Reduced order modeling of reacting shear flow

Abstract

Thermoacoustic instability in premixed c ombustors occurs occasionally at multiple frequencies, especially in configurations where flames are stabilized on separating shear layers that form downstream of sudden expansions or bluff bodies. While some of these frequencies are related to the acoustic field, others appear to be related to shear flow instability phenomena. It is shown in this paper that shear flows can support self-sustained instabilities if they possess absolutely unstable modes. The associated frequencies are predicted using mean velocity profiles that resemble those observed in separating flows and for profiles obtained from numerical simulations, and are shown to match those derived from experimental and numerical investigations. It is also shown that the presence of density profiles compatible with premixed combustion can affect this frequency and can change the absolute instability mode into a convectively unstable mode thereby reducing the possibility of the generation of self-sustained oscillations. A qualitative prediction of the pressure amplitudes resulting from these shear layer modes is shown to be consistent with experimental measurements. The results from the stability analysis are combined with those using the Proper Orthogonal Decomposition (POD) method to yield a reduced-order model.

Stochastic estimation of a separated-flow field using wall-pressure-array measurements

“…As shown in Fig. The absolute instability mechanism suggested by Wee et al 36,37 and its relation to the formation of large-scale structures in the back-step flow are similar to the flow behavior in the wake of bluff bodies where the process of vortex shedding has been linked to the existence of an absolute-instability mechanism as well ͑Oertel 39 ͒. 38 Thus, within this location, it is likely that an absolute instability exists, which leads to the rollup of the large-scale vortex.…”

“…Hence, the distinction of the two modes is likely to primarily affect the flow characteristics within the separation bubble rather than downstream of reattachment. Wee et al 36,37 found that large-scale vortices periodically formed at the middle of the reattachment zone before shedding downstream. Only one other recent study indicates a scenario similar to that identified here.…”

“…Figures 27 and 28 provide an idealized sketch of the coherent structures developing in the separation bubble for the shear-layer and wake modes, respectively. Wee et al 36,37 state that absolute modes are most likely to originate in a region with strongest backflow. The study is conducted by Wee et al 36,37 using a random vortex method, numerical simulation of the flow field downstream of a sudden expansion.…”

Optimal mixing in recirculation zones

“…For instance, the shear-layer dynamics at the upper stagnation point has been shown to be of large importance at backward-facing steps 40,41 and in dump combustors, 42 but this effect is neglected in the present study. Similarly, the non-negligible effect of turbulent fluctuations is not considered.…”

Extensions of adaptive slope-seeking for active flow control

“…All controller parameters (u 0 , v sin , a, k, f 0 ref ) are the same as before. For equation (10), m 5 2 and n 5 2 are chosen.…”