Lagrangian modeling of large volcanic particles: Application to Vulcanian explosions

[1] A new 2D/3D Lagrangian particle model (named LPAC) for the dynamics of clasts ejected during explosive eruptions is presented. The novelty of the model lies in the one-way coupling of the carrier flow field, given by a Eulerian multiphase flow code, and the particles. The model is based on a simplification of the Basset-Boussinesq-Oseen equation, expressing the Lagrangian equation of a particle as the sum of the forces exerted on it along its trajectory. It is assumed that particles are non-interacting and do not affect the background carrier flow and that the drag coefficient is constant. The model was applied to large clasts produced by Vulcanian explosions, in particular those occurring in August 1997 at Soufriere Hills Volcano, Montserrat (West Indies, UK). Simulation results allowed parametric studies as well as semi-quantitative comparisons between modeling results and field evidence. Major results include (1) the carrier flow was found to play a fundamental role even for meter-sized particles—a 1 m diameter block is predicted to reach a distance that is about 70% greater than that predicted without the effect of the carrier flow (assuming the same initial velocity), (2) assumption of the initial velocity of the particle was dropped thanks to the description of both the acceleration and deceleration phases along the particle trajectory, (3) by adopting experimentally based drag coefficients, large particles were able to reach greater distances with respect to smaller particles consistently with field observations and (4) the initial depth of the particle in the conduit was found to mainly influence the ejection velocity while the initial radial position with respect to the conduit axis was found to play a major role on the distance reached by the particle.

[1]  Kendall E. Atkinson.  An introduction to numerical analysis , 1978 .

[2]  P. Saffman.  The lift on a small sphere in a slow shear flow , 1965, Journal of Fluid Mechanics.

[3]  Lionel Wilson,et al.  Explosive Volcanic Eruptions-II The Atmospheric Trajectories of Pyroclasts , 1972 .

[4]  Larry G. Mastin,et al.  A simple calculator of ballistic trajectories for blocks ejected during volcanic eruptions , 2001 .

[5]  K. Kelfoun,et al.  Characterisation of the 1997 Vulcanian explosions of Soufrière Hills Volcano, Montserrat, by video analysis , 2003 .

[6]  V. Lorenz.  Some aspects of the eruption mechanism of the Big Hole Maar , 1970 .

[7]  A. Sherwood.  Effect of air drag on particles ejected during explosive cratering , 1967 .

[8]  Dimitri Gidaspow,et al.  Dense, vertical gas‐solid flow in a pipe , 1992 .

[9]  Gary H. Ganser,et al.  A rational approach to drag prediction of spherical and nonspherical particles , 1993 .

[10]  S. Self,et al.  Vulcanian eruption mechanisms , 1979, Nature.

[11]  Daniela Mele,et al.  The analysis of the influence of pumice shape on its terminal velocity , 2005 .

[12]  Andrew W. Woods,et al.  Explosive Volcanic Eruptions , 2001 .

[13]  Lionel Wilson,et al.  Explosive volcanic eruptions—VII. The ranges of pyroclasts ejected in transient volcanic explosions. , 1993 .

[14]  G. S. Gorshkov.  Gigantic eruption of the volcano bezymianny , 1959 .

[15]  Hugo Delgado-Granados,et al.  Experimental determination of drag coefficient for volcanic materials: Calibration and application of a model to Popocatépetl volcano (Mexico) ballistic projectiles , 2006 .

[16]  V. Lorenz,et al.  External ballistic of volcanic explosions , 1983 .

[17]  B. Voight,et al.  Transient dynamics of vulcanian explosions and column collapse , 2002, Nature.

[18]  T. Minakami.  5. On the Distribution of Volcanic Ejecta(Part I.) : The Distributions of Volcanic Bombs ejected by the Recent Explosions of Asama , 1942 .

[19]  Efficient calculation of the history force at finite Reynolds numbers , 2007 .

[20]  Houston C. Saunderson,et al.  Equations of motion and ballistic paths of volcanic ejecta , 2008, Comput. Geosci..

[21]  L. Wilson,et al.  Explosive Volcanic Eruptions-I The Rate of Fall of Pyroclasts , 1971 .

[22]  J. Riley,et al.  Equation of motion for a small rigid sphere in a nonuniform flow , 1983 .

[23]  B. Voight,et al.  The eruption of Soufrière Hills Volcano, Montserrat from 1995 to 1999 , 2002 .

[24]  Dimitri Gidaspow,et al.  Collisional viscosity of FCC particles in a CFB , 1996 .

[25]  Stephen Self,et al.  Ukinrek Maars, Alaska, II. Deposits and formation of the 1977 craters , 1980 .

[26]  Carlo Cavazzoni,et al.  A parallel multiphase flow code for the 3D simulation of explosive volcanic eruptions , 2007, Parallel Comput..

[27]  M. Sommerfeld,et al.  Multiphase Flows with Droplets and Particles , 2011 .

[28]  P. Thomas.  On the influence of the Basset history force on the motion of a particle through a fluid , 1992 .

[29]  Andrew W. Woods,et al.  On the dispersal of clasts from volcanic craters during small explosive eruptions , 1996 .

[30]  W. Melson,et al.  Ejecta velocities, magma chamber pressure and kinetic energy associated with the 1968 eruption of arenal volcano , 1971 .

[31]  R. Isaia,et al.  Turbulent boundary layer shear flows as an approximation of base surges at Campi Flegrei (Southern Italy) , 2004 .

[32]  B. Voight,et al.  Computational modelling of the transient dynamics of the August 1997 Vulcanian explosions at Soufrière Hills Volcano, Montserrat: influence of initial conduit conditions on near-vent pyroclastic dispersal , 2002, Geological Society, London, Memoirs.

[33]  N. K. Sinha,et al.  Drag on non-spherical particles: an evaluation of available methods , 1999 .

[34]  Dimitri Gidaspow,et al.  Multiparticle simulation of collapsing volcanic columns and pyroclastic flow , 2003 .