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NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. IV - Aerodynamic lift on a thin cylinder in convective flows

The aerodynamic lift exerted on a long circular cylinder immersed in a convective flow pattern in an ideal fluid is calculated to establish the equilibrium position of the cylinder. The calculations establish the surprising result that the cylinder is pushed out the upwellings and the downdrafts of the convective cell, into a location midway between them. The implications for the intense magnetic flux tubes in the convection beneath the surface of the sun are considered.

Tsinganos, K. C.↗

NASA NTRS1979

Sunspots and the physics of magnetic flux tubes. VI - Convective propulsion. VII - Heat flow in a convective downdraft

The effect of negative aerodynamic drag in an ideal fluid subject to convective instability is considered. It is shown that a cylinder moving in such a fluid is propelled forward in its motion by the convective forces and that the characteristic acceleration time is comparable to the onset time of convective motions in the fluid. It is suggested that convective propulsion plays an important role in the dynamics of flux tubes extending through the surface of the sun. The suppression of the upward heat flow in a Boussinesq convective cell with free upper and lower boundaries by a downdraft is then analyzed. Application to the solar convection zone indicates that downdrafts of 1 to 2 km/s at depths of 1000 to 4000 km beneath the visible surface of the sun are sufficient to reduce the upward heat flux to a small fraction of the ambient value.

Parker, E. N.↗

NASA NTRS1979

Solution of a few nonlinear problems in aerodynamics by the finite elements and functional least squares methods

The numerical simulation of the transonic flows of idealized fluids and of incompressible viscous fluids, by the nonlinear least squares methods is presented. The nonlinear equations, the boundary conditions, and the various constraints controlling the two types of flow are described. The standard iterative methods for solving a quasi elliptical nonlinear equation with partial derivatives are reviewed with emphasis placed on two examples: the fixed point method applied to the Gelder functional in the case of compressible subsonic flows and the Newton method used in the technique of decomposition of the lifting potential. The new abstract least squares method is discussed. It consists of substituting the nonlinear equation by a problem of minimization in a H to the minus 1 type Sobolev functional space.

Periaux, J.↗

NASA NTRS1955

Impingement of Water Droplets on a Sphere

Droplet trajectories about a sphere in ideal fluid flow were calculated. From the calculated droplet trajectories the droplet impingement characteristics of the sphere were determined. Impingement data and equations for determining the collection efficiency, the area, and the distribution of impingement are presented in terms of dimensionless parameters. The range of flight and atmospheric conditions covered in the calculations was extended considerably beyond the range covered by previously reported calculations for the sphere.

Dorsch, Robert G.↗

NASA NTRS1982

Multidomain approach for calculating compressible flows

A multidomain approach for calculating compressible flows by using unsteady or pseudo-unsteady methods is presented. This approach is based on a general technique of connecting together two domains in which hyperbolic systems (that may differ) are solved with the aid of compatibility relations associated with these systems. Some examples of this approach's application to calculating transonic flows in ideal fluids are shown, particularly the adjustment of shock waves. The approach is then applied to treating a shock/boundary layer interaction problem in a transonic channel.

Cambier, L.↗

NASA NTRS1983

Modeling of transient disturbances in coronal-streamer configurations

Numerical simulations of the formation and propagation of mass ejection, loop transients in coronal streamers are discussed. The simulations are accomplished with numerical solutions of the single fluid, ideal MHD equations of motion in the meridional plane. The streamer is produced by simulating the relaxation of an initially radial hydrodynamic flow coupled with a dipole magnetic field. The simulated transient then results from an energy release at the base of the streamer. The legs of the loop transient produced remain essentially stationary while the loop expands mainly in the radial direction with velocities of 400 to 750 km s-1. Once the leading edge of the transient has passed out of the lower corona, the initial streamer configuration is restored after 15 to 24 hours. A second energy release 2 hours later than, and with an energy release identical to, the first does not produce a significant coronal disturbance.

Steinolfson, R. S.↗

NASA NTRS1984

A convective model for turbulent mixing in rotating convection zones

The effects of rotation are included in an analytical model for the convective motions in a plane-parallel layer of an ideal fluid. The turbulent stress tensor, formed by taking products and averages of the various velocity components, is calculated for an arbitrary eddy size and shape. Heuristic formulae presented for determining the size and shape of the dominant eddy then give a fully specified stress tensor. Applications for this stress tensor in problems of stellar internal dynamics, heat flow, scalar diffusion, and dynamo theory are suggested. The resultant stresses tend to produce differential rotation profiles with rapidly rotating equators and interiors. The dynamo activity associated with these convective motions tends to occur near the lower boundary of the convection zone.

