Self-sustained hydrodynamic oscillations in lifted jet diffusion flames: origin and control

Abstract

We use direct numerical simulation (DNS) of the Navier-Stokes equations in the low-Mach-number limit to investigate the hydrodynamic instability of a lifted jet diffusion flame. We obtain steady solutions for flames using a finite rate reaction chemistry, and perform a linear global stability analysis around these steady flames. We calculate the direct and adjoint global modes and use these to identify the regions of the flow that are responsible for causing oscillations in lifted jet diffusion flames, and to identify how passive control strategies might be used to control these oscillations. We also apply a local stability analysis to identify the instability mechanisms that are active. We find that two axisymmetric modes are responsible for the oscillations. The first is a high-frequency mode with wavemaker in the jet shear layer in the premixing zone. The second is a low-frequency mode with wavemaker in the outer part of the shear layer in the flame. We find that both of these modes are most sensitive to feedback involving perturbations to the density and axial momentum. Using the local stability analysis, we find that the high-frequency mode is caused by a resonant mode in the premixing region, and that the low-frequency mode is caused by a region of local absolute instability in the flame, not by the interaction between resonant modes, as proposed in Nichols et al. (Phys. Fluids, vol. 21, 2009, article 015110). Our linear analysis shows that passive control of the low-frequency mode may be feasible because regions up to three diameters away from the fuel jet are moderately sensitive to steady control forces.

Diffusion-flame flickering as a hydrodynamic global mode

“…A pocket of absolutely unstable flow, away from boundaries, was also found by Qadri et al (2015) in the context of nonbuoyant flames for their "mode B". 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.…”

“…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.…”

“…Preferential diffusion effects, associated with light and heavy fuel molecules, could be addressed in the infinitely fast reaction limit by using coupling-function formulations accounting for reactant Lewis numbers that differ from unity (Liñán 1991). Consideration of finite-rate effects would be needed to examine the stability characteristics of lifted flames, studied in previous work (Qadri et al 2015) under buoyancy-free conditions. While the present work pertains to laminar flames, the global instability analysis could also be applied to turbulent conditions, with the steady base flow obtained for instance by time averaging results of large-eddy simulations, as done earlier in connection with local spatiotemporal analyses of jet flames (See & Ihme 2014).…”

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

“…(15) was introduced in thermo-acoustics to calculate the effect of external feedback mechanisms, such as a hot wire, and design-parameter changes, such as the flame inlet geometric ratio, in the stability [7][8][9] via appropriate models for the thermo-acoustic perturbation δJ . We introduce the concept of intrinsic sensitivity , extending the structural sensitivity used in [7,18] , defined as the eigenvalue's sensitivity to intrinsic physical mechanisms. Here, the perturbation operator of the eigenvalue's sensitivity formula (15) is the Jacobian itself, i.e., δJ = εJ .…”

“…We use a Discrete Adjoint approach [7,25] to ensure that the adjoint spectra match the complex conjugate of the direct spectra to machine precision. The code was validated against the solutions of [18] and the spectra matched with an error smaller than 0.5%. To test our method, we use the coaxial jet combustor of [14,15] , which is schematically shown in Fig.…”