Dimensional analysis of droplet size and ligament length during high-speed rotary bell atomization
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Dimensional analysis of droplet size and ligament length during high-speed rotary bell atomization Lutz Go¨deke , Walter Oswald, Norbert Willenbacher, Peter Ehrhard
Ó The Author(s) 2020 Abstract Modern spray-coating processes are based on high-volume, low-pressure, airless atomization or high-speed rotary bell atomization, often assisted by electrostatic charging to increase the transfer efficiency. The process from the liquid film flow beneath the bell, through ligament formation and consecutive disintegration to droplet deposition, has been constantly explored during the evolution of automotive spray coating. This work proposes a set of dimensionless groups that fully describe the process from film flow to ligament disintegration, including shear and elongational flow effects during atomization of particle laden, shear thinning, viscoelastic fluids. Keywords Dimensional analysis, High-speed rotary bell atomization, Elongational flow, Ligament disintegration, Droplet size, Acrylic thickener, Plate-like particles
Introduction High-speed rotary bell atomization is the state-of-theart technology for paint application in the automotive industry. In recent years, research on this topic has been published in experimental, theoretical, and numerical form, dealing with both the formation of droplets and the measurement methods used. FundaL. Go¨deke (&), P. Ehrhard Fluid Mechanics, Biochemical and Chemical Engineering, TU Dortmund, Emil–Figge–Strasse 68, 44227 Dortmund, Germany e-mail: [email protected] W. Oswald, N. Willenbacher Applied Mechanics, Institute of Mechanical Process Engineering and Mechanics, KIT, Gotthard–Franz–Straße 3, 76131 Karlsruhe, Germany
mental work has been done by Hinze and Milborn.1 Their publication deals with the atomization of an idealized film flow and ligament disintegration of Newtonian liquids for nonserrated bells. The process is well described starting with an analytical solution for the film flow and leading to a thorough analysis of the ligament formation with experimental data validation. Domnick et al.2 used measurement data as a basis for numerical models to predict the spraying process. Mescher3 and Kamplade et al.4 carried out experiments on ligament disintegration at transverse flow and subsequent numerical investigations to optimize the gas flow with respect to the resulting droplet size distribution. Kalmbach et al.5 used a comparable theoretical approach and validated the asymptotic solutions of linear stability analysis with experiments. A detailed analytical investigation of the resulting drop size from an emerging jet of a rivulet inside a bore of a spinning cup was carried out by Kuhnhenn et al.6 The obtained results for water droplets, under consideration of the appearing strain rate e_ , provide a good prediction for the experimental data by using a function of the capillary breakup time after Rayleigh7 and the strain rate e_ . Furthermore, Tratnig et al.8 investigated the pressure-swirl atomization of various particle-laden opaque Carreau–Yasuda liquids by m
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