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NASA NTRS1959

On Fully Developed Channel Flows: Some Solutions and Limitations, and Effects of Compressibility, Variable Properties, and Body Forces

An examination of the effects of compressibility, variable properties, and body forces on fully developed laminar flow has indicated several limitations on such streams. In the absence of a pressure gradient, but presence of a body force (e.g., gravity), an exact fully developed gas flow results. For a liquid this follows also for the case of a constant streamwise pressure gradient. These motions are exact in the sense of a Couette flow. In the liquid case two solutions (not a new result) can occur for the same boundary conditions. An approximate analytic solution was found which agrees closely with machine calculations.In the case of approximately exact flows, it turns out that for large temperature variations across the channel the effects of convection (due to, say, a wall temperature gradient) and frictional heating must be negligible. In such a case the energy and momentum equations are separated, and the solutions are readily obtained. If the temperature variations are small, then both convection effects and frictional heating can consistently be considered. This case becomes the constant-property incompressible case (or quasi-incompressible case for free-convection flows) considered by many authors. Finally there is a brief discussion of cases wherein streamwise variations of all quantities are allowed but only a such form that independent variables are separable. For the case where the streamwise velocity varies inversely as the square root distance along the channel a solution is given.

Maslen, Stephen H.↗

NASA NTRS1983

Labyrinth seal forces on a whirling rotor

An experimental investigation of air labyrinth seal forces on a subsynchronously whirling model rotor is described and test results are given for diverging, converging, and straight two-strip seals. The effects of pressure drop, provide basic experimental data needed in the development of design methods for predicting and preventing self-excited whirl of turbine rotors and other machines having labyrinth seals. The total dynamic seal forces on the whirling model rotor are measured accurately by means of an active damping and stiffness system that is adjusted to obtain neutral whirl stability of the model rotor system. In addition, the whirling pressure pattern in the seal annulus is measured for a few test conditions and the corresponding pressure forces on the rotor are compared with the total measured forces. This comparison shows that either radial and axial pressure gradients in the seal annulus or drag forces on the rotor are significant. Comparisons made between the measured seal forces and theoretical results show that present theory is inadequate.

Wright, D. V.↗

NASA NTRS1983

Labyrinth seal forces on a whirling rotor

An experimental investigation of air labyrinth seal forces on a subsynchronously whirling model rotor is described and test results are given for diverging, converging, and straight two-strip seals. The effects of pressure drop, back pressure, whirl direction, and whirl frequency are shown. These results provide basic experimental data needed in the development of design methods for predicting and preventing self-excited whirl of turbine rotors and other machines having labyrinth seals. The total dynamic seal forces on the whirling model rotor are measured accurately by means of a novel active damping and stiffness system that is adjusted to obtain neutral whirl stability of the model rotor system. In addition, the whirling pressure pattern in the seal annulus is measured for a few test conditions and the corresponding pressure forces on the rotor are compared with the total measured forces. This comparison shows that either radial and axial pressure gradients in the seal annulus or drag forces on the rotor are significant.

Wright, D. V.↗

NASA NTRS1975

Shock wave relations in lunar ash flow

A detailed analysis of steady normal shock waves in a layer of lunar ash by the theory of two phase flow of a mixture of a gas and small solid particles is presented. New terms of pressure gradient and virtual mass forces in the particle momentum equation and the particle kinetic energy and work done in the particle energy equation are included in the fundamental equations and their influences are investigated. The flow variables as functions of the free stream Mach number, initial particle volume fraction and the density ratio G are presented. The thickness of the relaxation zone is found to increase with decreasing initial particle volume fraction and almost independent of G for any given values of free stream Mach number. A new empirical relation of the drag coefficient for the spherical particles in the mixture is proposed to fit experimental data.

Pai, S. I.↗

NASA NTRS1984

Contactless pellet fabrication

A small object is coated by holding it in the pressure well of an acoustic standing wave pattern, and then applying a mist of liquid coating material at low velocity into the pressure well. The pressure gradient within the well forces the mist particles to be pushed against the object. A lower frequency acoustic wave also can be applied to the coated object, to vibrate it so as to evenly distribute the coated material. The same lower frequency vibrations can be applied to an object in the shape of a hollow sphere, to center the inner and outer surfaces of the sphere while it remains suspended.

