Numerical study on drag coefficient of deformable alumina droplet in compressible flows
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摘要:
针对固体火箭发动机喷管，利用流体体积（VOF）函数方法模拟液滴-气体两相流，同时结合模糊理论和比例微分控制方法（PD）控制液滴达到准静止状态，从而对可变形氧化铝液滴在流场中的受力特性进行研究。结果表明：引入模糊控制理论可以更加高效和稳定地控制液滴达到准静止状态。液滴的曳力系数会随着变形程度和流场与液滴之间的相对马赫数的增加而增加，相对马赫数和韦伯数的影响几乎没有耦合性。固体火箭发动机两相流场的精确计算需要同时考虑液滴形变与绕流流场可压缩性对气-液两相间相互作用的影响，相比于刚性球曳力系数模型，液滴的变形会使固体火箭发动机喷管的气相推力损失更多，也会造成喷管内无颗粒区更小。
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关键词:
- 液滴 /
- 曳力系数 /
- 可压缩流 /
- 流体体积（VOF）方法 /
- 模糊控制
Abstract:In view of the solid rocket motor nozzle, the volume of fluid (VOF) method was used to simulate the droplet-gas two-phase flow, and the fuzzy theory and proportional differential control (PD) method were combined to control the droplet to reach a quasi-static state, so as to study the force characteristics of deformable alumina droplet in the flow field. The results showed that the fuzzy theory coupled with PD controller can make the droplet reach the quasi-steady state more efficiently and stably. The drag coefficient of the droplet increased with the increase of deformation degree and the relative Mach number between the flow field and the droplet, and there was no significant coupling between the relative Mach number and Weber number. The effect of droplet deformation and compressibility of flow field on gas-liquid phase interaction should be considered in accurate calculation of two-phase flow field for solid rocket motor. Compared with the drag coefficient model of the rigid sphere, droplet deformation could cause more thrust loss in the gas phase of solid rocket motor nozzle, and also result in smaller particle-free zone in the nozzle.
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Key words:
- droplet /
- drag coefficient /
- compressible flows /
- volume of fluid (VOF) method /
- fuzzy control
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图 7 横纵比和液滴曳力系数随无量纲时间的变化
Figure 7. Variation of aspect ratio and droplet drag coefficient with the dimensionless time
图 8 液滴震动周期随液滴半径的变化
Figure 8. Variation of droplet oscillation periods with radius of droplets
图 9 液滴形状与流场流线（Ma=0.3, $ t^{*} $=250）
Figure 9. Droplet shapes and streamlines （Ma=0.3, $ t^{*} $=250）
图 11 不同马赫数下液滴形状，流线和压力系数分布（We = 9）
Figure 11. Droplet shapes, streamlines and distribution of pressure coefficient at different Mach number （We = 9）
图 15 氧化铝液滴曳力系数Cd随Ma的变化
Figure 15. Variation of drag coefficient Cd of alumina droplet with Ma
图 16 粒径为20 μm的刚性球和氧化铝液滴的速度分布和部分轨迹线
Figure 16. Velocity distribution and trajectory lines of rigid spheres and alumina droplets which particle diameter is 20 μm
图 17 液滴颗粒的相对雷诺数Re沿轨迹线的变化
Figure 17. Relative Reynolds number Re of the droplet vary along the trajectory lines
图 18 液滴颗粒与气流的相对马赫数Ma沿轨迹线的变化
Figure 18. Relative Mach number Ma of the droplet vary along the trajectory lines
表 1 kd的模糊规则调节表
Table 1. Fuzzy rule table of kd
Ev/Ec NB NM NS ZO PS PM PB N ZO ZO ZO NM NB NB NB ZO NM NM NM NM ZO ZO ZO P NB NB NM NM ZO ZO ZO 
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表 2 不同网格细化方案的计算结果
Table 2. Calculation results of different grid division schemes
方案 R0/$ \Delta x $ Cd 1 7.5 1.4020 2 10 1.1770 3 15 1.1471 4 20 1.1257 5 30 1.1180
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表 3 不可压缩气流中液滴曳力系数数值计算结果与参考文献对比
Table 3. Compared the results of numerical simulation with references for drag coefficient of droplet
工况 Re We ${\rho ^*}$ ${\mu ^*}$ Cd数值
计算结果Cd文献中试验结果 Dandy等[25] Helenbrook等[14] Feng[26] Youngho等[15] （a） 10 1 0.91 4 4.460 4.01 （b） 20 1 1000 100 2.822 2.72 2.947 （c） 60 4 1000 100 1.630 1.61 1.702 1.67 1.700 （d） 100 1 1000 100 1.147 1.1349 （e） 200 1 1000 100 0.812 0.7961 （f） 300 1 1000 100 0.658 0.6456
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