Showing papers on "Hydrostatic equilibrium published in 1987"

A model for resin flow during composite processing: Part 1—general mathematical development

Abstract: A generalized three-dimensional model for resin flow during composite processing has been developed. The model is based on a theory of consolidation and flow through a porous medium, which considers that the total force acting on a porous medium is countered by the sum of the opposing forces, including the force due to the spring-like effect of the fiber network and the hydrostatic force due to the pressure of the liquid within the porous medium. The flow in the laminate is described in terms of Darcy's Law for flow in a porous medium, which requires a knowledge of the fiber network permeability and the viscosity of the flowing fluid. Unlike previous resin flow models, this model properly considers the flows in different directions to be coupled and provides a unified approach in arriving at the solution. Comparison of numerical solutions with the closed form analytical solution shows good agreement. Resin pressure profiles show that the pressure gradients in the vertical and horizontal directions are not linear, unlike the assumption of linearity made in several previous resin flow models. The effects on the resin pressure of both linear and nonlinear stress-strain behavior of the porous fiber network were considered. The nonlinear behavior simulates a rapidly stiffening spring and the resin pressure decreases much more rapidly after a given initial period compared to the linear stress-strain behavior.

The stability of accretion tori. II - Non-linear evolution to discrete planets

Abstract: Hawley has shown through two-dimensional computer simulations that a slender torus in which a linear Papaloizou-Pringle (PP) instability with azimuthal wavenumber m, is excited evolves non-linearly to a configuration with m nearly disconnected 'planets'. We present an analytical fluid equilibrium that we believe represents his numerical planets. The fluid has an ellipsoidal figure and is held together by the Corio lis force associated with the retrograde fluid motion. There is a bifurcation between the torus and planet configurations at precisely the vorticity below which the PP instability switches on. Although the solution is three-dimensional, there is perfect hydrostatic equilibrium and the motion is entirely two-dimensional. We analyse the linear modes of the analytical planet and find that there are numerous instabilities, though they are not as violent as the PP instability in the torus. We also discuss the energy and vorticity of neutral modes, and we argue that when the torus breaks up into planets, neutral modes with negative energy and non-zero vorticity are excited in order to conserve total energy and specific vorticity. We speculate that the fluid in Hawley's simulations may be approaching two-dimensional turbulence.

Mean Fields Induced by Local Gravity-Wave Forcing in the Middle Atmosphere

Abstract: The role of geostrophic adjustment in the middle atmosphere for given wave packet forcing by a three-dimensional hydrostatic model is examined. It is shown that the induced fields consist of two different kinds of modes. One, produced by forcing vorticity only, is steady quasi-geostrophic flow; this is restricted to the forcing region. The other, produced by both forcing vorticity and forcing divergence, is oscillatory, and is in the form of gravity waves propagating out of the forcing region plus inertial oscillations in the forcing region. The scales and amplitudes of the induced gravity waves are determined by the forcing. For a typical example, a 200 km x 200 km gravity wave packet of momentum flux 0.5 N/sq m absorbed in a layer of 5 km thickness centered near 18 km altitude, the gravity waves spread to a larger region about 1000 km x 1000 km at a level 7 km above the forcing region. At that level, the horizontal and vertical wavelengths of the induced waves are about 300 km and 7 km respectively, and the momentum flux is substantially reduced to 0.0004 N/sq m. The results suggest that geostrophic adjustment processes may play an important role in specifying the gravity wave spectrum in the middle atmosphere.

On stable hydrostatic equilibrium configurations of the galaxy and implications for its halo

Abstract: Using a variety of observations, it is shown that the gaseous, magnetic field, and cosmic-ray components in the local region of the Galaxy may be in a large-scale hydrostatic equilibrium that is stable against Parker-type instabilities. Lower limits for the density of the halo are derived as a function of its scale height. The temperature of the hot medium in the disk and at large distances from the plane is found to be typically about a million K in a stable equilibrium, whereas around z roughly 1-3 kpc the temperature could be only 200,000-300,000 K. The scale height of the sum of cosmic-ray and magnetic field pressures in a stable hydrostatic equilibrium state is found to be only weakly dependent on the scale height of the gaseous halo. 109 references.

Quasi-static winds from neutron stars

Abstract: A series of numerical models is constructed for radiatively driven, quasi-static winds from the surfaces of hot neutron stars. A mathematical technique is devised that in many cases facilitates the integration of the fluid equations in the vicinity of the sonic point, and an improved treatment of radiative transfer is developed that is appropriate to the exotic physical conditions encountered in the models. Boundary conditions which are more realistic than previous ones are used in these models. In agreement with earlier studies, it is found that radiatively driven winds are likely to be directly relevant to the existence of precursors in fast X-ray transients and to apparent radius variations during the course of some type I bursts, and that the presence of such a wind should prevent the bolometric luminosity of a neutron star from exceeding the Eddington limit by more than a small fractional amount. Formulas describing the wind models are presented which are usable as boundary conditions for calculations of the evolution of the deeper, hydrostatic layers of a neutron-star envelope.