Lee, M. C.↗

NASA NTRS2006

General Relativistic Magnetohydrodynamic Simulations of Jet Formation with a Thin Keplerian Disk

We have performed several simulations of black hole systems (non-rotating, black hole spin parameter a = 0.0 and rapidly rotating, a = 0.95) with a geometrically thin Keplerian disk using the newly developed RAISHIN code. The simulation results show the formation of jets driven by the Lorentz force and the gas pressure gradient. The jets have mildly relativistic speed (greater than or equal to 0.4 c). The matter is continuously supplied from the accretion disk and the jet propagates outward until each applicable terminal simulation time (non-rotating: t/tau S = 275 and rotating: t/tau S = 200, tau s equivalent to r(sub s/c). It appears that a rotating black hole creates an additional, faster, and more collimated inner outflow (greater than or equal to 0.5 c) formed and accelerated by the twisted magnetic field resulting from frame-dragging in the black hole ergosphere. This new result indicates that jet kinematic structure depends on black hole rotation.

Mizuno, Yosuke↗

NASA NTRS2011

FTEs: Theory, Simulation, and Observations

Flux transfer events (FTEs) are ropes of interconnected magnetosheath and magnetospheric magnetic field lines generated by bursty reconnection at the dayside magnetopause. Theory predicts that the combined pressure gradient and magnetic curvature forces should determine the speed at which the events move and the locations where they can be observed. We present results indicating that events form on the dayside magnetopause for both northward and southward IMF orientations, but that the events for northward IMF orientations exhibit far weaker signatures until they reach the magnetospheric flanks and argue that this is consistent with observations indicating that events on the dayside tend to occur for southward IMF orientations, but those on the flank do not. We show that the component and antiparallel reconnection models predict events in strikingly different quadrants outside the flanks of the magnetotail.Observations of events in all four quadrants indicate that both models are required. The motion of events inferred from multispacecraft timing during periods of northward IMF orientation is generally consistent with the component reconnection model.

Siebeck, David G.↗

NASA NTRS1986

Quasistatic evolution of magnetostatic coronal structures

Four separate but related studies of coronal magnetostatic equilibria under a variety of boundary conditions and distributions of coronal current are reviewed. Physically, all four studies assume an axisymmetric corona whose radial magnetic field at the coronal base is dipolar. Electric currents in the model coronas are assumed to flow in the azimuthal direction, giving rise to Lorentz forces that must be balanced by pressure gradients and gravity. Mathematically, such coronas are described by the equation of magnetostatic force balance and Ampere's law. Although highly idealized, the axisymmetric magnetostatic models described provide insights into the behavior of a variety of coronal structures. The models show how more realistic current sheet boundary conditions and coronal density variations may be modeled.

Wolfson, Richard↗

NASA NTRS1990

A self-consistent two-dimensional resistive fluid theory of field-aligned potential structures including charge separation and magnetic and velocity shear

A self-consistent two-fluid theory that includes the magnetic field and shear patterns is developed to model stationary electrostatic structures with field-aligned potential drops. Shear flow is also included in the theory since this seems to be a prominent feature of the structures of interest. In addition, Ohmic dissipation, a Hall term, and pressure gradients in a generalized Ohm's law, modified for cases without quasi-neutrality, are included. In the analytic theory, the electrostatic force is balanced by field-aligned pressure gradients (i.e., thermal effects in the direction of the magnetic field) and by pressure gradients and magnetic stresses in the perpendicular direction. Within this theory, simple examples of applications are presented to demonstrate the kind of solutions resulting from the model. The results show how the effects of charge separation and shear in the magnetic field and the velocity can be combined to form self-consistent structures such as are found to exist above the aurora, suggested also in association with solar flares.

Hesse, Michael↗

NASA NTRS1989

Comparison between pressure gradient method and MAC method on high Re calculation

A cavity flow driven by shear and buoyancy forces is used as a test problem in the application of a nonstaggered pressure gradient (PG) method in solving the two-dimensional incompressible Navier-Stokes equations. Twelve finite differencing schemes are used to solve the cavity flow problem. The schemes consist of various combinations of grid arrangements, upwinding treatments, and conservativeness of convection terms. An artificial source term is introduced, and the solutions are compared with those obtained by the conventional marker-and-cell (MAC) method. The comparisons favor the PG method. Numerical results obtained by the twelve schemes are compared with exact solutions in order to assess the stability and accuracy of each scheme.

