Consolidation of a 1D isentropic analytical model for predicting particle velocity in cold spray

• Analytical model was consolidated through extensive experimental measurements. • Model captures trends in velocity with pressure, temperature, and particle size. • Numerical-experimental deviations of 5.37% and 5.26% for Al and Cu, respectively. • The model reproduced the velocity trends associated with particle size within ± 3.6% A robust validation of the one-dimensional isentropic model for predicting particle velocities in the cold spray process was carried out using a substantially larger and diverse experimental dataset to enable its safe application for data generation. We conducted high-speed laser imaging measurements over three stagnation pressures and four gas temperatures using aluminum and copper powders. To further assess the model’s accuracy, three Al particle-size distributions were also evaluated. Velocity data from the plume centerline matched model assumptions. The model reproduced key trends—velocity increases with temperature and pressure, and particle-size effects—with mean absolute deviations of 5.37% for Al and 5.26% for Cu. Although the overall trend was consistent, deviations up to 12–17% were observed in just two Al cases. In the case of Cu, all predictions presented deviations lower than 7% due to its higher sphericity, matching better with the model assumptions. While coarse-particle predictions were highly accurate, fine fractions were slightly overestimated, likely due to turbulence and nozzle shock waves not captured in the model. These results confirm that, with its extended validation, the model is a reliable, fast, and cost-effective alternative to Computational Fluid Dynamics simulations (CFD) for early-stage cold spray design and data generation.