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Dec 1961

Volume 4, Issue 12, pp. 1451-1575


Testing Time and Contact‐Zone Phenomena in Shock‐Tube Flows

William J. Hooker

Phys. Fluids 4, 1451 (1961); http://dx.doi.org/10.1063/1.1706243 (13 pages) | Cited 42 times

Online Publication Date: 9 December 2004

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Measurements have been made in a shock tube of the hot‐flow duration, the structure of the contact front, and the nature of the mixing zone. The flow duration was obtained by spectroscopically detecting the first arrival of the driver gas, and is observed to become vanishingly small with decreasing initial driven gas pressure. These data and the data of Roshko and Duff are compared with predictions of Roshko's (laminar) theory and the numerical example of Anderson's (turbulent) theory. Agreement with the one point of Anderson's prediction is surprisingly good, while the agreement with Roshko's theory ranges from excellent to unsatisfactory. Approximations in Roshko's treatment which contribute to the lack of correlation with the data obtained in the smaller diameter shock tubes of Duff and the present work are emphasized and a formulation of the flow model is developed which better predicts the actual shock‐tube flow durations.

Effect of Boundary‐Layer Growth in a Shock Tube on Shock Reflection from a Closed End

George Rudinger

Phys. Fluids 4, 1463 (1961); http://dx.doi.org/10.1063/1.1706244 (11 pages) | Cited 27 times

Online Publication Date: 9 December 2004

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The pressure behind a shock wave propagating in a constant‐area duct increases slightly with time as a result of the growing boundary layer. This rise is considerably magnified by the shock reflection from the closed end of the duct. Analysis of the local interaction of the reflected shock with the boundary layer yields information on the shock configuration, but the combined effects of the waves produced by the growing boundary layer along the entire shock tube must be considered to obtain the state of the gas behind the reflected shock. The theory of the flow field behind the incident shock is modified to allow for effects in addition to boundary‐layer growth which cause deviations from an ideal shock‐tube flow. Experimental observations of the pressure rise behind the reflected shock, obtained for shock pressure ratios up to about 4.5 are in satisfactory agreement with the computed results, and estimates for stronger shock waves are presented.

Interaction between a Magnetic Field and an Electrically Produced Shock Wave

John Paul Barach

Phys. Fluids 4, 1474 (1961); http://dx.doi.org/10.1063/1.1706245 (4 pages) | Cited 7 times

Online Publication Date: 9 December 2004

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Shock flows of speeds up to 1 cm∕μsec in krypton have been observed to interact with a magnetic field of 5700 gauss. A reflected shock is observed and deceleration of the flow is measured. Gas flows of up to Mach 63 are produced by an annular electric shock tube powered by a capacitor discharge of long time constant. A radial magnetic field geometry provides closed paths within the gas flow for the induced currents. The speed of the wave reflected off the magnetic field is found to increase slightly with interaction strength. The flow momentum lost per particle as the flow traverses the field region is calculated and is compared to the impulse delivered each particle by the magnetic field. Approximate agreement is found over a wide range of experimental conditions, validating the magnetohydrodynamic picture of the interaction and the use of the scalar gas conductivity.

Viscous Flow through Porous Media

Stephen Prager

Phys. Fluids 4, 1477 (1961); http://dx.doi.org/10.1063/1.1706246 (6 pages) | Cited 59 times

Online Publication Date: 9 December 2004

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The resistance of a porous medium to a fluid streaming through it is estimated by minimizing the rate of energy dissipation for a class of trial stress distributions. Rigorously valid lower bounds on the resistance are obtained in terms of certain two‐ and three‐point averages characterizing the medium. Results are given for flow both with and without slip at the pore walls.

Shear Coefficients for a Viscoelastic Substance in the Sonic Region

D. O. Miles

Phys. Fluids 4, 1482 (1961); http://dx.doi.org/10.1063/1.1706247 (6 pages) | Cited 10 times

Online Publication Date: 9 December 2004

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A pure sinusoidal shear is applied to a sample of diphenyl hexachloride at several temperatures in the frequency range 20 to 103 cps. The shear rigidity and shear viscosity are obtained as functions of frequency at each temperature. Comparison of viscosity at low frequencies and rigidity at high frequencies with measurements by others is within experimental errors. The experimental data deviate slightly from single relaxation theory for the Debye‐Frenkel model of liquids. Comparison of the distribution with that observed for compressional processes reveals a difference in shape, also predicted by the Debye‐Frenkel model. The temperature dependence of the high‐frequency shear rigidity is obtained and the expected plateau is observed below the glass transition.

