Suppression of global modes in low-density axisymmetric jets using coflow

Abstract

Experiments conducted in helium axisymmetric jets with an annular coflowing air stream yield critical values of the velocity ratio U2∕U1 needed to suppress global instability inherent in these low-density flows. Global mode suppression was achieved for coflowing velocities less than approximately 20% of the jet centerline velocity, though the critical velocity ratio displayed a nonmonotonic relationship with the initial shear layer momentum thickness. The experiments are supported by spatio-temporal inviscid stability theory, where the convective-absolute transition was tracked in an operating domain including U2∕U1 and D∕θ. For initially thick shear layers, the experimental observations are in good agreement with linear theory, but deviate considerably as the separating shear layer thickness is reduced.

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

“…The results of figure 1(a) also suggest that the hyperbolic-tangent velocity and density profiles (dotted lines), with their inflection points coinciding at the same radial position, do not provide good representations of the flow in the near field of a low-density jet. Similar conclusions can be drawn from figure 1(b), where the solid lines show the base-flow profiles, at a downstream position X = 10 −3 , obtained by integrating the boundary-layer equations (2.4)-(2.8) for a hot jet with D/θ 0 = 80 and S = 0.63, corresponding to one of the experiments of Monkewitz et al (1990), while the dashed lines show the corresponding profiles obtained by integrating (2.4)-(2.5) together with (2.9)-(2.11) for a light jet with D/θ 0 = 62.5 and S = 0.5, corresponding to one of the experiments of Hallberg et al (2007). Note in figure 1(b) that, since velocities have been non-dimensionalized with the mean velocity, U m , the centreline velocity U j is greater than unity.…”

“…The particular case of free submerged jets emerging from injectors has been widely studied due to its central role in applications involving mixing, combustion and propulsion. Pioneering experiments with isothermal jets of helium/air mixtures discharging into air (Sreenivasan, Raghu & Kyle 1989;Kyle & Sreenivasan 1993), as well as heated air jets Raghu & Monkewitz 1991), clearly demonstrated that round jets with density sufficiently smaller than that of the ambient sustain intense self-excited oscillations consistent with the existence of a supercritical Hopf bifurcation at a certain critical value of the density ratio (see also Hallberg & Strykowski 2006;Hallberg et al 2007). These experiments were motivated by previous theoretical investigations that revealed that jets with thin shear layers become absolutely unstable when the jet-to-ambient density ratio S becomes smaller than a certain critical value S c .…”

“…Base flow We consider the linear stability of cylindrical laminar low-density gas jets emerging from an injector of radius a, differentiating between hot mono-component jets and light jets with a non-uniform composition. To describe the local base-flow velocity and density profiles, the commonly used combination of a hyperbolic-tangent velocity profile U(r) with momentum thickness θ , together with the Crocco-Busemann relation to obtain the corresponding base-flow density profileρ(r) for a given jet-to-ambient density ratio S (Jendoubi & Strykowski 1994;Hallberg et al 2007;,…”

“…These experiments were motivated by previous theoretical investigations that revealed that jets with thin shear layers become absolutely unstable when the jet-to-ambient density ratio S becomes smaller than a certain critical value S c . In the case of an incompressible inviscid vortex sheet (Michalke 1970;Huerre & Monkewitz 1985), the critical density ratio was found to be S c 0.66, but its particular value is known to depend on other relevant control parameters, such as the shear-layer thickness and the values of the Mach, Reynolds and Richardson numbers, and is also strongly affected by the presence of ambient coflow or counterflow (Monkewitz & Sohn 1988;Jendoubi & Strykowski 1994;Sevilla, Gordillo & Martínez-Bazán 2002;Hallberg et al 2007;Nichols, Schmid & Riley 2007;Coenen, Sevilla & Sánchez 2008;Srinivasan, Hallberg & Strykowski 2010).…”

“…Most of the previous studies of the spatiotemporal stability properties of parallel low-density jets use parametric model velocity and density profiles, typically hyperbolic tangents, to represent the basic parallel jet flow (Jendoubi & Strykowski 1994;Sevilla et al 2002;Hallberg et al 2007;Nichols et al 2007;Srinivasan et al 2010). The question then naturally arises as to what extent do these parametric representations account for the actual stability properties associated with realistic velocity and density profiles downstream of the injector.…”