Stability of a Liquid Jet Impinging on Confined Saturated Sand

Abstract

This work focuses on the dynamics of a liquid jet impacting the surface of a confined, immersed granular bed. Although previous works have considered the erosion process and surface morphology, less attention has been given to the jet hydrodynamics. Based on laboratory experiments, we show that when the liquid jet forms a crater, two situations arise. In the case of weak/no erosion or open craters, the jet is stationary. For vertical or overhanging crater walls, the jet displays a wide range of behaviors, from quasi-periodic oscillations to symmetry breaking and exploration of different states in time. An analysis of the different system states leads to the emergence of a bifurcation diagram depending on a dimensionless parameter, J, comparing the jet impact force to the force necessary to eject a grain. The frequency of the jet oscillations depends on the inertial velocity, the jet dispersion and the ratio between the injector cross-section and the confinement length.

Oscillations of a particle-laden fountain

“…Figure 7 displays the Strouhal number St as a function of the parameter J. Similar to the jet impingement configuration [28], all data points collapse on a single curve and St exhibits a power-law behavior, St = βJ γ , with β 0.06 and γ −5/2. Interestingly, although in both the jet impingement or the upward jet configuration the Strouhal number decreases with J, the exponent of the power-law behavior is drastically different (γ −1 in the reverse configuration [28]).…”

“…Note that it also corresponds to the square root of a Shields number. Here α 7 • , of the order of the value measured by Vessaireet al [28]. Figure 7 displays the Strouhal number St as a function of the parameter J.…”

“…The frequency of the particle-laden jet oscillations can be expressed in a dimensionless form by the Strouhal number St = f L/u 0 J where the characteristic length is L = h g and u 0 J = Q/S i is the jet velocity at the nozzle exit, with S i = πd 2 i /4 the surface through which the fluid is injected at the cell bottom. Following [28], we introduce a dimensionless number corresponding to the velocity ratio between the particle-laden jet, u J , at height h g and a single grain velocity u. The jet velocity is derived in confined geometry as u J Q/(2eh g tan α), where e is the cell gap and α the jet half-angle.…”

“…In a recent work, Vessaire et al investigated a liquid jet impinging on a confined saturated granular bed [28]. This configuration unraveled a puzzling phenomenon: in a given range of parameters, the jet is strong enough to form a crater containing suspended particles and exhibits oscillations.…”

Fluid-particle suspension by gas release from a granular bed

“…To tackle this question, we consider particle entrainment immersed granular beds. The resuspension of particles forming this solid-like settled state and the induced erosion, chimney or crater formation have been investigated using different mechanisms such as shearing flow [14,15], the impact of liquid jets [16][17][18][19], thermal convection or plume emission [20][21][22][23][24], underground cavity collapse [25], fluidization [26], etc. The present paper focuses on gas release from a granular bed, a scenario highlighted in the above applications.…”