A Fully Coupled Variable Properties Thermohydraulic Model for a Cryogenic Hydrostatic Journal Bearing

Abstract: The goal set forth here is to continue the work started by Braun et al. (1984-1985) and present an integrated analysis of the behavior of the two row, 20 staggered pockets, hydrostatic cryogenic bearing used by the turbopumps of the Space Shuttle main engine. The variable properties Reynolds equation is fully coupled with the two-dimensional fluid film energy equation. The three-dimensional equations of the shaft and bushing model the boundary conditions of the fluid film energy equation. The effects of shaft eccentricity, angular velocity, and inertia pressure drops at pocket edge are incorporated in the model. Their effects on the bearing fluid properties, load carrying capacity, mass flow, pressure, velocity, and temperature form the ultimate object of this paper.

A Forced Gravity Wave Model of Serf-Organizing Convection

Abstract: A two-dimensional, hydrostatic, nonrotating numerical model with a cumulus paramelerizafion is developed to study the early stages of mesozcale convective systems. Amplifying, forced gravity waves occur when peneirative downdrafts are present. Updraft heating by itself is unable to cause convective sysiems to intensify. Propagation speeds are in rough agreement with those observed in midlatitude mesoscale convective systems. The conditionalityof the convection and the horizontal advection of precipitation by the relative wind produce las between lifting and convection that are not found in conventional wave-CISK models. These lags slow the growth and reduce the propasation speeds of forced gravity waves.

Measurement of heat capacity under hydrostatic pressure between 0.5 K and 15 K

Abstract: An experimental method for measurement of the low-temperature heat capacity at hydrostatic pressures and external magnetic fields was developed. Also, a suitable pressure-transmitting medium (Apieson-J oil) was found which had good thermal properties for the present method to measure the thermal and magnetic properties of a single crystal of CuCl22H2O (TN=4.33 K) at hydrostatic pressures of up to 6 kbar.

The Mechanics of Equibiaxial Hydrostatic Deformation in Solid State: Isotactic Polypropylene

Abstract: Equibiaxial, hydrostatic deformation of isotactic polypropylene (i‐PP) of an intermediate weight average molecular weight (29×105) has been achieved by uniaxial compression between two axially aligned circular cylinders at the desired draw temperature (TDR) Independent measurements of load (ie, stress) and displacement (ie, strain) are made during the course of deformation A systematic variation in TDR (from 30–130°C) at a ram speed of 025 in/min has been studied The stress‐strain data corrected for machine compliance has been compared to a theoretical model This model assumes a rigid‐plastic behavior with a hydrostatic pressure effect The shear stress at the wall, caused by metal‐polymer contact, is coulombic friction As the compressive force (and, hence the hydrostatic pressure) is increased, the frictional shear stress (in the central portion of the compressed sample) exceeds the maximum shear stress (also changing with hydrostatic pressure), causing the i‐PP to yield on the surface (refe

Balanced Flow States Resulting from Penetrative, Slantwise Convection

Abstract: Analytic solutions representing rectilinear flow in geostrophic and hydrostatic balance are constructed using the conformal mapping technique of Gill. Two types of mapping are used to characterize the state of a fluid after a parcel convects to a position of neutral buoyancy. The first mapping corresponds to the homogeneous intrusion in a rotating, stratified fluid studied by Gill. The second mapping describes an internal discontinuity of finite length, embedded in a fluid of uniform potential vorticity. In the idealized physical problem represented by these conformal transformations, an elliptical region of undisturbed fluid is considered to be “saturated” and in a state of unstable equilibrium. On perturbing the system, the saturated parcel convects to a new level distant from its initial position and is rendered homogeneous in absolute momentum and potential temperature by internal mixing. The resulting equilibrium configuration involves a two-dimensional fluid lens, which 1ocally distorts the...

