Laboratory studies of volcanic jets

Abstract

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.