Properties of two point boundary value functions
Two point boundary value problems of quasi- differential equations, discussing conditions for continuous and increasing lower bounds of functions
Bogar, G. A.↗
SEARCH · Search NASA
Results for “Continuity equation”
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.
Mathematical model of water transport in Bacon and alkaline matrix-type hydrogen-oxygen fuel cells
Based on general mass continuity and diffusive transport equations, a mathematical model was developed that simulates the transport of water in Bacon and alkaline-matrix fuel cells. The derived model was validated by using it to analytically reproduce various Bacon and matrix-cell experimental water transport transients.
Prokopius, P. R.↗
Fixed interval smoothing with discrete measurements.
Smoothing equations for a linear continuous dynamic system with linear discrete measurements, derived from the discrete results of Rauch, Tung, and Striebel (1965), (R-T-S), are used to extend, through recursive updating, the previously published results of Bryson and Frazier (1963), (B-F), and yield a modified Bryson and Frazier, (M-B-F), algorithm. A comparison of the (M-B-F) and (R-T-S) algorithms leads to the conclusion that the former is to be preferred because it entails less computation, less storage, and less instability. It is felt that the presented (M-B-F) smoothing algorithm is a practical mechanization and should be of value in smoothing discretely observed dynamic linear systems.
Bierman, G. J.↗
Calculation of turbulent shear stress in supersonic boundary layer flows
Turbulent shear stress distributions for supersonic boundary layer flows have been computed from experimental mean boundary layer data. The computations have been made by numerically integrating the time averaged continuity and streamwise momentum equations. Distributions have been obtained for flows upstream and downstream of shock-wave-boundary layer interactions and for both two-dimensional and axisymmetric flows. The computed results are compared with recently reported shear stress measurements which were obtained by hot wire anemometer and laser velocimeter techniques.
Sun, C. C.↗
A plate with a crack, stiffened by a partially debonded stringer
The effect of a partially debonded infinite stringer on the stress intensity factor at the crack tip is investigated. It is assumed that the stringer is bonded to an isotropic plate through an adhesive, along a line perpendicular to the crack. Due to the high stress concentration around the crack tip and on the adhesive, partial debonding is assumed to develop between the stringer and the plate. The integral equation, obtained from the continuity of displacements along the line where the stringer and the plate are bonded, is solved numerically to give the shear stress distribution between the plate and the stringer and the stress intensity factors at both crack tips.
Arin, K.↗
Prediction of pressure and flow transients in a gaseous bipropellant reaction control rocket engine
An analytic model is developed to predict pressure and flow transients in a gaseous hydrogen-oxygen reaction control rocket engine feed system. The one-dimensional equations of momentum and continuity are reduced by the method of characteristics from partial derivatives to a set of total derivatives which describe the state properties along the feedline. System components, e.g., valves, manifolds, and injectors are represented by pseudo steady-state relations at discrete junctions in the system. Solutions were effected by a FORTRAN IV program on an IBM 360/65. The results indicate the relative effect of manifold volume, combustion lag time, feedline pressure fluctuations, propellant temperature, and feedline length on the chamber pressure transient. The analytical combustion model is verified by good correlation between predicted and observed chamber pressure transients. The developed model enables a rocket designer to vary the design parameters analytically to obtain stable combustion for a particular mode of operation which is prescribed by mission objectives.
Markowsky, J. J.↗
A note on the effect of lateral bending stiffness of stringers attached to a plate with a crack
An infinite stringer which is assumed to be partially bonded to a plate through a layer of adhesive is considered. The stringer is assumed to have bending as well as longitudinal stiffness. The effect of the stringer's bending rigidity on the stress intensity factor at the tip of the crack is illustrated. Shear stress distribution between the plate and the stringer and the stress intensity factors will be obtained from the solution of a system of Fredholm integral equations which represent the continuity of displacements along the line of bond.
Arin, K.↗
Effect of electric fields on the daytime high-latitude E and F regions
We have obtained solutions of the coupled continuity, momentum, and energy equations for NO(+), O(+), and O2(+) ions for conditions appropriate to the daytime high-latitude E and F regions. Owing to the rapid increase of the reaction O(+) + N2 yielding NO(+) + N with ion energy, high-latitude electric fields and consequent perpendicular-E x B drifts deplete O(+) in favor of NO(+). For electric field strengths less than about 10 mV/m the depletion of O(+) is small, and the altitude profiles of ion density are similar to those found at mid-latitudes. However, for moderate electric field strengths (50 mV/m), NO(+) is substantially increased in relation to O(+) and becomes an important ion throughout the F region. For large electric fields (200 mV/m), NO(+) completely dominates the ion composition to at least 600 km, decreasing at high altitudes with a diffusive equilibrium scale height. Since the overall F region electron density decreases markedly with increasing electric field strength, it appears that high-latitude, daytime electron density troughs are directly related to the presence of ionospheric electric fields.
Schunk, R. W.↗
Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 1: Computational technique
A numerical procedure has been developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second order accurate finite difference scheme is used to integrate the three dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.
Marconi, F.↗
Development of a computer code for calculating the steady super/hypersonic inviscid flow around real configurations. Volume 2: Code description
A numerical procedure was developed to compute the inviscid super/hypersonic flow field about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects of blunt nose entropy layers are computed in detail. Real gas effects for equilibrium air are included using curve fits of Mollier charts. Typical calculated results for shuttle orbiter, hypersonic transport, and supersonic aircraft configurations are included to demonstrate the usefulness of this tool.
