The temporal analysis of symmetric (dilatational) and asymmetric (sinusoidal) perturbations at the interface of a water sheet in a co-flowing air stream focuses on low gas Weber number region (Weg < 0.4), namely Rayleigh breakup zone. The motive for this investigation is to acquire a better insight of breakup phenomena involved, rather than technical relevance, by utilizing Kelvin-Helmholtz instability. Accordingly, perturbations are introduced on the basic flow whose stability is to be examined by the method of normal (Fourier) modes. The temporal growth-rate of perturbations are traced to extract the wavenumber associated with maximum growth-rate. Thus, the critical wave-length, in conjunction with the phase velocity of the disturbance will facilitate to obtain the corresponding breakup frequency of the liquid sheet. The analytical findings on liquid sheet breakup frequency with increasing Weber number ratio exhibit the dominance of symmetric wave over asymmetric wave. It also shows independent evolution of breakup frequency with respect to Weber number ratio for the respective perturbation modes, which appears to be a pointed profile. That is, the frequency contour for dilatational mode dips, whereas it rises for the sinusoidal mode and at the Weber number ratio of 0.518 the crossover occur. The theoretical results were substantiated by high speed flow visualization studies that discerns the coexistence of low-frequency (primary) and high-frequency (intermediate) breakup events. Furthermore, the empirical average frequency data tracks reasonably well with the dilatational instability.
Dr. Sivadas V., Karthick S., and Balaji K., “Symmetric and Asymmetric Disturbances in the Rayleigh Zone of an Air-Assisted Liquid Sheet: Theoretical and Experimental Analysis”, Journal of Fluids Engineering, Transactions of the ASME, vol. 142, no. 7, pp. 071302 (1-12), 2020.