TasksTasks 4.1 4.1 4.2 4.2

Department of Civil and Environmental EngineeringDepartment of Civil and Environmental Engineering

University of TrentoUniversity of Trento

Wallingford (UK), Wallingford (UK), MayMay 16 16thth-17-17thth 2002 2002IMPACT Investigation of Extreme Flood Processes & Uncertainty

Composition of the Composition of the group:group:a.armaninia.armaninil.fraccarollol.fraccarollom.larcherm.larcherg.rosattig.rosattie.toroe.toro

c.dalrìc.dalrìe.zorzin e.zorzin

A Godunov method for the computation of erosional shallow water transients

L. Fraccarollo, H. Capart, and Y. Zech

submitted to the Int. Journal of Numerical Methods in Fluids, 2002.

EquationsEquations

0)()(

mmmb uhx

hzt

0)()(

mssb uhx

hzt

w

bsmsmmsmmsm x

z)hrh(gghrghu)hrh(

xu)hrh(

t

2

212

212

g

uuhh m

mss

2eq )(

1D with sections having varying shape and dimensions1D with sections having varying shape and dimensions

inclusions of non-erodible sections at assigned positionsinclusions of non-erodible sections at assigned positions

Undergoing AdvancementsUndergoing Advancements

AdaptationAdaptation processes processes

SelectionSelection processes processes

Boundary conditionsBoundary conditions

True two phase flowsTrue two phase flows

                    2D model for flows over mobile bed2D model for flows over mobile bed

during extreme eventsduring extreme events

w

byb

w

bxb

bb

b

y

zghchvghc

y

huvcx

hvct

x

zghchuvc

y

hughcx

huct

chvy

chux

chzct

hvy

hux

hzt

)1()1(

)1()1(

)1()1(

)1()1(

0)()()(

0)()()(

2221

2221

Governing equations

0)(

xxt xU

UHFU

)(USU

xt

A splitting technique is adopted, spanned over two steps for each direction.

First step. The numerical integration in the time-space domain concerns the following PDE

Second step. The numerical integration in the same domain of the following ODE:

X-splitting

0

x)(

x

)(

t

UUH

UFU

*2/1

*2/1

1

iini

ni x

tFFUU

L*2/1

R*2/1

1

iini

ni x

t

nib

nib

ni

ni

ii

nib

nib

ni

ni

ii

zzcc

gSS

S

zzcc

gSS

S

)()(2

11

)()(2

11

11

LR

R*2/1

R*2/1

11

LR

L*2/1

L*2/1

w

nibxn

in

i

iini

ni

t

x

t

1)2/1()1(

L*2/1

R*2/1

2/1

ˆ

Non conservative flux + Source terms

121 costan/ˆ

nnbw

nibx c u

2D Numerical model2D Numerical model

2D Numerical model2D Numerical model

inclusions of non-erodible sections at assigned positionsinclusions of non-erodible sections at assigned positions

Undergoing AdvancementsUndergoing Advancements

AdaptationAdaptation processes processes

SelectionSelection processes processes

Boundary conditionsBoundary conditions

True two phase flowsTrue two phase flows

Rheological modelRheological model

mesh-cells fitting to boundaries (I.e.:cut-cell methods)mesh-cells fitting to boundaries (I.e.:cut-cell methods)

OBLIQUE FRONTDEVIATION ANGLE

DEFLECTION ANGLE

10

15

20

25

30

35

0 50 100 150 200 250

Serie1

Task 4.2Task 4.2

belt

flume slit

6.0 m

Recirculating experimental channel for Recirculating experimental channel for uniform granular flowuniform granular flow

uniform granular uniform granular flowflow

uniform mud flowuniform mud flow

Recirculating experimental Recirculating experimental channel for uniform granular flowchannel for uniform granular flow

Recirculating experimental Recirculating experimental channel for uniform granular flowchannel for uniform granular flow

Flow regimesFlow regimes

Voronoï 2D (Capart et al., 2002)Voronoï 2D (Capart et al., 2002)

