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At least 307 records · Page 17

On the relationship between the growth and expansion phases of substorms and magnetospheric convection

It is suggested that the definition of the growth and expansion phases of substorms should rest on magnetospheric convection theories and data because of the ambiguities in interpretation of ground magnetometer records from which these concepts arose originally. Data such as that discussed in the report offers strong evidence for the validity and usefulness of the concepts of the growth and expansion phases.

Mozer, F. S.↗

Asymptotic expansion of an impulse for an optimal finite burn

Closed form expressions are derived for the position and velocity of a spacecraft during a finite burn using the method involving the theory of asymptotic expansion of the optimal impulsive solution. The small parameter is given by the reciprocal of the mass flow rate. The expansion is given in terms of the impulsive solution and holds up through third-order for the velocity and fourth-order for the position.

Pines, S.↗

Application of matched asymptotic expansions to lunar and interplanetary trajectories. Volume 2: Derivations of second-order asymptotic boundary value solutions

Previously published asymptotic solutions for lunar and interplanetery trajectories have been modified and combined to formulate a general analytical solution to the problem of N-bodies. The earlier first-order solutions, derived by the method of matched asymptotic expansions, have been extended to second order for the purpose of obtaining increased accuracy. The complete derivation of the second-order solution, including the application of a regorous matching principle, is given. It is shown that the outer and inner expansions can be matched in a region of order mu to the alpha power, where 2/5 alpha 1/2, and mu (the moon/earth or planet/sun mass ratio) is much less than one. The second-order asymptotic solution has been used as a basis for formulating a number of analytical two-point boundary value solutions. These include earth-to-moon, one- and two-impulse moon-to-Earth, and interplanetary solutions. Each is presented as an explicit analytical solution which does not require iterative steps to satisfy the boundary conditions. The complete derivation of each solution is shown, as well as instructions for numerical evaluation. For Vol. 1, see N73-27738.

Lancaster, J. E.↗

Thermal expansion method for lining tantalum alloy tubing with tungsten

A differential-thermal expansion method was developed to line T-111 (tantalum - 8 percent tungsten - 2 percent hafnium) tubing with a tungsten diffusion barrier as part of a fuel element fabrication study for a space power nuclear reactor concept. This method uses a steel mandrel, which has a larger thermal expansion than T-111, to force the tungsten against the inside of the T-111 tube. Variables investigated include lining temperature, initial assembly gas size, and tube length. Linear integrity increased with increasing lining temperature and decreasing gap size. The method should have more general applicability where cylinders must be lined with a thin layer of a second material.

Watson, G. K.↗

Pilot model expansion tunnel test flow properties obtained from velocity, pressure, and probe measurements

Velocity-profile, pitot-pressure, and supplemental probe measurements were made at the nozzle exist of an expansion tunnel (a modification to the Langley pilot model expansion tube) for a nozzle net condition of a nitrogen test sample with a velocity of 4.5 km/sec and a density 0.005 times the density of nitrogen at standard conditions, both with the nozzle initially immersed in a helium atmosphere and with the nozzle initially evacuated. The purpose of the report is to present the results of these measurements and some of the physical properties of the nitrogen test sample which can be inferred from the measured results. The main conclusions reached are that: the velocity profiles differ for two nozzle conditions; regions of the flow field can be found where the velocity is uniform to within 5 percent and constant for several hundred microseconds; the velocity of the nitrogen test sample is reduced due to passage through the nozzle; and the velocity profiles do not significantly reflect the large variations which occur in the inferred density profiles.

Friesen, W. J.↗

On the relationship between the growth and expansion phases of substorms and magnetospheric convection.

The definition of the growth and expansion phases of substorms is considered in terms of temporal sequences of magnetospheric convection. It is suggested that the definition of these phases should rest on magnetospheric convection theories and data because of the ambiguities in the interpretation of ground magnetometer records from which these concepts arose originally. Reviewed data are shown to offer strong evidence for the validity and usefulness of the concepts of substorm growth and expansion phases.

Mozer, F. S.↗

Thermal expansion compatibility of ceramic chip capacitors mounted on alumina substrates.