Hathaway, D. H.↗

NASA NTRS1985

Deceleration of a supersonic flow behind a curved shock wave with isentropic precompression

Three-dimensional supersonic flows of an ideal fluid in the neighborhood of bodies formed by being cut out along the streamlines of an axisymmetric flow are investigated. The flow consists of a region of isoentropic compression and a region of vortex flow. An exact solution with variable entropy is used to describe the flow in the vortex region. In the continuous flow region an approximate solution is constructed by expanding the solution in a series in a small parameter. The effect of the shape of the excision and the vorticity of the flow on compression of the jet and and the total pressure loss coefficient is studied.

Dulov, V. G.↗

NASA NTRS1986

A model of Comet P/Giacobini-Zinner

A computer model of Comet P/Giacobini-Zinner is presented which contains photoprocesses, gas-phase chemical kinetics, energy balance, multifluid hydrodynamics with a transition to free molecular flow, and solar wind interaction. Recently the physics for electrons in the model has been improved by including electron impact ionization and dissociation and separately accounting for electron energetics. Electron heating and cooling mechanisms include photoprocesses, recombination processes, inelastic and elastic collisions with heavy molecules, and expansion cooling. The model incorporates an internally consistent interaction of the solar wind with the coma gas using the axisymmetric ideal fluid dynamic equations. The nuclear size and composition have been chosen to make the calculations relevant to the September 11, 1985 International Cometary Explorer (ICE) encounter with Comet P/Giacobini-Zinner. Model profiles of the temperature, velocity, and number density of the electrons are in good agreement with measurements along ICE's trajectory. The results indicate the probe passed through a region of the coma at the onset of the plasma tail.

Boice, D. C.↗

NASA NTRS1990

Nonaxisymmetric instabilities in a slender torus - Two- and three-dimensional simulations

Nonaxisymmetric instabilities in accretion disks are investigated in terms of the slender, non-self-gravitating, ideal fluid torus model. Nonlinear simulations are carried out in two and tree dimensions, using Cartesian-grid finite differencing. The fastest growing instability is the principal mode. This mode saturates with the formation of ellipsoidal density distributions, designated as 'planets'. The simulations provide evidence for nonlinear mode-mode coupling. When several wavenumbers m are unstable, multiple 'planets' form that subsequently merge. Sources of numerical error are examined, and the effects are contrasted with those of the physical instability. The same qualitative evolution is seen in both the two- and the three-dimensional simulations, even though strict vertical hydrostatic equilibrium is no longer rigorously maintained after mode saturation.

Hawley, John F.↗

NASA NTRS1990

Acoustic waves superimposed on incompressible flows

The use of incompressible approximations in deriving solutions to the Lighthill wave equation was investigated for problems where an analytical solution could be found. A particular model problem involves the determination of the sound field of a spherical oscillating bubble in an ideal fluid. It is found that use of incompressible boundary conditions leads to good approximations in the important region of high acoustic wave number.

Hodge, Steve↗

NASA NTRS1990

Dynamical effects of annihilation in pair-dominated winds

The steady, spherically symmetric flow of an ideal fluid dominated by photons and ultrarelativistic electron-positron pairs is analyzed. A new wind equation and a set of critical point conditions are obtained which describe the relativistic flow of an annihilation gas in which the flow velocity exceeds the diffusion velocity of the photons. Numerical results are reported which suggest the possible existence of trapped, pure-pair winds driven by the combined pressure of the pairs and the photons. Most of the annihilation occurs below the critical radius in trapped flows, and a substantial fraction of the total energy of the injected pairs is converted into kinetic energy and radiation. Accurate numerical solutions for the flow velocity and the positron loss rate in optically thin, Newtonian winds are obtained, and a useful approximate analytic relation between the positron loss rate and the flow velocity is derived which suggests that a large number of pairs may survive the annihilation region, ultimately escaping the potential well.

