Modeling of Spray-Formed Materials: Geometrical Considerations

suming and not economical. Hence, computer simulation is SPRAY forming is a manufacturing technique in which a useful approach to investigatingthe formationand developpartially solidified metal droplets are dispersed upon a subment of round billets. Several mathematical models have strate to produce an almost fully dense material in tonnage been developedto calculate the growth of round billets. quantities.Availablestudies show that the thermal and solidiThese models aim at the selection of optimal processing fication conditions that are present during spray forming parameters, the design of spray-forming chambers and promote several desirable characteristics, such as microplants, and the investigation of the thermal transfer. structural refinement, extended solubility, and, in In related studies, Frigaard et al. formulated a mathematisome cases, the appearance of nonequilibriumphases. For cal model to investigate the growth dynamics of spraythe production of near-net-shape deposits, the droplet size formed billets. In their model, a partial differential and spatial distribution are of interest because the deposit equation describing the average motion of a billet’s surface shape resembles the spatial distributionof dropletmass arrivis formulated. Numerical solution of the partial differential ing at the deposition surface. The droplet size and spatial equation is then implemented to study both transient billet distribution are related to the type of atomizer used and to growth and steady-state crown shapes of spray-formed aluoperating variables. In the atomization of metals, circular minum billets, and the atomizer scanner angle function for gas jet nozzles represent a type of atomizer that is commonly a perfect shape billet is computed. used. Therefore, there exists a limitation in that the droplet Mathur et al., Muhamad et al., and Elgobashi et mass distribution exhibits a Gaussian distribution centered al. [25] have independentlyestablished theirmodels to predict about the spray axis. To that effect, specific experimental the buildup of round billets. They divided the substrate surarrangementshave been taken to approach a variety of geomface into many grid points. Using a scanning spray mode, etries, including rings, billets, tubes, and cylinders, while they obtain the shape of billets by accumulating the height using circular atomizers. growth in all grid points. Considering the fact that, in pracExperimental and simulation efforts have been conducted tice, sticking efficiency is less than 100 pct, Mathur et al.[24] on the geometry of plates[7–11] and tubes.[12] However, threeincorporate sticking efficiency into shape calculation, in dimensional growth during buildup of round billets leads to order for shape modeling to reflect the real situation. complexities in the required control protocols, as a result of More recently, Seok et al.[15,16] formulated a three-dimentransient phenomena that develop under certain conditions. sional model to predict the motion dynamics of a billet’s One example of such transient phenomena is described in surface. In their formulation, the surface is obtained by the literature as a shadowing effect, which leads to the determining the position of all points at any instant. Moreformation of columnar porosity. Exploring the optimal over, Seok et al. use computer graphics to illustrate the