ATOMIZATION CHARACTERISTICS OF HYDRAULIC NOZZLES USING FRACTAL GEOMETRY

Fractal scalings of the V(x X) . Xd type have been used in this work for cumulative volume (V) distribution applied through spray nozzles in size x droplets, smaller than the characteristic size X. From exponent d, the fractal dimension (Df), which measures the degree of irregularity of the medium, has been deduced. This property consists of the repetition of the irregularity itself over a certain range of scales, and it is called self-similarity. The objects or sets that have this property are named fractals. Based on the considerations below, and supposing that the droplet set from a spray nozzle is self-similar, an algorithm has been developed to relate a nozzle type with a Df value. The data input for this algorithm were the droplet size spectra factors corresponding to 10%, 50%, and 90% (Dv0.1, Dv0.5, and Dv0.9, respectively) as measured at different operating pressures for different nozzle types. Multivariate, multilinear, and polynomial models were conducted to predict droplet size spectra factors based on Df and operating pressure (multilinear model) and based on Df, operating pressure, and orifice diameter (polynomial model). Df values showed dependence on nozzle geometry and independence of operating pressure. Significant coefficients of determination (r2) at the 95% confidence level were found for the fitted models. An exception occurred in one case, associated with Dv0.9. Thus, r2 values were higher for the polynomial models than for the multilinear models, except for a case associated with Dv0.1. These models could be useful to compare the behavior of different nozzles under the same operating conditions, or the same nozzle under different operating conditions. Because Df is related to nozzle geometry, the inclusion of Df in models to predict droplet size spectra factors will allow us to detect the geometric differences between nozzles, which are otherwise difficult to measure. Similar procedure could be carried out for other nozzles types.

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