Global stability of a jet in crossflow

Abstract

A linear stability analysis shows that the jet in crossflow is characterized by selfsustained global oscillations for a jet-to-crossflow velocity ratio of 3. A fully threedimensional unstable steady-state solution and its associated global eigenmodes are computed by direct numerical simulations and iterative eigenvalue routines. The steady flow, obtained by means of selective frequency damping, consists mainly of a (steady) counter-rotating vortex pair (CVP) in the far field and horseshoe-shaped vortices close to the wall. High-frequency unstable global eigenmodes associated with shear-layer instabilities on the CVP and low-frequency modes associated with shedding vortices in the wake of the jet are identified. Furthermore, different spanwise symmetries of the global modes are discussed. This work constitutes the first simulation-based global stability analysis of a fully three-dimensional base flow. IntroductionThe generic flow configuration of a jet in crossflow is ubiquitous in a great variety of industrial applications, ranging from the control of boundary-layer separation to pollutant dispersal from chimneys, from film cooling of turbine blades to the injection of fuel into combustion chambers and furnaces. The flow structures, mixing properties and general dynamics of jets in crossflow have therefore been the subject of numerous experimental and computational studies. In general four main coherent structures (see e.g. Fric & Roshko 1994;Kelso, Lim & Perry 1996;Muppidi & Mahesh 2007 and the references therein) characterize the jet in crossflow: (i) the counter-rotating vortex pair (CVP), which originates in the near field of the jet and essentially follows the jet trajectory and dominates the flow field far downstream; (ii) the shear-layer vortices which are located at the upstream side of the jet and take the form of ring-like or loop-like filaments; (iii) horseshoe vortices forming in the flat-plate boundary layer upstream of the jet exit and corresponding wall vortices downstream of the exit close to the wall; and (iv) 'wake vortices/upright vortices' which are vertically oriented shedding vortices in the wake of the jet. The accurate description of these relevant features is a prerequisite for a sound understanding of the perturbation dynamics of jets in crossflow and a first step in an attempt to manipulate it.Recent advances in computational methods have enabled global stability analyses of flows with nearly arbitrary complexity and have furnished the possibility to assess fully two-and three-dimensional base flows as to their stability and response behaviour to general three-dimensional perturbations. Specifically, the combination of new efficient † Email address for correspondence: henning@mech.kth.se

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