A new drag law for irregularly shaped particles is presented here. Particles are described by a shape factor that takes into account both sphericity and circularity, which can be measured via the most commonly used image particle analysis techniques. By means of the correlation of the drag coefficient versus the particle Reynolds number and the shape factor, a new drag formula, which is valid over a wide range of Reynolds number (0.03–10,000), is obtained. The new model is able to reproduce the drag coefficient of particles measured in terminal velocity experiments with a smaller scatter compared to other laws commonly used in multiphase flow engineering and volcanology. Furthermore, the new formula uses only one equation, whereas previous models, to insure validity over an ample range, made use of a step function that introduces a discontinuity at the switch of equations. Finally, this drag law works in the whole range of variation, from extremely irregular particles to perfect sphere. A code of the iterative algorithm for the drag coefficient calculation and terminal velocity is included in the supporting information both as a Fortran routine and a Matlab function.

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The source conditions of volcanic plumes and collapsing fountains are investigated by means of large-scale experiments. In the experiments, gas-particle jets issuing from a cylindrical conduit are forced into the atmosphere at different mass flow rates. Dense jets (high particle volumetric concentration, e.g., C 0 > 0.01) generate collapsing fountains, whose height scales with the squared exit velocity. This is consistent with Bernoulli's equation, which is a good approximation if air entrainment is negligible. In this case, kinetic energy is transformed into potential energy without any significant loss by friction with the atmosphere. The dense collapsing fountain, on hitting the ground, generates an intense shear flow similar to a pyroclastic density current. Dilute hot jets (low particle volumetric concentration, e.g., C 0 < 0.01) dissipate their initial kinetic energy at much smaller heights than those predicted by Bernoulli's equation. This is an indication that part of the total mechanical energy is lost by friction with the atmosphere. Significant air entrainment results in this case, leading to the formation of a buoyant column (plume) from which particles settle similarly to pyroclastic fallout. The direct measurement of entrainment coefficient in the experiments suggests that dense collapsing fountains form only when air entrainment is not significant. This is a consequence of the large density difference between the jet and the atmosphere. Cold dilute experiments result in an entrainment coefficient of about 0.06, which is typical of pure jets of fluid dynamics. Hot dilute experiments result in an entrainment coefficient of about 0.11, which is typical of thermally buoyant plumes. The entrainment coefficients obtained by experiments were used as input data in numerical simulations of fountains and plumes. A numerical model was used to solve the classic top-hat system of governing equations, which averages the field variables (e.g., column velocity and density) across the column. The maximum heights calculated with the model agree well with those observed experimentally, showing that our entrainment coefficients are compatible with a top-hat model. Dimensional analysis of the experimental data shows that a value of 3 for the source densimetric Froude number characterizes the transition between dense collapsing fountains and dilute plumes. This value delimits the source conditions (exit velocity, conduit radius, and particle volumetric concentration) for pyroclastic flow (<3) and fallout (>3). © 2014 Springer-Verlag Berlin Heidelberg

[1] It is currently impractical to measure what happens in a volcano during an explosive eruption, and up to now much of our knowledge depends on theoretical models. Here we show, by means of large-scale experiments, that the regime of explosive events can be constrained on the basis of the characteristics of magma at the point of fragmentation and conduit geometry. Our model, whose results are consistent with the literature, is a simple tool for defining the conditions at conduit exit that control the most hazardous volcanic regimes. Besides the well-known convective plume regime, which generates pyroclastic fallout, and the vertically collapsing column regime, which leads to pyroclastic flows, we introduce an additional regime of radially expanding columns, which form when the eruptive gas-particle mixture exits from the vent at overpressure with respect to atmosphere. As a consequence of the radial expansion, a dilute collapse occurs, which favors the formation of density currents resembling natural base surges. We conclude that a quantitative knowledge of magma fragmentation, i.e., particle size, fragmentation energy, and fragmentation speed, is critical for determining the eruption regime.

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Large‐scale experiments generating ground‐hugging multiphase flows were carried out with the aim of modelling the rate of sedimentation, of pyroclastic density currents. The current was initiated by the impact on the ground of a dense gas‐particle fountain issuing from a vertical conduit. On impact, a thick massive deposit was formed. The grain size of the massive deposit was almost identical to that of the mixture feeding the fountain, suggesting that similar layers formed at the impact of a natural volcanic fountain should be representative of the parent grain‐size distribution of the eruption. The flow evolved laterally into a turbulent suspension current that sedimented a thin, tractive layer. A good correlation was found between the ratio of transported/sedimented load and the normalized Rouse number of the turbulent current. A model of the sedimentation rate was developed, which shows a relationship between grain size and flow runout. A current fed with coarser particles has a higher sedimentation rate, a larger grain‐size selectivity and runs shorter than a current fed with finer particles. Application of the model to pyroclastic deposits of Vesuvius and Campi Flegrei of Southern Italy resulted in sedimentation rates falling inside the range of experiments and allowed definition of the duration of pyroclastic density currents which add important information on the hazard of such dangerous flows. The model could possibly be extended, in the future, to other geological density currents as, for example, turbidity currents.

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