Marconi, F.↗
Ionospheric composition in SAR-arcs
Theoretical ion and electron density profiles in the SAR-arc region are calculated using a model of the ionosphere based on the coupled continuity, momentum, and energy equations for O(+), NO(+), and O2(+). It is found that an increase in the reaction O(+) + N2 yields NO(+) + N, which results from enhanced N2 vibrational excitation due to the high electron temperatures found in SAR arcs, can cause a reduction in F-region electron densities by up to a factor of two. The increase in the O(+) + N2 reaction rate is shown to result in a marked change in the ion composition in SAR arcs, with NO(+) being an important ion up to altitudes of about 350 km at night. Since observed electron-density depressions in SAR arcs generally vary between factors of two and seven, it is concluded that the increase in the O(+) + N2 reaction rate cannot account for these depressions by itself.
Raitt, W. J.↗
A theory for creep crack growth
The paper derives an analytical expression for creep crack growth rate based on a model in which the higher and concentrated stresses ahead of the crack tip enhance creep deformation, thus progressively causing stress rupture and continuous crack advance. The equation derived for creep crack growth rate is expressed in terms of a geometrical factor in the stress intensity expression and in terms of the crack tip radius whose lower limit estimate is the fracture mechanics crack-tip opening displacement. The functional features of the derived creep crack growth rate equation can be compared with those of a pertinent empirical equation. The analytical expression provides some guidelines for alloy and microstructure design.
Purushothaman, S.↗
Helium ion outflow from the terrestrial ionosphere
For situations where ion outflow occurs from the topside ionosphere, steady-state solutions for the He(+) continuity, momentum, and energy equations have been obtained self-consistently, yielding density, velocity, and temperature profiles of He(+) from 200 to 2000 km altitude. The study indicates that the outflowing He(+) has density profiles of similar shape to those of H(+), for basically different reasons; the effect of the perpendicular electric field differs considerably for H(+) and He(+); the fractional heating of He(+) due to the He(+)-O(+) relative flow is not as effective in heating He(+) as the flow is in heating H(+); during magnetospheric disturbances the He(+) peak density decreases only by approximately a factor of 2; and the He(+) escape flux over the winter pole is approximately a factor of 20 greater than the He(+) escape flux over the summer pole. The possibility of interhemispheric He(+) flux from winter to summer on high-latitude closed field lines is considered.
Raitt, W. J.↗
An improved supersonic, three-dimensional, external, inviscid flow field code
A numerical procedure was developed to compute the inviscid super/hypersonic flow fields about complex vehicle geometries accurately and efficiently. A second-order accurate finite difference scheme is used to integrate the three-dimensional Euler equations in regions of continuous flow, while all shock waves are computed as discontinuities via the Rankine-Hugoniot jump conditions. Conformal mappings are used to develop a computational grid. The effects for equilibrium air are included using curve fits of Mollier charts. This report deals only with modifications to these procedures in four specific areas: inlet mass ingestion, subsonic axial Mach number, improved conformal mappings, and vehicles flying at yaw. In each area both the modifications to the computational procedures and computer code are discussed.
Marconi, F.↗
The solar ultraviolet heating efficiency of the midlatitude thermosphere
In this paper we quantify the major channels by which solar UV energy is transferred to the atmosphere, and determine the UV heating efficiency for the thermosphere. Current knowledge of the solar ultraviolet fluxes, thermospheric chemistry and neutral atmosphere is used in a steady state, interhemispheric solution of the ionospheric continuity, momentum and energy equations. The heating efficiency is found to be a strong function of altitude, and peaks near the altitude of maximum EUV deposition at a value of approximately 50%.
Torr, M. R.↗
Two-dimensional zonal mean flow model
The interactions of dynamics, photochemistry and radiation in the stratosphere can be described by the continuity, momentum, and energy equations. A more comprehensive model for stratospheric transport theory was developed for the purpose of aiding predictions of changes in the stratospheric ozone content as a consequence of natural and anthropogenic processes. This model is time dependent and the dependent variables are zonal means of the relevant meteorological quantities which are functions of latitude and height. The detailed formulation of a numerical model both in physics and mathematics is given. A set of fundamental dynamical equations, and the numerical method used in the integration are described.
Chen, H. C.↗
High-latitude ionospheric model - First step towards a predictive capability
In order to study the plasma density features associated with both weak and strong convection in the winter high-latitude F-region, a simple plasma convection model was combined with an ionospheric-atmospheric composition model. In a model calculation, a field tube of plasma is followed as it moves along a convection trajectory through a moving, neutral atmosphere. The altitude profiles of the ion densities are obtained by solving the appropriate continuity, momentum and energy equations, including many high-latitude processes. The result of following many such plasma field tubes is a time-dependent, three-dimensional ion density distribution for the ions NO(+), O2(+), O(+), N(+), and He(+). The high-latitude ionosphere is covered over one complete day above 42 deg N magnetic latitude, at altitudes of 160-800 km.
Schunk, R. W.↗
Seasonal variations of the high-latitude F region for strong convection
A plasma convection model is combined with an ionospheric-atmospheric composition model in order to study the seasonal variations of the high-latitude F region for geomagnetic conditions leading to strong convection. In a model calculation, a field tube of plasma is followed as it moves along a convection trajectory through a moving neutral atmosphere. Altitude profiles of the ion densities are obtained by solving the appropriate continuity, momentum, and energy equations including numerous high-latitude processes. It is found that the high-latitude ionosphere exhibits a significant UT variation both during the winter and summer. In general, the electron density at high-latitudes is lower in winter than in summer. In both summer and winter, the major region of low electron density is associated with the 'main' or mid-latitude' trough.
Sojka, J. J.↗