Numerical and analytical analyses of the impact of monodisperse and bidisperse granular flows on a baffle structure

Abstract

Baffle structure, a promising countermeasure in reducing the destruction power of rapid granular flows, needs more investigation especially with focus on the physically based design strategy. To contribute to this point, we conduct a series of numerical modeling tests to investigate the impact dynamics of monodisperse and bidisperse granular flows against the baffle array, based on which a jet-based model for estimation of the peak impact force and run-up height is proposed for baffle design. The results show that the energy loss due to interparticle interaction increases with the Froude number; the hard contact of larger particles and the arching effect of debris–baffle interaction are important to the impact dynamics on baffle structure; the baffle design could ignore the static force component, at least for rapid granular flow with the smaller ratio of the baffle slit size to the particle size; and for the bidisperse granular flow impact, the effect of larger particles is only dominant when the percentage of larger particles is large because fine debris could provide a cushioning effect. A jet-based model considering conservation equations for momentum and energy is then proposed for baffle design with the introduction of jamming-related momentum and energy discharge process. The model is verified using numerical data in terms of the run-up height and impact force. On the basis of the proposed model, baffle design is further discussed considering flow material inhomogeneity and unsteady flow dynamics.

Appendix. DEM contact model

The DEM simulations in this paper are conducted using EDEM software, which offers an efficient contact model referred to as a Hertz–Mindlin (no-slip) contact model combined with an anti-rolling model to compensate for the simplification of the real particle shape in DEM simulation:

$$\begin{array}{c}{F}_{n}^{c}=-{K}_{n}{\lambda }_{n}+{D}_{n}{v}_{n}^{rel},\end{array}$$

(22)

$$\begin{array}{c}{F}_{t}^{c}=min\left\{{K}_{t}{\lambda }_{t}+{D}_{t}{v}_{t}^{rel}, {\mu }_{s}{F}_{n}^{c}\right\},\end{array}$$

(23)

$$\begin{array}{c}{M}_{r}={-\mu }_{r}{F}_{n}^{c}{d}_{i}{\widehat{\omega }}_{i}.\end{array}$$

(24)

Here, the subscripts n and t respectively indicate the normal and tangential directions. And the definitions of variables are presented in Nomenclature.

Nomenclature
DEM contact model	${F}_{n}^{c}$, ${F}_{t}^{c}$: normal and tangential contact force; K: elastic stiffness constant; D: damping coefficient; $\lambda$: overlap; ${v}^{rel}:$ relative velocity; ${\mu }_{s}:$coefficient of Coulomb friction; ${\mu }_{r}$: rolling friction coefficient; ${d}_{i}$: distance between the contact point and center of mass; ${\widehat{\omega }}_{i}$: unit angular velocity.
Baffle layout	${L}_{B}$: baffle array spacing; ${S}_{B}$: slit spacing; ${W}_{F}$: flume width; ${h}_{B}$: baffle height; ${W}_{B}$: baffle width; B: opening ratio.
Flow properties	${h}_{f}$: flow depth; ${u}_{f}$: flow velocity; $\delta$: particle diameter; ${u}_{f}$: flow velocity; ${\phi }_{f}$: solid volume fraction; ${\rho }_{s}$: particle density: ${N}_{Fr}$: Froude number; ${E}_{k}$: kinetic energy: ${E}_{p}$: potential energy; ${E}_{d}$: dissipated energy; ${E}_{r}$: energy loss due to particle removal; ${E}_{s}$: elastic strain energy.
Design Parameters	${F}_{n}$: total impact force; ${F}_{n}^{s}$: static force component; ${F}_{n}^{d}$: dynamic force component; ${\Psi }_{m}$: momentum reduction coefficient; ${\Psi }_{u}$: velocity reduction coefficient; ${h}_{r}$: run-up height; ${\Psi }_{e}$: energy reduction coefficient; ${\kappa }_{f}$: longitudinal pressure coefficient; ${\gamma }_{r}$: empirical coefficient for compensation of the overestimation of run-up height; ${\alpha }_{0}$: force correction coefficient.