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# Flow and turbulence in sharp open-channel bends

The sustainable development of rivers requires a knowledge on the three-dimensional mean flow field and the turbulence in complex morphologies. In a future, the computational capacity will be sufficient to simulate numerically the fine details of the flow. Our physical knowledge, however, is at present insufficient: the overwhelming majority of experimental research concerns straight-uniform flow and even complex numerical models are based on straight-uniform-flow knowledge. A sound understanding of the relevant physical processes will always be essential in complicated problems such as the river management, which concern a variety of different fields, and this irrespective of the available computational capacity. This PhD investigates, mainly experimentally, the mean-flow field and the turbulence in open-channel bends; this situation is considered as a generic case for complex highly three-dimensional flow. The experimental investigation is rendered feasible by the availability of a powerful Acoustic Doppler Velocity Profiler (ADVP), developed in our laboratory. The principal objectives of this PhD are: To provide a high-quality data base on three-dimensional open-channel flow, including all three mean velocity components and all six Reynolds stresses on a fine grid. To document interesting features of the flow field and the turbulence, such as the multi-cellular pattern of secondary circulation, the curvature influence on the turbulence, etc. To gain insight in the relevant physical mechanisms and processes underlying these features. To apply the acquired knowledge in an engineering sense, mainly by evaluating, improving and developing numerical simulation techniques. First, a limited series of experiments was conducted in a small laboratory flume, with the aim of testing the feasibility of the project. Subsequently, extended series of experiments have been designed in a large and optimized laboratory flume. The small-flume experiments yielded results beyond all expectations and form the core of this dissertation. The large-flume experiment are intended to confirm those results and to investigate newly emerged questions. Only few large-flume results are included in this dissertation; more large-flume results will be reported in literature in the future. The structure of this dissertation follows the above-mentioned objectives. In PART I "Instrumentation and experimental set-up", the experimental set-up, the ADVP and the measuring strategy are presented. Furthermore, a method is proposed to improve acoustic turbulence measurements. PART II "Experimental observations" provides high-quality data on the mean flow and the turbulence and documents the most interesting features: The downstream velocity increases in outward direction and its vertical profiles are flatter (increased/decreased velocities in the lower/upper part of the flow depth) than in straight flow. A relatively small and weak outer-bank cell of secondary circulation exists besides the classical center-region cell (helical motion). The turbulence activity is reduced in the outer half of the cross-section in the investigated bend, as compared to a straight-uniform flow. Linear models that are commonly used to account for the effect of the secondary circulation in depth-integrated flow models are inaccurate for moderately to strongly curved flows. PART III "Fundamental research" investigates the physical mechanisms and processes underlying these observations, mainly by making term-by-term evaluations of the relevant flow equations (momentum, vorticity, turbulent kinetic energy) and by considering the instantaneous flow behavior. The distribution of the downstream velocity is dominated by both cells of secondary circulation, whereby the outer-bank cell has a protective effect on the stability of the outer bank by keeping the core of maximum velocity at distance. The center-region cell is mainly generated by the vertical gradient of the centrifugal force, : the non-uniform outward centrifugal force and the nearly-uniform inward pressure gradient, due to the super-elevation of the water surface, are on the average in equilibrium; their local non-equilibrium, however, gives rise to the centerregion cell. There exists a strong negative feedback between the vertical profile of the downstream velocity, vs, and the center-region cell: the center-region cell flattens the vs-profiles, which on its turn leads to a reduction of and a weakening of the center-region cell. Linear models that are commonly used to account for the effect of the secondary circulation in depth-integrated flow models perform poorly because they neglect this feedback. Similar outer-bank cells exist in straight turbulent flow as well as in curved laminar flow. In straight turbulent flow, they are induced by the anisotropy of turbulence whereas they come into existence in curved laminar flow when the curvature exceeds a critical value: the vs-profiles flatten to such an extent that the gradient of the centrifugal force changes sign near the water surface, < 0, provocating the generation of the outer-bank cell. In curved turbulent flow, both mechanisms have a comparable contribution to the generation of the outer-bank cell and strengthen each other, whence the outer-bank cell is stronger in a curved turbulent flow than in a curved laminar or a straight turbulent flow. The restitution of kinetic energy from the turbulence to the mean flow plays an important role in the generation of the outer-bank cell, and the deficiency of standard k-ε turbulence closures to accurately simulate them is due to their inherent incapability to account for such kinetic-energy restitution. The turbulence structure is fundamentally different than in a straight-uniform flow: for the same amount of turbulent kinetic energy, there is less shear in a curved flow. This change in turbulence structure is responsible for the observed reduced turbulence activity. An analysis of the instantaneous flow behavior suggests that the turbulence fluctuations can be decomposed into two fundamentally different parts: a wave-like oscillation of the pattern of circulation cells embedded in background turbulence. PART IV "Applied research" tries to apply the acquired knowledge in an engineering sense. It proposes a non-linear model to account for the effect of the secondary circulation in depth-integrated flow models, that simulates the negative feedback between the downstream velocity profile and the center-region cell. Contrary to the commonly used linear models, this non-linear model agrees well with experimental data for strongly curved flow from both the small and the large-flume experiments. The model depends on the curvature ratio, the friction factor and the spanwise distribution of the downstream velocity, which can all be incorporated in a newly defined bend parameter, that allows an objective definition of weak, moderate and strong curvature. The linear model is found as the asymptotic solution for vanishing curvature. An evaluation for natural rivers has shown that differences between the linear model and the non-linear model are relevant. Moreover, outer-bank cells have been successfully simulated by means of a non-linear k-ε turbulence closure. As mentioned before, the small-flume experiments yielded results beyond all expectations. As a side-effect, the analysis of the large-flume experiments could not be accomplished within this dissertation and the work that is presently in progress is briefly described in PART V "Work in progress". Finally, PART VI summarizes the main conclusions of this dissertation.

Section de génie civil

Faculté de l'environnement naturel, architectural et construit

Institut des infrastructures, des ressources et de l'environnement

Laboratoire d'hydraulique environnementale

Jury: Huib de Vriend, Peter Egger, Wilhelm Hager, Peter Monkewitz, Anton Schleiss, Yves Zech

Public defense: 2002-5-3

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Record created on 2005-03-16, modified on 2016-08-08