Study of Linear Steady Atmospheric Flow above a Finite Surface Heating

Abstract: The steady-state atmospheric responses to a finite surface heating through thermal eddy diffusion are studied. The effects of the mean wind, the earth's rotation, and the thermal stratification are considered in a linear system. Scale analysis reveals the limit of the hydrostatic approximation. It shows that the classical aspect ratio is not sufficient in determining the validity of the hydrostatic approximation. It shows that the classical aspect ratio is not sufficient in determining the validity of the hydrostatic approximation, and what the diffusive aspect ratio, the stratification aspect ratio and the Rossby number should be included. Various circulation patterns are presented for different horizontal heating scales and shapes and for different atmospheric mean conditions. In a comparison paper, this study I In a composition paper, this study is extended to investigate the lake-effect nownstorms in the vicinity of Lake Michigan.

Liquid thickness vs. vertical pressure gradient in a model of the pleural space.

Abstract: In recent studies using relatively noninvasive techniques, the vertical gradient in pleural liquid pressure was 0.2–0.5 cmH2O/cm ht, depending on body position, and pleural liquid pressure closely approximated lung recoil (J. Appl. Physiol. 59: 597–602, 1985). We built a model to discover why the vertical gradient in pleural pressure is less than hydrostatic (1 cmH2O/cm). A long rubber balloon of cylindrical shape was inflated in a plastic cylinder. The “pleural” space between the balloon and cylinder was filled with blue-dyed water. With the cylinder vertical, we measured pleural pressure by a transducer through side taps at 2-cm intervals up the cylinder. The pressure was measured with different amounts of water in the pleural space. With a clear separation between the balloon and the container, the vertical gradient in pleural liquid pressure was hydrostatic. As water was withdrawn from the pleural space, the balloon approached the wall of the container. Over an 8-cm-long midregion of the model where the balloon diameter matched the cylinder diameter, the vertical gradient was not hydrostatic and was virtually absent. In this region, the pleural liquid pressure was uniform and equal to the recoil of the balloon. In this section we could not see any pleural space. By scintillation imaging using 99mTc-diethylenetriamine pentaacetic acid in the water, we estimated the thickness of this flat “costal” pleural space to be approximately 20 microns. Radioactive tracer injected at the top of the pleural space appeared by 24 h at the bottom, which indicated a slow drainage of liquid by gravity.(ABSTRACT TRUNCATED AT 250 WORDS)

The evolution of cooling flows. I - Self-similar cluster flows

Abstract: The evolution of a cooling flow from an initial state of hydrostatic equilibrium in a cluster of galaxies is investigated. After gas mass and energy are injected into the cluster at an early phase, the gas approaches hydrostatic equilibrium over most of the cluster and cooling becomes important in the dense central regions. As time passes, cooling strongly affects an increasing amount of gas. The effects of mass removal from the flow, the inclusion of magnetic or cosmic-ray pressure, and heat conduction are considered individually.

Moist Convection at a Surface Cold Front

Abstract: The motion of a surface cold front in an environment that is unstable to moist convection is studied with the aid ofboth hydrostatic and nonhydrostatic two-dimensional models. Simulations with the hydrostatic model essentially extend the work reported by Ross and Orlanski. It is shown that when deep convection occurs, Coriolis turning of the flow into the convective line creates a poleward low-level jet ahead of the front. It is also shown that after the generation and decay of the first convective element, another line develops on the order of a day later. It is found that the intensity of this line increases significantly ira north-south gradient of moisture is specified. The periodicity in convective activity at the front is explained in terms of an inertial gravity oscillation in the low-level convergence. The first convective system, which decays when the subeloud layer is dried out by the convection, forces a geostrophic imbalance in the surface front and the surrounding environment. In ret...

Device for measuring the quantity of fluid contained in a tank

Abstract: Device for measuring the quantity of fluid 3 contained in a tank 1 disposed in a vehicle According to the invention, this device is noteworthy in that hydrostatic measurement means 5 deliver at least one output signal 12 representing the hydrostatic pressure difference between an upper measurement point 9 and a lower measurement point 8 provided in the tank 1, in that the means 15 generating the signal connected to the attitude of the vehicle deliver at least the vertical component of the acceleration to which the said tank 1 is subjected and in that the said computer 18 calculates a magnitude equal to the ratio between the hydrostatic pressure difference and the product of the density of the fluid with the vertical component of the acceleration Gauging liquids

The shape of a planet in hydrostatic equilibrium. An application to the Earth

Abstract: A new technique for computing gravitational equilibrium surfaces (considering gravitational and rotational potential) as a function of depth is presented here for a hydrostatic planet,i.e. a planet where rigidity is neglected. This work was formerly approached by Clairaut, and more recently by Lanzano; in this paper a new technique is developed that solves the problem without making use of the Clairaut differential equation. It is possible to define the gravitational potential of a planet by dividing it intoN shells, each of constant density, with a greater accuracy than in previous works; we can compute the equilibrium surface of each shell with an iterative technique,i.e. by modifying the solution by little steps until the desired accuracy is obtained. In the case of the Earth the geoid is found to be flatter than this ideal surface (this had already been observed also by means of completely different methods, for example by investigating the precession of the Earth). A possible reason for such a discrepancy is that it is too great an approximation to consider the Earth's density as being a function only of the depth.

