The mass eruption rate from the perspective of an analog experience

P. Dellino, R. Büttner, F. Dioguardi, D. Doronzo, T. Dürig, D. Mele, I. Sonder, R. Sulpizio, B. Zimanowski

Why is the mass eruption rate so important?

• For volcanologists it is useful as a measure of the “bigness” of an eruption and helpsdefining the boundary between diverse eruption categories.

• For atmosphere scientists it is important for controlling the amount and the fate of the volcanic ash that intrudes the atmosphericboundary layer

Collapsing column

Convective plumeV

olc

ano

logy

Atm

osh

pe

ric

scie

nce MER= rmixV0pr2

rmix=rsC+rg(1-C)

Since volcanic particles (ash,lapilli) have a density, rs, at least3 order of magnitude higherthan gas rg even if particlevolumetric concentration, C, atconduit exit is very low (smallerthan 1%), most of the mass inthe eruptive mixture isrepresented by “rocky” particles(magma fragments).

The fate of the gas-particlemixture, both in theVolcanological and in theAtmospheric domain, is stronglyinfluenced by the rock fragmentscharacteristics and their rate ofproduction upon magmafragmentation.

Fallout

Pyroclastic flow

The basic questions of this work are:

2) How to sustain MER by magma fragmentation?

1)What is the consequence of MER on the eruption regime? (plume vs collapse)

The experiment setup

Convective plume experiment: particle fallout

Collapsing column experiment: pyroclastic flow

Range of experiment conditions

• Temperature up to 300°C• Particle mass up to 600 kg• Exit velocity up to 50 m/s• Conduit radius up to 0.3 m• Natural volcanic particles ranging from fine ash to coarse lapilli• Particle volumetric concentration at conduit exit from 0.002 to 0.15• Mixture density at conduit exit from 5 to 240 kg/m3

• Duration of conduit flow alimentation longer than time for theestablishment of maximum height (sustained column)

• Specific mass flow rate at conduit exit: 60 to 1200 kg/m2s (in scalewith natural MER50 from 5x105 to 107 kg/s)

• Scaling parameters: Re>106; Fr0’ : 0.3 to 10.4• Sedimentation rate scaled 1:1 to natural eruptions (about 0.1 to 100

kg/m2s)

Boundary between eruptive styles: i.e. the Froudenumber dependence of the entrainment rate

The entrainment rate, e, expresses the velocity of entrance of atmosphere air into the eruptive column Ue as compared with

column vertical velocity U

e=Ue/U

The entrainment rate is not constant in an eruptive column but it is a function of the densimetric Froude number at the source, Fr0’

Fr0’= V0/(r0g’)0.5

g’=(rmix-rair)/rair

A convective plume generating particle fallout

• Entrainment rate = 0.1• Fr’

0 = 10• “Mortonian” style:

constant entrainmentrate along main flow direction: self-similarplume structure

When air entrainment issignificant, convection iseffective, the density of the hot gas-particle mixture gets lowerthan air and becomes buoyant

• Entrainmentrate: about 0

• Fr’0 = 1.4

• “Bernoullian” style: conservation of mass flow rate and totalpressure alongmain flow directionH=V0

2/2g

A collapsing column generating a pyroclastic flow Without air entrainment the mixture density cannot get lower than atmoshpere and the eruptive column collapses under its own weight after the source momentum has beenconsumed at the expenses of gravity

The boundary between eruptive condition allowingor precluding air entrainment, and the formation of a convective plume at conduit exit, is Fr0’=3 (consistently with the recent engineering experiments on jets)

Collapsing columnsNo air entrainment

Convective plumese=0.1 for hot plumes

Fr0’=3

Numerical simulation of experiments

Classificatory abacus based on the Froude number threshold

Why is magma fragmentation relevant to MER and to the evolution of a convective plume?

• Big Plinian eruptions (MER about 107 to 108 Kg/s) form the largestplumes. They last for many hours to days, and represent the mostimportant eruptive events both for Volcanologists and forAtmoshpere Scientists.

