EFFECTS OF COMPRESSIBILITY ON THE INSTABILITY OF LIQUID SHEETS

The effect of compressibility of fluids on the instability of a liquid sheet issued from a nozzle into an ambient gas is investigated by use of linear stability analysis. It is found that increasing the gas Mac h number from subsonic to transonic causes the maximum growth rate, do minant wave number, and cut-off wave number of disturbances to increas e. Liquid compressibility has a minimal effect on instability. At a co nstant wave number, the growth rate of disturbances increases as the g as Mach number tends to 1 and then begins to decline with further incr ease in the gas Mach number. Hence, liquid sheet breakup is due to sur face disintegration not gross fracturing in agreement with experimenta l observations. At small values of wave number, antisymmetrical distur bances grow faster than symmetrical ones while the growth rate of both types of disturbances approach each other at large wave numbers. At s mall Weber number, antisymmetrical disturbances exhibit a higher maxim um growth rate and a lower dominant wave number than symmetrical distu rbances. However, the maximum growth rate and dominant wave number of the two types of disturbances are almost identical when Weber number b ecomes large. An increase in the gas-to-liquid density ratio enhances the instability. Surface tension always opposes the development of ins tability.