Asynchronous and synchronous quenching of a globally unstable jet via axisymmetry breaking

Abstract

We explore experimentally whether axisymmetry breaking can be exploited for the open-loop control of a prototypical hydrodynamic oscillator, namely a low-density inertial jet exhibiting global self-excited axisymmetric oscillations. We find that when forced transversely or axially at a low amplitude, the jet always transitions first from a period-1 limit cycle to $\mathbb {T}^2$ quasiperiodicity via a Neimark–Sacker bifurcation. However, we find that the subsequent transition, from $\mathbb {T}^2$ quasiperiodicity to $1:1$ lock-in, depends on the spatial symmetry of the applied perturbations: axial forcing induces a saddle-node bifurcation at small detuning but an inverse Neimark–Sacker bifurcation at large detuning, whereas transverse forcing always induces an inverse Neimark–Sacker bifurcation irrespective of the detuning. Crucially, we find that only transverse forcing can enable both asynchronous and synchronous quenching of the natural mode to occur without resonant or non-resonant amplification of the forced mode, resulting in substantially lower values of the overall response amplitude across all detuning values. From this, we conclude that breaking the jet axisymmetry via transverse forcing is a more effective control strategy than preserving the jet axisymmetry via axial forcing. Finally, we show that the observed synchronization phenomena can be modelled qualitatively with just two forced coupled Van der Pol oscillators. The success of such a simple low-dimensional model in capturing the complex synchronization dynamics of a multi-modal hydrodynamic system opens up new opportunities for axisymmetry breaking to be exploited for the open-loop control of other globally unstable flows.

Multifractality and scale-free network topology in a noise-perturbed laminar jet

“…This transition can be viewed as a Hopf bifurcation from a fixed point perturbed by noise to a limit cycle associated with nonlinear global oscillations (Huerre & Monkewitz 1990; Kyle & Sreenivasan 1993; Hallberg & Strykowski 2006; Li & Juniper 2013 b ; Kushwaha et al. 2022). Such oscillations can be useful in some processes (e.g.…”

“…Above a critical Reynolds number, a low-density jet can become globally unstable, transitioning from a spatial amplifier of extrinsic disturbances to a self-excited oscillator with intrinsic dynamics prescribed by a wavemaker (Chomaz, Huerre & Redekopp 1988;Lesshafft & Marquet 2010;Coenen et al 2017;Chakravarthy, Lesshafft & Huerre 2018). This transition can be viewed as a Hopf bifurcation from a fixed point perturbed by noise to a limit cycle associated with nonlinear global oscillations (Huerre & Monkewitz 1990;Kyle & Sreenivasan 1993;Hallberg & Strykowski 2006;Li & Juniper 2013b;Kushwaha et al 2022). Such oscillations can be useful in some processes (e.g.…”

Self-excited vortex-acoustic lock-in in a bluff body combustor

“…2019; Kushwaha et al. 2022). (ii) Study of lock-in due to the interaction between two self-excited systems.…”

“…Several experimental (Poinsot et al 1987;Emerson & Lieuwen 2015) and theoretical (Matveev & Culick 2003) investigations highlight the role of vortex shedding in thermoacoustic instability. Vortical structures in combustors are observed due to two mechanisms: (i) (absolute) wake instability in an unexcited flow (Monkewitz 1988) and (ii) longitudinal (Poinsot et al 1987;Candel 1992) and transverse (Rogers & Marble 1956;Kushwaha et al 2017) acoustic excitations. In-turn vortices perturb the heat release rate by affecting the flame surface area (Emerson & Lieuwen 2015), equivalence ratio (Lieuwen & Zinn 1998) etc.…”

“…The system can be a hydrodynamic (Li & Juniper 2013a;Emerson & Lieuwen 2015) or a thermoacoustic (Balusamy et al 2015;Kashinath et al 2018) system. Extensive studies on the characterization of lock-in boundary (Li & Juniper 2013a,b,c), exploration of an open-loop control strategy through asynchronous quenching were performed (Guan et al 2019a;Mondal et al 2019;Kushwaha et al 2022). (ii) Study of lock-in due to the interaction between two self-excited systems.…”