SIMULATION OF DUST DEVILS

Zhaolin GU, PhD, ProfessorXi’an Jiaotong University October , 2006, CCFD Forum , Tokyo University

Background

Atmospheric dust has important impacts on

global and regional climates.

Some specific convective wind systems in the

convective boundary layer (CBL), such as, dust

storms, dust devils etc., can carry dust into the

atmosphere.

Dust transportation in Northwestern arid area of China

Dust stormMeso-scale meteorological process

Dust devilMicro-scale meteorological process

About dust storms – Some pictures

The vision of Lanzhou Train Station at 16:00, April 10, 2004

The vision of Dunhuang Grottoes at 16:00, April 10, 2004

The vision of Xi’an City Wall, April 9, 2006

The destroyed window by the dust storm, April 9, 2006

About dust storms – Meteorological aspects

A Mesoscale meteorological process, composed of strong convection cells Height of dust front 300-400 m Length of dust front around 100 km second dust front 10-20 km Horizontal velocity more than 20 ms-1 Vertical velocity more than 15 ms-1

Temperature increment (T ) 4–8 K Pressure depression (p) 2.0–3.5 hPa

ΔT and Δp are departures from ambient values of temperature and

pressure.

About dust devils – Meteorological aspects

A special case of convective vortex occurring in the atmosphere boundary layer.

The most common, small-scale dust transmitting system.

Maybe the primary atmospheric dust-loading mechanism in non-storm seasons

Mixing grains in dust devils becoming tribo-electrified.

Typical Observed Dust Devil Physical Characteristics

Diameter Tens to 141 m Height 300–660 m Horizontal velocity 5-20 ms-1 Vertical velocity 3–15 ms-1

Rotation sense Random Temperature increment (ΔT ) 2–8 K Pressure depression (Δp) 2.5–4.5 hPa

ΔT and Δp are departures from ambient values of temperature and pressure.

Inducement of dust devils—Background vorticity

The Benard’s Convection in atmospheric boundary layer

Inducement of dust devils—Background vorticity

Inducement of dust devils— Surface roughness

2/1 1 z C

tv z C e

At h=5.2m and h=9.4m (V7 and V31 in the figure), the value of tangential velocities at r=50m is different, where is far from the dust devil center and maybe the boundary of the dust devil. (P. C. Sinclair, 1973)

Inducement of dust devils— Buoyancy

Heat radiation from the sun causing the rise of

surface temperature

The temperature difference between the ground

surface and the near-surface air parcels is over

20-30K at sunny mid-day in deserts (Li J. F. ,

Desert Climate, Meteorological Press, Beijing,

2002)

The temperature difference is related to the heat

flux on the surface.

Tool and methods for dust devil study

Field observation and

test

Laboratory experiment,

e.g. dry ice simulator in

Arizona University

Numerical simulation

gas-solid two-phase flow

Numerical simulation

C. B.Leovy, Nature, 424 ,2003 Promise to be an important tool for interpreting labor

atory and field observations of dust devils (C. B.Leovy, Nature, 424 ,2003) Getting insights into the dynamics of boundary-layer

vortices Two scale methods: convective boundary layer (CBL) sc

ale simulation, and dust devil-scale simulation

Dust devil-scale simulation method LES- Lagrangian discrete phase model (LDPM) model

LES for the turbulent flow LDPM for the grain movement—one way coupling Lifting of dust not actually appearing to be of major dyn

amical importance for the development of these vertical vortices ( P. C. Sinclair, J. Appl. Meteorol. 8,1969)

0j

j

u

x

0jc

j

u

xContinuity equation

3

i j ji iSGS c i

j i j j i

u u uu uPg T T

t x x x x x

Momentum equation

Pr Prj SGS

j j SGS j

u ee et x x x

Energy equation

2SGS C S

12

2 ij ijS S S

LES Equations

12

ij ij

ij ij

L MC

M M

Least-squares approach, Lilly (1992)

1

23ij kk ij ijL L CM

2 2 2ij ij ij

M S S S S

2

12

jiij

j i

uuS

x x

1/2

2 ij ijS S S

Dynamic subgrid scheme

Dust devil scale LES model—boundary conditions

Involution of dust devils

a) Weak vortex phase; b) Single cell phase;c) Transition phase of single cell to double cell; d) Double cell phase .

