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Higher Orders Instability of a Hollow Jet Endowed with Surface Tension

Radwan A. E., Ahmed N. A.

Mechanics and Mechanical Engineering

2008

Vol. 12, nr 1

69-77

The higher orders instability of a gas cylinder ambient with an incompressible inviscid liquid endowed with surface tension is analyzed. The perturbation equations up to third order are derived and solved. The surface displacements, the velocity potentials and the dispersion relations are derived for each order of axisymmetric perturbation. It is found that, up to third order, a transition from instability to stability states occurs when the perturbed wavelength equals the circumference of the gas cylinder. The stability discussions for the present model have been done and for the nonhollow jet as well. The hollow jet instability is much larger than that of the nonhollow model. It is found that the maximum temporal amplification prevailing in the hollow jet is much higher than that of the full fluid jet. These results are consistent with some data of the experimental work of Kendall [9], in the first order perturbation.

Stability of Compressible Magnetized Hollow Cylinder Pervaded by Azimuthally Field

Radwan A. E.

Mechanics and Mechanical Engineering

2007

Vol. 11, nr 1

87-96

The stability of compressible magnetized hollow cylinder (gas jet embedded into a liquid) pervaded by varying azimuthally magnetic field has been developed for all symmetric m = 0 and asymmetric m ≠ 0 pertubation modes (m transverse wavenumber). The problem is formulated well, apart from the singular solutions the different variables are determined, the stability criterion is derived and discussed. The axial field in the liquid region is stabilizing for all short and long wavelengths and that effect is independent of m values. In contrast, the azimuthal field in the gas is destabilizing or not according to restrictions and m values. The capillary force along the gas { liquid interface is destabilizing only for m = 0, for small longitudinal wavenumber and stabilizing in the rest. The compressibility has a strong stabilizing effect for all m ≥ 0 disturbance modes. Here the instability due to azimuthal field and the capillary force could be completely suppressed under restrictions and stability sets in.