Voronoï 3D (Spinewine et al., 2002)Voronoï 3D (Spinewine et al., 2002)

PIVPIV (Lorenzi et al., 2002) (Lorenzi et al., 2002)

Measurement TechniquesMeasurement Techniques

Local stress relationsLocal stress relationsNormal stress local equilibrium

)y(cc )y(TT

Deriving along y direction:

z

y

rigid bed

water and particles in motion

hw

vs

TcGrcdg

y

c swsws )41)(/1(cos)(0

)c1(2

)c21()c(r

3)1(2

)2()(

c

ccG

dy

dc

)( 2221 sss wuT

Tangential stress local equilibrium

Deriving along y and substituting dc/dy we obtain:

dy

du

cG

GTcrddg

y

c ssww

2

21

212

08

51

121

5

/18sin1

Second order equation to get velocity profile

02

2

Edy

duB

dy

udA

T-experimental results

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014

T [m2/s2]

z [m

]

T-experimentalresults

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800

c [-]

z [m

]

c-theoreticalprofile

c-exsperimentalprofile

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.000 0.500 1.000 1.500 2.000

u [m/s]

z [m

]

u-theoreticalprofile

u-exsperimentalprofile

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.000 0.500 1.000 1.500 2.000

u [m/s]

z [m

]

u-theoretical profile-noadded mass effects

u-theoretical profile-added mass effect

u experimental profile

No added mass effect on velocity profile

Feed pipe

Pneumatic piston (23° max)

flume

inflow

outflow

Valve

Pump

hopper

Forced flux between pump and

hopper

Experimental installation for mud-Experimental installation for mud-flowflow

Mud-flow (Sarno material)Mud-flow (Sarno material)

steady condition

Ultrasound doppler velocimeterUltrasound doppler velocimeter

Particle trackingParticle tracking

High-frequency radarHigh-frequency radar

Measurement TechniquesMeasurement Techniques

Ultrasound Doppler Velocimeter

It has been used for medical applications in the 60es;

Cardiovascoular surgery

Food industry

Metallergic industry

Ultrasound beam survey

Acoustic field intensity along the transducer

zza

λ

πsin

I

I 222

o

z

Divergence of ultrasonic beam

D

1.22λsinδ 1

Near field(blind zone)

Far field 4λ

DZ

2

Sampling volume

Burst lenght

Beam geometry

Working scheme

2

Tcp d

12prf12 TT2

ccosθTv)p(p

12e TTf2πδ

cosθ2f

cf

Tcosθ2f

δcv

e

d

prfe

Frequency difference between the sent and the received signal

c

cosθcosθvff 21e

d

Pulsed doppler ultrasound

Doppler effect

Shift phase of the received echo

Particle velocity

Sound celerity measure

Sound celerity geometric field

kinematic field

determines

Micrometer2MHz probe

water 1498 m/s

mud 30 %

mud 40 %

2100 m/s

2790 m/s

mud 50%Signal

Completely absorbed

Steel plate

Operative procedure

X

Y

ZFlow direction

Side measurements Bottom measurements

Motion along Z

Motion along X

Doppler

angle

Ultrasonic Gel

Y is constant

Doppler Angle

500 kHz probe

Partial ultrasound beam Complete ultrasonic beam

Experiemntal measurements

Instrument setting parameters

Side measurements 3D velocity profile

Profili di velocità trasversali

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200

Larghezza [mm]

velo

cità

[m

m/s

]

Concentration variation along the section?

Wall reflection effect?

Other effects?

Mean value over 1000 profiles

Experimental measurements

Conclusions about the velocimeter

Advantages:

- Opaque fluids measurement

- Instantaneous geometric-kinematic information

Disadvantages:

- Distruction of the ultrasonic beam with d> 1.5 mm

- Rapid absorption, power increase

- High divergence of the sonic field

- Invalid data

- High Signal Noise Ratio

- Sound celerity constant for every fluid