Conduit models (WK-1, YK-1) to investigate transition between explosive and effusive eruptions

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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.
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Explosive or Effusive
Unzen, 1991
Pinatubo, 1991
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Key observations
What is the minimal model to explain these
extreme eruption styles?
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Basic Equation for WK-1
(Woods and Koyaguchi, 1993)
Mass conservation
liquid
gas
Momentum conservation
Equation of State
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A method to systematically investigate the
features of solutions (Shooting method)
lithostatic
Normalized depth
hydrostatic
for different mass flux
Normalized pressure
Determine exit pressure by systematically
changing mass flux, Q
Obatain the relationship between DP and Q
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Multiple steady solutions and negative friction
Exit pressure
Mass flux
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General features of results
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Geological implication of the presence of
multiple solutions
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Origin of the multiple solutions
Pressure drop due to viscous friction
Exit pressure
Mass flux
Mass flux
Decrease in total friction due to descending
fragmentation surface
Exit pressure
Mass flux
Pressure drop due to turbulent friction
Exit pressure
Mass flux
Mass flux
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Purpose of YK-1
(Yoshida and Koyaguchi, 1999)
Gas may escape vertically.
Gas-loss through conduit wall
What is the minimal model to express the effects
of relative velocity?
WK-1
YK-1
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Basic equations for YK-1

• 2-velocity model
• presence of fractured turbulent flow regime

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Constitutive equation describing wall friction
Before fragmentation
? Poiseuille flow
After fragmentation
?Trubulent flow
Tentatively critical void fraction (f0.8) was
chosen as a fragmentation criterion.
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Constitutive equations describing gas-liquid
friction
Bubbly flow
Fractured turbulent flow
? turbulent pipe flow
Gas-particle flow
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Essense of YK-1
Whatever the details of the constitutive
equations may be
Wall friction friction between liquid and
gas Both are determined by gas viscosity.
Wall friction gtgtfriction between liquid and gas
Determined by gas
viscosity Determined by liquid viscosity.
Wall friction friction between liquid and
gas Both are determined by liquid viscosity.
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General features of results
Void fraction
depth
pressure
velocity
pressure
pressure
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End