goals and intent of cflow explosivity of lava domes estimate of gas overpressure heterogeneity of...

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