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Results for “EQUATIONS - STRESSES PLATES”

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.

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At least 325 records · Page 18
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Diffusion flame extinction in slow convection flow under microgravity environment

A theoretical analysis is presented to study the extinction characteristics of a diffusion flame near the leading edge of a thin fuel plate in slow, forced convective flows in a microgravity environment. The mathematical model includes two-dimensional Navier-Stokes momentum, energy and species equations with one-step overall chemical reaction using second-order finite rate Arrhenius kinetics. Radiant heat loss on the fuel plate is applied in the model as it is the dominant mechanism for flame extinguishment in the small convective flow regime. A parametric study based on the variation of convective flow velocity, which varies the Damkchler number (Da), and the surface radiant heat loss parameter (S) simultaneously, is given. An extinction limit is found in the regime of slow convective flow when the rate of radiant heat loss from fuel surface outweighs the rate of heat generation due to combustion. The transition from existent envelope flame to extinguishment consists of gradual flame contraction in the opposed flow direction together with flame temperature reduction as the convective flow velocity decreases continuously until the extinction limit is reached. A case of flame structure subjected to surface radiant heat loss is also presented and discussed.

Chen, Chiun-Hsun↗
NASA NTRS1988

Implications of truncating semi-infinite physical domains on the accuracy of the solutions to the N-S equations

Numerical techniques for solving the Navier-Stokes equations of laminar incompressible flow over a forward-facing step on a semiinfinite flat plate are evaluated analytically and by means of sample computations. A primitive-variable method with pseudocompressibility and full mapping of the semiinfinite domain is compared with a vorticity/stream-function method with a truncated domain, applying a flux-corrected explicit finite-difference procedure to solve the discretized transport equations. The results are presented in graphs and compared with published experimental data. The solutions obtained with the truncated-domain methods are shown to be inaccurate, even in cases when they are smooth.

Dekruif, Jeffery S.↗
NASA NTRS1983

A finite element model for sound transmission through panels

A finite element method (FEM) is applied to predicting coupled frequencies and pressures within an acoustic cavity in order to characterize sound transmission through a panel. Structural equations of motion are defined and the FEM model is configured with four-noded plate elements, the lateral displacement and two slopes being the unknowns at every node. Each element then has 12 degrees of freedom (DOF) and the displacement variation is expressed by a 12-term nonconforming polynomial. A consistent mass matrix is used to represent the panel mass matrix and a wave equation governs the acoustic volume. Analysis of pressure and displacement over the panel yields a square coupling matrix, and an eigenanalysis leads to a solution of the forced vibration problem.

Ramakrishnan, J. V.↗
NASA NTRS1971

Calibration of a laboratory spectrophotometer for specular light by means of stacked glass plates.

Stacked glass plates have been used to calibrate a laboratory spectrophotometer, over the spectral range 0.5-2.5 microns, for specular light. The uncalibrated instrument was characterized by systematic errors when used to measure the reflectance and transmittance of stacked glass plates. Calibration included first, a determination of the reflectance of a standard composed of barium sulfate paint deposited on an aluminum plate; second, the approximation of the reflectance and transmittance residuals between observed and computed values by means of cubic equations; and, finally, the removal of the systematic errors by a computer. The instrument, after calibration, was accurate to 1% when used to measure the reflectance and transmittance of stacked glass plates.

Allen, W. A.↗
NASA NTRS1974

Numerical solution of the time-dependent compressible Navier-Stokes equations in inlet regions

The results of a study to determine the effects of compressibility on the viscous flow through channels that have straight, parallel walls are presented. Two channel configurations are considered, the flow between two semi-infinite flat plates with uniform flow prescribed at the inlet plane and a cascade of semi-infinite flat plates with uniform flow introduced upstream. The flow field is modeled by using the time dependent, compressible Navier-Stokes equations. Time dependent solutions are obtained by using an explicit finite difference technique which advances the pressure on near field subsonic boundaries such that accurate steady state solutions are obtained. Steady state results at Reynolds number 20 and 150 are presented for Mach numbers between 0.09 and 0.36 and compared with the incompressible solutions of previous studies.

