High Sound Speed Research Articles

Geologic nozzles

Sonic velocities of geologic fluids, such as volcanic magmas and geothermal fluids, can be as low as 1 m/s. Critical velocities in large rivers can be of the order of 1–10 m/s. Because velocities of fluids moving in these settings can exceed these characteristic velocities, sonic and supersonic gas flow and critical and supercritical shallow‐water flow can occur. The importance of the low characteristic velocities of geologic fluids has not been widely recognized, and as a result, the importance of supercritical and supersonic flow in geological processes has generally been underestimated. The lateral blast at Mount St. Helens, Washington, propelled a gas heavily laden with dust into the atmosphere. Because of the low sound speed in this gas (about 100 m/s), the flow was internally supersonic. Old Faithful Geyser, Wyoming, is a converging‐diverging nozzle in which liquid water refilling the conduit during the recharge cycle changes during eruption into a two‐phase liquid‐vapor mixture with a very low sound velocity. The high sound speed of liquid water determines the characteristics of harmonic tremor observed at the gyeser during the recharge interval, whereas the low sound speed of the liquid‐vapor mixture influences the fluid flow characteristics of the eruption. At the rapids of the Colorado River in the Grand Canyon, Arizona, the channel is constricted into the shape of a converging‐diverging nozzle by debris flows that enter from tributary canyons. Both subcritical and supercritical flow occur within the rapids. The transport capacity in the rapids can be so great that the river contours the channel to a characteristic shape. This shape can be used to interpret the flood history of the Colorado River over the past 10³–105 years. The unity of fluid mechanics in these three natural phenomena is provided by the well‐known analogy between gas flow and shallow‐water flow in converging‐diverging nozzles.

The surface pressure spectrum induced by boundary-layer turbulence on a rough wall

The low-wavenumber surface pressure spectrum induced on a rough plane by boundarylayer turbulence at low Mach number is investigated by using the Lighthill theory of aerodynamic sound. If the patch of turbulence is of sufficiently large extent, then the magnitude of spectral elements with nearly sonic phase speeds is found to be dominated by the presence of trapped surface waves. The effect of roughness on a coated flat plate is also investigated. A sufficiently thick coating with a higher sound speed than the surrounding fluid is found to reduce the magnitude of the spectral elements with nearly sonic phase speed.

Laboratory studies of volcanic jets

The study of the fluid dynamics of violent volcanic eruptions by laboratory experiment is described, and the important fluid‐dynamic processes that can be examined in laboratory models are discussed in detail. In preliminary experiments, pure gases are erupted from small reservoirs. The gases used are Freon 12 and Freon 22, two gases of high molecular weight and high density that are good analogs of heavy and particulate‐laden volcanic gases; nitrogen, a moderate molecular weight, moderate density gas for which the thermodynamic properties are well known; and helium, a low molecular weight, lowdensity gas that is used as a basis for comparison with the behavior of the heavier gases and as an analog of steam, the gas that dominates many volcanic eruptions. Transient jets erupt from the reservoir into the laboratory upon rupture of a thin diaphragm at the exit of a convergent nozzle. The gas accelerates from rest in the reservoir to high velocity in the jet. Reservoir pressures and geometries are such that the fluid velocity in the jets is initially supersonic and later decays to subsonic. The measured reservoir pressure decreases as the fluid expands through repetitively reflecting rarefaction waves, but for the conditions of these experiments, a simple steady‐discharge model is sufficient to explain the pressure decay and to predict the duration of the flow. Density variations in the flow field have been visualized with schlieren and shadowgraph photography. The observed structure of the jet is correlated with the measured pressure history. The starting vortex generated when the diaphragm ruptures becomes the head of the jet. Though the exit velocity is sonic, the flow head in the helium jet decelerates to about one‐third of sonic velocity in the first few nozzle diameters, the nitrogen head decelerates to about three‐fourths of sonic velocity, while Freon maintains nearly sonic velocity. The impulsive acceleration of reservoir fluid into the surrounding atmosphere produces a compression wave. The strength of this wave depends primarily on the sound speed of the fluid in the reservoir but also, secondarily with opposite effect, on the density: helium produces a relatively strong atmospheric shock while the Freons do not produce any optically observable wave front. Well‐formed N waves are detected with a microphone far from the reservoir. Barrel shocks, Mach disks, and other familiar features of steady underexpanded supersonic jets form inside the jet almost immediately after passage of the flow head. These features are maintained until the pressure in the reservoir decays to sonic conditions. At low pressures the jets are relatively structureless. Gas‐particle jets from volcanic eruptions may behave as pseudogases if particle concentrations and mass and momentum exchange between the components are sufficiently small. The sound speed of volcanic pseudogases can be as large as 1000 m s−1 or as small as a few tens of meters per second depending on the mass loading and initial temperature. Fluids of high sound speed produce stronger atmospheric shock waves than do those of low sound speed. Therefore eruption of a hot gas lightly laden with particulates should produce a stronger shock than eruption of a cooler or heavily laden fluid. An empirical expression suggests that the initial velocity of the head of supersonic volcanic jets is controlled by the sound speed and the ratio of the density of the erupting fluid to that of the atmosphere. The duration of gas or pseudogas eruptions is controlled by the sound speed of the fluid and the ratio of reservoir volume to vent area.

The equation of state of D2O determined from sound speeds

The equation of state of D2O valid over the ranges 0–60 °C and 0–1000 bar has been determined from the high pressure sound speeds of Chen and Millero. The precision of the equation of state is ±0.01×10−6 bar−1 in the isothermal compressibility, ±10×10−6 cm3 g−1 in the specific volume, and ±2×10−6 deg−1 in the thermal expansibility. The results agree reasonably well with the equations of Fine and Millero and with the refit equation of Emmet and Millero.

