Showing papers on "Rarefaction published in 1974"

Nuclear Fusion Reactions in Fronts Propagating in Solid DT

Abstract: The use of strong shocks in controlled thermonuclear devices was thought about long agol. However, it turns out that a so-called “thermonuclear shock” should have a tremendously high velocity of propagation2. Many means are known which drive strong shocks through matter: high explosives, magnetic fields, electron beams, laser beams. The shock may or may not be followed by some kind of rarefaction.

On the dynamics of hypervelocity liquid jet impact on a flat rigid surface

Abstract: The phenomena associated with the impact of a right circular fluid cylinder with a flat rigid surface are studied with the aid of a two-dimensional axisymmetric finite difference code. Both sub-and supersonic initial conditions are investigated. It is shown that, contrary to earlier reports, the maximum pressure sustained is precisely the one-dimensional maximum, i.e., the shock Hugoniot. The relaxation time corresponds to the time for the edge rarefaction, initiating at the impact corner, to traverse the jet radius. The maximum lateral speed, at the impact corner, was found to be nearly twice that of impact, slightly higher for very low Mach number and slightly lower for supersonic impact.

Velocity lag of solid particles in oscillating gases and in gases passing through normal shock waves

Abstract: The velocity lag of micrometer size spherical particles is theoretically determined for gas particle mixtures passing through a stationary normal shock wave and also for particles embedded in an oscillating gas flow. The particle sizes and densities chosen are those considered important for laser Doppler velocimeter applications. The governing equations for each flow system are formulated. The deviation from Stokes flow caused by inertial, compressibility, and rarefaction effects is accounted for in both flow systems by use of an empirical drag coefficient. Graphical results are presented which characterize particle tracking as a function of system parameters.

Compression of matter to superhigh densities by an accelerating heat wave

Abstract: A one‐dimensional analytical model is presented for the compression of matter (e.g., thermonuclear fusion fuel to densities of more than 103 times the solid density) by an accelerating subsonic heat wave. The heat wave, driven possibly by the absorption of a temporally tailored laser pulse, launches a large number of successive weak shock waves which compress and heat the target quasiadiabatically in order to keep the energy expenditure at a minimum. The net power to drive this heat wave must have a stepwise increase in time approximated by W = 98ρ0c03K2/τ2, where K = Dfρf/D0ρ0 is the fraction of the initial target mass (of density ρ0 and thickness Df) which reaches the final state (of ρf and Df. The adiabatic ondition sets the requirement that K should be much smaller than one. The time t is scaled as τ = 1 − t/t8, where t8 = D0/c0 and c0 is the initial sound speed. The sound speed in the compressed matter, from which pressure and density can be obtained using the adiabatic equations of state, will incre...

On the temperature dependence of the thermal conductivity of ceramic materials with rarefaction of the gas medium

Abstract: The results of an experimental study of the temperature dependence of the thermal conductivity of ceramic materials under conditions of rarefaction of the gas medium are explained by processes of degassing of the material during the experiment.

Rectification of Acoustic Waves

Abstract: The difference in the behavior of the denser and the rarer regions of a longitudinal travelling acoustic wave is utilized to produce the phenomenon of rectification of ultrasonic waves. It has been shown that, under appropriate conditions, the energy density of sound in the regions of rarefaction can be increased while in the regions of compression the energy density is decreased. It is found that under suitable conditions, the pressure amplitude in the rarer regions is about 4% larger than that in the denser regions. The measurement of this difference in amplitude can be used to determine the parameter of nonlinearity.

Impact of a freely expanding gas on a wall

Abstract: A study is made of the flow which results when an initially uniform gas expands into a vacuum through a complete one‐dimensional rarefaction wave, and then strikes either a solid wall or a similar opposite facing rarefaction. A Knudsen number K n is defined by the ratio of the undisturbed mean free path to the distance between the center of the rarefaction and the wall. The direct simulation Monte Carlo method has been used to obtain numerical solutions over a range of K n from 10−4 to 103. Results for the wall pressure profile were also obtained from experiment and from approximate continuum calculations. The pressure profile on the wall or the line of symmetry was found to be insensitive to assumptions about the initial highly rarefied stage of the reflection. On the other hand, when considering the temperature history of the gas adjacent to the wall, a proper molecular analysis of the initial stage of reflection was required for all values of the Knudsen number.

The energy density of a shock wave

Abstract: An expression is proposed for the energy-momentum density of a first-order gravitational shock wave.

Density distribution in rarefaction wave produced by rupture of diaphragm in a shock tube

Abstract: The effect of the finite time of opening of the diaphragm in a shock tube on the formation of the rarefaction wave was investigated experimentally. The density distribution in the rarefaction wave was measured in relation to the coordinate and time and was compared with the known self-similar solution.

Reply by Author to A. Wortman

Abstract: along the kernel radius. The secondary shock wave is initially so weak that it is swept outward by the expanding flow but it gains strength arid, as shown by Friedman, at about the time that the rarefaction fan reaches the origin the secondary shock wave is moving inward, even in stationary coordinates. This shock wave is initially quite weak so that it reaches the origin about 0.1 y/sec after the rarefaction fan is reflected. The reflected shock front now establishes an order of magnitude variation of temperature along the radius, but this time the maximum is at the origin. Successive reflections and interactions with the contact surface reverse the temperature gradients along the kernel radius with a period of about twice the characteristic time of the problem. The assumption of uniform kernel temperature cannot be justified. The power law and exponential expression for the temperature depen4ence of the reaction rates magnify the order of magnitude errors introduced by the incorrect gas dynamics model assumed by Ref. 1 and thus, the whole calculation is meaningless. A further point which, although relatively minor compared to the fundamental objections raised above, nevertheless deserves mention in order to view the work of Zajac and Oppenheim in the proper perspective. In the calculations of the flowfield ahead of the expanding spherical kernels, Ref. 1 did not predict the existence of the primary shock wave at the head pf the disturbed flow. The absence of the shock wave ahead of the accelerating contact surface was dismissed with the statement that "Shock waves were generated only in the case of plane and cylindrical flows, the increase of the cross-sectional area in the spherical case having been evidently too large for this purpose." The inability to calculate a shock wave suggests numerical difficulties; moreover, the accompanying statement cannot be accepted since it contradicts directly the discussion on p. 428 of Courant and Friedrichs, who demonstrate clearly that even a uniformly expanding sphere generates a shock wave.

Amplification of tkiangular shock waves in a flammable two-phase medium

Abstract: In [1, 2] values are established for the parameters of a compression wave with a triangular pressure variation such that when the wave interacts with a two-phase gas-liquid medium it can produce nonstationary combustion. More complicated to study, but of greater practical interest, is the interaction of longitudinal compression waves with a burning two-phase medium.