Transcript Experimental and numerical investigations of stationary mixed flows in 2D flume http://www.hach.ulg.ac.be N.V.

Experimental and numerical investigations of
stationary mixed flows in 2D flume
http://www.hach.ulg.ac.be
N.V. Nam, F. Kerger, S. Erpicum, B. Dewals, P. Archambeau & M. Pirotton
Hydrology, Applied Hydrodynamics
and Hydraulic Constructions (HACH)
Liège,14/11/2011
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Outline
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• Introduction
• Methodology
• Physical experiment
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• Numerical modeling
• Conclusions
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Introduction
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• Mixed flows: are known as the simultaneous occurrence of free-
surface and pressurized flows.
1- Water supply systems
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3- Storm water systems
2- Sewer systems
4- Hydroelectric systems
and so on.
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Introduction
• Mixed flows: have been investigated mainly for 1D
configurations (Wiggert (1972), Cardle et al. (1989),
Gómez and Achiaga (2001), Vasconcelos and Wright
(2005), Erpicum et al. (2008), Kerger et al. (2008),
Wright et al. (2008), etc.)
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• But mixed flows present often 2D
characteristics
 experimental and numerical
investigation of 2D mixed flows
1st step: - simple configurations
- steady flow
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Methodology
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2D rectangular cross-section channels connected by a conduit
 Three geometries
– Model A: Uniform rectangular cross-section conduit
c r o ss-sec t io n
pl a n v iew
– Model B: Convergent rectangular cross-section conduit
c r o ss-sec t io n
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pl a n v iew
– Model C: Parallel an uniform rectangular cross-section pressure conduit
and an uniform rectangular cross-section free surface channel.
c r o ss-sec t io n
pl a n v iew
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Methodology
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Geometries
Model A
Model B
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Experiment
modeling
Model C
Numerical
modeling
Q=[5-45(l/s)]
(8-10) tests/model
Comparison of
flow characteristics
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Physical experiments
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1- Experiment facility:
b
d
c
e
f
pipe d 150
1
pl a n v iew
A
A
g a te
d
c
e
b
- two 4.2 m long channel reaches made
of clear glass
1 - a 2 m long closed conduit made of
exterior type plywood
- an upstream tank and a collection box
- a gate made of thin steel plate
- pumping and piping system, etc.
f
sec tio n 1-1
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l eg en d :
y
x
a
f eed in g pipe
d
c o n d uit
b
upstr ea m ta n k
e
d o w n str ea m f l ume
c
upstr ea m f l ume
f
d o w n str ea m ta n k
a) Sketch of physical model
b) Picture of physical model
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Physical experiments
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2- Water alimentation and boundary condition
– Water alimentation system:
7
8
6
4
9
5
3
12
d 50
400 m3
11
1
10
2
sket c h o f w a t er a l imen t a t io n syst em
– Boundary condition:
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• Upstream boundary condition is the discharge into the model
• Downstream boundary condition is a gate (used as an free-weir or a raising
one)
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3- Measurement devices:
•
Using an electro magnetic (EM) probe to measure the velocity (fig a);
•
Using 8 ultrasound sensors to determine the water level (fig b);
•
Using 8 piezoresistive pressure transducers for pressure measuring (fig c);
•
Using an electromagnetic discharge meter to control the discharge (fig d);
(a)
(b)
(c)
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(d)
Physical experiments
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4- Example of results (model A)
- Velocity results with free weir, Q=10l/s
h =26c m
h =26c m
1
4
7
10
13
2
5
8
11
14
3
6
9
12
15
Q =10l / s
u bc =320m m
d bc =310m m
v el o c it y a t l o c a t io n t
h =16c m
h =16c m
1
4
7
10
13
2
5
8
11
14
3
6
9
12
15
Q =10l / s
u bc =320m m
d bc =310m m
v el o c it y a t l o c a t io n c
h =5c m
h =5c m
1
4
7
10
13
2
5
8
11
14
3
6
9
12
15
v el o c it y a t l o c a t io n b
300
250
t
c
b
t
c
b
t
c
b
Section 10-11-12
200
Vx [mm/s]
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Q =10l / s
u bc =320m m
d bc =310m m
150
100
B
50
C
T
0
-50 0
200
400
600
800
1000
-100
-150
Y [mm]
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Physical experiments
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– Pressure field results with free weir
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– Pressure field results with raising gate
9
14
10
12
15
Q=20 l/s
18
Q=42.5 l/s
16
12
Q=24 l/s
10
Q=30 l/s
8
6
Q=34.3 l/s
4
Q=40 l/s
2
0
Q=44 l/s
0 10 20 30 40 50 60 70 80 90100
Y [mm]
Section 8-9-10
H/h[-]
Q=20 l/s
14
H/h[-]
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8
18
16
14
12
10
8
6
4
2
0
Q=24 l/s
Q=30 l/s
Q=34.3 l/s
Q=40 l/s
Q=42.5 l/s
Q=44 l/s
0 10 20 30 40 50 60 70 80 90100
Y [mm]
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Section 14-12-15
Numerical modeling
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1- Shallow water equations
+ Preissmann slot model:
h ub vb


0
t x
y
Continuity
equation
J
J
z
z
mesh
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z
z
ub u 2b uvb g  (2h  b)b



  ghb b  ghr r  ghJ J x
t
x
y
2
x
x
x
z
z
vb uvb v 2b g  (2h  b)b



  ghb b  ghr r  ghJ J y
t
x
y
2
y
y
y
–
–
–
–
–
–
u, v: Velocity components
h: Pressure
b: Conduit height
Zb, Zr: Bottom and roof elevations
hb, hr, hJ: Equivalent pressure terms
Jx, Jy: Friction slope components
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Momentum
equations
Numerical modeling
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+ WOLF applicability
• Finite volume discretization, with multiple blocks using constant
space step (accuracy and computation time)
• Original FVS (WOLF – HACH), upwinding regarding the flow velocity
(momentum upstream, pressure terms downstream)
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• Bottom slope term discretized in agreement with the FVS (water at
rest)
• Bottom friction with Manning’s formula
•Explicit RK time integration scheme with CFL number condition
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Numerical modeling
2- Example of results (model A)
– Velocity field results with free weir, Q=10l/s
– Velocity field results with raising gate, Q=30l/s
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- Pressure field results with free weir, Q=10l/s
- Pressure field results with raising gate, Q=30l/s
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Conclusions
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• Study aims at studying 2D mixed flows using
- Experimental modeling
- Numerical modeling
• Choice of 3 configurations, tested with a wide range of steady
discharges
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• Results for comparison:
 Velocity and pressure distribution in two directions
 Mixed flows visualization in detail
Comparisons under progress…
• Perspectives:
 Perform unsteady modeling
 Consider the effect of air entrainment
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Thanks For Your Attention!
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