The Piano Key Weir is a type of labyrinth weir using overhangs to reduce the footprint of the foundation. These are directly placed on a dam crest. Together with its high discharge capacity for low heads, this geometry makes these weirs interesting in dam rehabilitation. However, the Piano Key Weir is a new weir type, first designed in 2001 and built from 2006 by Electricité de France. Even though experimental studies confirmed its appealing discharge capacities, the flow upstream, over and downstream of this complex structure is still not well known. This research presents experimental test results performed on a 1:10 scale model. The experiments aim at determining the flow features along the weir depending on the upstream head. The flow conditions are characterized in terms of specific discharge, velocity, pressure, water level and streamlines along the weir.

Piano Key Weirs are an effective solution for dam rehabilitation as well as new dam projects with a high level of hydraulic constraints. In order to improve the efficiency of their design, an experimental study of the influence of the main geometric parameters has been performed. Thirty one configurations were tested for a wide range of discharges. The results of the study show the influence of the weir height, the keys widths and the overhangs lengths on the discharge capacity and flow characteristics. Based on hydraulic considerations, optimum values of the main geometric ratios are provided. An analytical formulation is developed to predict the discharge capacity of the weir as a function of its geometry. It shows an accuracy of 10% compared to the experimental results of this study and from other sources.

With inertia and gravity representing the dominant forces for most open channel flow applications (e.g. weir flow), Froude similitude is commonly used for scaling hydraulic performance data from the model to prototype structures. With weir flow, as the upstream head decreases, however, the relevance of surface tension and viscosity forces can increase to the point when the model and prototype similitude is not fully achieved through Froude scaling. Such discrepancies are referred as size-scale effects, and among other things, can result in variations in the head–discharge relationship, nappe trajectory, and air entrainment. Published criteria for avoiding significant size-scale effects for free flow over linear weirs have suggested that minimal heads of ∼0.02 to 0.07 m be respected, independently of the model size. In this study, the size-scale effect, minimum upstream head, and Weber number limits are investigated for four piano key weirs with geometric model scales of 1:1, 1:7, 1:15, and 1:25.

Experimental model data are compared with numerical computations of dike-break induced flows, focusing on the final steady state. An idealized scale model was designed reproducing the specific boundary conditions of dike breaks. Discharges, water level, and depth profiles of horizontal velocities were recorded and validated by numerical modeling. The latter was performed by two different models solving the two-dimensional depth-averaged shallow water equations, namely a total variation diminishing Runge-Kutta discontinuous Galerkin finite element method, and a finite volume scheme involving a flux vector splitting approach. The results confirmed convergence and general applicability of both methods for dike-break problems. As regards their accuracy, the basic flow pattern was satisfactorily reproduced yet with differences compared to the measurements. Hence, additional simulations by the finite volume model were performed considering various turbulence closures, wall-roughnesses as well as nonuniform Boussinesq coefficients.

With the availability of high resolution DEMs, relevant and detailed inundation maps may now be routinely computed provided that suitable flow models are available. The full 2D flow model presented in this paper has been used to compute such maps on 800 km of the main rivers of the Walloon Region in Belgium. The use of grid spacing of 1 m, similar to the DEM resolution, enables the accurate prediction of the pattern of flood depth. This is confirmed by several application examples, which also demonstrate the ability of the model to reproduce depth measurements for a wide range of flood discharges without the need for recalibration of the roughness coefficient. The numerical model has been systematically validated by comparison with observations during recent real flood events. It shows a very good agreement with field data, in particular the free surface elevations and inundation extension.