# Flow and Sediment Transport in a Laboratory Model of a stretch of the Elbe River

## Best Practice Advice for the AC

1. Key Fluid Mechanics

The application challenge concerns the laboratory representation of flow, sediment transport and bed deformation in a stretch of the river Elbe. This configuration involves flow in an open channel with complex, irregular geometry which changes with time due to bed deformation, has groynes on the sides and is curved. A particular feature is the relatively large width compared with the depth (a factor of 30 to 40) so that the flow is rather shallow. The flow is highly turbulent and complex due to secondary motions and local separation zones. Another key element is the movable bed and the presence of important bed-load sediment transport which is highly dependent on the bed shear stress and deforms the bed, causing highly irregular geometry even if this was regular in the beginning. The bed-load sediment transport itself is a very complex mechanism in which bed material is transported in a bed-load layer due to rolling, sliding or saltations of sediment particles. The quantities to be calculated by CFD (DOAPs) are the velocity distribution and bed deformation as they develop with time and the water-level distribution as well as the cross-section averaged sediment transport rates.

The UFRs 4-04 (curved rectangular duct flow) and 4-05 (curved duct / pipe flow – accelerating) have been associated with this AC. However, both are really not relevant for this application challenge: the flow in UFR 4-04 is in a very narrow channel corresponding to a width to depth ratio of 1/3, has rectangular geometry and hence right-angle corners and this is very far from shallow open channel flow with sloping bed. UFR 4-05 concerns flow in passages between turbine blades; apart from the fact that the flow is curved there is no resemblance with the river flow considered.

2. Application Uncertainities

In situations with large river models the uncertainties are larger than in small-scale laboratory experiments. They arise from highly irregular geometry, the imprecision concerning fine details of the geometry and their representation in a numerical model, the movable bed introducing a time dependence of the geometry. There are also uncertainties about the sediment input at the inflow boundary as well as the flow conditions at the inflow which are not known in detail, especially the turbulence quantities, and must be estimated. Then there is also uncertainty about the value of the non-equilibrium adaptation length Ls which appears as an adjustable parameter in the bed-load sediment-transport model. The sensitivity of the DOAP predictions to these uncertainties is difficult to judge – it is probably not too high as reasonable agreement with the measurements was obtained in the calculations in spite the considerable uncertainties. It should be noted that great accuracy cannot be expected from the experiments so that the uncertainties in the predicted DOAP’s due to application uncertainties are generally not larger than the uncertainties in the experimental results. However, the influence of the parameter Ls in the sediment-transport model on the sediment-transport and hence on the bed-deformation calculations must be investigated further. It should be added at the end that in real river situations the uncertainties are considerably larger than for the laboratory situation of this AC.

Computational Domain and Boundary Conditions

After choosing the river stretch to be covered in the calculations, one has to specify the bed geometry prevailing at the start of the calculations from the experimental set-up (or from the bathymetry information available in the case of calculations of a real river) and has then to represent this geometry as closely as possible by the numerical grid.

Boundary conditions:

In 3-D calculations, wall functions should be used at the bed and also at walls of any structures, such as groynes. The roughness parameter in the wall functions should be related to the Manning roughness coefficient which can usually be estimated for the river section considered. At the free surface, the vertical gradients of the horizontal velocity components and turbulent energy k should be specified as zero and the dissipation rate ε should be related to the surface value of k and to the water depth. At the inflow, distributions of the mean velocity must be estimated and need to be consistent with the specified discharge. Distributions of turbulence quantities such as k and ε must also be estimated. For these estimations empirical formulae for the variation of the quantities over the depth in open channel flow should be used. At the outflow boundary zero gradient conditions should be applied except for the surface elevation for which the experimental value must be specified. The rate of sediment inflow into the calculation domain must be prescribed from the experiment.

Discretisation and Grid Resolution

In the calculations described in the D30, a hybrid central/upwind differencing scheme was used for the convective fluxes. The use of a more accurate higher-order scheme would be desirable. The calculations were obtained on a curvilinear grid that conformed to the main channel, with the groynes blocked out. Only one grid was used so that the numerical accuracy and in particular grid independence could not be shown. But from previous channel flow calculations it was found that 25 grid points over the channel depth are sufficient when wall functions are used. The grid should, however, adjust to the varying depth, i.e. the same number of grid points should always be used over the depth. From previous calculations it was also found that 60 grid points over the width in open channel flow with sloping beds at the boundaries is sufficient. However, if one wants to resolve details of the flow around groynes, more points should be used in these regions. The number of grid points in the streamwise direction depends, of course, on the length of the river stretch calculated, but the mesh size in this direction should be similar to the mesh size in the lateral direction.

Physical Modelling

In the calculations presented in the D30, only the k-ε turbulence model with wall functions was used. This model is recommended for this type of flow. Any secondary currents occurring are pressure-driven and do not need a more sophisticated turbulence model; the use of such a model would not be warranted anyway due to the considerable application uncertainties described in 2., particularly when real river situations are considered. The non-equilibrium bed-load sediment-transport model sketched in the D30 is recommended for simulating bed-load transport, but as with all sediment transport models this is highly empirical and must be considered rather crude involving considerable uncertainties. In particular, the value to be chosen for the important parameter Ls, which is the non-equilibrium adaptation length, is uncertain. The advice is to put Ls equal to the average value if the mesh sizes is in the two horizontal directions, but further studies on the sensitivity to and the proper choice of Ls are necessary.

Recommendations for Future Work

- Further calculations on the AC-case should be carried out to asses/improve the numerical accuracy, using higher order discretization schemes and finer grids

- The greatest uncertainty in the AC-calculations lies in the sediment transport model. Further studies should be carried out to investigate the sensitivity of the results to the parameters in this model, in particular the non-equilibrium adaptation length Ls. Other advanced sediment transport models proposed in the literature should also be tested. Further, the model used assumed the sediment particles to have uniform size, while in reality there is a size distribution. Models allowing for graded sediment transport should also be tested.

- The following UFR test cases are proposed:

(i) straight and curved open channel flow (with realistic width to depth ratios) with simple geometries (rectangular, trapezoidal)

(ii) flow around groynes, again for situations with simple, regular geometry

(iii) simple cases to test the sediment transport model under well-controlled conditions, e.g. with sediment transport in only one direction and hence 1-D bed deformation.