Adaptive cross-section segmentation method for aircraft fuel mass properties calculation
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摘要:
针对飞机燃油系统方案设计阶段截面连续变化的飞机油箱，提出了具有截面自适应性的燃油质量特性计算方法。首先根据飞行姿态和过载计算油面法向量，确定最低油面位置；然后根据等效燃油实体确定分割步长进行首次分割，并根据截面面积的变化情况，通过后续分割对误差进行补偿，直至分割精度达到预设精度阈值要求；最后对分割后的燃油实体进行燃油质量特性测量和计算。针对某型无人机燃油系统中多种不同类型的截面连续变化油箱进行仿真验证，表明该方法具有截面自适应性，且相比共轭梯度寻优算法，能够在保证计算精度的情况下，计算效率提升71.43%~92.31%，适用于飞机燃油系统方案设计阶段通过燃油质量特性计算快速准确地判断设计方案在重心方面的可行性。
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关键词:
- 燃油质量特性 /
- 截面自适应分割 /
- 油面法向量 /
- 燃油实体 /
- 飞机燃油系统方案设计
Abstract:For aircraft fuel tanks with continuously varying cross section in aircraft fuel system design, a method for calculating fuel mass properties with cross-section adaptability is proposed. Firstly, the fuel level normal vector is calculated using flight attitude and overload to determine the location of the lowest fuel level. Secondly, the split step is determined based on equivalent fuel entity to perform the first segmentation, and errors will be compensated through subsequent segmentations according to the cross-sectional area changes until the segmentation accuracy reaches preset accuracy threshold. Finally, fuel mass properties are measured and calculated for the segmented fuel entities. The simulation carried out for different types of fuel tanks with continuously varying cross section in fuel system of a certain type of UAVs shows that this method has the cross-section adaptability and can improve calculation efficiency by 71.43%-92.31% compared with conjugate gradient optimization algorithm, while ensuring calculation accuracy. It is suitable for quick and accurate determination of feasibility of design schemes in terms of gravity center by calculating fuel mass properties.
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表 1 精度等级
Table 1. Accuracy levels
精度等级 误差计算公式 1级 ±(4%ind+2%fq) 2级 ±(2%ind+0.75%fq) 3级 ±(1%ind+0.5%fq) 注：ind—指示值；fq—满油量。 
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表 2 飞机燃油质量特性计算参数
Table 2. Parameters of aircraft fuel mass properties calculation
序号 参数 描述 赋值计算
方法1 Vtotal 满油状态时燃油实体模型的总体积 测量赋值 2 m 分割完成后的燃油实体质量 3 x 分割完成后的燃油实体重心x坐标 4 y 分割完成后的燃油实体重心y坐标 5 z 分割完成后的燃油实体重心z坐标 6 Vtarget 指定剩余油量 人为指定 7 n 精度调节指数 8 Vacc 精度阈值 公式关系
计算9 HMax 分割平面最大偏移高度 10 hi 第i次分割的分割平面偏移高度 11 hi-1 第i-1次分割的分割平面偏移高度 12 Δhi 第i次分割的分割步长 13 Vi 第i次分割后的燃油实体体积 14 ΔVi 第i次分割后的油量差值 15 Si 第i次分割后的截面面积 16 Na 截面自适应分割法的分割次数 系统计数 17 Ng 共轭梯度寻优算法的分割次数
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表 3 实际剩余油量及精度等级误差
Table 3. Actual remaining fuel and error corresponding to different accuracy levels
剩余
油量/%实际剩余油量/L 精度等级误差/L 油箱1 油箱2 油箱3 油箱1 油箱2 油箱3 1级 2级 3级 1级 2级 3级 1级 2级 3级 90 283.437 351.021 98.635 17.636 8.031 4.409 21.841 9.946 5.460 6.137 2.795 1.534 80 251.944 312.018 87.675 16.376 7.401 4.094 20.281 9.166 5.070 5.699 2.575 1.425 70 220.451 273.016 76.716 15.117 6.771 3.779 18.721 8.385 4.680 5.261 2.356 1.315 60 188.958 234.014 65.756 13.857 6.141 3.464 17.161 7.605 4.290 4.822 2.137 1.206 50 157.465 195.012 54.797 12.597 5.511 3.149 15.601 6.825 3.900 4.384 1.918 1.096 40 125.972 156.009 43.838 11.337 4.881 2.834 14.041 6.045 3.510 3.945 1.699 0.986 30 94.479 117.007 32.878 10.078 4.252 2.519 12.481 5.265 3.120 3.507 1.480 0.877 20 62.986 78.005 21.919 8.818 3.622 2.205 10.921 4.485 2.730 3.069 1.260 0.767 10 31.493 39.002 10.959 7.558 2.992 1.890 9.361 3.705 2.340 2.630 1.041 0.658
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表 4 分割平面最大偏移距离
Table 4. Maximum offset distance of segmentation plane
油箱1最大偏移距离/mm 油箱2最大偏移距离/mm 油箱3最大偏移距离/mm 油面法
向量A油面法
向量B油面法
向量C油面法
向量A油面法
向量B油面法
向量C油面法
向量A油面法
向量B油面法
向量C834.300 927.187 925.413 552.067 671.856 662.010 208.815 301.095 595.075
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表 5 第1次分割后剩余油量误差及精度等级
Table 5. Remaining fuel error and accuracy levels after the first segmentation
剩余
油量/%油箱1剩余油量误差/L 油箱2剩余油量误差/L 油箱3剩余油量误差/L 油面法
向量A油面法
向量B油面法
向量C油面法
向量A油面法
向量B油面法
向量C油面法
向量A油面法
向量B油面法
向量C90 8.164(1) 21.403 16.225(1) 9.453(2) 34.149 18.800(1) 9.219 9.051 9.677 80 8.230(1) 20.998 18.019 4.217(3) 54.758 18.653(1) 12.632 13.198 14.291 70 7.058(1) 15.881 12.154(1) -3.095(3) 60.693 6.303(2) 12.511 13.872 13.048 60 5.065(2) 9.568(1) 4.506(2) -11.210(1) 51.788 -12.855(1) 10.319 11.346 7.912 50 2.658(3) 2.654(3) -3.695(2) -19.684 33.735 -33.268 7.341 5.780 2.929(1) 40 0.250(3) -4.260(2) -11.791 -28.079 14.309 -51.858 4.335 -1.627(2) -1.900(1) 30 -1.743(3) -10.573 -19.126 -35.931 -5.026(2) -62.699 1.328(2) -8.259 -6.615 20 -2.915(2) -15.697 -24.558 -40.861 -23.051 -58.543 -1.675(1) -10.927 -10.105 10 -2.872(2) -17.965 -20.480 -29.680 -25.692 -35.924 -3.890 -8.563 -8.245 注：括号()内数字为精度等级，未标注精度等级的说明未能达到1级精度。
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