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Publication# Experimental study on the influence of abrupt slope changes on flow characteristics over stepped spillways

Abstract

Application of stepped spillways increases the energy dissipation rate along the spillway and may reduce the dimensions of the terminal energy dissipation structure. This pronounced energy dissipation makes stepped chutes attractive under various conditions, namely as service spillways on RCC gravity dams and on valley flanks near earth dams. For both, in some cases, an abrupt slope change may be required to be implemented on stepped chutes in order to follow the site topography and to minimize the needed excavations and hence respective costs. An abrupt slope change along stepped spillways can influence the flow properties such as the air entrainment, velocity and pressure distribution, and the energy dissipation. A quite limited number of stepped spillways have been built with an abrupt slope change, whereas no systematic scientific investigation for designing such type of configuration has been conducted to date. Accordingly, comprehensive information on the effect of an abrupt slope change on the flow features is missing. Therefore, the present experimental research work aimed to examine the effect of an abrupt slope change (from steep to mild) on the skimming flow features, by analysing the air entrainment, flow bulking, velocity and dynamic pressure development and energy dissipation along the stepped chute. Physical modelling was conducted in a relatively large scale facility with slope changes from 50º to 18.6º and 50º to 30º. Detailed air-water flow measurements were conducted at several cross-sections (step edges) along the chute, upstream and downstream of the slope change. In addition, dynamic pressure measurements were obtained on both vertical and horizontal faces of several steps in the vicinity and far downstream of slope change cross-section. The results indicated a substantial influence of abrupt slope changes on the flow properties for the tested range of flow rates, particularly in comparison with typical results for constant sloping stepped spillway flows. Four main local sub-regions have been found to describe the typical air-water flow patterns in the vicinity and further downstream of the slope change, namely with regard to the mean (depth-averaged) air concentration, air concentration distribution, pseudo-bottom air concentration, air-phase frequency and characteristic flow depths. The relative head loss corresponding to the reach under the influence of the slope change was found to vary between 38% to 51%, for the tested range of flow rates and slope change configurations. Mean pressures up to approximately 21 times the equivalent clear water depth (approximately 13 times the step height) were observed on the horizontal step faces in the vicinity of slope change cross-section for the tested range of flow rates. In conclusion, for the first time, the influence of an abrupt slope change on skimming flow properties on stepped spillways was investigated with systematic experiments on two slope change configurations and for a wide range of relative critical flow depths. This thesis report describes and discusses the achieved results mainly on the air entrainment and flow bulking, velocity and dynamic pressure distributions, as well as the energy dissipation.

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Uncontrolled overtopping during flood events can endanger embankment dams. Erosion of the downstream slope and scouring of its base caused by the high velocity and energy of the overflow can indeed lead to breach formation until complete failure. In this context and faced with the important number of overtopped embankment dams to be rehabilitated, since the early eighties, researchers have investigated surface protection solutions for downstream slope. Overlays against erosion such as seeded goetextile or cable-tied cellular concrete blocks, are not sufficient. In fact, they can resist only short events with low discharge and velocity. Solution to overcome more severe overflow lies in overlays which dissipate flow energy along the downstream embankment slope. Conventional steps resulting from Roller Compacted Concrete (RCC) techniques fulfill efficiently this challenge. However, flows over steep stepped chutes are quite complex, characterizing by great aeration, high turbulence and confused wavy free surface. Then, most of hydraulic studies of such flows are performed on physical model. Yet, understanding and definition of flow behaviour and accurate approach to estimate energy dissipation are still lacking. General guidelines of hydraulics of aerated flows over stepped macro-roughness chutes and for optimal design of protection overlay remain confusing. To contribute to reduce these uncertainties, experimental study of flow over stepped chutes equipped with macro-roughness elements is performed in a laboratory gated flume for mild (~ 1:7H : 1V ) and weak (~ 3H : 1V ) chutes. Thus, they are representative of the range of embankment dams and spillways slopes. Three types of stepped macro-roughness overlays are assessed, namely rectangular conventional steps, steps equipped with endsills fixed on their nose over all the flume width and steps equipped with rectangular spaced blocks. Endsills overlays were characterized with different longitudinal distributions whereas blocks overlays consisted in different transverse patterns. Tests were conducted for the three nappe, transition and skimming flow regimes. Results can be extrapolated to 1/5 to 1/15 scaled prototypes using the Froude similarity with negligible scale effects. Flow depth, local air concentration and longitudinal velocities are measured with a double fiber-optical probe. Pressures at macro-roughness faces are taken with piezo-resistive sensors. Sequent depths of the hydraulic jump forced in the stilling basin at the flume base are measured with ultrasound sensors. Thus, this experimental phase of the thesis has allowed: to define flow parameters (regimes, depths, velocity and air concentration distributions, hydrodynamic forces) for tested overlays, to highlight that air-water flow depth is divided into: a rough boundary layer influenced by shear stress and by drag form (macro-turbulence) caused by macro-roughness, a homogeneous aerated layer which represents the main portion of flow involved in energy dissipation mechanism, a free surface layer which must be considered in the side walls design, to stress that energy dissipation is mainly a question of drag losses, to validate indirect method of hydraulic jump for energy dissipation estimation, to estimate relative energy loss for several stepped macro-roughness overlays. Tests finally show that an optimal alternative to dissipate the overflow energy during an overtopping event consists in spaced blocks, with transverse space larger than the width of block and fixed alternately on conventional steps. However, experimental results remain related and limited to their tested domains. Then, in order to provide more general governing equations of aerated flows over macro-roughness stepped chutes, a numerical modeling of two phase flows over conventional stepped flume was performed in collaboration with the Laboratory of Applied Hydrodynamics and Hydraulic Constructions at University of Liège. A quasi-2D numerical model based on the finite volume method was developed. It consists in applying the classical depth-averaged simplified Navier-Stokes equations (viscosity and Coriolis terms neglected) to a 1D incompressible air-water mixture flow over mild and steep slopes with a stepped topography. Self-aeration process is modeled by a transport equation of depth-averaged air concentration whereas turbulent structures are indirectly implemented through the Boussinesq coefficient. This first 1D-approach of semi-theoretical description of aerated flow over steps is tested for a 30o gated stepped flume and a 52° crested spillway laboratory model. This numerical model leads to realistic results regarding mixture depth, mean flow velocity, air concentration and wave amplitudes of the flow free surface. Finally, on the basis of existing protections of embankment dams and previous studies, the present experimental and numerical results contribute to extend the knowledge of high velocity aerated flows over macro-roughness and to provide elements of guidelines to optimize stepped macro-roughness overlays for embankment dams safety.

