DMD analysis for velocity fields of a laminar premixed flame with external acoustic excitation
Introduction
Combustion instability is a significant issue in the development of aircraft engines and gas turbines. The prediction and control of combustion system is required in practical combustion systems [1], [2]. The mechanism of combustion instability is complicated, which may be induced by many factors [3], [4], [5]. For premixed combustion, the interaction between the flame and acoustic plays an important role in combustion instability [5], [6], [7], [8]. Therefore, many studies have focused on this issue in order to understand and characterize the flame response to external perturbations. On the theoretical level, G-equation is one useful model to describe the dynamics of flame front [9]. Once the velocity model in fresh zone is determined, flame transfer function (FTF) between the heat release and the incoming velocity perturbation would be obtained. Many studies have been carried out to build the upstream velocity model of perturbed laminar flames [10], [11], [12], [13]. In the early works, the velocity perturbations in the upstream flow were assumed to be uniform [10], [11]. However, the phase of the FTF obtained from the uniform model could not match with the experimental data [14], [12]. With the development of experimental conditions, the PIV technique has been adopted to obtain the perturbed flow fields [15], [16]. Study by Thierry [13] indicated that the transverse flow would be significant under certain conditions and developed the convective velocity model. When the convective model was taken into account, the predicted FTFS would be consistent with the experimental one [13]. The measured velocity fields are also beneficial to verify and improve the theoretical velocity model in FTF [12], [13]. The studies dedicated to the FTF of conical flames [12], [17], [18] and multiple-configuration flames [19], [20], [21], [22] are now available for providing theoretical, experimental and numerical methods to obtain the FTFs.
Apart from developing the velocity model, the interaction mechanisms between the flame and acoustic by experimental methods have become a significant topic. Bourehla et al. [14] investigated the appearance and stability of a laminar conical premixed flame with acoustic excitation by LDV and image processing method, exhibiting the response chart of vibrating flame as a function of forcing frequency and perturbation intensity. Durox et al. [23] investigated the effect of strong acoustic forcing on conical premixed flame by schlieren visualisation, exhibiting that the conical flames would deform to a quasi-hemispherical shape under an intense acoustic field.
Recently, high-speed PIV technique has become possible to investigate the flame-acoustic interactions [24]. Ferguson et al. [25] obtained the velocity fields in an oscillating Bunsen flame by the PIV technique and pointed out that flow motion was related to the forcing frequency. Chen et al. [26], [27] investigated the flow fields of perturbed diffusion flames in a tube by combining the PIV technique and schlieren visualisation. Kravtsov et al. [28] investigated the dynamics of flame front in perturbed conical flame by using combined PIV and PLIF techniques, and indicated that the axial symmetry of flame front would be broken when the obstacle is present. Zheng et al. [29] studied the lift and reattached behavior of perturbed laminar premixed flame by schlieren visualisation and PIV method, results indicated that the external forcing would promote the flame height fluctuation due to the appearance of the separated flame pocket. Meanwhile, the interaction between acoustic and flame flickering was observed, but the detailed velocity fields lacked in the work. Fu et al. [30] investigated the perturbed flames with simultaneous high-speed LII and stereo PIV, exhibiting that the external forcing would play the role in the formation of an oval-shaped shoot region. Birbaud et al. [31] used PIV and LDV techniques to study the dynamics of the velocity fields in the fresh reactants and indicated that the anchor-points could leave effects on the nearby flow fields of the reaction layer, similar work has been carried out for the free jet [32].
Although much work has been carried out on the flame response to external acoustic excitation, the interactions between flame wrinkles and flow fields are rarely reported. Especially, the detailed mechanisms that how the flame front acts on the nearby flow field remains to be determined. Therefore, the present work aims to obtain the velocity fields of perturbed flames in both fresh and burnt zones, and to elaborate the interaction mechanisms between axial and radial components by extracting the corresponding excitation mode. The effects of wrinkled flame on nearby flow fields are discussed in detail by extracting the vorticity distributions. The article is organized as follows: The experimental apparatuses are described in Section 2. Results of experiments conducted for a laminar premixed flame subjected to acoustic excitations are presented and discussed in Section 3. The conclusions are briefed in Section 4.
Section snippets
Experimental setup
The experimental setup for this work is shown in Fig. 1. The experiments were carried out in a Bunsen burner, whose diameter is 9.5 mm. The compressed air and propane gases were perfectly mixed through a Venturi tube. The temperature of the premixed gas was set at approximately 290 K in the experiment. The premixed gas was fed into the plenum and then flowed through a honeycomb to reduce random fluctuations and get a relatively uniform flow. The loudspeaker located at the bottom of the plenum
The propagated motion of axial velocity fields
Phase-locked axial velocity fields of the perturbed flame are shown in Fig. 4. For Hz, the flame size varies synchronously with the acoustic modulations. Pronounced velocity fluctuations are observed in the unburnt regions during an acoustic perturbation cycle. The burnt gases flow sideways after the expansion over the flame front, similar to those in the unperturbed flame. Moreover, the velocity dip above the flame tip still exists. The dip zone follows with the periodic movement of the
Conclusion
Even though many studies show that premixed flames are sensitive to acoustic excitation, the detailed experimental investigations about the interactions between wrinkled flames and nearby flow fields are rarely reported. The present work is an attempt to investigate the flame-acoustic interactions by PIV methodology and elaborate the interaction mechanisms between radial and axial components. DMD method is adopted to extract and distinguish the corresponding oscillatory mode, the curl of
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This work was supported by the National Key RD Program of China (Grant No. 2020YFA0400700) and the National Science Foundation of China (No. 51976184, 91841302).
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