conduit models (wk-1, yk-1) to investigate transition between explosive and effusive eruptions t....
Post on 21-Dec-2015
214 Views
Preview:
TRANSCRIPT
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 Mitanietc.
Basic Equation for WK-1
Mass conservation
Momentum conservation
Equation of State
(1 )0
d n v
dz
1dv dPv g Fdz dz
P
nRTn
l
11
1/ 2[ { (1 )}] wv n sP n Qdz
2
2
8
0.0025
v
rF
v
r
2 ( ) /w h hQ rn K P P
gas :
liquid :
T constant
(Woods and Koyaguchi, 1993)
: overpressure parameter
2/10 sPnn
Obatain the relationship between P and Q
Determine exit pressure by systematically changing mass flux, Q
for different mass flux
hydrostatic
lithostatic
Nor
mal
ized
dep
th
Normalized pressure
A method to systematically investigate the features of solutions (Shooting method)
Overpressure para meter ( α )~ 1 atm
Mass flux
Exi
t p
ress
ure
Multiple steady solutions and “negative friction”
Geological implication of the presence of multiple solutions
出口の圧力
Mass flux
Dome eruption Explosive eruption
Dome collapseSub-sonic solution
Sonic solution
Exi
t pre
ssur
e
Atmospheric pressure + load
Increase of chamber pressure
Pressure drop due toviscous friction
Decrease in total friction due to descending fragmentation surface
Mass flux
Pressure drop due toturbulent friction
Mass flux
Mass flux
Exi
t pre
ssur
e
Mass flux
Exi
t pre
ssur
eE
xit p
ress
ure
Mass flux
Origin of the multiple solutions
Purpose of YK-1
WK-1 YK-1
Gas-lossthroughconduit wall
Gas may escape vertically.
(Yoshida and Koyaguchi, 1999)
What is the minimal model toexpress the effects of relative velocity?
Basic equations for YK-1・ 2-velocity model
・ presence of fractured turbulent flow regime
1 .l l lQ u const
.g g gQ u const
lg l1 (1 )l l l w
d dPQu g F F
dz dz
lgg g g gw
d dPQ u g F F
dz dz
gP RT
:
:
:l
g
Q
Q
Gas volume fraction
Gas mass flux (kg/m2 ・ s)
Liquid mass flux (kg/m2 ・s)
Mass conservation
Momentum conservation
Equation of state
12
8, 0lw gw
c
F u Fr
20, sgn( )4w
lw gw g g gc
F F u ur
← Poiseuille flow
←Trubulent flow
Constitutive equation describing wall friction
Before fragmentation
After fragmentation
Tentatively critical void fraction (=0.8) was chosen as afragmentation criterion.
1
lg 2lg 2
3: (1 )( ) (1 )( ) sgn( )
4
t t
g l g g l g lb b
F u u u u u ur r
0.6
0.7 0.6t
0.6 0.7
1
lg 2lg
3: (1 )( ) sgn( )
4 8
t t
Dg g l g l
b a
CF u u u u
r r
0.8
0.85 0.8t
0.8 0.85
lg 2
3: (1 )( )g l
b
F u ur
0.6 ←Stokes’ terminal veolcity
lg 2lg: (1 )( ) sgn( )
4 g g l g lc
F u u u ur
0.7 0.8 ← turbulent pipe flow
2lg
3: (1 )( ) sgn( )
8D
g g l g la
CF u u u u
r 0.85 ←high Re terminal
velocity
Constitutive equations describing gas-liquid frictionBubbly flow
Fractured turbulent flow
Gas-particle flow
Essense of YK-1
Wall friction >>friction between liquid and gas
Wall friction ~ friction between liquid and gasBoth are determined by liquid viscosity.
Wall friction ~ friction between liquid and gasBoth are determined by gas viscosity.
Determined by gas viscosityDetermined by liquid viscosity.
Whatever the details of the constitutive equations may be…
top related