<p>Particle erosion is an important process in both natural and manmade environments. &nbsp;For example, in natural environments particle or sediment erosion rates determine the course of rivers, streams, and deltas. &nbsp;The interplay between erosion rates and flow patterns can have dramatic impacts on shorelines. &nbsp;For example, where hydrodynamic jet flows or rip currents change direction, sediments may acculate or disperse altering the shape of coastlines and the ecosystems and economies that rely on them. &nbsp;In man made systems, jet flows may be used to mobilize particles from surfaces or within industrial scale mixing tanks. &nbsp;For example, in the nuclear industry, impinging jet mixers may be used to mobilize and suspend sludges at the bottom of waste tanks. &nbsp;In each of these examples, the Shields diagram is useful to determine the conditions under which erosion occurs. &nbsp;This diagram plots the scaled critical shear stress for erosion as a function of the particle size as embedded in particle Reynolds numbers, Archimedes numbers or their equivalents. &nbsp;Although the data are largely in agreement with mathematical models, for the smallest particles, model predictions diverge from each other and from experimental data. &nbsp;Indeed, there is substantial uncertainty about the Shields diagrams at relatively small particle sizes and flow rates. &nbsp;<br>
&nbsp;&nbsp; &nbsp;To date, the low particle Reynolds number (also called the grain or roughness Reynolds number) condition has been a matter of debate. &nbsp;Shields originally proposed a slope of -1 on a log-log plot of the Shields parameter versus particle Reynolds number (Mantz, 1977). &nbsp;In contrast, many empirical results suggest that the Shields parameter takes a more modest slope or asymptotes to a constant value at low particle Reynolds numbers (Mantz, 1977; Paphides, 1999; Miedema, 2016). &nbsp;The plots of Wiberg and Smith (1987) also show the Shields parameter asymptotes similarly, though this limit may not be recoverable from their equations. &nbsp;At least one potential cause of this uncertainty is the potential transition from laminar to turbulent flow. &nbsp;Thus far, the analysis of the critical shear stress for erosion above has been developed exclusively for turbulent flow conditions. &nbsp;At sufficiently low particle Reynolds numbers, however, the flow eventually becomes laminar. &nbsp;Recognizing when the flow regime has changed is important to knowing when the turbulent solution may be applied correctly. &nbsp;Therefore, the purpose of this paper is to evaluate the influence of laminar flow, particularly laminar jet flows, on critical shear stresses for erosion as they appear on the Shields diagram.<br>
&nbsp;&nbsp; &nbsp;Here we evaluate critical shear stresses for erosion under laminar jet flow. &nbsp;We first derive an expression for the critical shear stress for erosion under laminar jet flow. &nbsp;We then scale the expression as the Shields parameter versus particle Reynolds numbers, Archimedes numbers, and d* (the cube root of the Archimedes number). &nbsp;We show that at lower particle Reynolds numbers the turbulent and laminar Reynolds numbers, the curve on the Shields diagrams, have the same slopes. &nbsp;This analysis is particularly important for mobilization of the smallest particles. &nbsp;We find the Shields parameter to be inversely proportional to the particle Reynolds numbers under laminar jet flow conditions similar to turbulent conditions.</p>

Critical Shear Stress for Erosion Under Laminar Jet Flow

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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