Journal of Fluid Mechanics

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Vorticity structure and evolution in a transverse jet

YOUSSEF M. MARZOUKa1 p1 and AHMED F. GHONIEMa1

a1 Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

Abstract

Transverse jets arise in many applications, including propulsion, effluent dispersion, oil field flows, and V/STOL aerodynamics. This study seeks a fundamental, mechanistic understanding of the structure and evolution of vorticity in the transverse jet. We develop a high-resolution three-dimensional vortex simulation of the transverse jet at large Reynolds number and consider jet-to-crossflow velocity ratios r ranging from 5 to 10. A new formulation of vorticity-flux boundary conditions accounts for the interaction of channel wall vorticity with the jet flow immediately around the orifice. We demonstrate that the nascent jet shear layer contains not only azimuthal vorticity generated in the jet pipe, but wall-normal and azimuthal perturbations resulting from the jet–crossflow interaction. This formulation also yields analytical expressions for vortex lines in the near field as a function of r.

Transformation of the cylindrical shear layer emanating from the orifice begins with axial elongation of its lee side to form sections of counter-rotating vorticity aligned with the jet trajectory. Periodic roll-up of the shear layer accompanies this deformation, creating complementary vortex arcs on the lee and windward sides of the jet. Counter-rotating vorticity then drives lee-side roll-ups in the windward direction, along the normal to the jet trajectory. Azimuthal vortex arcs of alternating sign thus approach each other on the windward boundary of the jet. Accordingly, initially planar material rings on the shear layer fold completely and assume an interlocking structure that persists for several diameters above the jet exit. Though the near field of the jet is dominated by deformation and periodic roll-up of the shear layer, the resulting counter-rotating vorticity is a pronounced feature of the mean field; in turn, the mean counter-rotation exerts a substantial influence on the deformation of the shear layer. Following the pronounced bending of the trajectory into the crossflow, we observe a sudden breakdown of near-field vortical structures into a dense distribution of smaller scales. Spatial filtering of this region reveals the persistence of counter-rotating streamwise vorticity initiated in the near field.

(Received April 29 2005)

(Revised September 18 2006)

Correspondence:

p1 Present address: Sandia National Laboratories, Livermore, CA 94551, USA.

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