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 AND COMPRESSIBLE FLOW INCOMPRESSIBLE FLOW BUBBLY SECTION MAGMA CHAMBER Exsolution level INTEGRATION DOMAIN SCHEMATIC VIEW OF A VOLCANIC CONDUIT ORIGINALITY: 2-D METHOD: Finite Element

 = -2  e  (. v)  + P g  - K (.v).v)  PgPg : Gas pressure  Shear viscosity K : Bulk viscosity  P g = P + K (.v) RHEOLOGY (1) VISCOSITY+COMPRESSIBILITY GAS OVERPRESSURE DOME EXPLOSIVITY

b R P g  o, p f  PmPm  l K,  RHEOLOGY (2) =p g - 2  b -4 µ l ˙ RR 2 b b 3 R 3 [  r r ] r=R () K= 4 3 µ l 1 -   [  r r ] r=R =p m -3K ˙ R R p m =p b - 2  b

0 z r a h H  zz = p s u = 0  zz = p= p atm u = 0 or  rz = 0 u = 0 w = 0 u = 0  rz = 0 DOMAIN AND BC

BASIC EQUATIONS Artificial time Mass lumping Petrov Galerkin weighting [ D ] U = S U [ D ] W = S W [ M ]  = S  Conservation of momentum Conservation of mass Criteres d’arret Criteres d’arret

 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 P0-pa =  P K+4/3   a2a2 H2H2 = D

EXAMPLE RESULT (1) U = 0  = 10 6 Pa.s x 0 = 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) x 0 = 0.5 Wt% P(0,H) = 0.56 MPa Variable viscosity (Hess and Dingwell, 96)  rz = 0 P(a,H) = 1.5 MPa

EXAMPLE RESULT (3) x 0 = 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 difference Cylindrical Geometry Steady state Variable viscosity Non-equilibrium degassing (H. Massol, T. Koyaguchi)

EVOLUTION OF DISSOLVED WATER IN THE MELT H=5000 m a = 50 m  0 = 10 6 Pa.s x 0 = 4wt%  = 0.02 N m -1 D = m 2 s -1

H=5000 m a = 50 m  0 = 10 6 Pa.s x 0 = 4wt%  = 0.02 N m -1 D = m 2 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