The mechanics of pyroclastic density currents Montserrat, British - - PowerPoint PPT Presentation

The mechanics of pyroclastic density currents

Montserrat, British Geological Survey Transport processes (not deposits)

The role of particle-scale processes

• n the large scale dynamics of

pyroclastic density currents

Michael Manga

Interrupt and ask questions anytime

Mutiphase flows in explosive eruptions

Pyroclastic Flow

• Particulate gravity current
• Particle+Gas Flow
• Interaction with water

Plinian Column

• Buoyant plume
• Particle+Gas Flow

Montserrat Univ West Indies St Helens D Swanson, USGS

Multiphase flows in explosive eruptions

• Controls of particle size?
• How fast?
• How far?
• Internal structure?
• Connect processes

to deposits

Montserrat, Univ West Indies St Helens, USGS

Challenge

• Wide range of length and time scales
• Many critical processes occur at the scale of

particles

• How to integrate the micro- and macro-scale

mass, momentum and heat transfer?

Challenge

• Wide range of length and time scales
• Many critical processes occur at the scale of

particles

• How to integrate the micro- and macro-scale

mass, momentum and heat transfer?

Multiple levels of coupling between discrete and continuous phases

Multiple levels of coupling between discrete and continuous phases Prolonged Frictional Contact

Multiple levels of coupling between discrete and continuous phases Instantaneous Collisions

Multiple levels of coupling between discrete and continuous phases

St= p/f

Mean field multifluid equations

Details of constitutive models, equations of state, turbulence models, in Dufek and Bergantz (2007) Key: determining closure models

Continuity Momentum Thermal Energy

(1 1 1ui) t + (1 1 1ui

1uj)

xi = N(,e)

pM0 2

• (1P)

xi + 1 Re

• xi

1 ij

• + 1

St

• (1ui 2ui)+

1 Frd

2

• ˆ

eg

1 1cp

1T t + 1Ui 1T xi

• =

1 Pe

• 1q

1xi + 1

ThSt

• 2T - 1T

( )

• t

1 1

( )+

x

1 1 1ui

( ) = 0

Sub-grid scale thermo-mechanical processes

1) Collisions between particles within pyroclastic flows (and in volcanic conduits in the afternoon) 2) Role of boundary conditions (over water vs

• ver land)

3) Heat transfer from particles to water

• 1. How much of this ash is made

WITHIN the flow?

Influence on flow mechanics, deposits?

Augustine, 1986 Maurice and Katia Krafft

Frictional ash production experiment

Cagnoli and Manga, JGR (2004)

24R = 1

y(u)

Collisional ash production experiment

Ash, not fractal size distribution (collision energy not large enough)

23R = 24 2

( )

2 3/ 2 2

( )g0

3/ 2

2d

( )

• 1. Generating ash within flows
• t(g g

) + xi (g g gUi ) = 0

• t(2 2

) + xi (2 2 2Ui ) = 23R

Mass loss due to collisional ash prodution

• 24R

Mass loss due to frictional ash prodution

• t(3 3

) + xi (3 3 3Ui ) = + 23R

Mass gain due to collisional ash prodution

• t(4 4

) + xi (4 4 4Ui ) = + 24R

Mass gain due to frictional ash prodution

• Continuity
• t(g g

Ui ) + xi (g g gUi

gUj ) = g

P xi ij + g ij xj + gIi + g g gi

• t(2 2

Ui ) + xi (2 2 2Ui

2Uj ) = 2

P xi ij + 2 ij xj + 2Ii + 2 2 gi 23R2Ui 24R2Ui

• t(3 3

Ui ) + xi (3 3 3Ui

3Uj ) = 3

P xi ij + 3 ij xj + 3Ii + 3 3 gi + 23R3Ui

• t(4 4

Ui ) + xi (4 4 4Ui

4Uj ) = 4

P xi ij + 4 ij xj + 4Ii + 4 4 gi + 24R4Ui

Momentum

g g

gcp g T t + gUi g T xi

• = g

q xi H g2 H g3 H g4

2 2

2cp 2 T t + 2Ui 2 T xi

• = 2

q xi + H g2

3 3

3cp 3 T t + 3Ui 3 T xi

• = 3

q xi + H g3

4 4

4cp 4 T t + 4Ui 4 T xi

• = 4

q xi + H g4

Thermal

Model problem

grid 1m x 5 m; time step < 0.1s initial velocity 50 m/s initial concentration 0.025 initial size 1 cm temperature 650 C

Flow over level terrain

1 cm pumice Collisional ash Frictional ash

Collisional and frictional ash are well mixed Travels far beyond pumice Total ash produced: 7%

Downslope Accelerating

1 cm pumice Collisional ash Frictional ash

1 cm pumice Collisional ash Frictional ash

Ash production rate

Ash generated in more energetic part of flow

1 cm pumice Collisional ash Frictional ash

Ash production rate

Conclusions

• A few to a few 10s of % of

flow is converted to ash

• Ash generation increases

runout distance

• Ash generated within flow

separates from larger particles (travels faster, higher, farther)

• Origin of rounding of larger

clasts

• St. Helens, USGS

rounded Lacroix 1902

• 2. Transport capacity of pyroclastic flows:

substrate-flow interactions

Kos Plateau tuff

Role of boundary condition

Particle-substrate interactions

Measure velocity before and after collision; whether particle bounces Variables: angle , velocity, mass, substrate

Air gun

Example (water substrate)

• Extract quantitative information . . .

