Temporal and spatial stability of liquid jet containing cavitation bubbles in coaxial swirling compressible flow

A dispersion equation for studying the relation between temporal and spatial stability of a liquid jet containing vapor bubbles in coaxial swirling compressible flow is presented by the use of two linear theories, temporal theory and spatial theory. The mathematical model and the corresponding solving methods to the two linear theories are verified by comparing with the data in the literature. Furthermore, the relation between temporal and spatial stability of a liquid jet containing vapor bubbles is investigated, and the effects of the gas rotational strength, the gas Mach number and the bubble volume fraction on the difference between temporal and spatial stability are then discussed. Some conclusions can be drawn from the results of this investigation, for a liquid jet with the given physical parameters, (1) there are no significant differences between temporal theory and spatial theory in respect of the dominant mode of disturbance on the jet surface, the dominant characteristic wave frequency and the smallest atomized droplet, (2) the interfacial disturbance amplitude with spatial theory is apparently larger than the disturbance amplitude with temporal theory, (3) the coaxial rotation of the surrounding gas is a factor to affect the difference between temporal and spatial theory, and there is a certain value of the non-dimensional gas rotational strength (E = 1.5) which makes the difference between the two linear theories reach the peak, (4) the effect of the gas compressibility is to increase the difference between temporal and spatial theory, and the effect of the gas compressibility is going to increase rapidly when the gas Mach number Ma2 ≥ 0.5, and (5) the effect of bubble volume fraction is to increase the difference between temporal and spatial theory, and the difference value is approximately proportional to the increasing of bubble volume fraction.