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Self-excited vortex formation in hot jets Hot subsonic jets, when their temperature exceeds a critical value, are known to break up into a street of highly regular vortex rings. This phenomenon is observed in numerical simulations, and can be explained and predicted theoretically from global instability concepts.
The spontaneous onset of self-excited formation of regular vortex streets in hot jets was first observed experimentally by Monkewitz et al. (1990). Recent direct numerical simulations performed in our group have allowed to further analyze this phenomenon.
Self-excited vortex roll-up in a globally unstable hot jet. Vorticity contours from direct numerical simulation (Lesshafft, Huerre, Sagaut & Terracol 2006). Parameters: S=0.4, R/q=10, Ma=0.1, Re=3750.
In good agreement with the original experiments, direct numerical simulations of axisymmetric jets confirm that self-excited oscillations set in as the jet-to-ambient density ratio falls below a critical value. For the entire range of parameters used in the simulations, it has further been demonstrated that this critical value is associated with a transition from convective to absolute instability of the steady flow state (see publications 1, 2 and 3). The onset of absolute instability in hot jets is due to the destabilizing effect of the baroclinic torque within the shear layer (see publication 4).
The bifurcation of the flow towards an oscillatory state can be described as the growth of a nonlinear global instability mode. On theoretical grounds, the instability of such a nonlinear global mode requires that a region of the jet displays local absolute instability. In agreement with theoretical predictions, our numerical simulations demonstrate that the frequency of vortex formation corresponds, to first order, to the absolute frequency of the steady flow state near the nozzle.
The parameter régimes for our direct numerical simulations are limited to small Mach numbers (zero and 0.1, based on speed of sound on the jet axis), moderate Reynolds numbers (max. 7500, based on jet diameter), large ranges of density ratios (between isothermal and 0.1), and values of the jet shear layer thickness between 10% and 4% of the jet radius.