Fluid dynamics of slender,thin, annular liquid jets

Perturbation methods are used to obtain the one-dimensional, asymptotic equations that govern the fluid dynamics of slender, thin, inviscid, incompressible, axisymmetric, irrotational, annular liquid jets from the Euler equations. It is shown that, depending on the magnitude of the Weber number, two flow regimes are possible: an inertia-dominated one corresponding to large Weber numbers, and a capillary regime for Weber numbers of the order of unity. The steady equations governing these two regimes have analytical solutions for the liquid's axial velocity component and require a numerical integration to determine the jet's mean radius for inertia-dominated jets. The one-dimensional equations derived in this paper are shown to be particular cases of a hydraulic model for annular liquid jets, and this model is used to determine the effects of gravity modulation on the unsteady fluid dynamics of annular liquid jets in the absence of mass injection into the volume enclosed by the jet and mass absorption. It is shown that both the convergence length and the pressure coefficient are periodic functions of time which have the same period as that of the gravity modulation, but undergo large variations as the amplitude, frequency and width of gravitational pulses is varied.