greater than about 0.9. Additional surface temperature measurements were made in contacts with rough surfaces where the composite surface roughness was approximately equal to the EHD film thickness. A regression analysis was done to obtain a predictive equation for surface temperatures as a function of pressure, sliding speed, and surface roughness. A correction factor for surface roughness effects to the typical flash temperature analysis was found.

Winer, W. O.↗

Ingrained: An Automated Framework for Fusing Atomic-Scale Image Simulations into Experiments

To fully leverage the power of image simulation to corroborate and explain patterns and structures in atomic resolution microscopy, an initial correspondence between the simulation and experimental image must be established at the outset of further high accuracy simulations or calculations. Furthermore, if simulation is to be used in context of highly automated processes or high-throughput optimization, the process of finding this correspondence itself must be automated. In this work, "ingrained," an open-source automation framework which solves for this correspondence and fuses atomic resolution image simulations into the experimental images to which they correspond, is introduced. Here, the overall "ingrained" workflow, focusing on its application to interface structure approximations, and the development of an experimentally rationalized forward model for scanning tunneling microscopy simulation are described.

36 MATERIALS SCIENCE↗

Validation of a computer code for analysis of subsonic aerodynamic performance of wings with flaps in combination with a canard or horizontal tail and an application to optimization

Extensive correlations of computer code results with experimental data are employed to illustrate the use of a linearized theory, attached flow method for the estimation and optimization of the longitudinal aerodynamic performance of wing-canard and wing-horizontal tail configurations which may employ simple hinged flap systems. Use of an attached flow method is based on the premise that high levels of aerodynamic efficiency require a flow that is as nearly attached as circumstances permit. The results indicate that linearized theory, attached flow, computer code methods (modified to include estimated attainable leading-edge thrust and an approximate representation of vortex forces) provide a rational basis for the estimation and optimization of aerodynamic performance at subsonic speeds below the drag rise Mach number. Generally, good prediction of aerodynamic performance, as measured by the suction parameter, can be expected for near optimum combinations of canard or horizontal tail incidence and leading- and trailing-edge flap deflections at a given lift coefficient (conditions which tend to produce a predominantly attached flow).

Carlson, Harry W.↗

On the breakup of viscous liquid threads

A one-dimensional model evolution equation is used to describe the nonlinear dynamics that can lead to the breakup of a cylindrical thread of Newtonian fluid when capillary forces drive the motion. The model is derived from the Stokes equations by use of rational asymptotic expansions and under a slender jet approximation. The equations are solved numerically and the jet radius is found to vanish after a finite time yielding breakup. The slender jet approximation is valid throughout the evolution leading to pinching. The model admits self-similar pinching solutions which yield symmetric shapes at breakup. These solutions are shown to be the ones selected by the initial boundary value problem, for general initial conditions. Further more, the terminal state of the model equation is shown to be identical to that predicted by a theory which looks for singular pinching solutions directly from the Stokes equations without invoking the slender jet approximation throughout the evolution. It is shown quantitatively, therefore, that the one-dimensional model gives a consistent terminal state with the jet shape being locally symmetric at breakup. The asymptotic expansion scheme is also extended to include unsteady and inerticial forces in the momentum equations to derive an evolution system modelling the breakup of Navier-Stokes jets. The model is employed in extensive simulations to compute breakup times for different initial conditions; satellite drop formation is also supported by the model and the dependence of satellite drop volumes on initial conditions is studied.

Papageorgiou, Demetrios T.↗

Strong-Weak Duality via Jordan-Wigner Transformation: Using Fermionic Methods for Strongly Correlated su(2) Spin Systems

The Jordan-Wigner transformation establishes a duality between $su(2)$ and fermionic algebras. We present qualitative arguments and numerical evidence that when mapping spins to fermions, the transformation makes strong correlation weaker, as demonstrated by the Hartree-Fock approximation to the transformed Hamiltonian. This result can be rationalized in terms of rank reduction of spin shift terms when transformed to fermions. Conversely, the mapping of fermions to qubits makes strong correlation stronger, complicating its solution when one uses qubit-based correlators. The presence of string operators poses challenges to the implementation of quantum chemistry methods on classical computers, but these can be dealt with using established techniques of low computational cost. Here, our proof of principle results for XXZ and J1-J2 Heisenberg (in 1D and 2D) indicate that the JW transformed fermionic Hamiltonian has reduced complexity in key regions of their phase diagrams, and provides a better starting point for addressing challenging spin problems.