Effective horizontal sound speeds

Effective horizontal sound speed, the speed at which most of the energy from shots in the deep ocean sound channel propagates, was computed for several source/receiver geometries in the Atlantic and Pacific Oceans. Results showed values ranging from 1476.8 to 1487.5 m/s, the higher sound speeds being associated with the deeper hydrophones and the lower latitudes and vice versa. These values were compared to measured sound speeds, which varied from 1479.9 m/s in the South Atlantic to 1464.9 m/s in the Northwest Pacific and 1484.6 m/s in the Central Pacific. Computed and measured values for the same travel path agreed within 1.5 m/s, or within 0.1%. Because effective horizontal sound speeds vary for diverse travel paths in the world's oceans, appropriate discrete sound speeds should be used for computation methods employing arrival times. [Work supported by AFTAC Code 1035.]

Ultrasonic properties of phenolic and poly(phenylquinoxaline) polymers

AbstractLongitudinal and shear sound speeds and absorptions were measured for a phenolic polymer and a poly(phenylquinoxaline) (PPQ) polymer, from room temperature to 70°C, at a frequency of 1.8 MHz. Phenolic specimens were cured at a maximum temperature of either 120°C, 135°C, or 180°C. The specimens varied in density from 1.217 to 1.229 g/cm3 with no correlation to curing temperature. Longitudinal sound speed in phenolic was found to depend only on density (or specific volume) and not directly on temperature or degree of crosslinking. Sound speeds and elastic constants, in phenolic, are not sensitive to cure temperature but sound a bsorption is: the higher the cure temperature, the lower the absorption. Hence ultrasonic absorption is a possible way to monitor or measure degree of crosslinking. Sound absorption is higher in phenolic than in PPQ, contrary to what is expected for a polymer with high sound speed. This high absorption indicates an additional mechanism of absorption in phenolic not found in PPQ. Also, the sound absorption increases with temperature in phenolic but is constant in PPQ. The Gruneisen parameter of phenolic appears high and that of PPQ about right when compared with other polymers. All of these results suggest there is a molecular transition in phenolic, but not PPQ. Further evidence for a transition comes from specific volume measurements as a function of temperature. The exact temperature of the transition and the molecular process responsible cannot, however, be determined from the measurements reported here.

Vibration of containing structures by sound in the contained fluid

A system which consists of a rigid rectangular box with one simply-supported flexible wall is analysed by numerical and statistical methods for the internal acousto-structural mode coupling factors and the corresponding modal average radiation efficiency. A lower limiting frequency is found above which the subcritical radiation efficiency is equal to that of a baffled panel radiating into free-field conditions but below which the radiation efficiency falls below the free-field values. This limit is important practically in the cases of small box volumes and gases of high sound speed. At supercritical frequencies, a value of radiation efficiency half that of a freely radiating panel is found. Measurements have confirmed the existence of the lower limiting frequency. It has also been observed in the case of a cylinder. Corrections to the normal statistical energy response and radiation equations are presented which take into account the fact that it may not be assumed, purely on the basis of modal density ratio considerations, that many acoustic modes couple with an individual structural mode.

Production of High Ion Densities in Helium by Means of High Explosives

Temperatures of about 20 000°K with ion densities ranging from 1017 to 1018 cm−3 have been produced in helium by means of explosive-driven shocks. Helium was used because of its relatively simple structure, but this choice eliminated usual shock methods because of the high sound speed and high ionization potential. Shock waves having sufficient strength and planarity were obtained by reflecting against a glass plate initially strong shock waves produced by high explosives. Equilibrium calculations based on smear camera velocities of accurately plane shocks were used to determine the state of the gas behind the reflected shock wave. The light emitted consisted of a continuum on which were superimposed shifted and broadened lines of the normal helium spectrum and forbidden lines as well. Time-resolved spectrograms showed evidence of a measurable relaxation time at the shock front but no evidence of significant radiative cooling of the gas behind the shock. Under the conditions of these experiments, it was demonstrated that a quantitative prediction of the behavior of the helium states with principal quantum numbers 2, 3, and 4 requires consideration of the effects of electrons as well as ions.

Analysis of Steady-State Supported One-Dimensional Detonations and Shocks

Consideration is given to the possible steady one-dimensional flows which can occur in a medium in which an arbitrary number of chemical reactions proceed behind an initiating shock, and the stability of solutions to the chemical rate equations is investigated. The theoretical apparatus is that of irreversible thermodynamics and nonlinear mechanics, with neglect of transport processes. Most of the discussion is concerned with detonations, but the analysis applies to all such reacting systems. For detonations, it is shown that under suitable conditions on the rate functions, there are stable solutions resulting in an equilibrium final state for detonation velocities equal to or greater than the ``equilibrium Chapman-Jouguet (C-J)'' value corresponding to tangency of the Rayleigh line and the equilibrium Hugoniot. The final state in such a flow is the high-pressure intersection of the Rayleigh line and the equilibrium Hugoniot. We suggest that these solutions correspond to piston-supported detonations after decay of initiation transients, and we further suggest that the equilibrium C-J detonation is stable with respect to removal of the piston support at sufficiently late times. The ``normal frozen C-J condition,'' corresponding to attainment of chemical equilibrium at a point where the flow velocity is sonic with respect to the ``frozen'' or high frequency sound speed, is shown to result in an unstable solution. Solutions corresponding to ``pathological detonations,'' in which the region of steady flow terminates at a point of incomplete reaction, are identified, but the conditions necessary or sufficient for their realization have not been obtained, nor has the nature of the subsequent time-dependent flow been elucidated. Thus their physical significance remains somewhat doubtful.