CFLOW H. Massol, C. Jaupart GOALS AND INTENT OF CFLOW 2-D PRESSURE STATE IN THE CONDUIT EXPLOSIVITY OF LAVA DOMES ESTIMATE OF GAS OVERPRESSURE MT UNZEN, JAPAN HETEROGENEITY OF GAS CONTENT IN FLOWS AND DOMES GAS LOSS THROUGH CONDUIT WALLS MT ST HELENS, USA
SCHEMATIC VIEW OF A VOLCANIC CONDUIT BUBBLY SECTION INTEGRATION DOMAIN Exsolution level VISCOUS AND COMPRESSIBLE FLOW
INCOMPRESSIBLE FLOW ORIGINALITY: 2-D METHOD: Finite Element MAGMA CHAMBER RHEOLOGY (1) = -2 e + 2 ( 3 .v) + Pg - K ( Pg = P + K ( .v)
.v) Pg: Gas pressure Shear viscosity K: Bulk viscosity VISCOSITY+COMPRESSIBILITY GAS OVERPRESSURE DOME EXPLOSIVITY RHEOLOGY (2) o , p f P
g b Pm l K, R [ r r ] r=R
2 RR 2 = pg - 4 l 3 b b ( 4 1- K = l 3 b3 1- 3
R ) [ rr ]r=R = pm - 3K 2 pm = pb b R R z
zz = p atm u=0 orrz = 0 DOMAIN AND BC H u=0 w=0 u=0
rz = 0 h 0 zz = ps r u=0 a Criteres Criteres darret
BASIC EQUATIONS darret 10-2 10-210-8 10-8 Conservation of momentum [ D ] U = SU [ D ] W = SW Conservation of mass [ M ] = S Artificial time Mass lumping
Petrov Galerkin weighting 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-Pa K+4/3 a2 = P
=D 2 P0-pa H EXAMPLE RESULT (1) U=0 = 106 Pa.s x0 = 0.5 Wt% P(0,H) = 0.56 MPa OVERPRESSURE AT THE CENTER OF THE CONDUIT EXIT
Compatible with the analytical solution EXAMPLE RESULT (2) rz =0 x0 = 0.5 Wt%
P(0,H) = 0.56 MPa P(a,H) = 1.5 MPa Variable viscosity (Hess and Dingwell, 96) EXAMPLE RESULT (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 NUCLASCENT (H. Massol, T. Koyaguchi)
Turbulent Flow 1-D Finite difference Cylindrical Geometry Steady state Variable viscosity Non-equilibrium degassing Fragmentation Level Laminar Flow Nucleation of Bubbles EVOLUTION OF DISSOLVED WATER IN THE MELT
H=5000 m a = 50 m 0 = 106 Pa.s x0 = 4wt% = 0.02 N m-1 D = 10-11 m2 s-1 EVOLUTION OF PRESSURE AND NUMBER OF BUBBLES H=5000 m a = 50 m 0 = 106 Pa.s x0 = 4wt% = 0.02 N m-1 D = 10-11 m2 s-1
OUTPUT OF THE MODEL BUBBLE SIZES BUBBLE DENSITY PRESSURE INSIDE BUBBLES NEXT STEP: CONTINUOUS BUBBLE SIZE DISTRIBUTION
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