Scanning PIV of turbulent flows over and through rough porous beds using refractive index matching

This paper presents image velocimetry measurements on turbulent flows adjacent to a permeable bed made of randomly packed glass particles. For measuring flow velocities inside the bed, the refractive index of the glass particles was matched with that of the fluid. By continuously scanning in the transverse direction, we measured the streamwise and vertical velocity components within a three-dimensional domain (3D2C-PIV), including first- and second-order turbulent statistics. We established how the scanning travel speed is associated with the laser sheet thickness and the space-time velocity fluctuations for collecting reliable measurements. The methodology was applied to free-surface flows over a sloping bed under low relative submergence and supercritical conditions. Space- and time-averaged profiles were obtained in a representative elementary volume as defined by the double-averaging procedure (Nikora et al. in J Hydraulic Eng.127(2):123-133, 2001). A turbulent boundary layer over the rough bed was observed when experiments were run at intermediate Reynolds numbers Re = O(1000). Apart from measuring subsurface velocities, this method shed light on the part played by the rough bed in the overall flow dynamics: the roughness layer was a buffer region within which porosity varied sharply and turbulent stress was rapidly dampened.

Turbulent Flows over Rough Permeable Beds in Mountain Rivers: Experimental Insights and Modeling

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.

EPFL2019

Modelling the vertical structure of turbulent free-surface flows over rough permeable beds

Christophe Ancey, Joris Heyman, Gauthier Paul Daniel Marie Rousseau

Understanding diffusive processes across the sediment-water interface is important for quantifying hyporheic exchanges and related biogeochemical processes (e.g., denitrification, biomass growth). Viscous, turbulent and dispersive effects all contribute to the hydrodynamics of flows over rough permeable beds, although their specific role across the interface remains poorly understood. In order to model mixing processes from the permeable bed to the free surface, we have run experiments on low submergence flows over sloping porous beds made of randomly packed glass beads. Fluid velocities were measured using Particle Image Velocimetry (PIV) and a technique called Refractive Index-Matched Scanning (RIMS) allowing the interior of the bed to be examined. By applying the double averaging methodology, we determined the following mesoscale profiles: porosity, mean velocity, turbulent and dispersive stresses from the subsurface to the free surface. We observed a turbulent boundary layer over the rough bed for at intermediate Reynolds numbers, i.e. Re = O(1000). Under these flow conditions, viscosity played a non-negligible role through the van Driest damping effect. Based on the Prandtl mixing length theory and mechanistic considerations, we propose a new theoretical model to reproduce turbulent and dispersive stress profiles. In contrast to existing boundary layer models, our model takes into account the continuity of the porosity profile and the associated damping effects on flow momentum in the roughness layer. A good agreement is found between the model and classic flow resistance laws employed for low-land and gravel-bed rivers (e.g. Chézy, Manning-Strickler, Keulegan). A 1D vertical effective diffusion model is derived from the hydrodynamic model and should contribute improving our understanding of depth dependent diffusive processes across the sediment-water interface and thus hyporheic exchanges in various settings.

2020

Modelling the vertical structure of turbulent free-surface flows over rough permeable beds

Christophe Ancey, Joris Heyman, Gauthier Paul Daniel Marie Rousseau

2020

Turbulent Flows over Rough Permeable Beds in Mountain Rivers: Experimental Insights and Modeling

Gauthier Paul Daniel Marie Rousseau

EPFL2019