Structural and Internal State Variables in the Description of Scalar Rate Processes in Fluids

R. E. Nettleton

Phys. Fluids 4, 1488 (1961); http://dx.doi.org/10.1063/1.1706248 (6 pages) | Cited 5 times

Online Publication Date: 9 December 2004

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Arguments are presented to show that the internal energy per molecule in a macroscopically small volume element of an infinite liquid should remain constant, in first approximation, during a sudden fluctuation in liquid structure at constant density and temperature. This result is shown to be consistent with a formulation of nonequilibrium thermodynamics in which the departures of structural parameters from their local equilibrium values appear as thermodynamic variables and in which there is no relaxing structural specific heat. However, it is shown that such a relaxing specific heat must appear in the treatment of variables which give the populations of internal states. Consistent with this fact a new theory of thermal relaxation, which includes inertial effects, is formulated. It is shown, on plausible assumptions, that one can calculate all the rate constants and relaxation times introduced to describe inertial effects, as well as the thermodynamic forces.

Virial Coefficients of Hydrogen‐Hydrocarbon Mixtures

J. F. Connolly

Phys. Fluids 4, 1494 (1961); http://dx.doi.org/10.1063/1.1706249 (6 pages) | Cited 11 times

Online Publication Date: 9 December 2004

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Virial coefficients have been obtained for mixtures of hydrogen with benzene, n‐octane, and 2,2,4‐trimethylpentane. The measurements were made by two methods and cover the temperature range 50° to 300°C. The mixed 2nd virial coefficients predicted by the Kihara intermolecular potential‐energy function are in better agreement with experiment than those predicted by that of Lennard‐Jones.

Conductivity of Slightly Ionized Gases

Leonard S. Taylor

Phys. Fluids 4, 1499 (1961); http://dx.doi.org/10.1063/1.1706250 (5 pages) | Cited 3 times

Online Publication Date: 9 December 2004

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A kinetic theory of the conductivity of a slightly ionized gas is developed to distinguish between alternate expressions derived by Desloge et al. from the Boltzmann transport equation. It is determined that the current in a Lorentzian model is obtained by averaging the electron drift velocity over a function resembling the zero field distribution shifted by the drift velocity. The linear term corresponds to one of the proposed expressions. Nonlinear terms may also be obtained. The quadrature current is increased by a factor proportional to the ratio of the average electron kinetic energy in the field to the kinetic energy in the absence of the field when the first nonlinear term is included.

Kirkendall Effect in Gaseous Diffusion. II. Absolute Determination of Diffusion Coefficients

E. A. Mason

Phys. Fluids 4, 1504 (1961); http://dx.doi.org/10.1063/1.1706284 (2 pages) | Cited 6 times

Online Publication Date: 9 December 2004

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It is shown how the Kirkendall effect in gaseous diffusion can be used to determine absolute values of diffusion coefficients, rather than only relative values, by extrapolation of the observed marker motion to zero capillary diameter. In this way the diffusion coefficient of He‐Ar at 30°C and 1 atm is found to be 0.761 cm2∕sec, in agreement with a directly measured value of 0.762 cm2∕sec.

Experiments on Alfvén‐Wave Propagation

John M. Wilcox, Alan W. DeSilva, and William S. Cooper

Phys. Fluids 4, 1506 (1961); http://dx.doi.org/10.1063/1.1706307 (8 pages) | Cited 26 times

Online Publication Date: 9 December 2004

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Torsional hydromagnetic waves are generated in a cylindrical hydrogen plasma. The device that generates the plasma is described. Spectroscopic observation of Stark‐broadened Balmer lines gives the ion density as a function of time and indicates that the plasma is highly ionized. Reflections of the hydromagnetic waves are observed from high‐ and low‐impedance boundaries, and from a plasma‐neutral gas interface. The phases of the reflected waves are found to agree with theory. The driving current that generates the waves is analyzed in terms of Newcomb's principal modes. The measured radial distribution of the wave magnetic field is in fair agreement with this analysis, and the observed wave magnetic field amplitude agrees to within 15% with that predicted on the basis of the voltage applied at the driving electrode, decreased by the measured damping factor. Two different types of measurement suggest that the decaying plasma is electrically isolated from the (conducting) walls.

