tasks 4.1 4.2 department of civil and environmental engineering university of trento wallingford...
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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