Experimental Perspective on Sedimentation from Plumes

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21 Φεβ 2014 (πριν από 3 χρόνια και 4 μήνες)

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Experimental Perspective on Sedimentation from
Plumes
M.Bursik
Department of Geology,University at Bualo,SUNY
Bualo,NY 14260
mib@buffalo.edu
IAVCEI Working Group on Modeling Volcanic Tephra-Fall Hazards
First Meeting,14 and 20 July 2003
Cities on Volcanoes 3Full ScreenJuly 21,2003Univ.Bualo
IntroductionUniv.Bualo 1
IntroductionThe conservation of mass ux of particles for multiple grain size fractions,M
i
,as a
function of time,t,is given by:
dM
idt
= 
w
s
M
ih
(1)
where w
s
is the settling speed of a particle in a given size class.Univ.Bualo 1
IntroductionThe conservation of mass ux of particles for multiple grain size fractions,M
i
,as a
function of time,t,is given by:
dM
idt
= 
w
s
M
ih
(1)
where w
s
is the settling speed of a particle in a given size class.
This was developed for systems with a oor (Hazen,1904)Univ.Bualo 1
IntroductionThe conservation of mass ux of particles for multiple grain size fractions,M
i
,as a
function of time,t,is given by:
dM
idt
= 
w
s
M
ih
(1)
where w
s
is the settling speed of a particle in a given size class.
This was developed for systems with a oor (Hazen,1904)
Used extensively in civil engineering for design of settling ponds in wastewater
treatment Univ.Bualo 1
IntroductionThe conservation of mass ux of particles for multiple grain size fractions,M
i
,as a
function of time,t,is given by:
dM
idt
= 
w
s
M
ih
(1)
where w
s
is the settling speed of a particle in a given size class.
This was developed for systems with a oor (Hazen,1904)
Used extensively in civil engineering for design of settling ponds in wastewater
treatment
Works for volcanic plumes and umbrella clouds (Bursik et al.,1992)Univ.Bualo 1
Advection-DiusionHazen's equation can be derived from the advection-diusion equation
Assume that there is no relative diusion
@
t
C
i
+r ~uC
i
= r
2
C
i
+ (2)Univ.Bualo 2
Layered EnvironmentNeeded to test Hazen's validity for layered systems
Set up two main types of experimental systems
In the layered environment,a light,particle-bearing uid lies atop a denser uid
with no particleUniv.Bualo 3
Univ.Bualo 4
Univ.Bualo 4
Settling PhenomenologyIn experiments on layered systems,we found that...
Particles do not always settle from the upper layer singly
There are particle-laden,descending plumesUniv.Bualo 5
Settling PhenomenologyUniv.Bualo 5
TheoryThe development of descending plumes has been characterized by Hoyal et al.
(1999a,b):
Convective sedimentation:Gr =
gC
0

3
1

2
; = w
s
t (3)
Double diusion:Gr =
gC
0

2
1
w
s
(4)
Criterion:Gr > 1000 (5)
(6)Univ.Bualo 6
Shear and Re-entrainmentShear at the boundary between layers can destroy the convection,if the turbulence
level in the upper layer is suciently vigorous (Gupta,2002)
The result is...Univ.Bualo 7
Shear and Re-entrainmentUniv.Bualo 7
TheoryBecause of in ow toward the plume caused by wind and atmospheric entrainment,
particles can be re-entrained.In general,Eqn1takes on a form:
dM
i dt
= f (w
s
w

)
M
ih
(7)
where w

is a re-entrainment speed.The function,f,can be determined empirically.Univ.Bualo 8
Lee Wave,Separation,Coanda Eect...For plumes in a highspeed cross ow,topography can have an eectUniv.Bualo 9
Lee Wave,Separation,Coanda Eect...For plumes in a highspeed cross ow,topography can have an eectBut is this the case even when the plume is less dense than underlying layers?Univ.Bualo 9
Over a range of Re,for the buoyant jet with ambient water density above plume
density,there is reattachment
The result is that particles that would otherwise settle through atmosphere are
deposited from a ground-hugging currentUniv.Bualo 10
PrognosisUniv.Bualo 11
PrognosisMost models do not provide full dynamic expression of separate phasesUniv.Bualo 11
PrognosisMost models do not provide full dynamic expression of separate phases
It is dicult to know what the turbulence intensity and spectrum inside a plume isUniv.Bualo 11
PrognosisMost models do not provide full dynamic expression of separate phases
It is dicult to know what the turbulence intensity and spectrum inside a plume is
There are unmodeled eectsUniv.Bualo 11
PrognosisMost models do not provide full dynamic expression of separate phases
It is dicult to know what the turbulence intensity and spectrum inside a plume is
There are unmodeled eectsUniv.Bualo 11
Volcanic Plume ConvectionUniv.Bualo 12
Volcanic Plume ConvectionUniv.Bualo 12