74 ATOMIC AND MOLECULAR PHYSICS↗

Water Uptake by Silica Nanopores: Impacts of Surface Hydrophilicity and Pore Size

Water uptake at 298 K by two mesoporous silicas with different pore sizes was studied using volumetric vapor sorption. Here, through variation of sample pretreatment temperature and time, the number of surface hydroxyl groups was varied, leading to marked changes in the water sorption behavior. With increasing surface hydroxyl density, the adsorption of water to the pore surfaces increases, leading to formation of a thicker and denser water sorption layer. The BET model was used to measure surface hydroxyl density from low pressure parts of water adsorption isotherms. Adsorption of water molecules scales with the number density of surface hydroxyl groups, and monolayer coverage is reached at reduced pressure of ca. 0.3. The onset of adsorption pore condensation of water shifts to lower reduced pressure with increasing surface hydroxyl density, indicating growing thickness of adsorption layers. However, the water pore condensation step of the desorption branch shifts to smaller reduced pressure with increasing surface hydroxylation, reducing the adsorption-desorption hysteresis width. An adsorbed phase model is utilized to calculate the distribution of pore water molecules between adsorbed and pore condensation phases, and characterize the density and thickness of the water sorption phase. In the smaller pores, the adsorbed phase forms a sparse monolayer, while approximately a bilayer is formed in the wider pores. The previously reported silica nanopore underfilling by water is confirmed and rationalized by a significantly reduced water density in the adsorbed phase with respect to bulk, while the pore core is filled with water of approximately bulk density.

36 MATERIALS SCIENCE↗

A preference-ordered discrete-gaming approach to air-combat analysis

An approach to one-on-one air-combat analysis is described which employs discrete gaming of a parameterized model featuring choice between several closed-loop control policies. A preference-ordering formulation due to Falco is applied to rational choice between outcomes: win, loss, mutual capture, purposeful disengagement, draw. Approximate optimization is provided by an active-cell scheme similar to Falco's obtained by a 'backing up' process similar to that of Kopp. The approach is designed primarily for short-duration duels between craft with large-envelope weaponry. Some illustrative computations are presented for an example modeled using constant-speed vehicles and very rough estimation of energy shifts.

Kelley, H. J.↗

Applicability of linearized-theory attached-flow methods to design and analysis of flap systems at low speeds for thin swept wings with sharp leading edges

Low-speed experimental force and data on a series of thin swept wings with sharp leading edges and leading and trailing-edge flaps are compared with predictions made using a linearized-theory method which includes estimates of vortex forces. These comparisons were made to assess the effectiveness of linearized-theory methods for use in the design and analysis of flap systems in subsonic flow. Results demonstrate that linearized-theory, attached-flow methods (with approximate representation of vortex forces) can form the basis of a rational system for flap design and analysis. Even attached-flow methods that do not take vortex forces into account can be used for the selection of optimized flap-system geometry, but design-point performance levels tend to be underestimated unless vortex forces are included. Illustrative examples of the use of these methods in the design of efficient low-speed flap systems are included.

Carlson, Harry W.↗

ISAC - A tool for aeroservoelastic modeling and analysis

This paper discusses the capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrate some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

ISAC: A tool for aeroservoelastic modeling and analysis

The capabilities of the Interaction of Structures, Aerodynamics, and Controls (ISAC) system of program modules is discussed. The major modeling, analysis, and data management components of ISAC are identified. Equations of motion are displayed for a Laplace-domain representation of the unsteady aerodynamic forces. Options for approximating a frequency-domain representation of unsteady aerodynamic forces with rational functions of the Laplace variable are shown. Linear time invariant state-space equations of motion that result are discussed. Model generation and analyses of stability and dynamic response characteristics are shown for an aeroelastic vehicle which illustrates some of the capabilities of ISAC as a modeling and analysis tool for aeroelastic applications.

