Multi-objective optimization and performance improvement of CD nozzle design parameters for cold spray coating process using RSM, ANN and GA

Abstract

This study presents the multi-objective optimization of the convergent-divergent (CD) nozzle for the cold spray (CS) process and investigates the impact of five key nozzle design parameters. A 2D axisymmetric baseline nozzle was optimized through face central composite design (FCCD), computational fluid dynamics (CFD) simulations, response surface methodology (RSM), artificial neural networks (ANN), and genetic algorithms (GA). The nozzle performance in the CS process advances the manufacturing technologies by significantly optimizing the four response variables. Comparative analysis shows that RSM models (R² = 0.9893) were more accurate on average than ANN models (R² = 0.9848), although ANN provided a deeper understanding of complex interactions with an overall correlation coefficient of 0.99191. Sensitivity analysis suggested that increasing convergent length (Lc) increases particle velocity (PV) before it stabilizes while particle temperature (PT) decreases due to cooling effects. Divergent length (Ld) increases PV to an optimal range, but reduces PT, indicating energy loss. Smaller injector inner diameter (Did) enhances PV but reduces PT. Injector length (Li) increases PV to a certain limit, beyond which benefits stabilizes, and also increases surface pressure (SP). Expanding the exit diameter (De) increases PV, drops PT and heat flux (HF), and reduces SP, indicating decreased flow resistance. Optimization with RSM coupled with numerical simulation (RSM-DF) improved PV, PT, HF, and SP by 9.1 %, 4.4 %, 17.9 %, and 27.6 % respectively. Further optimization with a 5–6–4 ANN and GA (NSGA-II) improved PV by 5 %, PT by 5.4 %, HF by 15.7 %, and reduced SP by 20.9 %. Integrating CFD, RSM, ANN, and GA provides an effective approach for optimizing CD nozzle parameters.