Transfer function model of sloshing force effect of liquid propellant and its application
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摘要:
面向液体推进剂小幅晃动引发运载器不良耦合运动的预测和控制需要，基于液体晃动数值计算结果，开展晃动力效应的传递函数模型辨识研究。对返回阶段水平飞行运载器内置的平放煤油贮箱示例，根据其飞行阶段关注的转动运动范围，建立力效应传递函数描述模型，在此基础上，进行晃动抑制设计，以期增加晃动阻尼并削弱晃动对飞行的影响。结果表明：传递函数辨识结果能够捕获液体推进剂晃动力效应，可以用于运载器飞行特性预测和晃动抑制设计。
Abstract:To predict and regulate the space vehicle’s undesirable coupling motion produced by tiny amplitude sloshing of liquid propellant, a transfer function model identification study is carried out based on the findings of numerical calculations. For an example of a horizontally placed kerosene tank in a vehicle, during the level flight in the re-entry phase, a force effect transfer function description model is established with the range of rotational motion of interest, based on which a sloshing suppression design is carried out to increase sloshing damping and weaken the impact of sloshing on flight. The findings show that the transfer function can capture the impacts of the liquid propellant sloshing force, which can be utilized to anticipate space vehicle flight characteristics and design sloshing suppression.
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图 2 2种设置下计算的液体剖面形态对比
Figure 2. Comparison of liquid profile form calculated under two settings
图 3 2种设置下液体对油箱纵向合力和合力矩对比
Figure 3. Comparison of longitudinal force and moment of liquid on tank between two settings
图 4 平放煤油贮箱与参考坐标系示意图
Figure 4. Schematic diagram of horizontally placed kerosene tank and reference coordinate system
图 6 滚转角速度-滚转力矩幅相特性
Figure 6. Amplitude-phase characteristic of roll rate to roll moment
图 7 滚转角速度-偏航力矩幅相特性
Figure 7. Amplitude-phase characteristic of roll rate to yaw moment
图 8 俯仰角速度-轴向力幅相特性
Figure 8. Amplitude-phase characteristic of pitch rate to axial force
图 9 俯仰角速度-法向力幅相特性
Figure 9. Amplitude-phase characteristic of pitch rate to normal force
图 10 俯仰角速度-俯仰力矩幅相特性
Figure 10. Amplitude-phase characteristic of pitch rate to pitch moment
图 11 滚转角速度-侧向力模型结果时域对比
Figure 11. Time domain comparison of roll rate to side force model result
图 12 滚转角速度-滚转力矩模型结果时域对比
Figure 12. Time domain comparison of roll rate to roll moment model result
图 13 滚转角速度-偏航力矩模型结果时域对比
Figure 13. Time domain comparison of roll rate to yaw moment model result
图 14 俯仰角速度-轴向力模型结果时域对比
Figure 14. Time domain comparison of pitch rate to axial force model result
图 15 俯仰角速度-法向力模型结果时域对比
Figure 15. Time domain comparison of pitch rate to normal force model result
图 16 俯仰角速度-俯仰力矩模型结果时域对比
Figure 16. Time domain comparison of pitch rate to pitch moment model result
图 17 滚转角速度-侧向力预测幅相特性
Figure 17. Amplitude-phase characteristic of roll rate to side force predictive result
图 18 滚转角速度-滚转力矩预测幅相特性对比
Figure 18. Comparison of amplitude-phase characteristic of roll rate to roll moment predictive result
图 19 滚转角速度-偏航力矩预测幅相特性对比
Figure 19. Comparison of amplitude-phase characteristic of roll rate to yaw moment predictive result
图 20 滚转角速度-侧向力预测模型结果时域对比
