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The complete development of the mathematical theory of hydrostatic equilibrium for the earth is recounted. Modifications of the first order theory are given along with the subsequent extension to the second order. In addition, the equations are presented which resulted from a revision of the second order theory to suit the new applications and data types of the post-artificial earth satellite era.
A flat seal having an angular misalinement is analyzed, taking into account the radial variations in seal clearance. An analytical solution for axial force, tilting moment, and leakage is presented that covers the whole range from zero to full angular misalinement. Nonaxisymmetric hydrostatic pressures due to the radial variations in the film thickness have a considerable effect on seal stability. When the high pressure is on the outer periphery of the seal, both the axial force and the tilting moment are nonrestoring. The case of high-pressure seals where cavitation is eliminated is discussed, and the possibility of dynamic instability is pointed out.
A description is presented of a sequence of one-dimensional fluid flow models of the transition zone and the inner corona. A hydrostatic model atmosphere in reasonable agreement with observations of closed, large-scale coronal structures found in the quiet sun is considered and various physical effects are introduced, one at a time, observing the response of the model. As a result of the investigations, a model is developed of the plasma flow in a coronal hole. It is shown that the data severely circumscribe the allowable range of possible models.
This report describes the application of a three-dimensional two-component model to the distribution of argon in the upper atmosphere of the earth. The Cira (1972) model is used to specify the background gas density and the temperature as functions of altitude, latitude, local time, and day of the year. Emphasis is placed on examining the effects of departures from hydrostatic equilibrium on the argon density distribution. Such effects are found to be significant, producing a strong summer argon bulge. Comparisons of the model results with observational data are discussed.
Critical current studies have been made on copper-clad Nb-Ti composite wire prepared under area reductions of 100:1 and 10,000:1 by hydrostatic extrusion (HE), wire drawing and HE plus drawing. Comparative evaluation of the thermomechanical processing equivalent of HE was performed.
Numerical solutions are presented for the fundamental natural frequency and mode shape of a rectangular plate loaded by in-plane hydrostatic forces for a wide variety of aspect ratios, boundary conditions, and load magnitudes. All six possible combinations of simply supported and clamped edges are considered. The limiting conditions of unloaded vibration and buckling are discussed in detail, with emphasis on the preferred mode shape. Design curves and approximate formulae are presented which provide a simple means of determining the fundamental frequency parameter.
Results of an investigation into the causes of the deterioration and premature failure of the grout under the hydrostatic bearing runner at DSS 14 are reported. Generic types of materials were screened and tested to find a grout material more resistive to the causes of grout failure. Emphasis was placed on the physical properties, strength, modulus of elasticity, and resistance to erosion and chemical attack by oil and unique requirements imposed by each material for mixing, placing, compacting, and cooling. The polymetric grout developed to replace the dry grout is described.
A device for damping radial motion of a rotating shaft is described. The damper comprises a series of spaced plates extending in a radial direction. A hydraulic piston is utilized to place a load in these plates. Each annular plate is provided with a suitable hydrostatic bearing geometry on at least one of its faces. This structure provides a high degree of dampening in a rotor case system of turbomachinery in general. The damper is particularly useful in gas turbine engines.
Baroclinic waves in the atmospherics general circulation experiment (AGCE) apparatus by the use of numerical hydrostatic primitive equation models were determined. The calculation is accomplished by using an axisymmetric primitive equation model to compute, for a given set of experimental parameters, a steady state axisymmetric flow and then testing this axisymmetric flow for stability using a linear primitive equation model. Some axisymmetric flows are presented together with preliminary stability calculations.
The vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating supply pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and the sleeve is solved numerically together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The results presented include Bode plots of bearing oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency. The results are compared with the results of an earlier study involving the response of a similar bearing to oscillating exhaust pressure.