Fine flow structure in the weak vortex phase

The updraft vectors and contours of updraft velocity

Fine flow structure in the single cell phase

The updraft vectors and contours of updraft velocity

Fine structure in transition phase of single cell to double cell

The updraft vectors and contours of updraft velocity

Fine flow structure in the double cell phase

The updraft vectors and contours of updraft velocity

Daughter vortices in the double cell phase

Grain tracks in the mature phase flow

100m 200m 300m

Dust lifting patterns in a dust devil

1-track of fine dust grains;2-track of medium grains;3-track of large grains;4-small vortices induced by the interaction of different sized grains; 5-general pattern of interactions.

An illustration of the electric dust devil—Farrell et al. J. Geophys. Res., 109,2004

Observed near-surface patterns of terrestrial dust devils

Modeled dust devils and typical parameters

ModelsMomentumroughness

(m)

Ground temperature

(K)

Initial vorticity

(ms-1)

Maximum rotating and updraught speed, v and w, and

pressure drop, Δp

A 4.0 343 2.5 v=12 ms-1, w=16 ms-1, Δp=2hPa

B 4.0 343 5.0 v=20 ms-1, w=22 ms-1, Δp=4.2hPa

C 4.0 323 2.5 v=10 ms-1, w=10 ms-1, Δp=1hPa

D 4.0 323 5.0 v=18 ms-1, w=17 ms-1, Δp=3.6hPa

E 2.0 343 2.5 v=12 ms-1, w=9.5 ms-1, Δp=3hPa

F 6.0 343 2.5 v=16 ms-1, w=38 ms-1, Δp=8.5hPa

Simulated near-surface patterns of dust devils

Near-surface shapes of dust devils simplified by the periphery of the rotating velocity contour of their cores.

Some problems in the numerical simulation

Grain size distribution The influence of electrostatic field on the

movement the positive-charged or negative-

charged particles

The collision of particles resulting in charge

neutralization and/or production, and then the

particle movement

Particle population balance model—an example

Particle population balance model

A method connecting the microcosmic behaviors

with the macroscopic token of dispersed phase

Description for different microcosmic behaviors in

various process, such as crystal, growth,

dissolution, breakage, aggregation, erosion, sinter

and so on

Dealing with some process— formation or

transformation of rain, snow and hail, aerosol,

sand storm, dust devils

Particle population balance equation (PPBE)

n (L, us, t, x) particle number density function;

us particle velocity;

L particle properties;

X dimension ;

T time ;

S(L, us, x, t ) source tem, relating to the dispersed phase

behaviors;

F forces acting on the dispersed phase.

( , ;x, )[ ( , ;x, )] [ F ( , ;x, )] ( , ;x,t)

s

ss s u s s

n L u tu n L u t n L u t S L u

t

Particle population balance equation (PPBE)

( ) ( ) ( ) ( )a a b bk k k k kS B t D t B t D t

( ) 3 3 /3 * ( ) *

1 1 1 1 1 1

1( ) ( )

2

q q q q q qN N N N N NN k k k k

kS t L L L a b L a

3 3 /3

0 0

1( ) ( ; ) ( , )( ) ( ; )

2a kkB t n t L L n L t dLd

0 0

( ) ( ; ) ( , ) ( ; )a kkD t L n L t L n t d dL

0 0

( ) ( ) ( | ) ( ; )b kkB t L a b L n t d dL

0

( ) ( ) ( ; )b kkD t L a L n L t dL

1

( ; ) ( ) [ ( )]aN

a aa

n L t t L L tTransformation

( )akB t

( )akD t

( )bkB t

( )bkD t

Source term with no reaction

Solution of the PPBE

Classification method (CM)—(N+1)-fluid model, one fluid corresponding to the gas phase and N fluids to the different size dispersed phase

Quadrature method of moment (QMOM) (McGraw, Aerosol. Sci. Technol., 27, 1997)

Direct Quadrature method of moment (DQMOM) (Marchisio et al., Chem. Eng. Sci., 58, 2003)

Monte Carlo Methods

Prospect of CFD coupling with PPBE-1

Extending the physical understanding of the dispersed phase behaviors and process

QMOM and DQMOM, based on the fundamental statistical concepts on the microscopic level, are the promise to solve the PPBE

Reformulation of the coalescence and breakage, consistent with QMOM and DQMOM

Improving the formulation of the turbulence effects, interfacial transfer fluxes

Improving the formation of the boundary conditions (inlet and outlet conditions, wall boundary)

Prospect of dust simulation

The evaluation of dust flux at a level of dust devil on different surface

The possibility evaluation of occurring of dust devils in the region

The evaluation of regional dust flux from dust devils

Thanks for your attention!