Luigi Fraccarollo

Rheological stratification in experimental free-surface flows of granular-liquid mixtures

Laboratory experiments are conducted to study the rheological behaviour of high-concentration granular-liquid mixtures. Steady uniform free-surface flows are obtained using a recirculating flume. Cases in which a loose deposit forms underneath the flow are contrasted with runs for which basal shear occurs along the flume bottom. The granular motions are observed through the channel sidewall, and analysed with recently developed Voronoi imaging methods. Depth profiles of mean velocity, solid concentration, and granular temperature are obtained, and complemented by stress estimates based on force balance considerations. These measurements are used to probe variations in rheological behaviour over depth, and to clarify the role of the granular temperature. The flows are found to evolve a stratified structure. Distinct sublayers are characterized by either frictional or collisional behaviour, and transitions between one and the other occur at values of the Stokes number which suggest that viscous effects intervene. The observed frictional behaviour is consistent with shear cell tests conducted at very low shear rates. On the other hand, the collisional data corroborate both the Bagnold description and the more recent kinetic theories of granular flows, provided that one accounts for the inertia of the interstitial liquid.

Two-dimensional simulation of debris flows in erodible channels

Debris flows are massive sediment transports of poorly sorted material that occur in small steep mountain catchments. The paper addresses the problem of the propagation of cohesionless debris flows, in which the erosion and sedimentation processes are important and the fixed bed assumption is not acceptable. The depth-averaged motion equations are integrated numerically in a two-dimensional domain. The model is based on a two-phase description of the flow with immediate adaptation of the transport to local flow conditions and with rheological closure valid in the grain-inertia regime. The set of partial differential equations is simplified in order to end up with a hyperbolic system that is solved numerically by means of a second order Godunov-type, finite volume scheme that is accurate in space and time. The scheme uses an approximated Riemann solver of LHLL type, which takes into account the non-conservative terms, and an implicit discretization of the bed shear-stress source terms. The model parameters are determined by means of laboratory flume tests on the site material. Two real-case applications show the effectiveness of the code and how it can be used in predictive situations as in the case of defensive work assessment and verification or hazard mapping.

Displacement characteristics of coarse fluvial bed sediment

[1] Previous work highlights the need for data collection to identify appropriate models for temporal evolution of tracer dispersal in rivers. Results of 64 gravel-bed field tracer experiments covering a wide range of flow and sediment supply regimes are compiled here to determine the probabilistic character of gravel transport. We focus on whether particle travel distances and waits are thin- or heavy-tailed. While heavy-tailed travel distance distributions are observed between successive monitoring events in different hydrological and sediment supply regimes, heavy-tailedness does not persist through total travel distance over multiple monitoring events, suggesting that individual monitoring events occur before particle travel distance exceeds the characteristic correlation length for the channel (such that particles that start in fast paths remain in fast paths and particles in slow paths remain in slow paths). After a large number of transport events, super-diffusive spreading was not observed at any of the gravel bed streams. Continuous-time tracking of x, y, z coordinates of tracers in natural streams is necessary to capture exact step and waiting time distributions.

A well-balanced approach for flows over mobile-bed with high sediment-transport

In this paper we deal with the numerical computation of one-dimensional, unsteady, free-surface flows over mobile-bed. We focus on flows characterized by high concentration of sediments and strong interaction between flow and bottom dynamics, as in hyper-concentrated- and debris-flows. These features are fully considered in the adopted system of equations. Challenging in its numerical approximation is the preservation of the coupling and the treatment of a non-conservative flux in the momentum equation. In order to devise a new Godunov-type approach, we analyzed in detail the Riemann problem associated with the mobile-bed phenomena and the peculiar features of its wave relations. The scheme we developed is based on two supports: well-balanced treatment of the variable updating at the new time-level and flux evaluation by three-wave approximations of the intercell Riemann-problem that, without any split, embody the effect of the non-conservative term. The properties of the new numerical strategy (named AWB) are assessed by comparison with exact solutions of Riemann problems, built by handling an inverse technique. Finally, AWB has been applied to cases of practical interest, where wave interaction and friction effects makes the flow more complex. The obtained results point out that the new method is able to predict faithfully the overall behaviour of the solution and of any type of waves. The use of AWB, in this one-dimensional frame, is therefore fostered in representing rapid transients in river/torrent flows with movable bed.