Vibration of a statically loaded, inherently compensated hydrostatic journal bearing due to oscillating exhaust pressure is investigated. Both angular and radial vibration modes are analyzed. The time-dependent Reynolds equation governing the pressure distribution between the oscillating journal and sleeve is solved together with the journal equation of motion to obtain the response characteristics of the bearing. The Reynolds equation and the equation of motion are simplified by applying regular perturbation theory for small displacements. The numerical solutions of the perturbation equations are obtained by discretizing the pressure field using finite-difference aproximations with a discrete, nonuniform line-source model which excludes effects due to feeding hole volume. An iterative scheme is used to simultaneously satisfy the equations of motion for the journal. The results presented include Bode plots of bearing-oscillation gain and phase for a particular bearing configuration for various combinations of parameters over a range of frequencies, including the resonant frequency.
The dynamics of hydrostatic gravity waves generated by the passage of a steady, stably stratified, moist flow over a two-dimensional topography is considered. Coriolis effects are neglected. The cloud region is determined by the dynamics, and within that region the Brunt-Vaisala frequency takes on a value smaller than the outside value. In both the dry and cloudy regions the Brunt-Vaisala frequency is constant with height. The moist layer is considered to be either next to the mountain or at midlevels and to be deep enough so that an entire cloud forms in that layer. The nonlinearity in the flow and lower boundary affects the dynamics of these waves and wave drag. The latter is found to depend upon: (1) the location of the moist layer with respect to the ground, (2) the amount of moisture, (3) the degree of nonlinearity and (4) the departure from symmetry in the bottom topography.
A computer algorithm for simulation of hydrostatic journal bearing pressure-flow behavior has been generated. The effects taken into account are inertia, cavitation, variable properties (isothermal bearing) and roughness. The program has been specifically tailored for simulation of the hybrid bearing of the cryogenic turbopumps of the main shuttle engine. Due to the high pressure (515 psia) of the supply line no cavitation has been found. The influence of the roughness effects have been found to become important only when the surface-roughness order of magnitude is comparable with that of the bearing clearance itself. Pocket edge inertia and variable properties have been found to have quite an important influence upon the pocket pressure, field pressure distribution and lubricant mass flow.
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.
Hydrostatic bearings used in advanced turbopump designs use the pumped propellant as the working fluid and supply the propellant to the bearing from pump discharge. The resulting rotordynamic coefficients are highly speed-dependent and in some instances can cause system natural frequencies to coincide with spin speed over a wide speed range. This paper discusses this 'synchronous tracking' phenomenon. The factors affecting it are defined, and specific examples are presented. Methods which identify synchronous tracking issues early in the design process are reported, and techniques for eliminating this undesirable characteristic are addressed.
The energy balance in the lower transition region is analyzed by constructing theoretical models which satisfy the energy balance constraint. The energy balance is achieved by balancing the radiative losses and the energy flowing downward from the corona. This energy flow is mainly in two forms: conductive heat flow and hydrogen ionization energy flow due to ambipolar diffusion. Hydrostatic equilibrium is assumed, and, in a first calculation, local mechanical heating and Joule heating are ignored. In a second model, some mechanical heating compatible with chromospheric energy-balance calculations is introduced. The models are computed for a partial non-LTE approach in which radiation departs strongly from LTE but particles depart from Maxwellian distributions only to first order. The results, which apply to cases where the magnetic field is either absent, or uniform and vertical, are compared with the observed Lyman lines and continuum from the average quiet sun. The approximate agreement suggests that this type of model can roughly explain the observed intensities in a physically meaningful way, assuming only a few free parameters specified as chromospheric boundary conditions.
Several modifications made to enhance utility of HBEAR, computer program for analysis and design of hydrostatic bearings. Modifications make program applicable to more realistic cases and reduce time and effort necessary to arrive at a suitable design. Uses search technique to iterate on size of orifice to obtain required pressure ratio.
The radiation of energy by hydrogen lines and continua in hydrostatic energy-balance models of the transition region between the solar chromosphere and corona is studied using models which assume that mechanical or magnetic energy is dissipated in the hot corona and is then transported toward the chromosphere down the steep temperature gradient of the transition region. These models explain the average quiet sun and also the entire range of variability of the Ly-alpha lines. The relations between the downward energy flux, the pressure of the transition region, and the different hydrogen emission are described.