Adams, William M., Jr.↗

Development of MLPG and LBIE Methods for Nonlinear Problems of Fracture

The truly meshless local Petrov-Galerkin (MLPG) method holds a great promise in solving boundary value problems, using a local symmetric weak form as a natural approach. In the present paper, in the context of MLPG and the meshless interpolation of a moving least squares (MLS) type, a method which uses primary and secondary nodes in the domain and on the global boundary is introduced, in order to improve the accuracy of solution. The secondary nodes can be placed at any location where one needs to obtain a better resolution. The sub-domains for the shape functions in the MLS approximation are defined only from the primary nodes, and the secondary nodes use the same sub-domains. The shape functions based on the MLS approximation, in an integration domain, have a single type of a rational function, which reduces the difficulty of numerical integration to evaluate the weak form. The present method is very useful in an adaptive calculation, because the secondary nodes can be easily added and/or moved without an additional mesh. The essential boundary conditions can be imposed exactly, and non-convex boundaries can be treated without special techniques. Several numerical examples are presented to illustrate the performance of the present method.

Atluri, Satya N.↗

Isogeometric large-eddy simulations of turbulent particle-laden flows

In recent years, isogeometric analysis (IGA) has attracted significant attention from the computational mechanics community due to its ability to integrate design and analysis. Besides, IGA is also a higher-order discretization technique for solving partial differential equations, showing high approximation capability per degree of freedom. In this paper, we extend the application realm of IGA to particle-laden flows based on Eulerian–Eulerian description that couples Navier–Stokes equations with a density transport equation through a Boussinesq approximation. The coupled systems are solved by using quadratic non-uniform rational B-spline (NURBS) functions and a recently developed residual-based variational multiscale (VMS) formulation, which introduces coupling between the fine velocity scales and density equation residuals. We deploy the proposed approach to perform large-eddy simulations (LES) of dilute particle-laden flows over a flat surface at Reynolds number = 10,000. We compare the simulation results against direct numerical simulation (DNS) results from the literature. We find that combining VMS and IGA, the proposed approach enables accurate prediction of a wide range of flow/particle statistics with a relatively lower mesh resolution.

Mathematics↗

Approximate techniques of structural reanalysis

A study is made of two approximate techniques for structural reanalysis. These include Taylor series expansions for response variables in terms of design variables and the reduced-basis method. In addition, modifications to these techniques are proposed to overcome some of their major drawbacks. The modifications include a rational approach to the selection of the reduced-basis vectors and the use of Taylor series approximation in an iterative process. For the reduced basis a normalized set of vectors is chosen which consists of the original analyzed design and the first-order sensitivity analysis vectors. The use of the Taylor series approximation as a first (initial) estimate in an iterative process, can lead to significant improvements in accuracy, even with one iteration cycle. Therefore, the range of applicability of the reanalysis technique can be extended. Numerical examples are presented which demonstrate the gain in accuracy obtained by using the proposed modification techniques, for a wide range of variations in the design variables.

Noor, A. K.↗

Information Theory - The Bridge Connecting Bounded Rational Game Theory and Statistical Physics

A long-running difficulty with conventional game theory has been how to modify it to accommodate the bounded rationality of all red-world players. A recurring issue in statistical physics is how best to approximate joint probability distributions with decoupled (and therefore far more tractable) distributions. This paper shows that the same information theoretic mathematical structure, known as Product Distribution (PD) theory, addresses both issues. In this, PD theory not only provides a principle formulation of bounded rationality and a set of new types of mean field theory in statistical physics; it also shows that those topics are fundamentally one and the same.

Wolpert, David H.↗