Tan, C.-H.↗

NASA NTRS1971

Proposed techniques for launching instrumented balloons into tornadoes

A method is proposed to introduce instrumented balloons into tornadoes by means of the radial pressure gradient, which supplies a buoyancy force driving to the center. Presented are analytical expressions, verified by computer calculations, which show the possibility of introducing instrumented balloons into tornadoes at or below the cloud base. The times required to reach the center are small enough that a large fraction of tornadoes are suitable for the technique. An experimental procedure is outlined in which a research airplane puts an instrumented, self-inflating balloon on the track ahead of the tornado. The uninflated balloon waits until the tornado closes to, typically, 750 meters; then it quickly inflates and spirals up and into the core, taking roughly 3 minutes. Since the drive to the center is automatically produced by the radial pressure gradient, a proper launch radius is the only guidance requirement.

Grant, F. C.↗

NASA NTRS1987

Spacecraft attitude control momentum requirements analysis

The relationship between attitude and angular momentum control requirements is derived for a fixed attitude, Earth orbiting spacecraft with large area articulating appendages. Environmental effects such as gravity gradient, solar radiation pressure, and aerodynamic forces arising from a dynamic, rotating atmosphere are examined. It is shown that, in general, each environmental effect contributes to both cyclic and secular momentum requirements both within and perpendicular to the orbit plane. The gyroscopic contribution to the angular momentum control requirements resulting from a rotating, Earth oriented spacecraft is also discussed. Special conditions are described where one or more components of the angular momentum can be made to vanish, or become purely cyclical. Computer generated plots for a candidate space station configuration are presented to supplement the analytically derived results.

Robertson, Brent P.↗

NASA NTRS1988

Model structure of a cosmic-ray mediated stellar or solar wind

An idealized hydrodynamic model is presented for the mediation of a free-streaming stellar wind by galactic cosmic rays or energetic particles accelerated at the stellar wind termination shock. The spherically-symmetric stellar wind is taken to be cold; the only body force is the cosmic ray pressure gradient. The cosmic rays are treated as a massless fluid with an effective mean diffusion coefficient k proportional to radial distance r. The structure of the governing equations is investigated both analytically and numerically. Solutions for a range of values of k are presented which describe the deceleration of the stellar wind and a transition to nearly incompressible flow and constant cosmic ray pressure at large r. In the limit of small k the transition steepens to a strong stellar wind termination shock. For large k the stellar wind is decelerated gradually with no shock transition. It is argued that the solutions provide a simple model for the mediation of the solar wind by interstellar ions as both pickup ions and the cosmic ray anomalous component which together dominate the pressure of the solar wind at large r.

Lee, M. A.↗

NASA NTRS2000

Diffusion Driven Combustion Waves in Porous Media

Filtration of gas containing oxidizer, to the reaction zone in a porous medium, due, e.g., to a buoyancy force or to an external pressure gradient, leads to the propagation of Filtration combustion (FC) waves. The exothermic reaction occurs between the fuel component of the solid matrix and the oxidizer. In this paper, we analyze the ability of a reaction wave to propagate in a porous medium without the aid of filtration. We find that one possible mechanism of propagation is that the wave is driven by diffusion of oxidizer from the environment. The solution of the combustion problem describing diffusion driven waves is similar to the solution of the Stefan problem describing the propagation of phase transition waves, in that the temperature on the interface between the burned and unburned regions is constant, the combustion wave is described by a similarity solution which is a function of the similarity variable x/square root of(t) and the wave velocity decays as 1/square root of(t). The difference between the two problems is that in the combustion problem the temperature is not prescribed, but rather, is determined as part of the solution. We will show that the length of samples in which such self-sustained combustion waves can occur, must exceed a critical value which strongly depends on the combustion temperature T(sub b). Smaller values of T(sub b) require longer sample lengths for diffusion driven combustion waves to exist. Because of their relatively small velocity, diffusion driven waves are considered to be relevant for the case of low heat losses, which occur for large diameter samples or in microgravity conditions, Another possible mechanism of porous medium combustion describes waves which propagate by consuming the oxidizer initially stored in the pores of the sample. This occurs for abnormally high pressure and gas density. In this case, uniformly propagating planar waves, which are kinetically controlled, can propagate, Diffusion of oxidizer decreases the wave velocity. In addition to the reaction and diffusion layers, the uniformly propagating wave structure includes a layer with a pressure gradient, where the gas motion is induced by the production or consumption of the gas in the reaction as well as by thermal expansion of the gas. The width of this zone determines the scale of the combustion wave in the porous medium.

