Chapter 7. Parabolic round jet in a shear cross flow Multimedia files Nos. 7.1 – 7.5 The results of researches presented in presentation are published in the following main articles: 1.Grek G.R., Kozlov V.V., Kozlov G.V., Litvinenko Yu.A. Instability modeling of a laminar round jet with parabolic mean velocity profile at the nozzle exit // Vestn. NSU. Seria: Physics Vol. 4. Vip. 1, pp , in Russian 2. Kozlov V.V., Grek G.R., Kozlov G.V., Litvinenko Yu.A. Physical aspects of subsonic jet flows evolution // The collection of proceedings «Successes of mechanics of continuum» to the 70-anniversary of academician V.A. Levin, Dalnauka, Vladivostok, pp , in Russian

Round jet with parabolic mean velocity profile at the nozzle exit. Jet instability to the weak cross flow.

Mean velocity profile at the nozzle exit 1 - Mean velocity profile at the nozzle exit without overlay 2 - Mean velocity profile at the nozzle exit with overlay Jet velocity (U 0 ) – 4 m/s, Cross flow velocity (U jet ) – 0.5 m/s.

Smoke visualization patterns of the jet cross sections Double click here Video file No. 7.1

Scheme of the jet folding into the counter rotating stationary vortex pair under action of a cross flow (Scheme is taken from the work by Lim et al., 2001 )

High – frequency secondary instability of the round jet tangential ejections caused by the cross flow Double click here Video file No. 7.2

CONCLUSIONS  It is found, that round jet instability to cross flow result in deformation of a jet as tangential ejections of gas from its periphery in ambient space.  It is revealed folding of ejections into the counter rotating vortex pair.  It is shown, that tangential ejections are subjected to high – frequency secondary instability.

Parabolic round jet in a shear cross flow (flat plate boundary layer) Direct numerical simulation (DNS) by S. Bagheri et al. Global stability of jet in cross flow // J Fluid Mech., vol. 624, pp

Experimental set - up Boundary layer mean velocity profile, x = 250 mm Round jet mean velocity profile at the nozzle exit

Smoke visualization of the jet in a flat plate boundary layer at K = U jet /U 0  3 (acoustic field frequency from 30 up to 180 Hz) Streamwise jet section Double click here Cross flow direction Video file No. 7.3

Smoke visualization of the jet in a flat plate boundary layer at K = U jet /U 0  3 (acoustic field frequency F = 180 Hz) Jet cross section at different distances from the flat plate Double click here Cross flow direction Video file No. 7.4

Smoke visualization of the jet in a flat plate boundary layer at K = U jet /U 0  3 (acoustic field frequency F = Hz) Jet cross section at different distances from the flat plate Double click here Cross flow direction Video file No. 7.5

KEY POINTS:  Characteristics of development of a round jet with a top hat and parabolic mean velocity profile at the nozzle exit essentially differ.  Instability of a round jet with a parabolic mean velocity profile leads to its deformation in the shape of the tangential ejections of gas from the jet periphery by means of cross flow into the ambient space, folding of ejections into the counter rotating vortex pair and thereof to reduction of the jet core size.  The round jet with a parabolic mean velocity profile in a cross shear flow is subjected by folding into the counter rotating stationary vortex pair.  The most unstable global modes with high frequencies represent wave packets on the counter rotating stationary vortex pair. These modes are connected with W- like vortex structures on a flow shear layer.  Global modes at low frequencies also have considerable amplitude in a jet wake closer to the wall.  Growth in jet penetration and reduction in the near-field entrainment of cross-flow fluid by a parabolic jet in cross flow is found.  The jet/crossflow interfaces of the parabolic jet in cross flow might have undergone a ‘‘stretching and thinning’’ process caused by the cross-flow.