Optimization of Nozzle Layout Parameters Based on a Corrected Free Spray Flow-Field Model for Textile Applications

Spray pretreatment is a key step in short-process textile cleaning, and spray deposition uniformity on the target plane directly determines the quality consistency of subsequent dyeing and finishing, with nozzle layout exerting a direct influence on this uniformity. However, the existing non-submerged free jet model suffers from physical distortions in planar flow projection, namely multi-valued flow at the origin and non-convergent far-field flow. To address this, the proportionality coefficient of the Gaussian distribution is redefined to establish a corrected planar flow distribution function with a unique origin flow and natural far-field convergence. Treating continuous fabric motion as equivalent nozzle translation, a cumulative flow superposition model for moving planes is constructed, and a collaborative optimization model for nozzle spacing, mounting height, and attitude angle is established using the Particle Swarm Optimization (PSO) algorithm, with adjacent nozzle pairs as the periodic unit. Experimental calibration shows that relative errors between theoretical and measured flow rates remain within 10%. Nozzle rotation about the local z-axis is identified as the most effective attitude variable for uniformity tuning; a 0.1 m increase in nozzle spacing reduces peak overlap flow by about 30% and overlap width by about 40%. For a dual-nozzle system on a 0.66 m-wide target plane, numerical simulation results show that the calculated cumulative flow variance decreases from 5.9193 to 1.1588, corresponding to an 80.4% reduction in the numerical uniformity index. This numerical optimization framework provides a quantitative reference for nozzle layout design in textile spraying processes.