GOALS AND INTENT OF CFLOW

EXPLOSIVITY OF LAVA DOMES

ESTIMATE OF GAS OVERPRESSURE

HETEROGENEITY OF GAS CONTENT IN FLOWS AND DOMES

GAS LOSS THROUGH CONDUIT WALLS

2-D PRESSURE STATE IN THE CONDUIT

MT UNZEN, JAPAN

MT ST HELENS, USA

CFLOW H. Massol, C. Jaupart

VISCOUS ANDCOMPRESSIBLEFLOW

INCOMPRESSIBLEFLOW

BUBBLY SECTION

MAGMA CHAMBER

Exsolution level

INTEGRATIONDOMAIN

SCHEMATIC VIEW OF A VOLCANIC CONDUIT

ORIGINALITY: 2-DMETHOD: Finite Element

= -2 e + 23

( .v) + Pg - K ( .v)

Pg: Gas pressure Shear viscosityK: Bulk viscosity

Pg = P + K ( .v)

RHEOLOGY (1)

VISCOSITY+COMPRESSIBILITY

GAS OVERPRESSURE

DOME EXPLOSIVITY

bR

Pg

o , p

f

Pml

K,

RHEOLOGY (2)

= pg -

2b

- 4µl

˙

RR2

b 31 -

b 3

R3[ r r ] r=R ( )

K =43µ

l

1 -

[ r r

] r=R = pm

- 3KR

R

p m

= p b-

2b

0

z

ra

h

H

zz = p s u = 0

zz = p atm

u = 0or rz = 0

u = 0w = 0

u = 0

rz = 0

DOMAINAND BC

BASIC EQUATIONS

Artificial time

Mass lumping

Petrov Galerkin weighting

[ D ] U = SU

[ D ] W = SW

[ M ] = S

Conservation of momentum

Conservation of mass

Criteres d’arret

10-2 10-8

Criteres d’arret

10-2 10-8

CAPABILITIES

VARIABLE MELT VISCOSITY

VARIABLE CONDUIT GEOMETRY

HORIZONTAL AND VERTICAL VELOCITY COMPONENTS

VARIABLE COMPRESSIBILITY

ASSUMPTIONS AND LIMITS

EQUILIBRIUM DEGASSING

ONLY VALID BEFORE FRAG. LEVEL

ANALYTICAL SOLUTION

HYPOTHESES

- No horizontal velocity - Constant compressibility - Constant viscosity

BUT: Gas pressure varies in both directions

Numerical model benchmark

RESULTS

PARABOLIC PRESSURE PROFILE ACROSS THE CONDUIT

DIMENSIONLESS NUMBER, D

PH-PaP0-pa

= P K+4/3

a2

H2= D

EXAMPLERESULT (1)

U = 0

= 106 Pa.s

x0 = 0.5 Wt%

P(0,H) = 0.56 MPa

OVERPRESSURE AT THE CENTER OF THE CONDUIT EXIT

Compatiblewith theanalytical solution

EXAMPLERESULT (2)

x0 = 0.5 Wt%

P(0,H) = 0.56 MPa

Variable viscosity(Hess and Dingwell, 96)

rz = 0

P(a,H) = 1.5 MPa

EXAMPLERESULT (3)

x0 = 0.5 Wt%

P(0,H) = 0.34 MPa

P(a,H) = 1.1 MPa

CONCLUSIONS

GAS PHASE IS OVERPRESSURED / DOME EXPLOSIVITY

HORIZONTAL PRESSURE GRADIENT / VITRIFIED MARGINS, HETEROGENEITY IN GAS CONTENT IN FLOWS AND DOMES

IMPORTANCE OF THE EXIT BOUNDARY CONDITIONS / CREASE STRUCTURE

FUTURE WORK

BOUNDARY CONDITIONS

- CONDUIT WALLS AND - COUPLING WITH FLOW

CRYSTALS

Fragmentation Level

Laminar Flow

Turbulent Flow

Nucleation of Bubbles

NUCLASCENT

1-D Finite differenceCylindrical GeometrySteady state

Variable viscosityNon-equilibrium degassing

(H. Massol, T. Koyaguchi)

EVOLUTION OF DISSOLVED WATER IN THE MELT

H=5000 ma = 50 m0 = 106 Pa.sx0 = 4wt%= 0.02 N m-1

D = 10-11 m2 s-1

H=5000 ma = 50 m0 = 106 Pa.sx0 = 4wt%= 0.02 N m-1

D = 10-11 m2 s-1

EVOLUTION OF PRESSURE AND NUMBER OF BUBBLES

OUTPUT OF THE MODEL

BUBBLE SIZES BUBBLE DENSITY

PRESSURE INSIDE BUBBLES

NEXT STEP: CONTINUOUS BUBBLE SIZE DISTRIBUTION