Set of measurement data from flume experiments on steady uniform debris flows

The paper documents a detailed set of measurements from laboratory experiments involving open–channel flows of granular–liquid mixtures. Polyvinyl Chloride pellets mixed with clear water are used, and represent simplified analogues of the mixtures of rocks and muddy water encountered in stony inertial debris flows. The flows are examined in steady uniform conditions, achieved by setting up a closed loop with an inclined channel and a high–speed conveyor belt. Such idealized conditions make it possible to estimate stresses within the flowing mixture, and to accumulate statistics of local granular configurations and motions. These are extracted from video sequences imaged through the sidewall, using algorithms based on the Voronoï diagram. Estimates of granular concentration and granular temperature are derived from local grain patterns and from a detailed analysis of Lagrangian and Eulerian velocity correlations. Depth profiles of kinematic and dynamic quantities are then obtained for various ratios of solid to liquid discharges. These data were earlier used to probe depth variations of rheological behaviour in granular–liquid flows. To make them available for other purposes, they are assembled here into a comprehensive dataset, and provided in digital form in the electronic supplement to this special issue.

Generalized Roe schemes for 1D two-phase, free-surface flows over a mobile bed

The problem of two-phase, free-surface flows over a mobile bed is characterized by a hyperbolic partial differential equations system that shows nonconservative terms and highly nonlinear relations between primitive and conserved variables. Weak solutions of the present problem were obtained resorting both to the distribution theory and to the integral formulation of momentum conservation: the comparison of these two approaches allowed us to give a physical insight into the meaning of the nonconservative term across a discontinuity. Starting from this result, we derived the conditions necessary to obtain generalized, well-balanced Roe solvers without using the concept of a family of paths. Two numerical schemes based on the same set of matrices have been developed, one in terms of conserved variables and one in terms of primitive variables. The friction-source term has also been included by using an upwind approach. The capabilities and limits of the proposed schemes have been analyzed by comparison with exact solutions of Riemann problems and with numerical solutions obtained with the AWB-3SRS scheme.

Three-dimensional flow evolution after a dam break

In this paper, the wave propagation on a plane dry bottom after a dam break is analysed. Two mathematical models have been used and compared with each other for simulating such a dam-break scenario. First, the fully three-dimensional Navier–Stokes equations for a weakly compressible fluid have been solved using the new smooth particle hydrodynamics formulation, recently proposed by Ferrari et al . ( Comput. Fluids , vol. 38, 2009, p. 1203). Second, the two-dimensional shallow water equations (SWEs) are solved using a third-order weighted essentially non-oscillatory finite-volume scheme. The numerical results are critically compared against the laboratory measurements provided by Fraccarollo & Toro ( J. Hydraul. Res. , vol. 33, 1995, p. 843). The experimental data provide the temporal evolution of the pressure field, the water depth and the vertical velocity profile at 40 gauges, located in the reservoir and in front of the gate. Our analysis reveals the shortcomings of SWEs in the initial stages of the dam-break phenomenon in reproducing many important flow features of the unsteady free-surface flow: the shallow water model predicts a complex wave structure and a wavy evolution of local free-surface elevations in the reservoir that can be clearly identified to be only model artefacts. However, the quasi-incompressible Navier–Stokes model reproduces well the high gradients in the flow field and predicts the cycles of simultaneous rapid decreasing and frozen stages of the free surface in the tank along with the velocity oscillations. Asymptotically, i.e. for ‘large times’, the shallow water model and the weakly compressible Navier–Stokes model agree well with the experimental data, since the classical SWE assumptions are satisfied only at large times.

Experimental investigation of mobile armoring development

Vertical sorting of bed material in rivers has received increasing attention, but very little experimental data are available so far. A recently developed nondestructive sampling technique allows the determination of bed material composition over vertical surfaces of the bed. This is particularly interesting for determining particle arrangement on the surface of and inside bed forms. Experiments were carried out using bimodal and trimodal sediment mixtures in two recirculating flumes. The development of surface coarsening was detected and measured at various stages of the process. Variations in the initial bed material composition brought very different responses in the bed geometry. The mobile armoring process was also strongly affected by bed material composition. The experimental procedures described in this work indicate a possible path to be followed for further experimental research on armoring processes.