The thermal expansion coefficients of a representative sample of BaTiO3 and TiO2 ceramic chip capacitors and alumina substrates have been examined. These data have revealed large potential mechanical stresses under thermal cycling. A mathematical analysis of a composite model of the capacitor to predict the thermal expansion and modulus of elasticity and an analysis of the capacitor-substrate system to predict the magnitude of thermally induced stresses have been conducted. In all cases studied, thermally induced stresses great enough to cause capacitor body rupture or termination failure was predicted.

Allen, R. V.↗

Glass-to-metal seals comprising relatively high expansion metals

A glass suitable for glass-to-metal seals that has a resistance to attack by moisture and a high coefficient of linear thermal expansion is introduced. Linear expansion covers the range from 12 to 14 x 10 to the minus 6 C between room temperature and 500 C. The glass is essentially composed of, by molar percent, about 9% of K2O, about 10% of Na2O, about 70% of SiO2, about 6% Al2O3, and about 5% of MgO.

Hirayama, C.↗

Computer extension and analytic continuation of Stokes' expansion for gravity waves

Stokes' infinitesimal-wave expansion for steady progressive free-surface waves has been extended to high order using a computer to perform the coefficient arithmetic. Stokes' expansion has been found to be incapable of yielding the highest wave for any value of the water depth since convergence is limited by a square-root branch-point some distance short of the maximum. By reformulating the problem using a different independent parameter, the highest waves are obtained correctly. Series summation and analytic continuation are facilitated by the use of Pade approximants. The method is valid in principle for any finite value of the wavelength and solutions of high accuracy can be obtained for most values of the wave height and water depth.

Schwartz, L. W.↗

Flow properties in expansion tube with helium, argon, air, and CO2

Test flow velocities from 5 to 7 km/sec were generated in a 6-in. expansion tube using helium, argon, air, and CO2 test gases. Pitot pressure profiles across the flow at the test section are presented for the four test gases, and measured flow quantities are compared to computer predicted values. Comparison of predicted and measured flow quantities suggests the expansion to be near thermochemical equilibrium for all test gases and implies the existence of a totally reflected shock at the secondary diaphragm. Argon, air, and CO2 flows were observed to attenuate while traversing the acceleration section, whereas no attenuation was observed for helium.

Miller, C. G.↗

Shock shapes on blunt bodies in hypersonic-hypervelocity helium, air, and CO2 flows, and calibration results in Langley 6-inch expansion tube

Shock shape results for flat-faced cylinders, spheres, and spherically blunted cones in various test gases, along with preliminary results from a calibration study performed in the Langley 6-inch expansion tube are presented. Free-stream velocities from 5 to 7 km/sec are generated at hypersonic conditions with helium, air, and CO2, resulting in normal shock density ratios from 4 to 19. Ideal-gas shock shape predictions, in which an effective ratio of specific heats is used as input, are compared with the measured results. The effect of model diameter is examined to provide insight to the thermochemical state of the flow in the shock layer. The regime for which equilibrium exists in the shock layer for the present air and CO2 test conditions is defined. Test core flow quality, test repeatability, and comparison of measured and predicted expansion-tube flow quantities are discussed.

Miller, C. G., III↗

Description and initial operating performance of the Langley 6-inch expansion tube using heated helium driver gas

A general description of the Langley 6-inch expansion tube is presented along with discussion of the basic components, internal resistance heater, arc-discharge assemblies, instrumentation, and operating procedure. Preliminary results using unheated and resistance-heated helium as the driver gas are presented. The driver-gas pressure ranged from approximately 17 to 59 MPa and its temperature ranged from 300 to 510 K. Interface velocities of approximately 3.8 to 6.7 km/sec were generated between the test gas and the acceleration gas using air as the test gas and helium as the acceleration gas. Test flow quality and comparison of measured and predicted expansion-tube flow quantities are discussed.

Moore, J. A.↗

Plasma processes in the expansion of the solar wind and in the interplanetary medium

Recent research into plasma processes involved in the expansion of the solar wind and the interplanetary medium is reviewed. Emphasized topics deal primarily with processes that drive the solar wind, the gross expansion of the interplanetary medium between 0.5 and 5 AU, recent observational results in the vicinity of 1 AU, and the microstructure of the interplanetary medium. Satellite measurements of the radial profile of the interplanetary medium out to 5 AU are discussed together with model calculations of the solar wind and its possible driving mechanisms. Studies of Alfven and magnetoacoustic waves in the solar wind are summarized. Possible roles are considered for thermal conduction in coronal energy transport, and observations of ion velocity distributions near 1 AU are described.

