1. SECOND ORDER MODELLING OF COMPOUND OPEN CHANNEL-FLOWS Laboratoire de Modélisation en Hydraulique et Environnement Prepared by : Olfa DABOUSSI Presened by Zouhaïer HAFSIA

2. 2 Plan Introduction. Secondary currents in compound open channel flow. Turbulence model. Numerical results. Conclusions. Experimental results.

3. 3 INTRODUCTION In laboratory, compound channel are represented by the main channel and one floodplain with rectangular sections. After strong rain. The compound channel is composed from many stages. The turbulence model : second order model R ij. We use the CFD code PHOENICS for numerical simulations. It is interesting to study the compound channel flow to understand main channel – floodplain interaction. Numerical results are compared to experimental data of Tominaga and al. (1989).

4. 4 THE RECTANGULAR OPEN COMPOUND CHANNEL FLOW I – Rectangular compound channel Symmetric Asymmetric Free surface

5. 5 Three cases of β values are simulated (Mesures of Tominaga and al., 1989). β = 0.5 β = 0.343 β = 0.242 λ = 2.07 II – Tested cases

6. 6 CasB (m)b (m)λ = B/bh (m)H (m)β = (H-h)/H W moy (m s -1 ) 10.1950.0942.070.05010.10010.5000.315 20.1950.0942.070.05010.06610.2420.32 30.1950.0942.070.05010.07630.3430.273 Tominaga and al. (1989) data

7. 7 NUMERICAL SIMULATIONS I – Governing Equations In incompressible Newtonian fluid and parabolic flow through the z direction, the Reynolds stress turbulence model of Launder and al. (1975) is written as : - Continuity : - Momentum :

8. 8 - Kinetic equation : - ε equation : - Reynolds stress : i, j, k = 1, 2, 3

9. 9 C 1, C 2 and C s are constants. - Boundary conditions : - Smooth wall logarithmic law : - Near walls, k, ε and R ij are : - The free surface is considered as a symmetric plane : - On the vertical symmetric plane :

10. 10 I – In PHOENICS There are four derivations of the R ij model : IPM, IPY, QIM and SSG. IPM is the Isotropisation of production model. IPY is the IPM model of Younis (1984). QIM is the quasi-isotropic model SSG is the model of Speziale, Sarkar and Gatski Where : PHOENICS use the finite volume numerical method.

11. 11 PHOENICS take the z axis as the main flow direction for the parabolic ones. The cell along z is a slab. The general form of the transport equations is :

12. 12 k-ε model : Using the CFD code PHOENICS, we have tested two cases for β = 0.5. The k- can not reproduce the isovelocity bulging shown experimentally RESULTS OF SIMULATIONS Results with coarse grid :

13. 13 The k-ε model is isotropic. The second order model R ij take account of the turbulence anisotropy. k- do not reproduce the isovelocity bulging Results with thin grid : Experience shows a strong anisotropy

14. 14 Results with the R ij model: The four derivations of R ij give the same results. Secondary currents : Main channel vortex Free surface vortex

15. 15 Tranversal velocity profils on X = 0.087 m : = 0.5 on X = 0.101 m : = 0.5 on X = 0.055 m : = 0.5

16. 16 Longitudinal velocity variations : Wall law at X = 0.02 m : β = 0.5 Vertical averaging of the velocity : β = 0.5

17. 17 Comparaison of numerical isovelocity with Tominaga et al. (1989) data : β = 0.5 The R ij model reproduce well the isovelocity.

18. 18 Wall shear stress variation : The shear stress on the floodplain raises near the main channel- floodplain junction. Momentum transfer from the main channel to the floodplain.

19. 19 The adimensional dispersion coefficient appears after integration of the momentum equation through the transversal section. Needs a closure law Two approches : Gradient closure : Correlation based on the momentum distribution THE ADIMENSIONAL DISPERSION COEFFICIENT

20. 20 Whith λ = 2.07, α varies as second degrees polynomial in function of as follow : α variation in function of β : Calculations show that α is different from 1. It depends of : from 1.04 to 1.35

21. 21 CONCLUSIONS Numerical computation show that the dispersion coefficient α is expressed as a polynomial function of β Secondary currents modify longitudinal iso-velocity. The first order k-ε model do not reproduce the isovelocity bludging The second order turbulence model can reproduce the interaction between the main channel and flood-plain (momentum transfer)