Simulation and analysis of SPH algorithm for interaction of aircraft tire-wet pavement
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摘要:
针对飞机在湿滑道面上的滑水问题，采用光滑粒子流体动力学(SPH)算法建立了飞机轮胎-湿滑道面有限元模型，与流固耦合算法(CEL)模型进行对比，显示了SPH算法的优越性，进而分析了不同轮胎速度及水膜厚度对轮胎与湿滑道面相互作用的影响规律。结果表明，SPH模型得到的临界滑水速度与CEL模型结果相差不超过5%；舰首波、侧向羽流等流体特征更为明显立体；平均运算效率较CEL模型提高36.5%。利用SPH模型分析可得，道面支撑力随轮胎速度增加呈先平缓下降再急速下降的趋势，水膜厚度为3～13 mm时，急速下降段所在轮胎速度区间为170～260 km/h，基本处于A320飞机的着陆滑跑速度范围内，应增强对飞机滑水事故风险的防范；位移阻力随着轮胎速度增加呈先增大后减小的趋势，且在轮胎达到临界滑水速度时取得最大值，进而提出利用位移阻力最大值确定临界滑水速度的方法；侧向羽流最大溅水高度随轮胎速度增加呈先升高后降低的趋势，在接近临界滑水速度时达到最大值；舰首波最大溅水高度低于侧向羽流最大溅水高度，且随轮胎速度增加而降低，达到临界滑水速度时舰首波接近消失，2种溅水特征的最大溅水高度值均低于A320飞机发动机的最小离地高度0.680 m，不会对发动机产生影响。
Abstract:In view of aircraft hydroplaning on wet and slippery pavement, a finite element model of aircraft tire-wet pavement was established by using the smoothed particle hydrodynamics (SPH) algorithm and compared with the coupled Eulerian-Lagrangian (CEL) model, which highlighted the superiority of SPH algorithm. Then, the influence of different tire speeds and water film thickness on the interaction between tire and wet pavement was analyzed. The results show that the difference between the critical hydroplaning speeds obtained by the SPH algorithm model and the CEL model is less than 5%. The fluid characteristics such as bow wave and lateral plume are more obvious. The average computing efficiency of the SPH model is 36.5% higher than that of the CEL model. Then, the SPH model is used to analyze and get the following conclusions: the pavement supporting force decreases gently at first and then rapidly with the increase in speed. When the thickness of accumulated water is 3–13 mm, the speed range of the rapidly decreasing section is 170–260 km/h, which is basically within the landing and taxiing speed range of A320 aircraft, and the prevention of the risk of hydroplaning accidents should be strengthened. The displacement resistance increases at first and then decreases with the increase in speed, and the maximum value is obtained when the tire reaches the critical hydroplaning speed. Then, a method of determining the critical hydroplaning speed by using the maximum value of displacement resistance is put forward. The maximum splashing height of the lateral plume increases at first and then decreases with the increase in speed and reaches a maximum value when approaching the critical hydroplaning speed. The maximum splashing height of the bow wave is lower than that of the lateral plume and decreases with increasing speed. When the critical hydroplaning speed is reached, the bow wave almost disappears. The maximum splashing height values of both splashing characteristics are lower than the minimum ground height of 0.680 m for the A320 aircraft engine and will not affect the engine.
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图 3 不同水膜厚度下流体特征
Figure 3. Characteristics of liquid under different water film thicknesses
图 6 SPH模型轮胎与积水道面接触特征
Figure 6. Contact feature between tire and wet pavement of SPH model
图 10 道面支撑力与位移阻力对比
Figure 10. Comparison of pavement supporting force and displacement resistance
表 1 轮胎物理参数
Table 1. Physical parameters of tire
直径/
cm内径/
cm宽度/
cm沟槽
宽度/mm沟槽
深度/mm胎压/
kPa单轮
轴载/kN116.8 50.8 43.2 10.0 9.0 1140.0 154.5 
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${\rho _{\text{w}}}/{\text{(}}{\mathrm{kg}} \cdot {{\mathrm{m}}^{-3}})$ $ {c}_{0}/({{\mathrm{m}} \cdot {\mathrm{s}}}^{-1}) $ $s$ ${\varGamma _0}$ $ \eta /({\mathrm{Pa}} \cdot {\mathrm{s}}) $ 1000 1480 0 0 1.79×10−3
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表 3 不同水膜厚度下临界滑水速度比较[19]
Table 3. Comparison of critical hydroplaning speeds under different water film thicknesses[19]
水膜厚度/mm 临界滑水速度/（km·h−1） 理论值与SPH算法
模拟值相对误差/%理论值 CEL算法 SPH算法 3 281.2 253.0 262.8 6.5 5 247.6 241.0 248.4 0.3 7.66 222.7 214.0 223.2 0.2 10 208.4 205.0 209.0 0.3 13 195.3 193.0 190.8 2.3
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表 4 不同轮胎速度工况下2种算法运算时间比较
Table 4. Comparison between operation time under different tire speeds by two algorithms
轮胎速度/
（km·h−1）运算时间/min 提升率/% CEL算法 SPH算法 144 373 245 34.3 162 332 223 32.8 180 293 182 37.9 198 251 153 39.0 209 236 145 38.6
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表 5 整体预计节省时间
Table 5. Expected time savings in all conditions
水膜厚度/mm 工况数量 预计节省时间/min 3 10 1070 5 7 749 7.66 8 856 10 6 642 13 5 535
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表 6 各水膜厚度对应临界滑水速度
Table 6. Critical hydroplaning speed corresponding to each water film thickness
水膜厚度/mm 临界滑水速度/（km·h−1） 位移阻力法 道面支撑力法 3 262.8 257～270 5 244.8 225～252 7.66 223.2 218～234 10 209 206～216 13 190.8 188～198
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