The structure of the absolutely unstable regions in the near field of low-density jets

Abstract

Link to this article: http://journals.cambridge.org/abstract_S0022112012004417How to cite this article: Wilfried Coenen and Alejandro Sevilla The structure of the absolutely unstable regions in the near field of lowdensity jets.The viscous spatiotemporal stability properties of low-density laminar round jets emerging from circular nozzles or tubes are investigated numerically providing, for the first time, a separate treatment of the two particular cases typically studied in experiments: a hot gas jet discharging into a quiescent cold ambient of the same species, and an isothermal jet consisting of a mixture of two gases with different molecular weight, discharging into a stagnant ambient of the heavier species. To that end, use is made of a realistic representation for the base velocity and density profiles based on boundary-layer theory, with account taken of the effect of variable transport properties. Our results show significant quantitative differences with respect to previous parametric studies, and reveal that hot jets are generically more unstable than light jets, in the sense that they have larger associated critical density ratios for values of the Reynolds number and momentum thickness typically used in experiments. In addition, for several values of the jet-to-ambient density ratio, S, the downstream evolution of the local stability properties of the jet is computed as a function of the two main control parameters governing the jet, namely the Reynolds number, Re, and the momentum thickness of the initial velocity profile, θ 0 /D. It is shown that, for a given value of S, the (Re, θ 0 /D) parameter plane can be divided in three regions. In the first region, defined by low values of Re or very thick shear layers, the flow is locally convectively unstable everywhere. In the second region, with moderately large values of Re and thin shear layers, the jet exhibits a localized pocket of absolute instability, away from boundaries. Finally, in the third region, that prevails in most of the (Re, θ 0 /D) parameter plane, the absolutely unstable domain is bounded by the jet outlet. All the experiments available in the literature are shown to lie in the latter region, and the global transition observed in experiments is demonstrated to take place when the absolutely unstable domain becomes sufficiently large. The marginal frequency of the resulting global self-excited oscillations is shown to be fairly well described by the absolute frequency evaluated at the jet outlet, in agreement with the numerical results obtained by Lesshafft et al. (J.

Global instability of low-density jets

“…Couairon & Chomaz (1999) and Lesshafft et al (2006) showed that when an absolutely unstable region is bounded by the jet outlet, the length x AC of this region needs to be sufficiently large for the global mode to be triggered. Coenen & Sevilla (2012) used the criterion x AC = C/ ω i (x = 0) (Chomaz et al 1988;Couairon & Chomaz 1999) that contains a free parameter C. They found that C = 0.85 gave good agreement with the experimental observations of Hallberg & Strykowski (2006). The same criterion would predict here that the length of the absolutely unstable region must be 4 radii.…”

“…Here k, ω, and t are non-dimensionalised using R * and U * m . Substitution of the normal modes into the equations of motion, linearised around the steady base flow, yields a system of ordinary differential equations that, together with appropriate boundary conditions, provides a generalised eigenvalue problem (see, for instance, Coenen & Sevilla 2012), to be interpreted as a dispersion relation D(k, ω; Re, S, D/θ 0 , . .…”

Diffusion-flame flickering as a hydrodynamic global mode

“…As in the present work, they found this region of local absolute instability to lie at the basis of the excitation of a global low-frequency flickering mode. In the buoyancy-free configuration analyzed by Qadri et al (2015) the density of the fuel jet upstream from the lifted flame is significantly lower than that of the surrounding atmosphere, causing a second instability mode ("mode A") to be present in their analysis, with a region of absolute instability that starts at the outlet of the jet, similar to that found by Coenen & Sevilla (2012) in the context of light jets.…”

“…This slenderness condition is satisfied in buoyancy-free jet flows, for which the eigenmodes scale with the jet radius, which is much smaller than the jet development length for the moderately large values of the Reynolds number that characterize the onset of the instability. For instance, local linear stability analyses of light gaseous jets (Coenen et al 2008;Coenen & Sevilla 2012) have shown to give predictions in agreement with those of DNS ) and of global stability analyses (Lesshafft et al 2015;Coenen et al 2016). This is in contrast with the buoyancy-induced flickering flames investigated below, for which the eigenmodes will be seen to scale with the flame length, rather than with the jet radius.…”

Effects of finite-rate chemistry and detailed transport on the instability of jet diffusion flames

“…Theoretical investigations suggest that the jet can become absolutely unstable if the density ratio is smaller than a critical value (Monkewitz & Sohn 1988). The effects of the base flow on the growth rate in these jet flows has been investigated by different groups (Nichols, Schmid & Riley 2007;Coenen, Sevilla & Sánchez 2008;Srinivasan, Hallberg & Strykowski 2010;Lesshafft & Marquet 2010;Coenen & Sevilla 2012), showing that critical transition conditions and the absolute growth rate depend on the base-flow profiles, density ratio, momentum thickness and the proximity of the inflection points for density and velocity.…”