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The purpose of this paper is to investigate the instability of
a high-speed liqud jet issued into a ambient compressible gas.
Firstly, we list the conservative equations of mass and
momentum with corresponding boundary conditions. The liquid is
an incompressible inviscid fluid and the gas is assumed to be a
compressible inviscid fluid. Here the system is subjected to
axisymmetrical and asymmetrical disturbance. Secondly, we
neglect the high order nonlinear terms by means of the linear
theory. A characteristic dispersion equation that accounts for
the growth of asymmetrical disturbing waves is then derived by
considering a normal mode analysis. Finally, we use numerical
method directly to find the solution, and the effects of the
stability of a compressible gas can be estimated at high-speed
liquid jet. The results show that in the subsonic region the
instability is proportional to the value of the Mach number,
Ma. Here the Mach number is the ratio of the inject speed of
liquid to the sonic speed of the compressible gas . In the
supersonic region the result is converse, i.e., the system is
most unstable on Ma=1. The results also display that the
compressibility of gas will make the liquid jet more unstable
than that in the incompressibl case when Ma<Mam, where Mam
denotes a certain Mach number in the supersonic region. The
region of disturbance of sinuous wave is larger than that of
dilational wave. We apply the Castleman's postulation to
analyze the mechanism of atomization, and the results show that
the radius of the drop is twice that at the low-speed liquid
jet for the disturbance of dilational wave. It is a closed
agreement between the results and the predictions from Rayleigh'
s mathematical analysis. Excepting the transonic region, the
fast liquid jet yields the larger radius of the drop for the
disturbance of sinuous wave.
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