Ablative surface recession and mass loss on large-angle sphere-cones.
Approximate method to predict ablative recession rate and mass loss on sphere cones in Martian atmosphere entry
Orlik-Rueckemann, K. J.↗
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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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Water-glycol system volume calculation
Two methods calculate the volume of a thermodynamic system. Integral method uses an iterative solution to determine volume based on constants of liquid mass and gas mass. Differential method approximates volume by its initial values plus first-order differential changes in volume as functions of temperature and pressure.
Liley, B.↗
Annular flows for measuring the second normal stress difference.
Second normal stress difference measurement by annular flows, giving approximate method for experimental data inversion
Tanner, R. I.↗
Perturbations in rectangular coordinates by iteration.
Orbits computation by Picard successive approximations method, discussing iterative numerical perturbation techniques
Broucke, R.↗
Two stochastic approximation procedures for identifying linear systems.
Robbins-Monro stochastic approximation method using algorithms for identifying finite memory time-discrete time-stationary linear system from noisy input-output measurements
Holmes, J. K.↗
Molecular collisions. X.
Rotational excitation and scattering of diatomic molecules by structureless atoms, comparing approximation methods
Bernstein, R. B.↗
Inviscid radiating flow behind a paraboloidal shock wave
Axisymmetric radiating flow behind paraboloidal shock in ideal inviscid gas hypersonic stream, using differential approximation method for blunt body solution
Adkins, C. N.↗
Efficient computation of the complex error function
Complex error function computation using approximation method with single algorithm
Gautschi, W.↗
Radiation of sound from an unflanged circular duct with flow
Sound radiation from unflanged circular waveguide duct with flow, calculating reflection coefficients, directivity pattern and power for comparison with approximate methods
Drischler, J. A.↗
The influence of changing end conditions on the resonant response of beams and plates
Approximation method for structural beam and plate resonances at elastic edge excitations
Egle, D. M.↗
Motion of a symmetric rigid body under the action of a body-fixed force
Approximative method for predicting motion of symmetric rigid body subjected to body-fixed force
Chia, B. S.↗
Design of subsystems in large structures
Approximation methods for design of spacecraft subsystems in large structures
Caughey, T. K.↗
The mixing of homogeneous co-axial streams
Series solution for unbounded mixing of two incompressible homogeneous coaxial fluids with constant properties, using successive approximations method
Montealegre, A. P.↗
Plate measurement techniques and reduction methods used by the West German satellite observers, and resulting consequences for the observation
The West German tracking stations are equipped with ballistic cameras. Plate measurement and plate reduction must therefore follow photogrammetric methods. Approximately 100 star positions and 200 satellite positions are measured on each plate. The mathematical model for spatial rotation of the bundle of rays is extended by including terms for distortion and internal orientation of the camera as well as by providing terms for refraction which are computed for the measured coordinates of the star positions on the plate. From the measuring accuracy of the plate coordinates it follows that the timing accuracy for the exposures has to be about one millisecond, in order to obtain a homogeneous system.
Deker, H.↗
The estimation of galactic cosmic ray penetration and dose rates
This study is concerned with approximation methods that can be readily applied to estimate the absorbed dose rate from cosmic rays in rads - tissue or rems inside simple geometries of aluminum. The present work is limited to finding the dose rate at the center of spherical shells or behind plane slabs. The dose rate is calculated at tissue-point detectors or for thin layers of tissue. This study considers cosmic-rays dose rates for both free-space and earth-orbiting missions.
Burrell, M. O.↗
Locally nonsimilar solutions for radiating shock layer about smooth axisymmetric bodies
Locally nonsimilar solutions for nongray radiating shock layers about smooth axisymmetric bodies have been obtained based on a newly developed approximate method. Good agreement is found with numerical solutions for inviscid cases (both radiating and nonradiating) and with series solutions for the radiating viscous case. For the inviscid case, the effect of radiative cooling is to destroy the entropy layer; at a distance far from the stagnation point, the shock layer is nearly isothermal. For the viscous case, the radiative wall flux approaches that of the inviscid case at a distance far downstream of the stagnation point. The method can also treat surface mass injection.
Chou, Y. S.↗
Evaluation of one-dimensional approximations for radiative transport in blunt body shock layers
One-dimensional approximations for the nongray radiative flux and flux divergence in radiating shock layers about a blunt entry body are compared with an exact three-dimensional treatment. A coupled radiative-gasdynamic analysis of the shock layer flow about the entire body provided the thermodynamic field used in these comparisons. In terms of calculating the total energy lost by the shock layer, the one-dimensional approximations to the radiative flux divergence are accurate to within a few percent. In terms of calculating the surface flux, the one-dimensional approximations introduce the largest errors of approximately 15 percent near the stagnation point. The source of these errors is the slab-like geometric representation of the shock layer inherent in all one-dimensional models. Finally, for both the radiative flux and its divergence, the tangent slab approximation provides more accurate results than differential approximation methods.
Wilson, K. H.↗
Vortex equations: Singularities, numerical solution, and axisymmetric vortex breakdown
A method of weighted residuals for the computation of rotationally symmetric quasi-cylindrical viscous incompressible vortex flow is presented and used to compute a wide variety of vortex flows. The method approximates the axial velocity and circulation profiles by series of exponentials having (N + 1) and N free parameters, respectively. Formal integration results in a set of (2N + 1) ordinary differential equations for the free parameters. The governing equations are shown to have an infinite number of discrete singularities corresponding to critical values of the swirl parameters. The computations point to the controlling influence of the inner core flow on vortex behavior. They also confirm the existence of two particular critical swirl parameter values: one separates vortex flow which decays smoothly from vortex flow which eventually breaks down, and the second is the first singularity of the quasi-cylindrical system, at which point physical vortex breakdown is thought to occur.
Bossel, H. H.↗