Alfvén Waves in Solid‐State Plasmas

S. J. Buchsbaum and J. K. Galt

Phys. Fluids 4, 1514 (1961); http://dx.doi.org/10.1063/1.1706308 (3 pages) | Cited 39 times

Online Publication Date: 9 December 2004

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Alfvén waves can be studied experimentally in certain solid‐state plasmas with greater facility than in gaseous plasmas. This results from the fact that in these solid‐state plasmas all the charge carriers have masses equal to or less than the free electron mass. Alfvén waves can thus be studied at microwave frequencies. Previously published experimental results on microwave absorption in bismuth are reinterpreted in terms of the properties of Alfvén waves.

Source and Reflection Problems in Magneto‐Ionic Media

William C. Meecham

Phys. Fluids 4, 1517 (1961); http://dx.doi.org/10.1063/1.1706309 (8 pages) | Cited 3 times

Online Publication Date: 9 December 2004

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The scattering problems involving electromagnetic radiation propagating in magneto‐ionic media are formulated. Because of the magnetic field the medium becomes anisotropic. A practical case of great interest is that in which the frequency of the radiation is very low, in the audio range. A Green's formula is derived which expresses the field in interior regions in terms of the value of the field on any scattering surfaces present and the effect of sources. The Green's formula involves the Green's function in the usual way. The Green's functions is obtained, using a representation in terms of the eigenmodes for electromagnetic radiation propagating in the medium. The Green's function is evaluated for the special case of very low frequency.

Influence of Ion Motions on Nonlinear Plasma Oscillations

Russel Vernon

Phys. Fluids 4, 1524 (1961); http://dx.doi.org/10.1063/1.1706310 (3 pages) | Cited 3 times

Online Publication Date: 9 December 2004

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The effect of ion motions on the structure of nonlinear stationary electrostatic oscillations of a cold plasma is investigated. A solution is found by means of an expansion in powers of the electron‐to‐ion mass ratio m∕M. The frequency of oscillation, which is independent of amplitude for vanishing m∕M, turns out to be a decreasing function of the amplitude when the ion motions are included.

Stability of the Sharp Pinch and Unpinch with Finite Conductivity

J. D. Jukes

Phys. Fluids 4, 1527 (1961); http://dx.doi.org/10.1063/1.1706311 (7 pages) | Cited 12 times

Online Publication Date: 9 December 2004

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The stability of the sharp linear pinch and unpinch is analyzed using a model in which the magnetic fields are separated by a thin current layer of large, but finite electrical conductivity. Elsewhere the contained fluid is assumed to have zero conductivity, a model which may, for example, approximate a plasma pinch heated by the intermixing of skew magnetic fields. The perturbed radial displacement of the layer is assumed to be constant across the layer and small wavelength perturbations comparable to the layer thickness are not considered. Viscosity is also neglected. The infinitely conducting, ``stabilized'' pinch and the unpinch are now shown to be overstable to perturbations whose helices are approximately orthogonal to the helix of the mean magnetic field across the layer. The overstable growth rate is typically one tenth of the geometric mean of a fundamental, oscillatory frequency and the Ohmic diffusion rate of the layer.

Rotating Plasma Experiments. I. Hydromagnetic Properties

D. A. Baker, J. E. Hammel, and F. L. Ribe

Phys. Fluids 4, 1534 (1961); http://dx.doi.org/10.1063/1.1706312 (15 pages) | Cited 18 times

Online Publication Date: 9 December 2004

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Experiments on Ixion III, the Los Alamos rotating plasma device, using electrostatic and magnetic probe techniques are discussed. Analysis of the data indicates the presence of a two‐liter annular volume of rotating plasma whose mean mass density is ∼ 1 × 10−8 g∕cm3 and whose rotation decays with the supply voltage in ∼ 300 μsec. The plasma energy content of ∼ 130 joules appears to be nearly equipartitioned between ordered rotational drift motion and random thermal motion. Under typical operating conditions the data show the existence of drift velocities of ∼ 8 × 106 cm∕sec (∼ 65 ev for deuterium) and temperatures of the order of 30 ev. The operation of Ixion as a hydromagnetic capacitor in an oscillatory circuit is described.

