Flow dynamics of volumes of large light particles released on submerged steep slopes

The aim of the study is to carry out two-phase gravity driven flows of large light particles on submerged steep slopes and, from their characteristics, identify the criteria that govern the transition between a purely dense and a mixed (dense-suspended) regime. For that, volumes of large light particles are released without any initial velocity at the top of a 2D flume immersed in a 20 m3 tank filled with tap water. The particles are spherical, monodisperse, with two different diameters: 10.6 and 14.4 mm. The volume expansion β, the height H and the front velocity $$U_f$$ of the heavy flows are investigated varying the volume released between 0.2 and 3 L, and the tilt angle of the flume (θ) between 30 and 60°. Two different regimes are observed, one where all the particles move in close contact with each other (dense regime), and as the volume and/or flume angle increases, another where part of the particles are suspended (mixed regime). We find that the overall dynamics of the flow is governed by a buoyancy/drag equilibrium ruled by the densimetric Froude number $$Fr=U_f/\sqrt{(\Delta \rho g/\rho _w) H}$$ , with g the gravity acceleration and $$\Delta \rho =\rho -\rho _w$$ . $$\rho $$ is the density of the flow and $$\rho _w$$ that of the ambient fluid: water. The corresponding drag coefficient exerted on the particles volume is found to vary as $$C_d\approx 2{Fr^{-1.6}}$$ . The key parameter for the onset of the flow of some of the particles in suspension and the transition to the mixed regime proves to be $$St_\theta =St\cos \theta /(1-St\sin \theta )$$ , with $$St=v_s/U_f$$ the Stokes number comparing the settling velocity of the particles to the flow front velocity. While pressure remains hydrostatic within the flow in the dense regime ( $$St_\theta >0.9$$ ), it increases as suspension occurs in the mixed case and $$St_\theta $$ decreases. The dynamic pressure at the forehead of the volume then evolves as $$ P_{s} \approx \Delta \rho gH\cos (\theta )(1.9 - St_{\theta } )^{2} $$ .