The work presented contributes to the development of an appropriate numeri-cal model that incorporates the motion of floating rigid bodies in the estima-tion of flood risk. It considers the two-dimensional transport of floating ob-jects, predicting their trajectories, orientation and the interaction with other bodies or with inline structures. Since the main focus is on large bodies, each object is treated as a single enti-ty, which is reflected in the Lagrangian approach of the Discrete Element Method, one-way coupled with the Eulerian solution of the Shallow Water Equations. The forces exerted by the flow control the translation and the rota-tion of the bodies. The development of the model requires to simplify the shape of the floating bodies, in order to focus on the equations and exclude complicated fluid-solid interactions. The proposed formulation focuses both on perfectly symmetric elements, spheres, and on cylinders, which are axial-symmetric and for which orientation matters. The equations of transport, i.e. of translation and rotation, take into account such variability with an appropriate computation of the forces. The translation equations are derived by the Maxey–Ryley equation, which was originally developed for small spheres in creeping flows and can be ex-tended to large bodies and higher Reynolds numbers by taking into account the flow velocity distribution along the body length. The extension to cylin-ders is obtained by including the variability of the drag and side coefficients with the body orientation. To simulate body rotation, the torque acting on each object and a term of re-sistance to rotation are computed. As regards spheres, the main effect of rota-tion is in the variation of the trajectory. For cylinders this datum is extremely important to predict orientation before the interaction with fixed inline struc-tures: bodies aligned with the flow have lower possibility to trigger the for-mation of an obstruction. In the dissertation, two formulations to model bod-ies rotation are presented, in order to evaluate which solution has the best performances in predicting the cylinder final orientation. This results to be the most critical aspect of the simulation, due to the high sensitivity of rotation to local turbulence, domain characteristics and features of the numerical scheme. To help the implementation of the mathematical formulation, experimental campaigns were also carried out. Firstly, the measure of the hydrodynamic coefficients of semi-submerged cylinders was performed, to obtain a law for the variation of the coefficients with orientation. The measurements were per-formed with a hydrodynamic balance, built and installed in a prismatic chan-nel at the Department of Civil Engineering and Architecture of the University of Pavia. The obtained results helped in increasing the reliability of the hy-drodynamic forces estimation. A second group of experiments was held at the laboratory of the Department of Science and Technology of Materials and Fluids of the University of Zara-goza, where rigid body transport was replicated in a channel with side obsta-cles of different shape and number, to provide useful information for the cal-ibration of the proposed model. The model calibration took advantage also of a real-scale experiment realized in a reach of the Rienz river by researchers of the University of Bolzano, who traced the movement of real logs during floods. The application of the model to this real-life fluvial case helped in adapting the formulation to a real-scale domain. The presence of distributed inline obstacles is taken into account, and wood deposition and remobilization are modelled, too.

### Eulerian–Lagrangian modelling of large floating debris transport during floods

#### Abstract

The work presented contributes to the development of an appropriate numeri-cal model that incorporates the motion of floating rigid bodies in the estima-tion of flood risk. It considers the two-dimensional transport of floating ob-jects, predicting their trajectories, orientation and the interaction with other bodies or with inline structures. Since the main focus is on large bodies, each object is treated as a single enti-ty, which is reflected in the Lagrangian approach of the Discrete Element Method, one-way coupled with the Eulerian solution of the Shallow Water Equations. The forces exerted by the flow control the translation and the rota-tion of the bodies. The development of the model requires to simplify the shape of the floating bodies, in order to focus on the equations and exclude complicated fluid-solid interactions. The proposed formulation focuses both on perfectly symmetric elements, spheres, and on cylinders, which are axial-symmetric and for which orientation matters. The equations of transport, i.e. of translation and rotation, take into account such variability with an appropriate computation of the forces. The translation equations are derived by the Maxey–Ryley equation, which was originally developed for small spheres in creeping flows and can be ex-tended to large bodies and higher Reynolds numbers by taking into account the flow velocity distribution along the body length. The extension to cylin-ders is obtained by including the variability of the drag and side coefficients with the body orientation. To simulate body rotation, the torque acting on each object and a term of re-sistance to rotation are computed. As regards spheres, the main effect of rota-tion is in the variation of the trajectory. For cylinders this datum is extremely important to predict orientation before the interaction with fixed inline struc-tures: bodies aligned with the flow have lower possibility to trigger the for-mation of an obstruction. In the dissertation, two formulations to model bod-ies rotation are presented, in order to evaluate which solution has the best performances in predicting the cylinder final orientation. This results to be the most critical aspect of the simulation, due to the high sensitivity of rotation to local turbulence, domain characteristics and features of the numerical scheme. To help the implementation of the mathematical formulation, experimental campaigns were also carried out. Firstly, the measure of the hydrodynamic coefficients of semi-submerged cylinders was performed, to obtain a law for the variation of the coefficients with orientation. The measurements were per-formed with a hydrodynamic balance, built and installed in a prismatic chan-nel at the Department of Civil Engineering and Architecture of the University of Pavia. The obtained results helped in increasing the reliability of the hy-drodynamic forces estimation. A second group of experiments was held at the laboratory of the Department of Science and Technology of Materials and Fluids of the University of Zara-goza, where rigid body transport was replicated in a channel with side obsta-cles of different shape and number, to provide useful information for the cal-ibration of the proposed model. The model calibration took advantage also of a real-scale experiment realized in a reach of the Rienz river by researchers of the University of Bolzano, who traced the movement of real logs during floods. The application of the model to this real-life fluvial case helped in adapting the formulation to a real-scale domain. The presence of distributed inline obstacles is taken into account, and wood deposition and remobilization are modelled, too.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11571/1218990`