An optimisation method for the cold-spray process: On the nozzle geometry, L. Alonso, M. A. Garrido, P. Poza, Materials & Design, 214, 110387, 2022, Online version,


Currently, the cold-spray process, or simply cold spray, is an extensively used technique in coating applications. The low temperature of the deposition process is the distinctive feature that makes it suitable for many additive manufacturing activities such as repair and restoration of damaged components. The reliability of the coatings is strongly dependent on the velocity of the powder during its impact on the target surface. Spraying conditions such as the pressure and temperature of the carrier gas and the geometry of the nozzle control the acceleration of the powder particles. Consequently, there is an increasing interest in the optimisation of nozzle geometry so as to maximise the acceleration of the particles through the nozzle path that they follow. In contrast with various extant approaches to achieve this aim (finite element modelling, experimental approach, and analytical methods), an alternative model based on the one-dimensional isentropic theory that accounts for the dynamics of the dilute two-phase flow was developed in this study. First, an analysis of the common hypotheses used to obtain the equation of motion of the particle was carried out. Subsequently, with the new insights revealed from the previous analysis, a new theoretical model for the optimisation of the divergent part of the nozzle was performed considering a geometric angle restriction. This model is based on the numerical integration of the equation of motion of the particle, ensuring the maximisation of the particle drag force by means of the Lagrange multiplier method. Once the analytical model is formulated, a set of curves describing the optimal geometric parameters for different conditions is obtained. Moreover, some optimal geometries are presented demonstrating the low influence of the angle restriction. Additionally, the inversely proportional relationship between stagnation pressure and temperature is revealed.