Experimental and numerical analysis of flow instabilities in rectangular shallow basins

Free surface flows in several shallow rectangular basins have been analyzed experimentally, numerically and theoretically. Different geometries, characterized by different widths and lengths, are considered as well as different hydraulic conditions. First, the results of a series of experimental tests are briefly depicted. They reveal that, under clearly identified hydraulic and geometrical conditions, the flow pattern is found to become nonsymmetric, in spite of the symmetrical inflow conditions, outflow conditions and geometry of the basin. This non-symmetric motion results from the growth of small disturbances actually present in the experimental initial and boundary conditions. Second, numerical simulations are conducted based on a depth-averaged approach and a finite volume scheme. The simulation results reproduce the global pattern of the flow observed experimentally and succeed in predicting the stability or instability of a symmetric flow pattern for all tested configurations. Finally, an analytical study provides mathematical insights into the conditions under which the symmetric flow pattern becomes unstable and clarifies the governing physical processes.

Influence of macro-roughness of walls on steady and unsteady flow in a channel

Tobias Meile

High-head storage hydropower plants mainly operate their turbines during periods of high energy demand. The sudden starting and stopping of turbines (hydropeaking) lead to highly unsteady flow in channels and rivers. Besides hydropeaking, other anthropogenic actions and natural events such as sluice gate operations, flushing of reservoirs, debris jam and break up, ice jam and break up, sudden stopping and starting of turbines of runoff river hydropower plants, flashfloods or dambreaks can also cause highly unsteady flow. From an ecological point of view, hydropeaking consists in a non-natural disturbance of the flow regime. Possible mitigation measures aiming to reduce the effect of hydropeaking in a river downstream of the powerhouse can be divided into the installation of detention basins and the improvement of the river morphology. Morphological measures such as macro-roughness at banks might increase the flow resistance as well as the passive retention, which both increase the natural retention capacity of rivers and thus modify the form of the surge wave. In prismatic and nearly prismatic channels, highly unsteady flow conditions can be calculated using the elementary surge wave theory or numerical methods based on the Saint-Venant equations, respectively. For channels with large-scale roughness at the side walls, which may occur by the arrangement of particular morphological measures, no systematic experimental investigations have been done so far on the propagation of surge waves including downstream water-depth and flow velocity. The aim of this research project was to study how macro-roughness elements at the channel banks influence the unsteady flow conditions due to surge waves. 41 configurations of macro-rough banks and various discharges have been tested in a 40 m long flume with a bed slope of 1.14‰. A special experimental setup has been designed which is able to generate surge waves characterized by different discharge ratios. The first step of the experimental investigations focused on the determination of the flow resistance under steady flow conditions caused by large scale roughness elements at the channel banks, namely rectangular cavities (depressions). In a second step, positive and negative surge waves induced at the channel entrance have been tested in the same geometries. Five different discharge scenarios have been considered for each geometry. For comparison, experiments have also been performed in a prismatic reference channel without macro-roughness elements at the banks. The analysis of the experiments for steady flow conditions results in the following conclusions: The total head-loss is governed by different phenomena such as vertical mixing layers, wake-zones, recirculation gyres, coherent structures and skin friction. The flow resistance is significantly increased in the macro-rough configurations due to the disturbance of the bank geometry. Three different approaches have been considered in order to relate the additional, macro-rough flow resistance fMR to the forms of the banks by empirical formulas. The first approach is based on a powerlaw optimization, the second one on a model based on form drag and the third one uses the Evolutionary Polynomial Regression method. By separating the observed flow conditions in a square grooved, a reattachment and a normal recirculating flow type, the developed macro-rough flow resistance formulas are in good agreement with the laboratory experiments. Formulas of the second approach are suggested for practical applications in river engineering. Water body oscillations in cavities have been observed in axi-symmetric macrorough configurations. They lead to water-surface oscillations and transverse velocity components. Peaking excitations with heavy oscillations occur for Strouhal numbers values at 0.42 and at 0.84. The analysis of the experiments with unsteady flow, namely surge waves, shows: The elementary surge wave theory for the prismatic reference configuration including secondary waves and wave breaking could be verified in the laboratory flume. The absolute surge wave celerity Vw and the celerity c are lower for the macro-rough configurations. The decrease of the absolute surge wave celerity Vw is mainly due to the increased flow resistance and lies between 5% and 25% for both, positive and negative waves coming from upstream. Due to the dispersive character, the positive and negative surges from upstream are characterized by a sudden change (front), followed by a progressive change (body) of the water level. The sudden change can be clearly distinguished from the progressive change in the prismatic channel. In the channel with macro rough banks the separation is often hardly visible. The front height decreases between 5% to 25% along the laboratory flume for the prismatic configuration. In the macro-rough channel, the decrease can reach 70%. Behind the wave front of a positive surge, the water level continuous rising to a level which is higher than in the prismatic channel due to the channel bank macro-roughness. The decrease of the height of the surge wave front along the channel could be approached fairly good with an empirical relationship applicable for prismatic and macro-rough configurations. Numerical simulations based on the boundary conditions of the experiments have been done for steady flow tests (2-D simulations). They reveal that the integration of the turbulent stresses is required for the reproduction of the steady flow tests. Test cases with unsteady flow (1-D simulations) show that surge waves in rivers can be computed by integrating the macro-rough flow resistance in the source terms as well as by a modification of the continuity equation taking into account the passive retention.