Olson, L. E.↗
NASA NTRS1980

Crack problems for a rectangular plate and an infinite strip

The general plane problem for an infinite strip containing multiple cracks perpendicular to its boundaries is considered. The problem is reduced to a system of singular integral equations. Two specific problems of practical interest are then studied in detail. The first problem explores the interaction effect of multiple edge cracks in a plate or beam under tension or bending. The second problem is that of a rectangular plate containing an arbitrarily oriented crack in the plane of symmetry. Particular emphasis is placed on the problem of a plate containing an edge crack and subjected to concentrated forces.

Civelek, M. B.↗
NASA NTRS1986

A mathematical approach for evaluating nickel-hydrogen cells

A mathematical equation is presented which gives a quantitative relationship between time-voltage discharge curves, when a cell's ampere-hour capacity is determined at a constant discharge current. In particular the equation quantifies the initial exponential voltage decay; the rate of voltage decay; the overall voltage shift of the curve and the total capacity of the cell at the given discharge current. The results of 12 nickel-hydrogen boiler plate cells cycled to 80 percent depth-of-discharge (DOD) are discussed in association with these equations.

Leibecki, H. F.↗
NASA NTRS1971

A model for the acoustic impedance of a perforated plate liner with multiple frequency excitation

A nonlinear resistance model is used in the one-dimensional equations of motion with an arbitrary exciting pressure function. The effects of high amplitude fluid motion, grazing flow, and spectral excitation can be studied together. Sample calculations of acoustic resistances are presented using a high amplitude discrete tone superimposed upon a simulated white noise spectrum. The tone amplitude is varied and its effect is shown both with and without a grazing flow velocity.

Rice, E. J.↗
DOE OSTI2025

Derivation of physical equations for high-speed laser welding using large language models

It is challenging to formulate complex physical phenomena that occur in a manufacturing process, particularly when the available data are limited, rendering conventional data-driven approaches ineffective. This study aims to predict humping onset in high-speed laser welding by introducing a novel framework, namely text-to-equations generative pre-trained transformer (T2EGPT). This method leverages the capabilities of large language models (LLMs), in combination with sparse experimental data and enriched literature data, to derive an interpretable and generalizable equation for predicting humping initiation. By capturing key correlations among physical parameters, T2EGPT generates a compact and dimensionless expression that accurately predicts hump formation. The equation reveals that humping arises from the interplay between inertia-driven backward melt flow and capillary-driven surface stabilization, where inertial forces drive molten metal backward and capillary forces resist surface deformation. Furthermore, compared to traditional data-driven models, T2EGPT demonstrates enhanced predictive accuracy and cross-material transferability. More broadly, this study highlights the potential of LLMs to integrate textual information with data-driven discovery, enabling the extraction of physical laws in data-scarce scientific domains.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Multiframe X-ray diffraction on the OMEGA EP laser

A method of measuring multiple temporally resolved powder x-ray diffraction measurements during a single dynamic compression laser experiment has been demonstrated on the OMEGA EP laser. Up to four time-gated snapshots of the x-ray diffraction pattern are collected on an ultrafast x-ray framing camera with a 2θ scattering angle coverage of 48°–65° and 400-ps temporal resolution with the potential for 10°–160° and 200-ps resolution. X-ray diffraction snapshots capture the transformation to a high-pressure β phase in ramp-compressed Zr, constraining the atomic structure and pressure–density equation-of-state in a single shot. Here, this platform will be used to constrain transition pressures, understand the role of kinetics, and verify the existence of hysteresis and metastability on phase transformations at the lattice level under single-shot dynamic compression.

47 OTHER INSTRUMENTATION↗
NASA NTRS1956

An Engineering Approach to the Variable Fluid Property Problem in Free Convection

An analysis is made for the variable fluid property problem for laminar free convection on an isothermal vertical flat plate. For a number of specific cases, solutions of the boundary layer equations appropriate to the variable property situation were carried out for gases and liquid mercury. Utilizing these findings, a simple and accurate shorthand procedure is presented for calculating free convection heat transfer under variable property conditions. This calculation method is well established in the heat transfer field. It involves the use of results which have been derived for constant property fluids, and of a set of rules (called reference temperatures) for extending these constant property results to variable property situations. For gases, the constant property heat transfer results are generalized to the variable property situation by replacing beta (expansion coefficient) by one over T sub infinity and evaluating the other properties at T sub r equals T sub w minus zero point thirty-eight (T sub w minus T sub infinity). For liquid mercury, the generalization may be accomplished by evaluating all the properties (including beta) at this same T sub r. It is worthwhile noting that for these fluids, the film temperature (with beta equals one over T sub infinity for gases) appears to serve as an adequate reference temperature for most applications. Results are also presented for boundary layer thickness and velocity parameters.

