Optimization of probe-drogue aerial refueling docking strategy based on pre-docking distance
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摘要:
软式空中加油中锥套的位置受到头波效应时难以控制，易导致对接失败。针对该问题，建立了软式空中加油对接的动态特性仿真平台,计算了受油机在不同预对接距离时锥套的位移响应。计算结果表明：不同的预对接距离对锥套的下沉量变化影响显著。预对接距离越大，对接过程持续时间越长，锥套受头波效应累积干扰的时间越久，导致对接全过程中下沉量的动态变化幅度越大。为解决头波效应对锥套下沉量影响过大的问题，计算了不同预对接距离下受油机能够成功对接的纵向初始位置包络。优化结果表明：对接前受油插头在瞄准锥套中心的基础上，根据预对接距离向上偏移50～70 cm，可显著提升对接成功率，该策略对大气扰动也表现出良好的鲁棒性。
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关键词:
- 软式空中加油 /
- 预对接距离 /
- 计算流体力学（CFD） /
- 头波效应 /
- 对接策略
Abstract:In probe-and-drogue aerial refueling, the position of the drogue is challenging to control under the bow wave effect, frequently leading to docking failure. To address this issue, a dynamic simulation platform for the probe-and-drogue aerial refueling docking process was developed to calculate the displacement response of the drogue at different pre-docking distances. The computational results indicated that the pre-docking distance significantly affected the variation in drogue sinkage. A larger pre-docking distance extended the duration of the docking process, thereby increasing the cumulative interference time of the bow wave effect, and resulting in a greater dynamic variation amplitude of sinkage throughout the process. To mitigate the excessive impact of the bow wave effect on drogue sinkage, the longitudinal initial position envelopes for successful docking were determined for different pre-docking distances. Optimization results demonstrate that, in addition to aligning with the center of the drogue, applying an upward offset of 50–70 cm based on the pre-docking distance can significantly enhance the docking success rate. Moreover, this strategy exhibits robust performance against atmospheric disturbances.
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图 1 软管-锥套系统离散化示意图
Figure 1. Schematic diagram of discretization for the hose-drogue system
图 2 二维相邻单元搜索算法示意图
Figure 2. Schematic diagram of the two-dimensional neighboring-cell search algorithm
图 3 不同弹性模量软管下的软管-锥套平衡状态
Figure 3. Equilibrium states of the hose–drogue system with different hose elastic moduli
图 4 不同线密度软管下的软管-锥套平衡状态
Figure 4. Equilibrium states of the hose–drogue system with different hose linear densities
图 5 不同锥套阻力系数下的软管-锥套平衡状态
Figure 5. Equilibrium states of the hose–drogue system with different drogue drag coefficients
图 10 不同大气条件下锥套z方向位移变化
Figure 10. Variation of drogue z-direction displacement under different atmospheric conditions
图 11 不同大气条件下锥套y方向位移变化
Figure 11. Variation of drogue y-direction displacement under different atmospheric conditions
图 12 可对接成功的受油机纵向位置包络
Figure 12. Longitudinal position envelope of the receiver for successful docking
图 13 可对接成功的受油机初始向上位移
