## 1 Introduction  
The predominant combustion in operational aero-engines remains spray combustion, resulting in non-premixed (diffusion) flames [1; 2; 3]. Lean-burn (global fuel/air ratio below stoichiometric) combustion is widely adopted in modern gas turbine combustors to reduce the emission of NOx pollutants. However, the accompanying danger of global extinction, called blowoff, occurs more frequently. Blowoff presents a significant hazard to aero-engines, especially when gliding or diving with the engine idling. In these cases, the air flow rate is high, and the fuel flow rate is low, that is, the global fuel/air ratios are beyond the blowoff limits [4; 5; 6]. Additionally, there is a high probability that aero-engine combustors run at high altitudes with low temperatures and pressures, and these operating conditions are highly susceptible to blowoff. If the aero-engines stall at high altitudes, the airplane must lower its altitude to an environment suitable for relighting, significantly jeopardizing flight safety. Therefore, it is of great interest to thoroughly investigate the combustion characteristics close to the blowoff limit and further understand the physical mechanism associated with the blowoff process to help avoid the blowoff phenomena and enlarge the flight envelope of modern aero-engines. Physical understanding and predictions regarding the blowoff transient are currently receiving significant attention. Previous studies of blowoff dynamics have shown that the heat release and the chemical radicals generated in combustion are insufficient to sustain the favorable reactions for a given flow rate, and then the flame will blow off [7]. In modern aero-engines, a local region with a reduced velocity and local strain rate in the flow field is created to guarantee enough time for the heat released from the burnt area to warm up the fresh fuel/air mixture for a successful ignition. In practical applications, this region is generally achieved by the bluff bodies and swirlers. A recirculation zone (RZ) is formed downstream of the bluff body, and the recirculated hot burned gases serve as the sources of continuous ignitors of unburned reactants [5; 8; 9]. The measurements of mixture fraction, temperature, and the concentration of stable species in the recirculation zone provide an opportunity to understand the chemistry and turbulence interaction in the flame stabilized on a bluff body [10; 11; 12]. The benefit of using swirling flows is that the tangential velocity in swirling flames induces a radial pressure gradient, resulting in a sub-ambient pressure near the centerline of the burner with reversal flow and, hence, recirculation. In addition, the swirling flows produce extra turbulence to enhance the mixing and combustion intensity, creating a compact flame with a higher level of mass recirculation than a non-swirling configuration [12; 13; 14; 15; 16]. Moreover, adding a swirler increases the residence time of the reactants and improves flame stability. [PERSON] et al. compared the blowoff limits with and without swirling in their work, concluding that the swirling extends the blowoff limit and enhances the stability of lean flames [17; 18; 19]. Currently, stable performance is ensured by operating the combustor with a wide margin above the uncertain blowoff limit, which can be easily influenced by noise and combustion instabilities caused by local flame extinction and heat release fluctuations [20; 21; 22]. When coupled with acoustics, the heat release oscillations can lead to significant pressure and velocity fluctuations in the reacting flow. Thus, the flame response can be controllable if an external acoustic excitation is introduced into the inlet flow [23], which is beneficial for scientific research. As observed in Refs. [24; 25; 26; 27; 28; 29; 30], the blowoff limits and stability mechanisms of forced flames differ from the unforced ones.