Gregg, J. L.↗
NASA NTRS1971

Prediction of windage power loss in alternators

Simplified equations and constants, based on laminar and turbulent flow theory between parallel plates, estimate windage loss in rotating electrical machinery. Comparison of calculated results and experimental data for smooth cylindrical rotor and slotted alternator yields 7 percent maximum variation between calculated and experimental data.

Vrancik, J. E.↗
NASA NTRS1972

A theoretical study of mixing downstream of transverse injection into a supersonic boundary layer

A theoretical and analytical study was made of mixing downstream of transverse hydrogen injection, from single and multiple orifices, into a Mach 4 air boundary layer over a flat plate. Numerical solutions to the governing three-dimensional, elliptic boundary layer equations were obtained using a general purpose computer program. Founded upon a finite element solution algorithm. A prototype three-dimensional turbulent transport model was developed using mixing length theory in the wall region and the mass defect concept in the outer region. Excellent agreement between the computed flow field and experimental data for a jet/freestream dynamic pressure ratio of unity was obtained in the centerplane region of the single-jet configuration. Poorer agreement off centerplane suggests an inadequacy of the extrapolated two-dimensional turbulence model. Considerable improvement in off-centerplane computational agreement occured for a multi-jet configuration, using the same turbulent transport model.

Baker, A. J.↗
NASA NTRS1982

Symmetric baroclinic instability of a Hadley cell

A symmetric baroclinic instability is examined in terms of a Boussinesq fluid contained between two horizontal plates to determine the effects of the Ekman and thermal layers. Governing equations are written for a rotating reference frame, taking into account the Rossby, Ekman, and Prandtl numbers. Equations are defined for the perturbation functions, treated as an eigenvalue problem, and a numerical integration of the full eighth order differential system is performed by a shooting technique. An instability is found to occur in the Hadley cell containing both Ekman and thermal boundary layers when the Richardson number is close to unity. If the Prandtl number is fixed the critical Richardson number decreases with an increasing Ekman number until the Ekman number reaches a certain value, at which time the fluid is stable.

Antar, B. N.↗
NASA NTRS1985

Upwind relaxation algorithms for the Navier Stokes equations

The development of upwind relaxation algorithms for obtaining efficient steady-state solutions to the compressible Navier-Stokes equations is described. The method is second-order accurate spatially and naturally disipative, using third-order flux splitting of the pressure and convective terms and second-order central differencing for shear and heat flux terms. A line Gauss-Seidel relaxation approach, shown to be unconditionally stable for model convection and diffusion equations, is used. The algorithm is demonstrated for several flows using the thin-layer form of the equations, including the problem of shock-induced separation over a flat plate.

Thomas, J. L.↗
NASA NTRS1987

An engineering study of hybrid adaptation of wind tunnel walls for three-dimensional testing

Solid wall tunnels having only upper and lower walls flexing are described. An algorithm for selecting the wall contours for both 2 and 3 dimensional wall flexure is presented and numerical experiments are used to validate its applicability to the general test case of 3 dimensional lifting aircraft models in rectangular cross section wind tunnels. The method requires an initial approximate representation of the model flow field at a given lift with wallls absent. The numerical methods utilized are derived by use of Green's source solutions obtained using the method of images; first order linearized flow theory is employed with Prandtl-Glauert compressibility transformations. Equations are derived for the flexed shape of a simple constant thickness plate wall under the influence of a finite number of jacks in an axial row along the plate centerline. The Green's source methods are developed to provide estimations of residual flow distortion (interferences) with measured wall pressures and wall flow inclinations as inputs.

Brown, Clinton↗