Quantitative modelling of the erosive removal of a thin soil deposit by impinging liquid jets

Abstract

Kaye et al. (1995, Wear, 186-187, 413-420) conducted an experimental investigation of the cleaning of thin soil layers by water jets generated from stationary nozzles of diameter 0.25-2 35 mm and velocities ranging from 6-40 m s -1 . The soil layers were prepared by drying a commercial cleaning suspension on polymethylmethacrylate plates. Several of their data sets have been re-analysed and are shown to fit the 'strong soil' model for cleaning by peeling reported by Bhagat et al. (2017, Food Bioproduct Proc., 102, 31-54). The model is demonstrated to be able to explain the trends in cleaning efficiency observed by Kaye et al. 40 quantitatively, including the transition in efficiency observed at longer times. Kaye et al. also investigated the case of cleaning by a moving nozzle for one set of jet conditions, and reported an increase in cleared area with nozzle velocity. This behaviour is not predicted for the 'strong soil' and the model was modified to incorporate a contribution from the milling action of the jet in its impingent zone. This 'very strong soil' result gave good agreement with the data for 45 the area cleared and the shape of the cleared region. NomenclatureRoman 50 a Radius of cleaned area, [m] ai Radius when cleaning front is first seen, [m] ai* Dimensionless radius when cleaning front is first seen, [-] ax Distance to cleaning front on jet path, [m] A Area of the cleared region, [m 2 ] 55 c1 Lumped parameters, 1 = 10 o 2 3 2 , [m -3 ] c2 Parameter, Eq. [8], [-] c3 Parameter, Eq. [9], [m -3 ] dN Nozzle diameter, [m] E Efficiency factor, [m -1 ] 60 EU Prefactor efficiency, [m -1 ] k' Lumped cleaning rate constant, [m s kg -1 ] L Distance from nozzle to target, [m] ṁ Mass flow rate, [kg s -1 ] M Momentum flow per unit width, [kg s -2 ] 65 p Radial distance to cleaning front, [m] p* Dimensionless radial distance to cleaning front, [-] Q Flow rate leaving nozzle, [m 3 s -1 ] r Radial co-ordinate, [m] rb Boundary layer radius, [m] 70 ro Jet radius, o = 1 2 N [m] Re Reynolds number, defined Re = UodN/µ t Time, [s] ti Induction time, [s] Uo Jet velocity, [m s -1 ] 75 V Jet's traversal velocity, [m s -1 ] WeG Weber number gaseous, defined We = GUo 2 dN/γ WeL Weber number liquid, defined We = LUo 2 dN/γ 80 4 Greek  Angle to direction of nozzle motion, [-] γ Surface tension, [N m -1 ]    Density, [kg m -3 ] µ  Dynamic viscosity, [Pa s] 85 σ Cleaning rate parameter, [m 2 s -1 ] Acronyms PMMA Polymethylmethacrylate RFZ Radial flow zone 90

Cleaning insoluble viscoplastic soil layers using static and moving coherent impinging water jets

“…Bhagat et al (2017) showed that the evolution in the hydrodynamics results in a transition in cleaning behaviour from a  t 1/2 close to the point of impingement to the point where the boundary layer reaches the free surface, b (which they labelled 'strong soil' behaviour), to a  t 1/5 at longer distances (which they labelled 'weak soil'). Oevermann et al (2019) demonstrated that these models gave a very good description of the experimental results of Kaye et al (1995) for adhesive removal of dried suspension layers by water jets featuring velocities up to 40 m s -1 . They also demonstrated that the model described removal by traversing jets.…”

“…ax > ro. Oevermann et al (2019) discussed the case where x < o and the peeling front only grew in the wake of the nozzle.…”

“…Non-Netwonian liquids exhibit more complex behaviour, resulting from the coupling of stresses between the cleaning liquid and the soil: Fuller and co-workers have investigated the cleaning behaviour of shear-thinning (Walker et al, 2012) and viscoelastic (Tsu et al, 2011) layers, respectively, subject to impinging jets. For immobile soils Bhagat et al differentiated between adhesive failure, where cleaning involved breaking of the soil/substrate bonds (peeling, reported for brittle dried suspension layers by Oevermann et al 2019) and cohesive failure, where shear stress wears the soil layer away (Murcek et al, 2019) Exposure of the soil layer to cleaning solution (e.g. soaking, Chee et al 2019) can convert it from an immobile to a mobile form, the dynamics of which are important factors for cleaning agent selection.…”

Modelling the cleaning of viscoplastic layers by impinging coherent turbulent water jets

“…More of the kinetic energy is employed in cleaning at small values of , i.e., when is high. This indicates that the most efficient way to clean a viscoplastic soil with impinging water jets is by using traversing nozzles, when the liquid film is continuously exposed to fresh soil [2,3,17,38]. The discontinuity in the predicted efficiency loci in Figure 17 arises from the jump in at [8] (see Figure 5-a).…”

“…fluid, soil layers. The cleaning of immobile (solid) layers has been studied by Oevermann et al [3] and Wilson et al [4]: both these studies involved peeling mechanisms, where the force imposed by the liquid film caused adhesive breakdown at the interface between the soil and the substrate.…”