Multiple-scale thermo-acoustic stability analysis of a coaxial jet combustor

Abstract

In this paper, asymptotic multiple-scale methods are used to formulate a mathematically consistent set of thermo-acoustic equations in the low-Mach number limit for linear stability analysis. The resulting sets of nonlinear equations for hydrodynamics and acoustics are two-way coupled. The coupling strength depends on which multiple scales are used. The double-time-double-space (2T-2S), double-time-single-space (2T-1S) and single-time-double-space (1T-2S) limits are revisited, derived and linearized. It is shown that only the 1T-2S limit produces a two-way coupled linearized system. Therefore this limit is adopted and implemented in a finite-element solver. The methodology is applied to a coaxial jet combustor. By using an adjoint method and introducing the intrinsic sensitivity, (i) the interaction between the acoustic and hydrodynamic subsystems is calculated and (ii) the role of the global acceleration term, which is the coupling term from the acoustics to the hydrodynamics, is analyzed. For the confined coaxial jet diffusion flame studied here, (i) the growth rate of the thermo-acoustic oscillations is found to be more sensitive to small changes in the hydrodynamic field around the flame and (ii) increasing the global acceleration term is found to be stabilizing in agreement with the Rayleigh Criterion.

Adjoint Methods as Design Tools in Thermoacoustics

“…Adjoint analysis was extended to a ducted compact diffusion flame in [158,159] to calculate the thermoacoustic sensitivity to the flame parameters, and to a premixed flame modelled by a flame front tracking equation [160]. By multiple-scale analysis, the authors of [161] proposed a thermoacoustic model that simulates the three-way interactions between all subsystems (Fig. 1).…”

Thermoacoustic combustion instability of propane‐oxy‐combustion with CO2dilution: Experimental analysis

“…They found that the shift from the natural acoustics to the vortex shedding modes corresponds to increase in flow velocity. Magri et al 40 reported that in regions of large heat release, hydrodynamics greatly impact the overall thermoacoustic stability. They reported that transient flame topology change (periodic change between V-shaped to M-shaped structure) results due to increase in wall temperature as combustor power increases before eventual attainment of the wall equilibrium temperature corresponding to that power input.…”

“…27 Bonciolini et al 28 studied the change in flame topology (of non-premixed flame) that is induced by increase in wall temperature resulting from higher combustor power transition. 40 A comprehensive review of the differences in dynamic response characteristics to forced excitation between premixed and non-premixed flames is conducted by Magina et al 17 While there is no such thing as a "stable fuel," combustion of hydrocarbon fuels is reported to exhibit different stability characteristics compared with other fuels like hydrogen-enriched hydrocarbons or syngas. The thermoacoustic stabilization of the flame corresponds to the M-shaped flame stabilization, which occurs at the equilibrium temperature.…”

“…39 The authors reported different frequencies of instability with different mixtures and Reynolds numbers. Magri et al 40 reported that in regions of large heat release, hydrodynamics greatly impact the overall thermoacoustic stability. Small changes in the hydrodynamic field around the coaxial jet diffusion flame were shown to influence the thermoacoustic oscillations.…”

“…The authors proposed the global acceleration term as a link between the acoustics and hydrodynamics that can be employed in thermoacoustic stability analysis without deviation from the Rayleigh Criterion. 40 A comprehensive review of the differences in dynamic response characteristics to forced excitation between premixed and non-premixed flames is conducted by Magina et al 17 While there is no such thing as a "stable fuel," combustion of hydrocarbon fuels is reported to exhibit different stability characteristics compared with other fuels like hydrogen-enriched hydrocarbons or syngas. 41 In other words, irrespective of the fuel, it is the interaction between the flame and the acoustics that leads to such instabilities.…”