A semi-empirical correlation for the swirl number of swirling jets generated by a radial-type swirler

Abstract

This work presents a semi-empirical correlation for the swirl number of a radial-type swirl generator under different conditions of both the Reynolds number and the angle of the swirler channels used to generate the flow tangential velocities. Quantitative velocity measurements are carried out via stereoscopic particle image velocimetry (PIV) to characterize the three-component velocity field of the swirling jets in the proximity of the nozzle exit for four values of the Reynolds number (i.e., 12,800, 20,800, 31,100 and 41,500) and nine swirl angles ranging from 0° to 20°. Such data is used to estimate the values of the swirl number from different theoretical formulations. Semi-empirical formulas are derived based on the mass and angular momentum conservation laws and analytical approximations of the quantities involved in the definition of the swirl number. These formulas elucidate the dependence of the swirl number on the geometrical parameters of the radial-type swirl generator, in particular on the swirl angle, and include coefficients estimated empirically from the velocimetry data, which essentially depend on the exit velocity distribution. The derived correlations may be useful for design and analysis purposes.