Particle fall throught the atmosphere

8/10/2019 Particle fall throught the atmosphere

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Particle Fall through theatmosphere

Lecture #5

Ashfall Class 2009


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Distance dtravelled by an object falling for

time t:

Time ttaken for an object to fall distance d:

Instantaneous velocity viof a falling object

after elapsed time t:

Instantaneous velocity viof a falling object

that has travelled distance d:

Average velocity vaof an object that has

been falling for time t(averaged over time):

Average velocity vaof a falling object that

has travelled distance d(averaged overtime):

use g= 9.8 m/s(metres per second squared; which might be thought

of as "metres per second, per second. Assuming SI units, gis measured

in metres per second squared, so dmust be measured in metres, tin

seconds and vin metres per second.

air resistance is neglected--- quite inaccurate after only 5 seconds
http://en.wikipedia.org/wiki/International_System_of_Unitshttp://en.wikipedia.org/wiki/International_System_of_Units


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Particle Fallout

After a very short time, ~4 seconds, particles

will reach a terminal velocityin earth's

atmosphere, with their gravitational attraction

to the earth balanced by air resistance. Small

particles have dominant air resistance (fall

slowly) while large particles have dominant

gravity (fall rapidly).
http://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.htmlhttp://hyperphysics.phy-astr.gsu.edu/hbase/airfri2.html


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Reynolds Number

Re

Reynolds number is a dimensionless number(i.e. it has no units) that is a measure of thetype of flow through a fluid. In the case of

falling particles, this describes the way that airflows around the particle. There are threebasic types:

laminarwhere Re < 0.4,

intermediate where 0.4 < Re < 500, and

turbulent where Re > 500.
http://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.htmlhttp://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.htmlhttp://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.htmlhttp://www-pgss.mcs.cmu.edu/Publications/Volume16/physics/Turb/Turb-II.html


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Laminar flow;

RN = 10-2Turbulent flow;

RN = 106RN = 20 RN = 40 RN = 104

Fast-falling

Large

Pyroclasts

Fluid dynamics applies dimensionless analysis of fall of spheres in the

atmosphere, which shows that experience with large pyroclasts might not applyto smaller ones which fall much more slowly

RN =dvt/

Medium and

small pyroclasts

10

m/s

D =

1mmD =1m

.01

cm/

s


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8

Conventional Wisdom:

Particle Settling

particle accelerates due to gravity

Drag force:

(i) viscous drag(friction betweenthe fluid and the

particle surface)(ii) form drag(inertial forcecaused by theacceleration offluid around theparticle as it falls)

Particle Reynoldsnumber, Rep:

ratio of inertial forceto viscous force perunit mass

Rep= Vtd/ v

Vt= particle terminal

fall velocity;d= particle diameter;v= fluid kinematic viscosity

Rep:

> 500 turbulent

1-500 transitional


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Larger pyroclasts,

those >2mm in

diameter, fall in aturbulent flow

regime (Re> 500)

through the

atmosphere. Smallpyroclasts,


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10

Particle Terminal Fall Velocity

For large particles (Rep> 500)

inertial forces dominate:

fd

fp

CgdtV

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d = particle diameter

p= particle density

f= fluid density

g = acceleration due to gravity

Cd= dimensionless drag coefficient

For small particles(Rep< 1)-viscous forces dominate:

18

2

gdV pt

p= particle density

g= acceleration due to gravity

d= particle diameter

v= kinematic viscosity


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Fall of spherical particles in earths atmosphere

Schneider et al., 1999, J Geophys Res 104 4037-4050


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12

Particle Terminal Fall Velocity

100 microndiameter

particle hasVtof ~4-7

ms-1

Mean particle sizeat ~330 km fromMSH (Ritzville,WA) was 20

microns; Vt~0.2-

0.4 ms-1


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13

Atmospheric Structure

Environmental parameters determined from the radiosonde sounding takenat Spokane International Airport at 1800 UTC on 18 May 1980.


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Bonadonna et al., 1998


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Figure 3. Digital elevation map produced from stereo-pair in Figure 2.

Figure 2 Typical stereo-pair taken at 8otilt angle.

Owen P Mills, MSthesis, Michigan Tech,

2007


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Ash is NOT

spherical!

Riley et al., 2003

Augustine ash P Izbekov


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Riley et al., 2003


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Rose W I, C M Riley and S Dartevelle, 2003, J Geology, 111:115-124.
http://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdfhttp://www.geo.mtu.edu/~raman/papers/Nebraska.pdf


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Riley et al., 2003


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Riley et al., 2003


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Riley et al., 2003


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Riley et al., 2003


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Riley et al., 2003

Particle fall throught the atmosphere

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