Becker, Peter A.↗

NASA NTRS1991

The optical analogy for vector fields

This paper develops the optical analogy for a general vector field. The optical analogy allows the examination of certain aspects of a vector field that are not otherwise readily accessible. In particular, in the cases of a stationary Eulerian flow v of an ideal fluid and a magnetostatic field B, the vectors v and B have surface loci in common with their curls. The intrinsic discontinuities around local maxima in absolute values of v and B take the form of vortex sheets and current sheets, respectively, the former playing a fundamental role in the development of hydrodyamic turbulence and the latter playing a major role in heating the X-ray coronas of stars and galaxies.

Parker, E. N.↗

NASA NTRS1992

Magnetic interchange instability of accretion disks

The nonlinear evolution of the magnetic interchange or buoyancy instability of a differentially rotating disk threaded by an ordered vertical magnetic field is investigated. A 2D ideal fluid in the equatorial plane of a central mass in the corotating frame of reference is considered as a model for the disk. If the rotation rate of the disk is Keplerian, the disk is found to be stable. If the vertical magnetic field is sufficiently strong, and the field strength decreases with distance from the central object, and thus the rotation of the disk deviates from Keplerian, if is found that an instability develops. The magnetic flux and disk matter expand outward in certain ranges of azimuth, while disk matter with less magnetic flux moves inward over the remaining range of azimuth, showing a characteristic development of an interchange instability.

Kaisig, M.↗

NASA NTRS1992

Homogeneous quantum electrodynamic turbulence

The electromagnetic field equations and Dirac equations for oppositely charged wave functions are numerically time-integrated using a spatial Fourier method. The numerical approach used, a spectral transform technique, is based on a continuum representation of physical space. The coupled classical field equations contain a dimensionless parameter which sets the strength of the nonlinear interaction (as the parameter increases, interaction volume decreases). For a parameter value of unity, highly nonlinear behavior in the time-evolution of an individual wave function, analogous to ideal fluid turbulence, is observed. In the truncated Fourier representation which is numerically implemented here, the quantum turbulence is homogeneous but anisotropic and manifests itself in the nonlinear evolution of equilibrium modal spatial spectra for the probability density of each particle and also for the electromagnetic energy density. The results show that nonlinearly interacting fermionic wave functions quickly approach a multi-mode, dynamic equilibrium state, and that this state can be determined by numerical means.

Shebalin, John V.↗

NASA NTRS1929

:Theoretical investigation of the effect of the ailerons on the wing of an airplane

The present work investigates, on the basis of Prandtl's wing theory, the form of the lift distribution when the ailerons are deflected in opposite directions. An ideal fluid and a wing with a rectangular form are assumed. The moments must not cause any rotation of the wing or any deviation from the rectilinear motion.

AILERONS - DISPLACEMENT↗

NASA NTRS1998

Stability of Capillary Surfaces in Rectangular Containers: The Right Square Cylinder

The linearized governing equations for an ideal fluid are presented for numerical analysis for the stability of free capillary surfaces in rectangular containers against unfavorable disturbances (accelerations,i.e. Rayleigh-Taylor instability). The equations are solved for the case of the right square cylinder. The results are expressed graphically in term of a critical Bond number as a function of system contact angle. A critical wetting phenomena in the corners is shown to significantly alter the region of stability for such containers in contrast to simpler geometries such as the right circular cylinder or the infinite rectangular slot. Such computational results provide additional constraints for the design of fluids systems for space-based applications.

Weislogel, M. M.↗

NASA NTRS2008

Simulating Sources of Superstorm Plasmas

We evaluated the contributions to magnetospheric pressure (ring current) of the solar wind, polar wind, auroral wind, and plasmaspheric wind, with the surprising result that the main phase pressure is dominated by plasmaspheric protons. We used global simulation fields from the LFM single fluid ideal MHD model. We embedded the Comprehensive Ring Current Model within it, driven by the LFM transpolar potential, and supplied with plasmas at its boundary including solar wind protons, polar wind protons, auroral wind O+, and plasmaspheric protons. We included auroral outflows and acceleration driven by the LFM ionospheric boundary condition, including parallel ion acceleration driven by upward currents. Our plasmasphere model runs within the CRCM and is driven by it. Ionospheric sources were treated using our Global Ion Kinetics code based on full equations of motion. This treatment neglects inertial loading and pressure exerted by the ionospheric plasmas, and will be superceded by multifluid simulations that include those effects. However, these simulations provide new insights into the respective role of ionospheric sources in storm-time magnetospheric dynamics.

Fok, Mei-Ching↗