SPATIAL INSTABILITY OF A SWIRLING JET - THEORY AND EXPERIMENT

To develop a foundation for active shear-layer control with swirl, spatial instability of a rotating jet is investigated both experimentally and theoretically. The hydrodynamic stability analysis is applied to an inviscid incompressible top-hat jet, with a swirl distribution of solid-body rotation and free vortex in and outside the vortex core, respectively. Both plane and helical instability modes are examined; i.e., m = 0, +/- 1, +/- 2, +/- 3. It is found that the top-hat jet with Rankine vortex swirl distribution is unstable in all of the modes studied. The higher the positive helicity (i.e., many-lobed disturbances spinning in the same direction as the rotating jet), the less spatially unstable the jet behavior; the higher the negative helicity (i.e., many-lobed disturbances of opposite spin), the more spatially unstable this behavior becomes. A comparison is made between theoretical results and limited experimental data of a low-intensity swirling jet (S = 0.12) for plane wave excitation (m = 0). The trend of the initial growth of the instability waves in the near field is qualitatively captured by the inviscid linear instability theory when excitation amplitude is sufficiently small, e.g., less than 1% of the mean axial velocity. At higher forcing amplitudes, the nonlinear interactions will render the linear theory inadequate.