Aldushin, A. P.↗

NASA NTRS2022

Gas-Liquid Flows Through Porous Media in Microgravity: Packed Bed Reactor Experiment-2

Modifications were made to the Packed Bed Reactor Experiment (PBRE) and flown on the ISS as PBRE-2 to eliminate external pressure oscillations at higher liquid flow rates and the packing diameter was reduced to increase the pressure gradient for lower flows. It is found that gas hold-up is a function of bed history at low liquid and gas flow rates whereas higher gas hold-up and pressure gradients are observed for the test conditions following a liquid only pre-flow compared to the test conditions following a gas only pre-flow period. Over the range of flow rates tested, the capillary force is the dominant contributor to the pressure gradient, which is found to be linear with the superficial liquid velocity but is a much weaker function of the superficial gas velocity, and varying inversely with the particle diameter.

Mahsa Taghavi↗

NASA NTRS2000

Noninvasive estimation of transmitral pressure drop across the normal mitral valve in humans: importance of convective and inertial forces during left ventricular filling

OBJECTIVES: We hypothesized that color M-mode (CMM) images could be used to solve the Euler equation, yielding regional pressure gradients along the scanline, which could then be integrated to yield the unsteady Bernoulli equation and estimate noninvasively both the convective and inertial components of the transmitral pressure difference. BACKGROUND: Pulsed and continuous wave Doppler velocity measurements are routinely used clinically to assess severity of stenotic and regurgitant valves. However, only the convective component of the pressure gradient is measured, thereby neglecting the contribution of inertial forces, which may be significant, particularly for nonstenotic valves. Color M-mode provides a spatiotemporal representation of flow across the mitral valve. METHODS: In eight patients undergoing coronary artery bypass grafting, high-fidelity left atrial and ventricular pressure measurements were obtained synchronously with transmitral CMM digital recordings. The instantaneous diastolic transmitral pressure difference was computed from the M-mode spatiotemporal velocity distribution using the unsteady flow form of the Bernoulli equation and was compared to the catheter measurements. RESULTS: From 56 beats in 16 hemodynamic stages, inclusion of the inertial term ([deltapI]max = 1.78+/-1.30 mm Hg) in the noninvasive pressure difference calculation significantly increased the temporal correlation with catheter-based measurement (r = 0.35+/-0.24 vs. 0.81+/-0.15, p< 0.0001). It also allowed an accurate approximation of the peak pressure difference ([deltapc+I]max = 0.95 [delta(p)cathh]max + 0.24, r = 0.96, p<0.001, error = 0.08+/-0.54 mm Hg). CONCLUSIONS: Inertial forces are significant components of the maximal pressure drop across the normal mitral valve. These can be accurately estimated noninvasively using CMM recordings of transmitral flow, which should improve the understanding of diastolic filling and function of the heart.

Non-NASA Center↗

NASA NTRS1982

Numerical simulations of unsteady transonic flow in diffusers

Forced and naturally occurring, self-sustaining oscillations of transonic flows in two-dimensional diffusers were computed using MacCormack's hybrid method. Depending upon the shock strengths and the area ratios, the flow was fully attached or separated by either the shock or the adverse pressure gradient associated with the enlarging diffuser area. In the case of forced oscillations, a sinusoidal plane pressure wave at frequency 300 Hz was prescribed at the exit. A sufficiently large amount of data were acquired and Fourier analyzed. The distrbutions of time-mean pressures, the power spectral density, and the amplitude with phase angle along the top wall and in the core region were determined. Comparison with experimental results for the forced oscillation generally gave very good agreement; some success was achieved for the case of self-sustaining oscillation despite substantial three-dimensionality in the test. An observation of the sequence of self-sustaining oscillations was given.

Liou, M.-S.↗

NASA NTRS1989

Steady hydromagnetic flows in open magnetic fields. II - Global flows with static zones

A theoretical study of an axisymmetric steady stellar wind with a static zone is presented, with emphasis on the situation where the global magnetic field is symmetrical about the stellar equator and is partially open. In this scenario, the wind escapes in open magnetic fluxes originating from a region at the star pole and a region at an equatorial belt of closed magnetic field in static equilibrium. The two-dimensional balance of the pressure gradient and the inertial, gravitational, and Lorentz forces in different parts of the flow are studied, along with the static interplay between external sources of energy (heating and/or cooling) distributed in the flow and the pressure distribution.

Tsinganos, K.↗