Hydrostatic Adjustment Time of the Solar Subconvective Layer

Abstract: One objection that has been raised against the suggestion that the solar cycle is driven by magnetohydromagnetic activity below the convective zone is that the Kelvin-Helmholtz time is a million years. In fact, as is argued here, the subconvective layer adjusts its hydrostatic structure in response to highly nonradial disturbances in a few years.

White Dwarf Stars: Laboratories for Strongly Coupled Plasma Physics

Abstract: The white dwarf phase corresponds to the final configuration in the evolution of the vast majority of stars. The Sun, for example, will end its life as a white dwarf. When nuclear fuel is exhausted in a typical star, gravity is no longer balanced by the internal pressure generated by nuclear energy sources and the star collapses on itself. Hydrostatic equilibrium is again restored when degenerate electron pressure takes over. At that stage, further contraction is prevented, the object has reduced its radius to about 1% of the solar radius, and we speak of a white dwarf star.

Turbulent Lubrication for a Hydrostatic Thrust Bearing with a Circular Recess : Vibration, Control Engineering, Engineering for Industry

Abstract: The paper is concerned with the characteristics of hydrostatic thrust bearings operating in the turbulent regime. Using the calculated results of the three-dimensional turbulent mean velocity between a rotating disk and a fixed wall, as already proposed, the pressure distribution, the load capacity and the oil flow rate of the hydrostatic thrust bearing with a circular recess are presented. Comparing the calculated results with the experimental ones, it has been found that the characteristics of the above bearing are little influenced by the transition to turbulence of the lubricant flow in the recess, but the transition in the land produces an extreme change in the bearing characteristics such as the load capacity and the lubricant flow rate.

Hydrostatic pressure dependence of the exponential optical absorption in CdInGaS4

Abstract: The optical‐absorption spectra in the semiconductor CdInGaS4 have been measured precisely at various hydrostatic pressures up to 20 kbar, and analyzed in the region below the fundamental absorption edges. It can be seen that the absorption coefficients plotted semilogarithmically vary linearly with photon energy below the fundamental absorption edges at each hydrostatic pressure. The steepness of the absorption edge is proportional to the inverse of hydrostatic pressure.

Accurate Pressure Gradient Calculations in Hydrostatic Atmospheric Models

Abstract: Most models of atmospheric flow which use the primitive equations require a diagnostic equation to determine local total pressure. In hydrostatic models, this equation is the vertically integrated hydrostatic equation. A frequently used approximation to this integration is to hold the temperature constant within model layers yielding a linear proportionality between Op or Mir (Exner’s function) and Az. This procedure yields static pressures with errors on the order of 10−3mb.

Structure of the Jovian Envelope and the Equation of State of Dense Hydrogen

Abstract: The interior composition of the planet Jupiter is deduced by comparing models generated from the equation of hydrostatic equilibrium and high-pressure equations of state with the known mass, equatorial radius, and gravitational multipole moments of the planet. The planet is primarily composed of liquid metallic hydrogen, but there appears to be a substantial admixture of denser elements present as well. Jupiter’s hydrogen-rich envelope is substantially enriched in material other than hydrogen and helium, containing approximately 20 to 60 earth masses of such material, in addition to 6 to 4 earth masses of such material in a distinct core. Thus Jupiter’s bulk composition differs from that of the sun. These conclusions are heavily dependent upon accurate pressure-density relations for pure metallic hydrogen in the pressure range from about 3 to 40 megabars, and at temperatures ranging from about 10000 to 20000 K. Experimental results for compression of hydrogen in the nonmetallic pressure range are helpful in constraining models, but accurate theoretical calculations of the thermodynamics of the liquid metallic phase provide the most help in constraining models. We discuss the state of the strongly-coupled plasma in the Jovian interior, and propose a phase diagram for dense liquid hydrogen.

Finite difference solution for a generalized Reynolds equation with homogeneous two-phase flow

Abstract: An attempt is made to relate elements of two-phase flow and kinetic theory to the modified generalized Reynolds equation and to the energy equation, in order to arrive at a unified model simulating the pressure and flows in journal bearings, hydrostatic journal bearings, or squeeze film dampers when a two-phase situation occurs due to sudden fluid depressurization and heat generation. The numerical examples presented furnish a test of the algorithm for constant properties, and give insight into the effect of the shaft fluid heat transfer coefficient on the temperature profiles. The different level of pressures achievable for a given angular velocity depends on whether the bearing is thermal or nonisothermal; upwind differencing is noted to be essential for the derivation of a realistic profile.

