Erosion threshold of a liquid immersed granular bed by an impinging plane liquid jet

Abstract

Erosion threshold of a model granular bed by a jet in a quasi bidimensional configuration has been studied experimentally in both laminar and turbulent regimes. The jet is a liquid sheet which impinges normally a packing of immersed beads monodisperse in size and density. The erosion threshold has been characterized at different impact distances of the jet on the sediment and for different grain size and fluid viscosity. In the explored range of parameters, we show that the erosion threshold is well described by a critical inertial Shields number based on the local flow velocity at the impinging point. This has been done by a careful analysis of the different jet flow regimes taking into account the position of the virtual origin of the jet.

Erosion onset of a cohesionless granular medium by an immersed impinging round jet

“…Most of the available references focus on the morphology of the scour crater, with the eroding fluid being either a liquid [1, 25,26,30] or a gas [6,17,27,28,32], the latter mainly motivated by the issue of a retrograde rocket landing on an extraterrestrial planet. In contrast, the present study disregards the crater morphology and concentrates solely on the onset of granular erosion under the action of an immersed impinging liquid jet, extending the recent results by Badr et al [5] obtained for a plane jet to the most usual 3D configuration of a round jet, and proposing an empirical model for erosion threshold inside the scouring crater.…”

“…As demonstrated by Badr et al [5], the characteristical hydrodynamic quantities of the fluid flow can be satisfactorily and consistently estimated from the classical self-similar free jet models, provided that a careful analysis is implemented, which in particular includes the introduction of a virtual origin as will be discussed more in depth in section III. Then, the hydrodynamical condition for particle dislodgement at the surface of the granular bed is classically quantified by the dimensionless Shields number Sh which compares the flow shear stress τ s to the buoyant weight of the soil particles [15].…”

“…Furthermore, a set of complementary experiments featuring a digital post-processing by means of the Particle Image Velocimetry (PIV) provide then the basis for a detailed analysis of the hydrodynamics of the impinging jet shown in section III and its comparison with the laminar self-similar theoretical model originally proposed by Schlichting [41]. Finally, section IV is devoted to an analysis of the experimental results: Firstly, two alternative definitions for the critical inertial Shields number referring to the free round jet model obtained in the previous section are examined and discussed, leading to the adoption of a final critical value fully consistent with Badr's results [5]; Then, a tentative empirical model accounting for the fluid velocity reduction inside the crater scoured in the granular sample is presented and some of its limitations are outlined.…”

“…Several previous studies have focused on the onset of particle motion in laminar flow condition with irregular granular substrates [16,18,29,34] or also regular ones [2]. Based on their results considering a planar impinging liquid jet, Badr et al [5] have concluded that the initiation of grain movement can be satisfactorily predicted by a critical inertial Shields number around 1 for particle Reynolds numbers ranging from 3 to 80, by assuming a simplified expression for the inertial flow stress derived from both laminar and turbulent free plane jet models [41] which therefore seem to be valid for a jet impinging on a granular sample. The present study provides an experimental contribution to a better understanding of the granular erosion mechanisms and most specifically to the definition of a critical inertial Shields number, based on a parametric analysis using artificial soils subjected to an impinging round jet.…”

“…To our knowledge, almost all previous works that have considered the implications for erosion assessment of natural soils, both cohesive or cohesionless, have directly made use of the results from turbulent wall impinging jets (plane or circular) [9,[24][25][26]30] without taking account of the significant differences in terms of roughness, permeability [43] and, above all, morphology once the scouring process has been initiated. An even simpler approach was adopted by Badr et al [5] for the case of granular erosion by both laminar and turbulent plane jets, considering as a strong assumption that, despite the complex flow configuration of a jet impinging on a sediment floor, the relevant shear-stress characteristic value exerted at the upper surface of the granular system was directly related to the maximal velocity predicted by the free jet models. Here we nevertheless decided to follow the same procedure and, referring to the free jet centerline velocity u 0 at a distance h 0 to the jet nozzle which is given by Eq.…”