Session: 04-08 Erosion, Slurry, Sedimentation

Paper Number: 85965

85965 - Jet Erosion of Particle Beds: Projecting Critical Suspension Velocities From Effective Clearing / Cleaning Radii 

Accurately describing jet driven erosion of particle beds is an important but challenging aspect of launch pad and airport design, slurry processing, semiconductor cleaning, dishwasher operation, and soil property characterization. In industrial processes such as the design of slurry process mixing vessels important process metrics include: 1) determining the region below the jet cleared or cleaned of particles as a function of time and 2) the jet nozzle velocity necessary to achieve cleaning to the vessel center by a jet positioned away from the center.  The former is termed the effective clearing/cleaning radius (ECR), while the latter is termed the critical suspension velocity, U_cs.  Although the two are intimately interrelated as outcomes of the same physics, their connection has not been probed previously. 

Prior analysis has considered separately ECR versus time and correlation of U_cs.  For example, Thomson and Edmondson (2010) developed a statistical power-law description of ECR after a jet flow has terminated.  Kuhn, et al. (2013), developed a model in which the rate of ECR growth with respect to time was proportional to the difference in the shear stresses applied by the fluid and resisted by particle forces, inversely proportional to the particle bed thickness, and proportional to an additional empirical constant that increased with particle concentration and was perhaps inversely proportional to the critical shear stress for erosion.

In this paper we explore the relationship between the ECR and U_cs.  Although one set of physics controls both the radial extent of erosion (i.e., the ECR) and the velocity needed to erode from the center of jet impingement to any given location (i.e., U_cs, typically defined to the vessel center), the relationship between these two remains unexplored quantitatively.  Here we advance the model of Kuhn, et al. (2013), as described by Pease, et al. (2017), to evaluate the relationship between the effective clearing/cleaning radius and the nozzle velocity.  We present both a closed form analytical but transcendental solution and a non-iterative approximation modeled after the Serghides approximation of Colebrook’s nonlinear equation for both ECR versus nozzle velocity and U_cs.  Comparison of the model to erosion radii measured in a 15 inch diameter vessel with a 2:1 semi-elliptical head and flume testing on a flat surface finds reasonable agreement.

Presenting Author: Judith Bamberger FEDSM2020 Chair and Senior Research Engineer, Pacific Northwest National Laboratory