Gauthier Paul Daniel Marie Rousseau

Steep mountain streams exhibit shallow waters with roughness elements such as stones and pebbles that are comparable in size to flow depth. Owing to the difficulty in measuring fluid velocities at the interface, i.e., from the rough permeable bed to the free surface, experimental results are rare although they are essential to improve models. Using a novel experimental procedure, this thesis attempts to improve predictions of the vertical structure of turbulent flows over rough permeable beds.
To explore flows at the bed interface, I devised an experimental set-up where a fluid flowed over glass spheres (8 mm < dp < 14 mm) in a narrow flume (W = 6 cm) with slopes varying from 0.5 % to 8 %. The Refractive Index Matching (RIM) technique has been employed. This involves matching the refractive index of the fluid with that of the glass spheres, thereby allowing the interior of the medium to be examined and velocities to be measured by Particle Image Velocimetry (PIV). Vertical profiles are retrieved by employing the spatiotemporal double averaging method.
In the course of this manuscript, flow processes are studied at the mesoscopic scale, i.e., by averaging quantities over distances ranging from 5 to 10 grain diameters. For open-channel flows over rough permeable beds, the spatial averaging procedure yields a continuous porosity profile. When applied to the Navier-Stokes equations, it produces a momentum equation with several terms including drag forces and three stresses: the turbulent, dispersive, and viscous stresses. The momentum equation was employed to devise a one dimensional (1D) model describing the vertical structure of unidirectional turbulent flow.
A turbulent boundary layer over the rough bed was observed while experiments were performed at intermediate Reynolds numbers, i.e., Re = O (1000). In such conditions, viscosity plays a critical role through the van Driest damping effect. To model vertical profiles, the Darcy-Ergün equation is well suited to the prediction of friction forces in the permeable bed, i.e., in roughness and subsurface layers. Based on the \textit{Prandtl mixing length theory}, turbulent stress is predicted from a mixing length distribution that considers dispersive effects and assumes a continuous porosity profile. This alternative contrasts with most existing boundary layer models which postulate a discontinuous porosity profile for permeable or impermeable walls.
Finally, hydraulic conditions collected by an Unmanned Aerial Vehicle (UAV) and classical flow resistance equations (Chézy, Keulegan, ...) were compared with profile simulations and demonstrate a good agreement between predictions and observations. It reveals the crucial role of fluid depth definition in equations in small submergence conditions. Furthermore, incipient sediment motion conditions have been estimated and compared to empirical results showing the importance of turbulence and lift force for grain entrainment.
With regard to fluid dynamics, mountain streams are a case study of the larger scientific family of turbulent flows interacting with porous structures. Insights and developments acquired in the course of this thesis are likely to be transferable to other domains working with these phenomena such as flows over buildings, vegetal canopies or rough wings.