Hydrostatic analysis of marine vehicles with trapped air cavities

Abstract: Results of a theoretical and experimental investigation of the contribution of trapped air cavities to the hydrostatic stability of marine vehicles is presented. The pneumatic compliance they afford reduces vessel motion in waves and is achieved through the use of open bottom tanks mounted on the vehicles. Semisubmersible and monohull vessels are considered.

Effect of hydrostatic pressure on the viscosity of failure of polymeric materials

Abstract: A setup and method were developed for studying the effect of hydrostatic pressure on the characteristics of the crack resistance of polymeric materials. The viscosity of failure of material K-4I based on butyl rubber was determined in a wide range of rates of crack propagation and hydrostatic pressures. It was found that an increase in the hydrostatic pressure increases the resistance to crack propagation in a polymeric material. The pressure-time analogy method, where the dependences of the viscosity of failure on the rate of crack growth are parallelly shifted to the value of the pressure-time shift and a generalized curve is formed, can be used for taking the effect of the pressure into consideration.

Computer Simulation of Hydrostatic Co-Extrusion of Bimetallic Compounds.

Abstract: 2.2 .1 Analytical Approaches ............................................................... 50 2 .2 .1 .1 Energy Method .............................................................. 50 2 .2 .1 .2 Slab A n a l y s i s .............................................................. 53 2 .2 .1 .3 Lower Bound Analysis ............................................. 54 2 .2 .1 .4 Upper Bound Analysis ............................................. 54 2 .2 .2 Numerical Approaches .................................................................... 55 CHAPTER 3 FINITE ELEMENT ANALYSIS OF METAL FORMING PROCESSES . . 57 3.1 I n t r o d u c t i o n ................................................................................................ 57 3.2 T h e o r y ............................................................................................................ 59 3.2 .1 Basic M e c h a n i c s .......................................................................... . 60 3 .2 .1 .1 Displacements .............................................................. 60 3 .2 .1 .2 S t ra in Measures ............................................................ 62 3 .2 .1 .3 S t ra in Rates ................................................................... 67 3 .2 .1 .4 S t ress Measures and S t ra in Rates ...................... 68 3 .2 .2 Governing Equations fo r E la s to -p la s t i c D e f o r m a t i o n .................................................................................... 70 3 .2 .3 Const i tu t ive Equations fo r E la s to -P la s t i c D e f o r m a t i o n .................................................................................... 72 3.3 The F in i te Element Program ..................................................................... 74 3.4 Simulation Parameters ............................................................................... 78 CHAPTER 4 HYDROSTATIC EXTRUSION EXPERIMENTS ...................................... 81 4.1 I n t r o d u c t i o n ................................................................................................ 81 4.2 Hydrostatic Extrusion Experiments ...................................................... 81 4.2 .1 Experimental F a c i l i t i e s .......................................................... 81 4 .2 .2 Experimental Procedure .............................................................. 83 4.3 Residual S t ress Measurements ............................................................... 86 4 .3 .1 Residual S t resses ....................................................................... 86 4 .3 .2 Sachs' Boring-out Technique .................................................. 87 4 .3 .2 .1 Radial S t resses ........................................................... 87 4 .3 .2 .2 Tangential S t resses ................................................... 89 4 .3 .2 .3 Longitudinal S tresses ............................................... 91 4 .3 .3 Electro-chemical Machining ...................................................... 92 4.4 Experimental S t ress Measurements ...................................................... 96 4.4 .1 Experimental F a c i l i t i e s and Materia ls ............................. 96 4 .4 .2 Sample Preparat ion ....................................................................... 99 4 .4 .3 Cal ib ra t ion o f Electro-chemical Machining .................... 100 4 .4 .4 Experimental Procedure ............................................................... 101

Turbulent lubrication for hydrostatic thrust bearing with a circular recess.

Abstract: This paper is concerned with the characteristics of hydrostatic thrust bearings operating in the turbulent regime. Using the calculated results of the three-dimensional turbulent mean velocity between a rotating disk and a fixed wall as already proposed, the pressure distribution, the load capacity and the oil flow rate of the hydrostatic thrust bearing with a circular recess are presented. Comparing the calculated results with the experimental ones, it has been found that the characteristics of the above bearing are little influenced by the transition to turbulence of the lubricant flow in the recess, but that the transition in the land produces an extreme change to the bearing characteristics such as the load capacity and the lubricant flow rate.