Linear stability analysis of three dimensional perturbations on swirling liquid sheet sheared by swirling gas flows
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摘要:
针对先进航空发动机燃烧室广泛采用的气动雾化形式,将核心物理现象简化为旋转液膜在内外侧旋流空气作用下的扰动破碎。从理论角度对这一过程进行了线性稳定性分析,给出了详细的推导与数值求解步骤。讨论了实验物性参数两相旋转运动对界面扰动特性的影响。内侧气流旋转运动对轴对称扰动有促进作用,外侧气流旋转有相反作用,主导扰动波数随液膜自身旋转强度增加而线性增长。对于高阶周向模态,内外侧旋转气流激发的扰动增长范围分别是轴对称模态的54.6%和35.1%。将理论结果与相近条件下的气动雾化隐式大涡模拟进行对比。内侧高速气流条件下,稳定性分析得到的主导扰动频率为2 546.5 Hz,与数值结果基本一致,外侧高速气流条件稳定性分析正确预测了扰动发展的趋势。通过理论计算,加深了对旋转条件气液相互作用机理的认识。
Abstract:Focus on the form of airblast atomization widely applied in advanced aeroengine combustor, the key physical phenomena are simplified to the perturbation and breakup of swirling liquid sheet under the influence of inner and outer swirling gas flows. Linear stability analysis was applied to this process from theoretical aspect and detailed derivation and numerical solving steps were presented. The influence on the characteristics of interfacial perturbations from two-phase swirling motions of experimental physical parameters was discussed. The swirling motions of inner gas flow had promoting influence on the axisymmetric perturbations, while swirling outer gas had inverse influence. The dominant perturbation wavenumber increased linearly with the increase of swirling strength of the liquid sheet. For the high-order circumferential modes, the perturbation growth ranges activated by inner and outer swirling gas were 54.6% and 35.1% of the axisymmetric modes separately. The theoretical results were compared with the implicit Large Eddy Simulations of airblast atomization under similar conditions. Under the condition of high velocity inner gas flow, the dominant perturbation frequency from stability analysis was 2 546.5 Hz, which was in accordance with numerical results. Under the condition of high velocity outer gas flow, the stability analysis correctly predicted the trends of perturbation development. The mechanisms of gas-liquid interaction under swirling conditions are further understood through theoretical computations.
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图 2 内侧轴向气液速度比对扰动增长率的影响$ {\overline{\rho }}_{\text{r}}=1.29\times {10}^{-3} $, $ {\overline{r}}_{\text{i}}=48,{\overline{r}}_{\text{o}}=50 $
Figure 2. Influence of inner gas-liquid axial velocity ratio on the perturbation growth rate $ {\overline{\rho }}_{\text{r}}=1.29\times {10}^{-3} $, $ {\overline{r}}_{\text{i}}=48,{\overline{r}}_{\text{o}}=50 $
图 4 内侧气流旋转强度对扰动增长率的影响$ {\overline{\rho }}_{\text{r}}=0.002 $, $ {\overline{u}}_{\text{i}{\textit{z}}}={\overline{u}}_{\text{o}{\textit{z}}}=2.0 $
Figure 4. Influence of inner gas swirling strength on the perturbation growth rate $ {\overline{\rho }}_{\text{r}}=0.002 $, $ {\overline{u}}_{\text{i}{\textit{z}}}={\overline{u}}_{\text{o}{\textit{z}}}=2.0 $
表 1 气动雾化过程数值模拟参数
Table 1. Simulation parameters for the airblast atomization process
参数 数值 计算域边长$ L $/mm 200 外侧旋转气流外直径$ {D}_{\text{o}} $/mm 14 外侧旋转气流厚度$ {h}_{\text{o}} $/mm 3.5 旋转液膜外直径$ {D}_{\text{l}} $/mm 7 旋转液膜厚度$ {h}_{\text{l}} $/mm 1 内侧旋转气流外直径$ {D}_{\text{i}} $/mm 5 内侧旋转气流厚度$ {h}_{\text{i}} $/mm 2 气相动力黏度$ {\mu }_{\text{g}} $/10−5 (kg/(m·s)) $ 1.8 $ 液相动力黏度$ {\mu }_{\text{l}} $/10−3 (kg/(m·s)) $ 1.8 $ 气相密度$ {\rho }_{\text{g}} $/(kg/m3) 1.293 液相密度$ {\rho }_{\text{l}} $/(kg/m3) 800.0 表面张力系数$ \sigma $/(kg/s2) 0.036 外侧气流入射速度$ {u}_{\text{g,o}} $/(m/s) 5.2, 23.2 内侧气流入射速度$ {u}_{\text{g,i}} $/(m/s) 23.2, 5.2 液膜入射速度$ {u}_{\text{l}} $/(m/s) 5.0 喷雾半锥角$ \theta $/(°) 30 -
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