Rotating Plasma Experiments. II. Energy Measurements and the Velocity Limiting Effect

D. A. Baker and J. E. Hammel

Phys. Fluids 4, 1549 (1961); http://dx.doi.org/10.1063/1.1706313 (10 pages) | Cited 20 times

Online Publication Date: 9 December 2004

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The total rotational energy and energy loss rate in Ixion III, the Los Alamos rotating plasma experiment, have been measured as functions of time. As the radial electric field is increased, a limiting velocity of rotation of approximately 1.3 × 107 cm∕sec is observed. Measurements indicate the presence of a region of fully ionized plasma whose contaminants radiate large amounts of energy in the form of line radiation in the vacuum ultraviolet. Mechanisms that have been proposed to explain the velocity limit are discussed in relation to the experimental results.

High‐β Injection into a Magnetic Mirror Field

F. R. Scott and O. C. Eldridge

Phys. Fluids 4, 1558 (1961); http://dx.doi.org/10.1063/1.1706314 (7 pages) | Cited 4 times

Online Publication Date: 9 December 2004

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Axial injection of a high‐density helium plasma into a magnetic mirror has been experimentally studied. Observations of the plasma‐field interaction were made with magnetic probes, electrostatic probes, piezoelectric probes, and an optical monochromator which analyzed emission‐line profiles. In the central plane of the mirror a density of 2 ± 1 × 1015 ions∕cm3 and a maximum ion temperature of 10 ev are indicated. In the upstream region ion temperatures of 35 ± 5 ev were recorded. Diamagnetic signals show that the high‐β plasma ``stagnates'' near the upstream throat of the mirror. Also, the derived plasma pressure measured on axis decreases exponentially downstream. Piezoelectric‐probe measurements show large axial‐momentum transfer rates in the downstream region of the mirror, where no diamagnetic signals are observed. The data are compared with a fluid model of a plasma which describes the injection, ``stagnation,'' and effusion along field lines. This experiment indicates that the axial injection of a collision‐dominate, high‐β plasma into a static mirror field is not efficient for producing and confining a high‐temperature plasma.
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Mach Reflection of 700‐kbar Shock Waves in Gases

B. B. Dunne

Phys. Fluids 4, 1565 (1961); http://dx.doi.org/10.1063/1.1706315 (2 pages) | Cited 1 time

Online Publication Date: 9 December 2004

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Abstract Unavailable

Magneto‐Fluid‐Dynamic Problem of a Shock Wave Attached to a Cone

J. R. Barthel and P. S. Lykoudis

Phys. Fluids 4, 1566 (1961); http://dx.doi.org/10.1063/1.1706316 (2 pages) | Cited 1 time

Online Publication Date: 9 December 2004

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Measurements of Electrode Drag and Conductance in a Supersonic Free Jet of Plasma

Sterge T. Demetriades and Richard W. Ziemer

Phys. Fluids 4, 1568 (1961); http://dx.doi.org/10.1063/1.1706317 (2 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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Novel Method of Measurement of Plasma Properties by Momentum‐Change Techniques

Sterge T. Demetriades

Phys. Fluids 4, 1569 (1961); http://dx.doi.org/10.1063/1.1706318 (2 pages) | Cited 2 times

Online Publication Date: 9 December 2004

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Injected Magnetic Compression Experiment

E. M. Little, J. Marshall, W. E. Quinn, and T. F. Stratton

Phys. Fluids 4, 1570 (1961); http://dx.doi.org/10.1063/1.1706319 (2 pages)

Online Publication Date: 9 December 2004

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Cyclotron Radiation from a Hot Plasma

Ernesto Tortia

Phys. Fluids 4, 1572 (1961); http://dx.doi.org/10.1063/1.1706320 (2 pages)

Online Publication Date: 9 December 2004

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Abstract Unavailable
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Comments on Theory of Electron‐Driven Shock Waves

H. D. Weymann

Phys. Fluids 4, 1573 (1961); http://dx.doi.org/10.1063/1.1706321 (2 pages)

Online Publication Date: 9 December 2004

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Answer to Comments by H. D. Weymann

R. G. Fowler

Phys. Fluids 4, 1574 (1961); http://dx.doi.org/10.1063/1.1706322 (2 pages)

Online Publication Date: 9 December 2004

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