Water substrate

sinkers Restitution coefficient: Fraction that sink:

Pumice substrate

Restitution coefficient: No effect of mass, impact velocity

Model problem

initial velocity 80 m/s Initial height 100 m initial concentration 0.025 or 0.40 density 1000 kg/m3 size: 95% are 10 microns, 5% are 0.5 mm temperature 700 K; air 300 K

Effect of boundary type

water pumice

Over land flows develop a dense bed-load region because particles are not lost from the flow

10 microns 10 microns 0.5 mm 0.5 mm

Add Lagrangian tracers

Interact with the flow, but do not affect the flow Introduced near inlet Size from 1 micron to 10 m

Over water

No concentrated bedload Concentration has little effect of large clast transport

concentration 0.025 concentration 0.40 > 1cm > 1cm < 1cm < 1cm furthest transport

• f 1 cm clast

Over land

With concentrated bedload, large clasts transported to the end of the flow! Flows travel further than over water concentration 0.025 concentration 0.40 > 1cm > 1cm < 1cm < 1cm furthest transport

• f 1 cm clast

Over water

1) Boundary condition has a small effect for dilute flows 2) Dense flows over land develop a particle-rich bedload which transports large clasts (over water, particles sink and no particle-rich bedload forms)

> 1cm < 1cm

Over land

0.025 0.025 0.40 0.40

Adding mass back into the current?

Can settling particles “splash” mass back into the current?

Experiments

Experiments

Mass ejected can exceed mass of incident particle

Fauria et al. (2016)

Scaling

New and literature data, new scaling law

Fauria et al. (2016)

Density current model

Compute concentration, velocity, temperature as a function of time (and distance) Assume turbulent gravity current (e.g., Dade and Huppert, 1995) more details in Fauria et al. (2016) Allow big particles to settle

Density current model

Allow small particles to splash Conserve energy more details in Fauria et al. (2016) Currents travel until either all particles settle,

• r they become buoyant

Splash cools flow, increases runout

Fauria et al. (2016)

Fauria et al. (2016)

Splash cools flow, increases runout

Fauria et al. (2016)

What we learned

Large clast transport is . . . 1) dominated by momentum exchange from smaller particles 2) suppressed over water because a dense bedload region does not develop (boundary effect is indirect through the concentration of particles in bedload region) 3) Resuspension can change runnout distance by an order-of-magnitude

• 3. Interaction with water

Hot flows, when they enter water, generate stream

• How much?
• How fast?
• Effects of steam generation?

Montserrat, Univ West Indies

Measurement of steam production rate

1) Measure mass of stream released 2) Measure time clasts float

(results in Dufek, Manga Staedter, J Geophys Res 2007)

100-700 oC Pumice, glass beads 3 mm - 2 cm

Stroberg, Manga and Dufek, JVGR 2010

Measurement of steam production rate

Rv =

p

( )

( ) p

( )

pcp

( )(pT wT )

mp[wcp(bT wT ) + L] = 6 p

( )

( ) pcp

( )(pT wT )

d3[wcp(bT wT ) + L]

Multiphase equations

• t(w w

) + xi (w w wUi ) = Rv

Mass loss due to phase change

• t(g g

) + xi (g g gUi ) = +Rv

Mass gain due to phase change

• t(p p

) + xi (p p pUi ) = 0

• t(g g

Ui ) + xi (g g gUi

gUj ) = g

P xi ij + g ij xj + gIi + g g gi + Rv

gUi Momentum gain to phase change

• t(w w

Ui ) + xi (w w wUi

wUj ) = w

P xi ij + w ij xj + wIi + w w gi Rv

wUi Momentum loss due to phase change

• t(p p

Ui ) + xi (p p pUi

pUj ) = p

P xi ij + p ij xj + pIi + p p gi

w

w wcp w T t + wUi w T xi

• = w

q xi + H wg H wp

Mean interphase heat transfer (particle-water)

• H s

wp Subgrid interphase heat transfer (particlewater)

• +

S

Mean field latent heat of vaporization

• +

Ss

Subgrid latent heat of vaporization

• g g

gcp g T t + gUi g T xi

• = g

q xi H gp H gw S

Mean latent heat of vaporization

• Ss

Subgrid latent heat of vaporization

• p p

pcp p T t + pUi p T xi

• = p

q xi + H gp + H wp

Mean interphase heat transfer (particlewater)

• +

H s

wp Subgrid interphase heat transfer (particlewater)

• Continuity

Momentum Thermal Energy

Application to July 12-13, 2003 littoral blast, Montserrat

grid 2 m x 10 m; time step , 0.1 s initial velocity 50 m/s initial concentration 0.1 initial sizes: 50% is 1 cm, 50% is 0.1 mm temperature 650 C

Landward directed base surge

• 0.6% flow forms landward-directed base surge

(Edmonds et al. (2006) estimate a volume of 0.75%)

• Landward directed flow is dry

Edmonds and Herd, Geology (2005)

steam landward directed blast

Conclusions

• Experimental measurements can be used to

link the micro- and macro-scale

• Particle-scale thermo-mechanical processes

and properties (ash production, vaporization of water, boundary conditions) matter - qualitatively and quantitatively

Suggested reading Dufek, J. (2016) The fluid mechanics of pyroclastic density currents, Annual Reviews of Fluid Mechanics, vol. 48, 459-485