ArGEnCo – MS²F - Hydrologie, Hydrodynamique Appliquée et Constructions Hydrauliques (HACH) Experimental and numerical investigations

ArGEnCo – MS²F - Hydrologie, Hydrodynamique Appliquée et Constructions Hydrauliques (HACH)

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Experimental and numerical investigations of stationary mixed flows in 2D flume

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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• Introduction

• Methodology

• Physical experiment

• Numerical modeling

• Conclusions

Outline Acomen 2011


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• Mixed flows: are known as the simultaneous occurrence of free-surface and pressurized flows. 1- Water supply systems 2- Sewer systems

3- Storm water systems 4- Hydroelectric systems

and so on.

Introduction Acomen 2011


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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

Introduction Acomen 2011

• 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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2D rectangular cross-section channels connected by a conduit Three geometries – Model A: Uniform rectangular cross-section conduit

– Model B: Convergent rectangular cross-section conduit

– Model C: Parallel an uniform rectangular cross-section pressure conduit and an uniform rectangular cross-section free surface channel.

Methodology Acomen 2011

pl an view

c r o ss-sec tio n

pl an view

c r o ss-sec tio n

pl an view

c r o ss-sec tio n


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Methodology Acomen 2011

Geometries

Model A Model B Model C

Experiment modeling

Q=[5-45(l/s)](8-10) tests/model

Numerical modeling

Comparison of flow characteristics


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1- Experiment facility: - two 4.2 m long channel reaches

made of clear glass- 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.

Physical experiments Acomen 2011

a) Sketch of physical model b) Picture of physical model

pipe d

150

pl an view

dbf

A

c e

g ateA

b

c

d

e

f

1 1

sec tio n 1-1

a feeding pipe

b upstr eam tank

c upstr eam fl ume

l eg end:

d c o nduit

e do wnstr eam fl ume

f do wnstr eam tankx

y


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2- Water alimentation and boundary condition– Water alimentation system:

– Boundary condition:• Upstream boundary condition is the discharge into the model

• Downstream boundary condition is a gate (used as an free-weir or a raising one)


6

7

8

1011

12

sketc h o f water a l imentatio n system

95

400 m3d50

1

2

3

4


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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) (d)


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4- Example of results (model A)- Velocity results with free weir, Q=10l/s


-150

-100

-50

0

50

100

150

200

250

300

0 200 400 600 800 1000

Vx

[mm

/s]

Y [mm]

Section 10-11-12

B

C

T

2

vel o c ity at l o c atio n t

1

3

5

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2

vel o c ity at l o c atio n c

1

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2

vel o c ity at l o c atio n b

1

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Q=10l /subc =320mmdbc =310mm

h=26c m h=26c m

h=16c m h=16c m

h=5c m h=5c m



bct

bct

bct


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– Pressure field results with free weir



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– Pressure field results with raising gate


0

2

4

6

8

10

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0 10 20 30 40 50 60 70 80 90100

H/h

[-]

Y [mm] Section 8-9-10

Q=42.5 l/s

Q=20 l/s

Q=24 l/s

Q=30 l/s

Q=34.3 l/s

Q=40 l/s

Q=44 l/s

8 9 10

02468

1012141618

0 10 20 30 40 50 60 70 80 90100

H/h

[-]

Y [mm] Section 14-12-15

Q=20 l/s

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

12 1514


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1- Shallow water equations

+ Preissmann slot model:

– 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

Numerical modeling Acomen 2011

0h ub vb

t x y

2 (2 )

2b r

b r J x

z zub u b uvb g h b bgh gh gh J

t x y x x x

2 (2 )

2b r

b r J y

z zvb uvb v b g h b bgh gh gh J

t x y y y y

Momentum

equations

Continuity

equation

J

z

z

mesh

J


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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)

• 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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2- Example of results (model A)

– Velocity field results with free weir, Q=10l/s

– Velocity field results with raising gate, Q=30l/s

- Pressure field results with free weir, Q=10l/s

- Pressure field results with raising gate, Q=30l/s



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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

• Results for comparison: Velocity and pressure distribution in two directions Mixed flows visualization in detailComparisons under progress…

• Perspectives: Perform unsteady modeling Consider the effect of air entrainment

Conclusions Acomen 2011


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Thanks For Your Attention!

Acomen 2011

Documents

ArGEnCo – MS²F - Hydrologie, Hydrodynamique Appliquée et Constructions Hydrauliques (HACH) Experimental and numerical investigations