Barnes, A.↗

A finite-difference analysis of the nozzle starting process in an expansion tunnel

A suitable finite-difference method for computing the quasi-one-dimensional unsteady flow in an expansion tunnel nozzle was identified. The difference equations are presented along with the appropriate stability limits. A parametric study of the starting process in an expansion tunnel nozzle is made, and acceptable operating conditions were determined.

Weilmuenster, K. J.↗

Solution of the exact equations for three-dimensional atmospheric entry using directly matched asymptotic expansions

The problem of determining the trajectories, partially or wholly contained in the atmosphere of a spherical, nonrotating planet, is considered. The exact equations of motion for three-dimensional, aerodynamically affected flight are derived. Modified Chapman variables are introduced and the equations are transformed into a set suitable for analytic integration using asymptotic expansions. The trajectory is solved in two regions: the outer region, where the force may be considered a gravitational field with aerodynamic perturbations, and the inner region, where the force is predominantly aerodynamic, with gravity as a perturbation. The two solutions are matched directly. A composite solution, valid everywhere, is constructed by additive composition. This approach of directly matched asymptotic expansions applied to the exact equations of motion couched in terms of modified Chapman variables yields an analytical solution which should prove to be a powerful tool for aerodynamic orbit calculations.

Busemann, A.↗

Measured opening characteristics of an electromagnetically opened diaphragm for the Langley expansion tunnel

Results from an experimental study of the opening characteristics of an electromagnetically opened, 15.24 cm diameter diaphragm are presented. This diaphragm consists of a polyester film bonded to a preformed wire and is opened by passing a current pulse (capacitor discharge) through the wire. The diaphragm separates the acceleration section of the expansion tunnel from the nozzle so that the nozzle may be at a lower pressure than the acceleration section prior to a test. Opening times and cleanness of the opened area were examined for dependence on diaphragm thickness, on wire diameter, on technique of bonding the wire to the diaphragm, and on voltage and energy level of the energy source. Time histories of the pitot pressure measured at the expansion-tunnel nozzle entrance location are presented for (1) no diaphragm, (2) a flow-opened diaphragm, and (3) an electromagnetically opened diaphragm.

Moore, J. A.↗

Free-jet expansions from laser-vaporized planar surfaces

Characteristics of free-jet vapor expansions created by the pulsed-laser vaporization of some refractory materials are examined. Such expansions were generated from planar surfaces at laser power densities up to 2.5 MW/sq cm. Time-integrated and time-resolved photography were used to show that the structure and pressures of such flows are correlated by the same relationship that is valid for free jets from orifice flows. Data show that the vapor velocity becomes sonic at or very near the vaporizing surface. A method is presented for deriving vaporization pressure from flow-field photos; such pressures from carbon-vaporization data for temperatures to 4500 K are in good agreement with extrapolated equilibrium vapor pressures. It is shown that this technique may be a means to determine vapor pressures of refractory materials at high temperatures.

Covington, M. A.↗

Flow-establishment times for blunt bodies in an expansion tube

Flow establishment results are presented as obtained from shock standoff distance, pressure, and heat transfer measurements in the Langley expansion tube. The models tested were flat-faced cylinders with varying radius and a sphere with a constant radius, and they were positioned at the acceleration section exit and tested in the open jet at zero angle of attack. The experimental results were obtained as spinoff from various studies using helium, air, and CO2 test gases at freestream velocities in the range 5-7 km/sec. Time histories of shock detachment distance illustrate that the shock formation about the smaller-radii flat-faced cylinders and the sphere is symmetrical, whereas a complex, asymmetric formation is observed for the larger-radii cylinders. Flow is shown to establish more readily about the sphere than a flat-faced cylinder of the same diameter. A quasi-steady flow exists about relatively large blunt models during two-thirds of the approximate 250-microsec expansion tube test period.

Miller, C. G.↗