a FULLY 3D NON-HYDROSTATIC MODEL FOR PREDICTION OF Flow, Sediment Transport and bed MORPHOLOGY IN open channels   

This study tries to develop and validate a model to predict the flow, bed load sediment transport and bed morphology changes in open channel flows.  The non-hydrostatic model solves the three-dimensional (3D) incompressible, Reynolds-Averaged Navier-Stokes (RANS) equations in generalized curvilinear coordinates and integrates the equations up to the wall such that the use of wall-functions is avoided.  The novelty of the model is the use of near-wall RANS models (SA and k-w) instead of the more popular and less computationally expensive models that employ wall functions.  The low-Reynolds-number version of the Spalart-Allmaras (SA) model and the k-ω model are implemented.  The k-w has the capability to account for small-scale bed roughness distribution via the wall boundary condition for w.  

The model uses adaptive grids in the vertical direction needed to account for changes in the free surface elevation and bathymetry.  At the free surface the proper kinematic and dynamic conditions are satisfied at convergence.  A non-equilibrium bed load sediment transport model similar to the one used in Wu, Rodi and Wenka (JHE, 2000) is used with the additional introduction of down-slope gravitational force effects.  

The model is used to predict flow through meandering open channels for which detailed validation data are available.   One of the experimental cases studied by Yen is used to validate the deformable free surface module and the experiments by Odgaard and Bergs (Water Resources Research, 1988) are used to validate the bed load transport module by predicting the flow and bed bathymetry at equilibrium.  The present simulation of the 180 degrees channel bend of Odgaard and Bergs uses around 360,000 mesh points (Fr=0.371, Re=65,500, d_50_sediment=0.35mm).  Only bed load transport is simulated.  For comparison the results of Wu, Rodi and Wenka obtained with the k-ε model with wall functions are included (both bed and suspended load are accounted for).  

Ultimately, our goal is to use hybrid RANS/LES approaches like Detached Eddy Simulation (DES) to predict scour in channels of complex geometries or around hydraulic structures. 

Figure: Sketch of the experiment. (a) experimental layout;  (b) cross-section of the flume.

Animation: Animation showing evolution of bed bathymetry and velocity magnitude from flat bed initial conditions to equilibrium deformed bed. Though the simulation is not time accurate, the animation allows us to can get an idea about how the bed evolves toward equilibrium.

Figure: Streamwise evolution of water depth at three positions in the 180° channel bend (near the two banks and centerline)

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Figure:  Comparison of bed levels between present simulations (SA and kw), k-e simulation of Wu et al. and measurement results.

Figure:  Contours of depth-averaged streamwise velocity in the channel bend

(a)    measurements; (b) k-ε with total load model (Wu et al.); (c) SA_SED; (d) kω_SED.

Figure: Contours of water depth in the channel bend; (a) measurements; (b) k-ε with total load model (Wu et al.); (c) SA_SED; (d) kω_SED.

REFERENCES

1.      Odgaard, A.J. and Bergs, M. 1988, Flow processes in a curved alluvial channel, Water Resources Research, 24:1, pp. 45-56.

2.      Wu, W., Rodi, W. and Wenka, T. 2000, 3D numerical modeling of flow and sediment transport in open channels, J. Hydraulic Engineering, ASCE, 126:1, pp. 4-15.

3.      Yen, C. L. 1967, Bed configuration and characteristics of subcritical flow in a meandering channel, Ph.D. Thesis, The University of Iowa, Iowa City, Iowa.