Numerical study on powder fluidization and conveying characteristics of powder supply device with built-in intake under high-pressure
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摘要:
针对粉末发动机中活塞驱动式燃料供给系统，设计了一种内置进气式供粉装置。基于欧拉-欧拉双流体模型，通过用户自定义函数实现活塞运动，建立了气体-粉末-活塞相互作用计算模型，开展了不同储箱内初始工作压力（0.6、1.2、1.8、2.4、3.0、3.6 MPa）对粉末燃料供给特性的数值研究。结果表明：不同初始工作压力下的气固分界面主要在进气口附近波动。随初始工作压力增大，粉末流量波动幅度降低，稳定输送阶段内的平均粉末流量更接近理论值，粉末层（粉末体积分数为0.1）面积波动幅度降低；在两相喷管喉道截面，固相平均体积分数随初始工作压力增大而增大，但拟颗粒温度的波动幅度随之减小。初始工作压力为3.6 MPa时的储箱内压力相比0.6 MPa能维持更长时间稳定，压力波动幅度降低了59.1%。
Abstract:A powder feeding device with a built-in intake channel was designed for the piston-driven powder fuel supply system in powder engines, the piston movement was realized by using the User Defined Function (UDF), and the action of the coupling of the gas-powder-piston was established. Numerical simulation was carried out to investigate the powder fuel supply characteristics under different initial operating pressures (0.6, 1.2, 1.8, 2.4, 3.0 and 3.6 MPa) in the powder storage tank based on the Eulerian-Eulerian two-fluid model. The results showed that the gas-solid interface mainly fluctuated around the intake under different initial operating pressures. With the increase of the initial operating pressure, the fluctuation amplitude of the powder flow rate decreased, the mean powder flow rate within the stable conveying stage was closer to the theoretical value, and the fluctuation amplitude of the powder layer (powder volume fraction of 0.1) area decreased; the area-averaged volume fraction of solid phase at the two-phase nozzle throat section increased with the increase of the initial operating pressure in the storage tank, but the fluctuation amplitude of the granular temperature decreased. The pressure in the storage tank at an initial operating pressure of 3.6 MPa was kept stable for a longer period compared with 0.6 MPa, and the pressure fluctuation in the storage tank was reduced by 59.1%.
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图 1 粉末储箱的几何结构（单位：mm）
Figure 1. Geometric configuration of powder storage tank （unit：mm）
图 5 瞬时粉末分布的数值计算与实验结果对比
Figure 5. Comparison between numerical simulations and experimental results of instantaneous powder distribution
图 7 出口平均粉末流量与理论值对比
Figure 7. Comparison of the mean outlet powder flow rate with the theoretical value
图 8 出口粉末流量均方差对比
Figure 8. Comparison of the standard deviation of the outlet powder flow rate
图 9 中心截面（Z = 0 m）处瞬时气固流型分布
Figure 9. Instantaneous gas-solid flow pattern distribution at the central section （Z = 0 m）
图 13 粉末体积分数变化和粉末云图分布
Figure 13. Area-averaged powder volume fraction variation and powder contour distribution
图 14 不同轴向位置处的面平均拟颗粒温度分布
Figure 14. Area-averaged granular temperature distribution at different axial positions
图 15 不同轴向位置处的拟颗粒温度均方差对比
Figure 15. Comparison of the standard deviation of the granular temperature at different axial positions
图 16 不同工况粉末储箱内压力随时间的变化规律
Figure 16. Variation law of pressure in the tank with time under different cases
图 17 不同工况粉末储箱内压力均方差对比
Figure 17. Comparison of the standard deviation of the pressure in the powder storage tank under different cases
Cd 阻力系数 ds 固相直径，mm e 粒子碰撞的恢复系数 g 重力加速度，m/s2 g0 径向分布函数 I 应力张量 I2D 偏应力张量的第二不变量 p 压力，N/m2 ps 固相压力，N/m2 Rg 气体常数，J/（mol·K） T 温度，K t 时间，s ug 气相速度，m/s us 固相速度，m/s Res 固相雷诺数 β 气相/固相动量交换系数，kg/（m3·s） $\gamma^{\varTheta}_{\mathrm{s}} $ 碰撞能量耗散，kg/（m3·s） $\varepsilon_{\mathrm{g}} $ 气相体积分数，% $\varepsilon_{\mathrm{s}} $ 固相体积分，% $\varepsilon_{\mathrm{s,max}} $ 固相最大打包极限，% $\varTheta_{\mathrm{s}} $ 拟颗粒温度，m2/s2 λg 气体体积黏度，Pa·s λs 固体体积黏度，Pa·s μg 气相剪切黏度，Pa·s μs 固相有效黏度，Pa·s μs,col 粉末碰撞黏度，Pa·s μs,fr 粉末摩擦黏度，Pa·s μs,kin 粉末动力黏度，Pa·s ρg 气相密度，kg/m3 ρs 固相密度，kg/m3 τg 气相应力应变张量，N/m2 τs 固相应力应变张量，N/m2 $\varPhi $ 内摩擦角，（°） 下标 g 气相 s 固相 
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表 1 计算工况
Table 1. Simulation cases
工况 活塞速度/
（mm/s）进气流量$ {\dot{m}}_{\mathrm{i}} $/
（g/s）初始工作压力/
MPa1 70 1（0.33%$ {\dot m_{{\text{pt}}}} $） 0.6 2 1.2 3 1.8 4 2.4 5 3.0 6 3.6
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表 2 计算条件参数
Table 2. Simulation condition parameters
参数 数值 颗粒粒径ds/mm 0.02 初始粉末装填率ε 0.55 最大粉末装填率εmax 0.63 重力加速度g/（m/s2） 9.81 颗粒黏度μg/10−5 （Pa·s） 1.72 颗粒密度ρs/（kg/m3） 2719 虚拟质量系数 0.5 恢复系数e 0.9
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