Figure 20. Time domain comparison of roll rate to side force predictive model result
图 21 滚转角速度-滚转力矩预测模型结果时域对比
Figure 21. Time domain comparison of roll rate to roll moment predictive model result
图 22 滚转角速度-偏航力矩预测模型结果时域对比
Figure 22. Time domain comparison of roll rate to yaw moment predictive model result
图 23 俯仰角速度-轴向力预测幅相特性对比
Figure 23. Comparison of amplitude-phase characteristic of pitch rate to axial force predictive result
图 24 俯仰角速度-法向力预测幅相特性对比
Figure 24. Comparison of amplitude-phase characteristic of pitch rate to normal force predictive result
图 25 俯仰角速度-俯仰力矩预测幅相特性对比
Figure 25. Comparison of amplitude-phase characteristic of pitch rate to pitch moment predictive result
图 26 俯仰角速度-轴向力预测模型结果时域对比
Figure 26. Time domain comparison of pitch rate to axial force predictive model result
图 27 俯仰角速度-法向力预测模型结果时域对比
Figure 27. Time domain comparison of pitch rate to normal force predictive model result
图 28 俯仰角速度-俯仰力矩预测模型结果时域对比
Figure 28. Time domain comparison of pitch rate to pitch moment predictive model result
图 30 2种挡板滚转角速度-侧向力幅相特性对比
Figure 30. Comparison of amplitude-phase characteristic of roll rate to side force with two different baffle settings
图 31 2种挡板滚转角速度-滚转力矩幅相特性对比
Figure 31. Comparison of amplitude-phase characteristic of roll rate to roll moment with two different baffle settings
图 32 2种挡板滚转角速度-偏航力矩幅相特性对比
Figure 32. Comparison of amplitude-phase characteristic of roll rate to yaw moment with two different baffle settings
表 1 数值计算模型参数设置
Table 1. Model parameter settings for numerical calculation
模型参数 软件算例设置 自建模型设置 网格生成器 表面重构
切割体网格单元生成表面重构
切割体网格单元生成网格基础尺寸/m 0.005 0.1 空间模型 三维 三维 时间模型 隐式非稳态 隐式非稳态 材料模型 多相流（水+空气）、VOF（分离流） 多相流（水+空气）、VOF（分离流） 湍流模型 K-Epsilon Spalart-Allmaras 自适应设置 自适应网格、自适应时间步 自适应网格、自适应时间步 求解器设置 一阶时间离散、时间步触发自适应 二阶时间离散、时间步触发自适应 内部迭代步数 15 50 
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表 2 滚转运动输入与输出系数
Table 2. Input and output coefficients of rolling motion
滚转输入参数 滚转输出参数 Aφ/(°) ωp/(rad·s−1) Ap/rad $ A_{F_y} $/N $ \varphi_{F_y} $/(°) $ A_{M_x} $/(N·m) $ \varphi_{M_x} $/(°) $A_{M_{\textit{z}}} $/(N·m) $ \varphi_{M_{\textit{z}}} $/(°) 10 1.57 0.27 25 0 50 0 24 180 2.09 0.37 35 0 50 0 35 180 3.14 0.55 105 0 50 0 115 180 3.70 0.65 250 0 47 0 290 180 6.28 1.10 120 −180 51 0 148 0 20 1.57 0.55 50 0 100 0 48 180 2.09 0.73 66 0 101 0 68 180 3.14 1.10 210 0 99 0 235 180 3.70 1.29 540 −45 95 0 660 135 6.28 2.19 215 −180 98 0 265 0 30 1.57 0.82 55 0 150 0 55 180 2.09 1.10 92 0 150 0 96 180 3.14 1.64 300 0 140 0 345 180 3.70 1.94 700 −135 160 0 750 45 6.28 3.29 290 −180 145 0 355 0
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表 3 俯仰运动输入与输出系数
Table 3. Input and output coefficients of pitching motion
