Response analysis of a laminar premixed M-flame to flow perturbations using a linearized compressible Navier-Stokes solver

Abstract

International audienceThe response of a laminar premixed methane-air flame subjected to flow perturbations around a steady state is examined experimentally and using a linearized compressible Navier-Stokes solver with a one-step chemistry mechanism to describe combustion. The unperturbed flame takes an M-shape stabilized both by a central bluff body and by the external rim of a cylindrical nozzle. This base flow is computed by a nonlinear direct simulation of the steady reacting flow, and the flame topology is shown to qualitatively correspond to experiments conducted under comparable conditions. The flame is then subjected to acoustic disturbances produced at different locations in the numerical domain, and its response is examined using the linearized solver. This linear numerical model then allows the componentwise investigation of the effects of flow disturbances on unsteady combustion and the feedback from the flame on the unsteady flow field. It is shown that a wrinkled reaction layer produces hydrodynamic disturbances in the fresh reactant flow field that superimpose on the acoustic field. This phenomenon, observed in several experiments, is fully interpreted here. The additional perturbations convected by the mean flow stem from the feedback of the perturbed flame sheet dynamics onto the flow field by a mechanism similar to that of a perturbed vortex sheet. The different regimes where this mechanism prevails are investigated by examining the phase and group velocities of flow disturbances along an axis oriented along the main direction of the flow in the fresh reactant flow field. It is shown that this mechanism dominates the low-frequency response of the wrinkled shape taken by the flame and, in particular, that it fully determines the dynamics of the flame tip from where the bulk of noise is radiated

Adjoint-based parametric sensitivity analysis for swirling M-flames

“…With our choice of chemical parameters we reach a flame speed of S d = 2.9ms −1 and a flame width of 0.007mm, which amounts to about 1% of the inlet-tube outer radius. Despite a discrepancy between parameters and values typically observed in real configurations, Blanchard et al (2015) showed that -for parameter values similar to ours -transfer functions could Table 3: Parameter values used in our study.…”

“…To achieve this we use the values shown in table 3. The most prominent compromise that had to be made is the low Reynolds number and the large Mach number compared to experimental values (Blanchard et al 2015), yielding a large velocity upstream of the combustion zone of 35ms −1 and a small outer radius of the inlet at 0.64mm. With our choice of chemical parameters we reach a flame speed of S d = 2.9ms −1 and a flame width of 0.007mm, which amounts to about 1% of the inlet-tube outer radius.…”

“…is used to present our results. This definition of the Strouhal number differs from the one traditionally used in non-reactive fluid problems (see, e.g., Garnaud et al (2013)), but is instead defined to allow for direct comparison with combustion experiments (Schuller et al 2003;Blanchard et al 2015).…”

Pressure wave generation from perturbed premixed flames

“…Flames submitted to a non-zero tangential velocity tend to propagate wrinkles along the flame front, as sketched in figure 1; this is true even for stable flame configurations (Blackshear 1953;Petersen & Emmons 1961;Boyer & Quinard 1990). This well-known behaviour was recently analysed within a linear framework (Blanchard et al 2015). Flame perturbations then appear as a superposition of (1) entropy and reaction waves, associated with flame-front displacement, and (2) vorticity waves that enforce mass conservation across the dilatation zone; at the flame tip, this set of waves becomes unstable before it disappears.…”

“…A chemistry model of this type has been used by Williams (1985) to analytically study planar flame fronts. Details about the numerical discretization of our governing equations can be found in Sandberg (2007) and Blanchard et al (2015). Our simulations use a conservative formulation of the state variable q = (ρ, ρu r , ρu θ , ρE, ρY f ) T with ρ as the density, (u r , u θ ) as the radial and angular velocity, respectively, E as the total energy and Y f as the fuel mass fraction.…”