Lecture 3. Governing equations for multiphase flows. Continuum hypothesis. Fragmentation mechanisms. Models of conduit flows during explosive eruptions and results. Volcanic plume dynamics in the atmosphere. Dynamics of dispersed systems. Bubbles. Mixture properties:. Particles.
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Continuity equations Mass fluxes
Momentum equations Momentum exchange
Energy equations Heat fluxes
Flow regimes and boundaries.
Homogeneous from magma chamber until pressure > saturation pressure.
Constant density, viscosity and velocity, laminar.
Vesiculated magma from homogeneous till magma fragmentation.
Bubbles grow due to exsolution of the gas and decompression.
Velocity and viscosity increases.
Flow is laminar with sharp gradients before fragmentation due to viscous friction.
Fragmentation zone or surface (?).
Gas-particle dispersion from fragmentation till the vent.
Turbulent, high, nonequilibrium velocities.
subsonic in steady case, supersonic in transient.Conduit flow during explosive eruption
Mass conservation for liquid and gas phases
intensity of mass transfer, bubble nucleation and diffusive growth
gravity forces, conduit resistance, inertia
momentum transfer between phases
energy transfer between phases
dissipation of energy by viscous forces
Bubble growth equation - nonequilibrium pressure distribution
Physical properties of magma - density, gas solubility, viscosity
Boundary conditions - chamber, atmosphere, between flow zonesModelling strategy
FP - fragmentation at fixed porosity.
overpressure in a
SR - critical
Need to calculate discharge rate
a - volume concentration of gas (1-a) - of condensed phase
b - volume concentration of crystals in condensed phase
r - densities, “m”- melt, “c”- crystals, “g” - gas
c - mass fraction of dissolved gas = k pg1/2
V - velocities, Q - discharge rates for “m”- magma, “g” - gas
n - number density of bubbles
r - mixture density
l - resistance coefficient
(32 - pipe, 12 -dyke)
k(a) - permeability
mg- gas viscosity
p- pressure “s”- mixture, “m”- condensed phase, “g”-gas
F - interaction forces:”sb” - between small and big particles
“gb” - between gas and big particles
High - comes to stratosphere
Ash fallout, climate change
Acid rains, aviation hazards
Pyroclastic flow generation