Predicting Abrasive Waterjet Penetration Through Depth-Dependent Velocity Decay: A Variable Wall-Drag Dimensionless Model

Abstract

Predicting how deep an abrasive waterjet (AWJ) penetrates is limited by the velocity the jet loses as it advances down the kerf, which earlier dimensional models handle with one constant wall-drag coefficient [8]. This study derives a dimensionless penetration model with a depth-dependent wall-drag law, governed by a drag number (Λ₀) and a drag-growth index (κ). Buckingham's π theorem reduces eight process variables to five dimensionless groups [28], and the depth follows from a closed-form expression for constant drag or a one-dimensional root problem for variable drag. A 16-run Taguchi L16 programme on EN 8 steel (pressure 275–380 MPa, abrasive flow 6.8–13.1 g/s, traverse speed 39.6–99.6 mm/min, stand-off 2–5 mm) supplied the data. Measured depths ranged from 2.45 to 5.41 mm. Traverse speed explained 55% of the variance and pressure 19%, while abrasive flow and stand-off each explained under 10%. The power-law model predicted left-out runs with a leave-one-out mean absolute percentage error (MAPE) of 13.3% and an RMSE of 0.64 mm, against 31.3% for the earlier dimensional model [9] and 13.1–13.7% for linear-regression and random-forest baselines. The zero-, constant- and variable-drag models fitted identically (nested F-tests, p > 0.8), so wall drag was not identifiable: the depths spanned only 3 to 7 nozzle diameters, where the drag correction is small. The fitted abrasive-flow exponent was close to zero (−0.07, 95% interval −0.37 to 0.24), which indicates abrasive saturation over the tested range. The study states the depth range and replication needed to detect wall drag in AWJ penetration data.