ASYMPTOTIC APPROXIMATION OF THE WIENER-HOPF TECHNIQUE AS APPLIED TO JET ATOMIZATION

An approximate Wiener-Hopf (WH) technique is developed for solving pro blems involving fine spatial structure. As an example of the applicati on of this method we investigate the atomisation of a liquid jet. The jet exits from a nozzle into an ambient fluid. Short interfacial waves become unstable and break into small particles. This problem is treat ed as a potential flow under the influence of capillary effects at the interface and the pressure fluctuation at the nozzle wall. Two simult aneous WH equations are obtained. To solve them, the singular parts in each equation are separated from the regular ones, that leads to a li near system of algebraic equations for the residues. The response-wave amplitudes are evaluated numerically and the instability diagram is p resented. It is found that resonance occurs at double roots of the dis persion relation. For a given azimuthal number m, the double roots for m two curves parametrised by the Weber number beta. They merge at a ce rtain critical point, where an even stronger resonance occurs. This fi nally selects the dominant modes. By gauging one parameter, namely the velocity ratio U, the theoretical prediction agrees quite well with e xperimental results of the jet atomisation.