Role of hydrodynamic shear layer stability in driving combustion instability in a premixed propane-air backward-facing step combustor

This paper presents a global hydrodynamic stability analysis of flow fields in a backward-facing step combustor, assuming weakly nonparallel flow. The baseline experiments in a “long” combustor of length of 5.0 m shows the presence of two combustion instability states characterized by coherent low- and high-amplitude acoustic pressure oscillations. The analysis is performed for propane-air mixtures at three values of $\varphi =0.63$, 0.72, and 0.85, which correspond to quiet, low-amplitude and high-amplitude instability states in the long combustor experiments. Base flow velocity and density fields for the hydrodynamic stability analysis are determined from time-averaged particle image velocimetry measurements made after the length of the duct downstream of the step has been shortened to eliminate acoustic pressure oscillations. The analysis shows that the shear layer mode is self-excited for the $\varphi =0.72$ case with an oscillation frequency close to that of the long combustor's fundamental acoustic mode. We show from an analysis of the weakly forced, variable density Navier-Stokes equations that self-excited hydrodynamic modes can be weakly receptive to forcing—suggesting that the low-amplitude instability in the long combustor is due to semi-open loop forcing of heat-release oscillations by the shear layer mode. At $\varphi =0.85$, the analysis shows that the flow is hydrodynamically globally stable but locally convectively unstable. Spatial amplification of velocity disturbances by the convectively unstable flow causes high-amplitude combustion instability in the long combustor case. These results show that combustion instability can be sustained by two different mechanisms by which acoustic and hydrodynamic modes being either strongly coupled result in fully closed loop forcing, or weakly coupled result in semi-open loop forcing of the flame by a self-excited hydrodynamic mode.

Figure 1

Fundamental mechanisms though which hydrodynamic instability modes and acoustic modes can couple during combustion instability: (a) semi-open loop, (b) fully closed loop.

Figure 2

Schematic of experimental setup.

Figure 3

Variation of overall sound pressure level with varying $\varphi$ for the propane-air case. The broken vertical lines are at the values of $\varphi$ analyzed in this paper. The arrows show the direction in which $\varphi$ was varied in each case. Figure adapted from data presented in Refs. [18, 19].

Figure 4

Typical base flow velocity and density profiles ($\varphi =0.72, x=0.26$). Time-averaged velocity data (symbols) from experiments (Ref. [19]) are overlaid for comparison. The density profile width is from the baseline estimate.

Figure 5

Time-averaged axial base flow velocity profiles at (a) $x/h=0.26$ and (b) $x/h=0.57$, measured using PIV by Hong et al. [19].

Figure 6

Variation of density base flow profile parameters (a) $y_f$ and (b) ${\delta }_f$, determined using seeding density change edges determined from raw PIV data (Ref. [19]).

Figure 7

Typical result from local stability analysis ($\varphi =0.63, k=3\pi , x=0.26$) (a) eigenvalue spectrum with the shear layer mode encircled and (b) $\widehat{v}$ eigenvector corresponding to the shear layer mode.

Figure 8

Variation of local absolute growth rate for the shear layer mode along the streamwise direction for the saddle point series that determines the complex global frequency.

Figure 9

Instantaneous $v^{\prime }$-velocity component of the global shear layer mode for (a) $\varphi =0.63$ (b) $\varphi =0.72$ and (c) $\varphi =0.85$.

Figure 10

Variation of the intensity of velocity fluctuations along the streamwise direction. The curves have been normalized by their value at $x=0.17$.

Figure 11

Spatial variation of (a) $|{\tilde{u}}^{†}|$ and (b) $|{\tilde{v}}^{†}|$ for $\varphi =0.85$. The step edge is at $(x,y)=(0,0)$.