One-dimensional adiabatic flow of equilibrium gas–particle mixtures in long vertical ducts with friction

Buresti, Guido; Casarosa, Claudio

doi:10.1017/s002211208900145x

Cited by 60 publications

(28 citation statements)

References 15 publications

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“…(5) We assume that the process is isothermal. This is a good approximation if the mass fraction of dissolved gas $J, , is sufficiently small (Buresti & Casarosa 1989). The heat capacity of the solid phase is sufficiently large that the vapour phase cannot cool as it expands.…”

Section: Formulation Of the Problemmentioning

confidence: 99%

A mathematical model of vulcanian eruptions

Turcotte¹,

Ockendon²,

Ockendon³

et al. 1990

Geophysical Journal International

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The problem of an expansion wave propagating into a saturated magma is solved and used as a model of a vulcanian eruption. In our model for an explosive eruption we assume that a drop in pressure leads to the exsolution of magmatic volatiles.Initially the exsolved vapours create bubbles in the magma. We model the subsequent part of the exsolution process in which a foam is created; this is believed to be an essential feature of explosive volcanic eruptions. The foam also has the advantage that it can be modelled as a mixture or 'pseudo-gas' without slippage between the phases. Eventually the foam breaks up and becomes volcanic ash.Assuming that the exsolution of vapour is given by Henry's law, that the temperature is constant, that the magma and vapour have equal velocities, and neglecting wall friction and gravitational effects, an analytic solution for pressure, velocity, and vapour fraction is obtained for the expanding mixture in a constant area duct. The exit velocity u for the mixture is where @o is the original mass fraction of dissolved vapour, R is the gas constant for the vapour, the constant temperature, and p o / p the pressure ratio across the expansion. With +o = 1 per cent, To = 1000"K, and p o / p = 100 we find uo = 300 m s-', consistent with observations for vulcanian eruptions.

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Section: Formulation Of the Problemmentioning

confidence: 99%

A mathematical model of vulcanian eruptions

Turcotte¹,

Ockendon²,

Ockendon³

et al. 1990

Geophysical Journal International

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show abstract

“…%, the cooling due to adiabatic expansion is small. We deduce that to leading order the mixture may be assumed to be isothermal [Buresti and Casarosa, 1989]. Figure 4a shows the result of a typical calculation in which the variation of the velocity, pressure, and void fraction is shown as a function of the height in the conduit.…”

Section: Models Of Conduit Flowmentioning

confidence: 99%

The dynamics of explosive volcanic eruptions

Woods¹

1995

Reviews of Geophysics

204

160

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Explosive volcanic eruptions involve the ejection of dense mixtures of ash and gas from a volcanic vent at high speed and pressure. This mixture is generated as liquid magma rises from a crustal magma chamber and decompresses, exsolving water vapor. As gas is exsolved, the mixture inflates, accelerates, and becomes foam‐like. Once the liquid films around the bubbles are unable to spread as rapidly as the bubbles are expanding through decompression, the films rupture, and a fragmented mixture of ash and volatiles ascends to the volcanic vent. On eruption from the vent, the material decompresses, either into a volcanic crater or directly into the atmosphere. In the case of free decompression, the mixture typically has a high speed, while decompression in a crater can lead to either very low or very high eruption speeds. After decompression, the hot, dense mixture begins to entrain and heat ambient air, thereby lowering the mixture density, but it also decelerates under gravity. If the eruption velocity is sufficiently high, then the material can become buoyant and will generate a buoyant ash plume, called a Plinian eruption column, which rises above the vent. In contrast, if the eruption velocity is small or the mass flux is very large, then the material will typically collapse back toward the Earth and form a dense, laterally spreading flow. Buoyant eruption columns are able to transport the material high into the atmosphere, since they provide an efficient means of converting the initial thermal energy of the mixture into potential energy through entrainment and heating of ambient air. The height of rise of such eruption columns depends upon the eruption rate, the stratification of the atmosphere, the degree of thermal disequilibrium between the particles and the air, and the amount of water vapor in the atmosphere. Dense, hot ash flows, generated by collapsing fountains, transport ash and clasts laterally from the vent, sedimenting many of the larger clasts and entraining air en route. As a result, the density of the mixture may fall below that of the atmosphere, and the finer‐grained solid material may thereby become buoyant and rise from the flow. The distance it travels increases with both the cloud mass and the mean particle size. The ensuing buoyant ash plume, called a coignimbrite eruption column, may have a source several kilometers from the original volcanic vent. Once the thermal energy of an eruption column has become exhausted, the ash intrudes laterally into the atmosphere. Ultimately, the cloud is swept downwind, where sedimentation of ash leads to fall deposits over hundreds of kilometers from the volcano.

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“…Therefore we assume that the chamber behaves as a thermaly isolated system during the eruption. This assumption would not be so valid in modeling the conduit, where cooling of the magmatic mixture by up to 100øC may occur [Buresti and Casarosa, 1989]. …”

Section: Physical Modelmentioning

confidence: 99%

A numerical model for temporal variations during explosive central vent eruptions

Folch¹,

Martı́²,

Codina³

et al. 1998

J. Geophys. Res.

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Abstract. An axisymmetrical numerical model has been developed in order to find the temporal evolution of pressure, the position of the exsolution level, the velocity field, the eruption rate, and the amount of erupted material of a shallow, volatile-rich, felsic magma chamber during a Plinian central vent eruption. The overpressure necessary to trigger the eruption is assumed to result from crystallization-driven volatile oversaturation. We solve the resulting set of equations using a finite element method. The results obtained show that the pressure at the conduit entrance decreases exponentially as the eruption proceeds. This produces a shifting of the exsolution level, so that deeper parts of the chamber become progressively volatile oversaturated during the eruption. We assess the influence of chamber geometry and the physical properties of the magma on the computed parameters using several numerical examples. The results are also compared with those predicted by previous models from the literature and are found to be in good agreement with documented eruptions. The model constitutes a first attempt to numerically model the dynamics and the temporal evolution of the most relevant physical parameters during withdrawal from a closed magma chamber.

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One-dimensional adiabatic flow of equilibrium gas–particle mixtures in long vertical ducts with friction

Cited by 60 publications

References 15 publications

A mathematical model of vulcanian eruptions

A mathematical model of vulcanian eruptions

The dynamics of explosive volcanic eruptions

A numerical model for temporal variations during explosive central vent eruptions

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