EPFL2007

High velocity aerated flow on stepped chutes with macro-roughness elements

Stéphanie Joëlle André

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.

EPFL2004

Simulation of shear-driven flows

Roland Bouffanais

The research work reported in the present dissertation is aimed at the analysis of complex physical phenomena involving instabilities and nonlinearities occurring in fluids through state-of-the-art numerical modeling. Solutions of intricate fluid physics problems are devised in two particularly arduous situations: fluid domains with moving boundaries and the high-Reynolds-number regime dominated by nonlinear convective effects. Shear-driven flows of incompressible Newtonian fluids enclosed in cavities of varying geometries are thoroughly investigated in the two following frameworks: transition with a free surface and confined turbulence. The physical system we consider is made of an incompressible Newtonian fluid filling a bounded, or partially bounded cavity. A series of shear-driven flows are easily generated by setting in motion some part of the container boundary. These driven-cavity flows are not only technologically important, they are of great scientific interest because they display almost all physical fluid phenomena that can possibly occur in incompressible flows, and this in the simplest geometrical settings. Thus corner eddies, secondary flows, longitudinal vortices, complex three-dimensional patterns, chaotic particle motions, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same geometry. This facilitates the comparison of results from experiments, analysis, and computation over the whole range of Reynolds numbers. The flows under consideration are part of a larger class of confined flows driven by linear or angular momentum gradients. This dissertation reports a detailed study of a novel numerical method developed for the simulation of an unsteady free-surface flow in three-space-dimensions. This method relies on a moving-grid technique to solve the Navier-Stokes equations expressed in the arbitrary Lagrangian-Eulerian (ALE) kinematics and discretized by the spectral element method. A comprehensive analysis of the continuous and discretized formulations of the general problem in the ALE frame, with nonlinear, non-homogeneous and unsteady boundary conditions is presented. In this dissertation, we first consider in the internal turbulent flow of a fluid enclosed in a bounded cubical cavity driven by the constant translation of its lid. The solution of this flow relied on large-eddy simulations, which served to improve our physical understanding of this complex flow dynamics. Subsequently, a novel subgrid model based on approximate deconvolution methods coupled with a dynamic mixed scale model was devised. The large-eddy simulation of the lid-driven cubical cavity flow based on this novel subgrid model has shown improvements over traditional subgrid-viscosity type of models. Finally a new interpretation of approximate deconvolution models when used with implicit filtering as a way to approximate the projective grid filter was given. This led to the introduction of the grid filter models. Through the use of a newly-developed method of numerical simulation, in this dissertation we solve unsteady flows with a flat and moving free-surface in the transitional regime. These flows are the incompressible flow of a viscous fluid enclosed in a cylindrical container with an open top surface and driven by the steady rotation of the bottom wall. New flow states are investigated based on the fully three-dimensional solution of the Navier-Stokes equations for these free-surface cylindrical swirling flows, without resorting to any symmetry properties unlike all other results available in the literature. To our knowledge, this study delivers the most general available results for this free-surface problem due to its original mathematical treatment. This second part of the dissertation is a basic research task directed at increasing our understanding of the influence of the presence of a free surface on the intricate transitional flow dynamics of shear-driven flows.

EPFL2007

High velocity aerated flow on stepped chutes with macro-roughness elements

Stéphanie Joëlle André

EPFL2004

Influence of macro-roughness of walls on steady and unsteady flow in a channel

Tobias Meile

EPFL2007

Simulation of shear-driven flows

Roland Bouffanais

EPFL2007