Figure 13. Feasible initial upward displacement of the receiver for successful docking
图 14 不同预对接距离向上调整不同距离的对接结果
Figure 14. Docking results with different upward adjustments at different pre-docking distances
图 15 大气扰动下锥套位移变化
Figure 15. Displacement response of the drogue under atmospheric disturbance
$ {C}_{{\mathrm{d}}0} $ 基线阻力系数 $ {C}_{{\mathrm{m}}\alpha } $/（°）−1 俯仰力矩对迎角的气动导数 $ {C}_{{\mathrm{l}}0} $ 基线升力系数 $ {C}_{{\mathrm{d}}\beta } $/（°）−1 阻力对侧滑角的气动导数 $ {C}_{{\mathrm{c}}0} $ 基线侧力系数 $ {C}_{l\beta } $/（°）−1 升力对侧滑角的气动导数 $ {C}_{{\mathrm{n}}0} $ 基线偏航力矩系数 $ {C}_{{\mathrm{c}}\beta } $/（°）−1 侧力对侧滑角的气动导数 $ {C}_{{\mathrm{m}}0} $ 基线俯仰力矩系数 $ {C}_{{\mathrm{n}}\beta } $/（°）−1 偏航力矩对侧滑角的气动导数 $ {C}_{{\mathrm{d}}\alpha } $/（°）−1 阻力对迎角的气动导数 $ {C}_{{\mathrm{m}}\beta } $/（°）−1 俯仰力矩对侧滑角的气动导数 $ {C}_{{\mathrm{l}}\alpha } $/（°）−1 升力对迎角的气动导数 锥套下沉量/m 锥套相对加油吊舱的竖直距离 $ {C}_{{\mathrm{c}}\alpha } $/（°）−1 侧力对迎角的气动导数 预对接距离/m 初始状态受油机受油插头相对锥套的水平距离 $ {C}_{{\mathrm{n}}\alpha } $/（°）−1 偏航力矩对迎角的气动导数 
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表 1 软管-锥套系统参数
Table 1. Parameters of the hose-drogue system
参数 数值 软管总长/m 14.3 软管内径/m 0.051 软管外径/m 0.067 软管密度/（kg/m） 4.09 软管弹性模量/108 Pa 2 锥套质量/kg 29.5 锥套阻力系数 0.83068
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表 2 本文仿真与文献对比结果
Table 2. Comparison between the simulation results in this paper and the results in the literature
速度/（m/s） h= 2286 mh= 7620 m$ {V}_{{\mathrm{d}}} $/m $ \Delta {V}_{{\mathrm{d}}} $/% $ {V}_{{\mathrm{d}}} $/m $ \Delta {V}_{{\mathrm{d}}} $/% 98 5.810 2.3 7.908 −1.1 108 5.091 2.7 7.227 0.8 118 4.455 2.5 6.580 2.3 129 3.856 0.6 5.715 −1.1 139 3.397 5.255 0.8 149 3.008 −0.5 4.812 2.0 159 2.679 −1.0 4.371 2.1 注：表中$ {V}_{{\mathrm{d}}} $表示锥套下沉量，即从拖曳点到锥套的高度差。$ \Delta {V}_{{\mathrm{d}}} $表示本章计算所得锥套下沉量与参考文献下沉量偏差百分比。
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表 3 软管-锥套系统参数
Table 3. Parameters of the hose-drogue system
参数 数值 软管总长/m 24 软管内径/m 0.076 软管外径/m 0.092 软管密度/（kg/m） 4.4 软管弹性模量/108 Pa 2 锥套质量/kg 35
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表 4 锥套气动参数
Table 4. Aerodynamic parameters of the drogue
参数 数值 基线气动 $ {C}_{{\mathrm{d}}0} $ 0.3695 $ {C}_{{\mathrm{l}}0} $ 0 $ {C}_{{\mathrm{c}}0} $ 0 $ {C}_{{\mathrm{n}}0} $ 0 $ {C}_{{\mathrm{m}}0} $ 0 相对迎角 $ {C}_{{\mathrm{d}}\alpha } $ 0 $ {C}_{{\mathrm{l}}\alpha } $ 0.00226 $ {C}_{{\mathrm{c}}\alpha } $ 0 $ {C}_{{\mathrm{n}}\alpha } $ 0 $ {C}_{{\mathrm{m}}\alpha } $ − 0.00411 相对侧滑角的气动参数 $ {C}_{{\mathrm{d}}\beta } $ 0 $ {C}_{{\mathrm{l}}\beta } $ 0 $ {C}_{{\mathrm{c}}\beta } $ − 0.00226 $ {C}_{{\mathrm{n}}\beta } $ − 0.00411 $ {C}_{{\mathrm{m}}\beta } $ 0
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表 5 大气扰动下对接结果
Table 5. Docking results under atmospheric disturbance
预对接
距离/m最终与锥套中心
z方向差值/m是否
对接成功2 0.02 √ 4 0.04 √ 8 0.02 √
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