Conduit models (WK-1, YK-1) to investigate transition between explosive and effusive eruptions T. Koyaguchi University of Tokyo Collaboration with: Andy Woods, Shigeo Yoshida, Helene Massol, Noriko Mitani etc.
Explosive or Effusive Pinatubo, 1991 Unzen, 1991
Key observations What is the minimal model to explain these extreme eruption styles?
Basic Equation for WK-1 Mass conservation Momentum conservation Equation of State gas ： liquid ： constant (Woods and Koyaguchi, 1993) overpressure parameter
Obatain the relationship between P and Q Determine exit pressure by systematically changing mass flux, Q for different mass flux hydrostatic lithostatic Normalized depth Normalized pressure A method to systematically investigate the features of solutions (Shooting method)
Overpressure para meter （ α ）～ 1 atm Mass flux Exit pressure Multiple steady solutions and “negative friction”
General features of results
Geological implication of the presence of multiple solutions 出口の圧力出口の圧力 Mass flux Dome eruption Explosive eruption Dome collapse Sub-sonic solution Sonic solution Exit pressure Atmospheric pressure + load Increase of chamber pressure
Pressure drop due to viscous friction Decrease in total friction due to descending fragmentation surface Mass flux Pressure drop due to turbulent friction Mass flux Exit pressure Mass flux Exit pressure Mass flux Origin of the multiple solutions
Purpose of YK-1 WK-1YK-1 Gas-loss through conduit wall Gas may escape vertically. (Yoshida and Koyaguchi, 1999) What is the minimal model to express the effects of relative velocity?
Basic equations for YK-1 ・ 2-velocity model ・ presence of fractured turbulent flow regime Gas volume fraction Gas mass flux (kg/m 2 ・ s) Liquid mass flux (kg/m 2 ・ s) Mass conservation Momentum conservation Equation of state
← Poiseuille flow ←Trubulent flow Constitutive equation describing wall friction Before fragmentation After fragmentation Tentatively critical void fraction ( =0.8) was chosen as a fragmentation criterion.
←Stokes’ terminal veolcity ← turbulent pipe flow ←high Re terminal velocity Constitutive equations describing gas-liquid friction Bubbly flow Fractured turbulent flow Gas-particle flow
Essense of YK-1 Wall friction >>friction between liquid and gas Wall friction ～ friction between liquid and gas Both are determined by liquid viscosity. Wall friction ～ friction between liquid and gas Both are determined by gas viscosity. Determined by gas viscosity Determined by liquid viscosity. Whatever the details of the constitutive equations may be…
pressure depth General features of results velocity Void fraction
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