• By the use of the classification abacus, if we assume a radius of50m and an exit velocity of 200 m/s, particle volumetricconcentration must be 0.01 or lower for a convective plume to bestable. It results in MER of about 107 kg/s. If the Plinian columnhas to be stable for long, magma fragmentation must occur at aconstant level in the conduit and “tranform” magma into particles(rocky fragments) at a rate smaller than about 2m/s. This is toosmall for a continuous brittle fragmentation process that is afunction of magma elastical properties (speed of sound of magmaof order of km/s).

The eruptive conditions assumed in the example of the previous slideare well within the range of a Plinian plume as calssically described inVolcanology lectures, therefore the apparent contraddiction betweenMER and magma fragmentation speed need to be resolved in orderto let the eruption “march forward”

Internet excerpt of an academic lecture in Volcanology about Plinian plumes

A myriad of fragmentation pulses (both magmatic and phreatomagmatic) merging up inthe atmosphere as a continuous plume with a time-averaged MER. Fragmentation isachieved when the critical elongational strain rate is reached in a parcel of magma.After fragmentation of one parcel, time is needed before the magma level is restoredinside the conduit by the ascent of a new parcel from the underlying reservoir. Thecycle can repeat for days and sustain a stable plume. At Eyjafjallajökull the pulsatorybehaviour was evident because videocameras were pointing directly at the crater exit.Probably, in other eruptions the only visible part was just the “merged up” plume.

One solution could be the “pulsating” fragmentation: Eyjafjallajökull is an example

After the plume is formed and the gas-particle mixture is intruded intothe atmospheric boundary layer, the aim is to quantify how much ashcan be transported far away from the volcano by wind, andsedimented at distance. The basic quantity for modelling the process isthe sedimentation rate from the plume margin Sr that is related to thecharacteristics at the source of the umbrella region (W, C, rs)

Where Pi is the probability that the ith particle-size class is sedimentedfrom suspension in the umbrella region. To define Pi , a probabilitydensity function linking terminal velocity Wti to the covariance of the fluctuating turbulent flow velocities needs to be defined.

We found a way to define it for pyroclastic flows, in the future we hopeto investigate it also in the context of plumes.

Atmosphere transportation and sedimentation

Sr = Wtii=1

n

å CirsiPi

U 'V '

For quantifying ash transportation and sedimentation, the basicparticle parameter is terminal velocity, Wt ,which is strongly affected by shape that influences the drag coefficient Cd.

Wt=(4gD(rs-rf)/3Cdrf)0.5

3D fractal dimension by x- raymicrotomography and newexperiments are helping us finding anew function valid both at high and lowRep

Particle characteristics

ReCdRe23DFD

Improvements needed for the advancements of the state of the art in modelling and monitoring

• New eperiments linking eruptive pulsationsto ash transportation

• Sensors for precise measurements of particlevolumetric concentration in plumes of Icelandic volcanoes.

Reference• Mass eruption rates in pulsating eruptions estimated from video analysis of the gas thrust-

buoyancy transition—a case study of the 2010 eruption of Eyjafjallajökull, Iceland. Earth, Planetsand Space (2015) 67:180 DOI 10.1186/s40623-015-0351-7 Tobias Durig, Magnús TumiGudmundsson, Sven Karmann, Bernd Zimanowski, Pierfrancesco Dellino,Martin Rietze and Ralf Buttner

• 2014. Volcanic jets, plumes, and collapsing fountains: evidence from large-scale experiments, with particular emphasis on the entrainment rate. DOI:10.1007/s00445-014-0834-6. pp.834. In BULLETIN OF VOLCANOLOGY - ISSN:0258-8900 vol. 76, Dellino P; Dioguardi F; Mele D; D’Addabbo M; Zimanowski B; Büttner R; Doronzo DM; Sonder I; Sulpizio...

• 2014. Integration of a new shape-dependent particle-fluid drag coefficient law in the multiphase Eulerian-Lagrangian code MFIX-DEM. pp.68-77. In POWDER TECHNOLOGY - ISSN:0032-5910 vol. 260 Dioguardi F; Dellino P; Mele D

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