A One-Way Coupled Hydrodynamic Advection-Diffusion Model to Simulate Congested Large Wood Transport

Abstract

An advection-diffusion model is proposed to simulate large wood transport during high flows. The mathematical model is derived from the wood mass balance, taking into consideration both the wood mass concentration and the log orientation, which affects log transport and, most importantly, wood accumulation. Focusing on wood mass transport, the advection-diffusion equation is implemented in a hydrodynamic model to provide a one-way coupled solution of the flow and of the floating wood mass. The model is tested on a large series of flume experiments, involving at least 30 logs and different control parameters (flow Froude number, log length, diameter, release point). The validation through the experimental data shows that the proposed model can predict the correct displacement of the most probable position of the logs and to simulate with a sufficient accuracy the planar diffusion of the wooden mass. Transversal wood distribution is more accurate than the streamwise one, indicating that a higher control on the longitudinal diffusion needs to be implemented.

Modeling Large Wood Transport in Semi-Congested Regime with Multiple Entry Points

“…Figure 4b shows the experimental velocity of a realization of uncongested transport, in which cylinders were released one by one, avoiding any interaction, at a transversal distance equal to 0.4 m. This is one of the experiments used to derive the transport velocity expressed by Equation ( 4) [30]. The experimental velocities for uncongested transport are less dispersed than those of semi-congested experiments (Figure 4a) since, in this case, only one release point was employed.…”

“…The numerical model ORSA2D, as modified in [30], is employed to model the transport of floating wood as a superficial pollutant. It is based on the one-way coupling of the shallow water equations and of the advection-diffusion equation for wood transport, which is derived from the continuity equation of the sole wood mass:…”

“…where t is the time and t 0 is the initial time, i c max indicates the cell where the maximum concentration is found, ∆t is the time step and ∆v is an empirical threshold calibrated on uncongested transport experiments (∆v = −0.16 m/s). Details of the mathematical derivation and on the transport velocity can be found in [30] (note that in the reference, the multiplication by fluid velocity is missing). The original hydrodynamic model, without the advection-diffusion equation, was applied to several tests and real case simulations, being capable of dealing with different geometries and hydraulic conditions, from dam-break flooding [37] to 2D circulations in shallow lakes [38].…”

“…Such an observation leads to a different perspective for numerical models, abandoning the deterministic approach, typical of Lagrangian models, in favor of an Eulerian approach that focuses on the transport of overall wooden mass. Following such an assumption, an Eulerian model was developed [29] and applied to a simple sinusoidal geometry [30]. By considering large wood as a floating pollutant, the model couples the diffusion equation with the shallow water equation to estimate the propagation of the wood mass.…”

“…Figure 2b shows the location of the average mass center for test 1 with a release distance of −0.4 cm. At the downstream boundary edge, the wood mass concentration is computed according to a Neumann boundary condition by setting its derivative equal to zero [30].…”