Vortex pairing in an axisymmetric jet using two-frequency acoustic forcing at low to moderate strouhal numbers

Hot-wire measurement and multi-smoke wire flow visualization method are employed to study vortex pairing in the jet column mode under two-frequency forcing with controlled initial phase differences. For the range of 0.3\St D \0.6, vortex pairing can be easily controlled by means of the fundamental and its subharmonic forcing with varying initial phase differences. As stable vortex pairing dominates, the variation of the subharmonic component with the initial phase difference changes from a sine shape to a cusp-like shape. The harmonics of the subharmonic also show similar trends. The detuning induces the amplitude and phase modulations of the u-signal in the time trace and the sideband growth in the spectra. The u-signal reflects the subharmonic variation with the initial phase difference in its envelope. For 0.6\St D \0.9, non-pairing advection of vortices due to improper phase difference is sometimes observed under single-frequency forcing. In this case, vortex pairing can be made to occur by the addition of a subharmonic with very small amplitude. As the initial level of this subharmonic is increased, the onset position of vortex pairing moves upstream. In this range, the initial phase difference is not an effective parameter in controlling vortex pairing. List of symbols a f fundamental amplitude at jet exit (u@ f /U e D x/0 ) a s subharmonic amplitude at jet exit (u@ s /U e D x/0 ) D jet diameter f fundamental frequency r radial coordinate r 0.1 radial position where U/U c \0.1 St D Strouhal number based on jet diameter ( fD/U e ) he Strouhal number based on initial momentum thickness ( fh e /U e ) U streamwise mean velocity u streamwise velocity fluctuation v radial velocity fluctuation x streamwise coordinate h momentum thickness (:r0.1 0 cc dr) d phase difference between fundamental and subharmonic / de phase difference at jet exit (/ d D x/0 ) Superscripts * complex conjugate @ root mean square Subscripts c jet center e jet exit f fundamental 2f fourth harmonic of subharmonic 3f/2 third harmonic of subharmonic r incoherent turbulent fluctuation s subharmonic t total fluctuation