Stephan the importance of confluences in hydraulic network models of rivers

DEPT. OF CIVIL ENGINEERING Hydraulics laboratory

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Source: The Internet

Stéphan Creëlle- [email protected] –Tom De Mulder

Belgian Hydraulics Day - 5/10/2015 – FHR Antwerp


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Confluence research @ Ugent

Laurent Schindfessel

Extreme discharge ratios

Large-eddy simulation

Stéphan Creëlle

Mixing & headloss prediction

Experiments

Promotor: Tom De Mulder



Hydraulics laboratory

pag. 3 Stéphan Creëlle- [email protected] –Tom De Mulder



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h3

Q1

Q2

h1

h2

Q1+Q2

?

?




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h1=h2

h1/h2 [-]

q [-]

Generally

accepted

Equation 1?

Equation 2?




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Multiple solutions reported in

literature

Equality model Energy approach Momentum approach

-simple

-easy to implement

h1=h2=h3

-simple

-errors up to

50% h3

E1+E2+ ΔE=E3

-empirical loss coeff.

-combines easily

with other energy

loss formulations

-limited information

M1,x+M2,x+ SF=M3,x

-allows for best calculation

of different terms

-additional computational

effort




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M1+M2 cos θ − M3=P3 − P1 − P2cos θ − PWALLS sin θ

3 1

M1,x+M2,x-M3,x =-SF

𝑀3, 𝑃3

𝑀2, 𝑃2

𝑀2, 𝑃2

𝑃𝑊𝐴𝐿𝐿𝑆




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Can be expressed with the variables of the problem:

𝑃 =𝜌ℎ2𝑊

2

? 𝑀 =

𝜌𝑄2

ℎ𝑊





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Taylor(1944)

ℎ𝑇𝐼𝑊 = ℎ𝑇𝑂𝑊 = ℎ2

Can be expressed with the variables of the problem:

𝑀 =𝜌𝑄2

ℎ𝑊

𝑃 =𝜌ℎ2𝑊

2

?





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Taylor(1944)




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Taylor(1944)




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Webber & Greated(1966)

Pressure difference over the

channel walls due to

contraction to the

downstream corner

Change in physical inflow

angle α in the TCS

Cause of deviations?




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PWALLS𝑴𝟐

= 𝟏 − 𝒒

𝒒

Ramamurthy(1988)

Hager(1998)

𝑴𝟐

𝒕𝒂𝒏 𝜶= PWALLS

α=8

9θ

α=acos [0.149 + 0.914 (1 − 𝑞)]

Hsu(1998)(for θ=90°)

Angle Wall pressure

difference

PWALLS sin θ




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0,95

1

1,05

1,1

1,15

1,2

1,25

1,3

1,35

1,4

0 0,2 0,4 0,6 0,8 1

h1/h

3 [

-]

q [-]

Hsu (1998) 30°

Hager (1989) 30°

Hsu (1998) 60°

Hager (1989) 60°

Hsu (1998) 90°

Hager (1989) 90°

equality

Fr3=0.55




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0,95

1,05

1,15

1,25

1,35

1,45

1,55

1,65

1,75

0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1

h1/h

3 [-]

Fr3

0.1 0.25

0.5

q [-]

0.75

0.9





Belgian Hydraulics Day - 5/10/2015 – FHR Antwerp pag. 16

Conclusions:

-Head losses near confluences become more significant when:

-Froude numbers increase

-The confluence angle increases

-For low angles and Froude numbers, the equality model can

suffice. For the other cases, an energy or momentum

approach should be incorporated.

-The momentum conservation approach delivers the most applicable

results, but for high angles the tributary momentum contribution should be

formulated accurately.


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Work in progress:

-Description of the tributary momentum contribution, based on

theoretical description of the velocity profiles in the tributary

branch, in order to obtain more reliable results, and to

eliminate the need for empirical expressions for the tributary

momentum contribution or inflow angle

-Experimental measurements of the flow behaviour of the flow

in the tributary branch in the approach of the confluence area.

-Description of the mixing, momentum exchange and

uniformization process in and downstream of the confluence,

based on experimental measurements of the surface

velocities.




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Thanks for your attention!




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References:

Taylor, E. H. (1944). Flow characteristics at rectangular open-channel

junctions. Trans. ASCE(107), 893–912.

Webber, N. B., & Greated, C. (1966). An investigation of flow behaviour at

the junction of rectangular channels. Paper presented at the ICE

Proceedings.

Hsu, C.-C., Wu, F.-S., & Lee, W.-J. (1998). Flow at 90 equal-width open-

channel junction. Journal of Hydraulic Engineering, 124(2), 186-191.

Hager, W. (1989). Transitional Flow in Channel Junctions. Journal of

Hydraulic Engineering, 115(2), 243-259. doi: doi:10.1061/(ASCE)0733-

9429(1989)115:2(243)




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Assumptions:

1) All channels have a rectangular shaped cross-section with width W,

2) The beds of the main channel and the tributary are concordant, fixed and

horizontal,

3) In the cross-sections 1, 2 and 3, the flow is uniform and the water surface is

horizontal,

4) Friction losses due to the banks and the beds can be neglected,

5) Pressure distributions are hydrostatic in the sections considered and along the

walls