俯仰输入参数 俯仰输出参数 Aθ/(°) ωq/(rad·s−1) Aq/rad $A_{F_x} $/N $ \varphi_{F_x} $/(°) $A_{F_{\textit{z}}} $/N $ \varphi_{F_{\textit{z}}} $/(°) $A_{M_y} $/(N·m) $ \varphi_{M_y} $/(°) 5 1.05 0.09 38 135 15 0 330 −45 1.26 0.11 50 123.75 22 0 300 −56.25 1.57 0.14 85 108 35 0 280 −78.75 2.09 0.18 95 45 55 0 130 −112.5 2.51 0.22 79 22.5 70 0 50 −78.75 3.14 0.27 68 22.5 100 0 100 0 10 1.05 0.18 65 135 30 0 500 −39.38 1.26 0.22 95 123.75 50 0 480 −50.63 1.57 0.27 140 108 75 0 420 −67.5 2.09 0.37 210 67.5 140 0 290 −90 2.51 0.44 156 22.5 160 0 120 −67.5 3.14 0.55 125 22.5 250 0 260 0 20 1.05 0.37 140 135 70 0 700 −33.75 1.26 0.44 170 123.75 100 0 680 −39.38 1.57 0.55 240 108 170 0 650 −56.25 2.09 0.73 330 78.75 320 0 550 −67.5 2.51 0.88 380 33.75 450 0 450 −33.75 3.14 1.10 250 22.5 600 0 650 0
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表 4 转动角速度-力效应拟合传递函数模型与评价
Table 4. Transfer function model and fitting evaluation of rotational rate to force effect
信号通道 传递函数 拟合度/% 幅频分散度/% p-Fy $ {G_{{F_y}}}\left( s \right) = {{\text{e}}^{ - 0.25s}}\dfrac{{ - 52.31{s^2} - 136.3s + 408.6}}{{{s^2} + 0.812\;6s + 14.64}} $ 80.2 1.93 p-Mx $ {G_{{M_x}}}\left( s \right) = \dfrac{{0.688\;3{s^2} + 281.1s + 574.4}}{{{s^2} + 1.998s + 0.053\;94}} $ 98.3 0.66 p-Mz $ {G_{{M_{\textit{z}}}}}\left( s \right) = {{\text{e}}^{ - 0.25s}}\dfrac{{68.11{s^2} + 142.9s - 349.6}}{{{s^2} + 0.807\;9s + 14.53}} $ 83.4 1.88 q-Fx $ {G_{{F_x}}}\left( s \right) = \dfrac{{ - 11.27{s^2} + 693.5s + 102.1}}{{{s^2} + 1.223s + 3.123}} $ 78.6 1.69 q-Fz $ {G_{{F_{\textit{z}}}}}\left( s \right) = {{ - 161}}{\text{.5}}s $ 72.7 2.55 q-My $ {G_{{M_y}}}\left( s \right) = {{\text{e}}^{ - 0.5s}}\dfrac{{5\;604{s^2} + 1\;777s + 4.001 \times {{10}^4}}}{{{s^3} + 3.446{s^2} + 12.44s + 1.095}} $ 91.8 3.92
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表 5 滚转角速度-力效应预测传递函数模型与评价
Table 5. Predictive transfer function model and evaluation of roll rate to force effect
信号
通道传递函数 拟合度/% 幅频
分散度/%p-Fy $ {G_{{F_y}}}\left( s \right) = {{\text{e}}^{ - 0.25s}}\dfrac{{ - 53.36{s^2} - 162.4s + 399.9}}{{{s^2} + 0.626\;8s + 15.07}} $ 64.3 2.10 p-Mx $ {G_{{M_x}}}\left( s \right) = \dfrac{{0.643\;9{s^2} + 281.1s + 552.1}}{{{s^2} + 1.921s + 0.053\;19}} $ 98.3 0.42 p-Mz $ {G_{{M_{\textit{z}}}}}\left( s \right) = {{\text{e}}^{ - 0.25s}}\dfrac{{69.31{s^2} + 174.1s - 334.6}}{{{s^2} + 0.607\;5s + 14.96}} $ 70.5 1.78
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表 6 俯仰角速度-力效应预测传递函数模型与评价
Table 6. Predictive transfer function model and evaluation of pitch rate to force effect
信号
通道传递函数 拟合度/% 幅频
分散度/%q-Fx $ {G_{{F_x}}}\left( s \right) = \dfrac{{8.038{s^2} + 743.1s + 100.7}}{{{s^2} + 1.328s + 3.087}} $ 81.0 1.66 q-Fz $ {G_{{F_{\textit{z}}}}}\left( s \right) = {{ - 160}}{\text{.4}}s $ 69.8 2.27 q-My $ {G_{{M_y}}}\left( s \right) = {{\text{e}}^{ - 0.5s}}\dfrac{{4835{s^2} + 676.1s + 3.5 \times {{10}^4}}}{{{s^3} + 2.826{s^2} + 11.21s + 1.116}} $ 96.1 3.24
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表 7 不同挡板传递函数幅频峰值特性
Table 7. Amplitude frequency peak characteristics of transfer function with different baffle settings
挡板设置 侧向力幅
值峰值/dB侧向力峰
值频率/(rad·s−1)偏航力矩
幅值峰值/dB偏航力矩
峰值频率/(rad·s−1)无挡板 63.1 4.1 64.9 4.1 挡板2 57.9 4.1 60.1 4.1 挡板1 53.6 4.0 55.3 4.0
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