Prediction of vortex height from mechanical mixing in metal matrix nanocomposite processing by means of dimensional analysis and scaling

Mechanical mixing can be used for initial dispersion and distribution of nanoparticle agglomerates in metal matrix nanocomposite (MMNC) fabrication. As vortex height increases, flow is enhanced as well as the risk of oxidate melt contamination. The goal of this study was to examine and predict vortex height using dimensional analysis while varying fluid and the angular speed of a pitched square-blade impeller. An equation proposed by Markopoulos et al. was verified for the present experimental conditions. The relevant dimensionless numbers were the Reynolds (Re), Froude (Fr) and Galilei (Ga) numbers. A modified Fr was defined (Fr*) including the shaft and blade angles of the impeller. Experiments allowed calculation of the dimensionless numbers. Two fluids, water and 50 vol% aqueous glycerine, were used. Angular clockwise speed varied from 200 to 900 rpm in 100 rpm increments. Vortex height was measured in lateral view digital images. Correlations of the dimensionless numbers yielded, first, a linear relationship of the product of dimensionless vortex height (H) and specific gravity (ρ*) with respect to Fr*. A polynomial relationship was found between H and ReFr* for each fluid. The polynomial coefficients, in turn, follow a power law behavior with respect to Ga. This allows a prediction of vortex height in other Newtonian fluids that satisfy the single-phase isothermal flow condition. Perhaps, molten aluminum used in MMNC fabrication, can be analyzed based on a simple, room temperature, low cost transparent fluid system. For the experimental conditions in this study, the equation proposed by Markopoulos et al. was valid. The predicting methodology was verified with experimental results using 25 vol% aqueous glycerine, resulting in an absolute percent error of 5.29%, comparable and lower than an error of 9.12% obtained by predicting vortex height with Markopoulos’ equation.