Experimental Measurements on the Coefficient of Restitution of Colliding Irregular Volcanic Particles

Dense volcanic granular flows are polydisperse in terms of grain size and density, and their flow characteristics are mainly governed by particle-particle collisions and frictional forces acting at the boundaries. The parameter measuring the energy dissipation during the collisions is the coefficient of restitution ($e$), which is proportional to the fraction of the original energy stored in the colliding particles that is restored to the same ones after the collision. $e$ is fundamental in computational fluid dynamics (CFD) numerical models to simulate multiphase granular flows because it is required to solve the particles motion and the particle-particle momentum exchange. The calculation of $e$ for irregular volcanic particles is an unsolved challenging problem, which is here addressed by colliding particles through a pendulum-type instrumental apparatus. $e$ was calculated for volcanic particles with different density ($\rho$), diameter ($d$) and particles size ratio ($d_{\text{ratio}}$), and the data were used to obtain linear relationships between $e$ and the investigated parameters. Afterward, a multicollinearity analysis and a multiple regression were applied to all data to adequately predict the value of $e$ knowing the values of $\rho$, $d$, and $d_{\text{ratio}}$. The empirical law was finally validated against some large-scale experiments by using the multiphase CFD simulation tool Multiphase Flow with Interphase eXchanges. The CFD simulations inserting the predicted $e$ showed a better agreement between simulated and experimental flow velocities, with an increase of the simulation accuracy up to 20%. Hence, the current paper proposes a simple instrumental apparatus to calculate $e$, demonstrating its importance in simulations of multiphase granular flows.