编队飞行中基于危险区域的后机最优位置研究

Optimal Position of Trailing Aircraft Based on Hazard Zone in Formation Flight

编队飞行是实现民航绿色发展的重要措施之一。在前机尾涡危险区域分析的基础上,科学确定后机最优位置是编队飞行的关键。首先,以随机两阶段尾涡消散模型为基础,利用Hallock-Burnham涡模型和诱导滚转力矩系数模型分析后机诱导滚转力矩系数的演变规律。然后,基于设定的安全阈值,给出前机尾涡危险区域,并考虑飞行高度、速度和风对危险区域的影响。最后,基于后机不同位置处的燃油流量减少率,得出编队飞行中后机最优位置。研究结果表明:后机诱导滚转力矩系数随着前、后机之间横向距离的增加,呈先增后减再增的趋势;随纵向距离的增加,呈先缓慢减小后快速减小的趋势;高度越高、速度越小,诱导滚转力矩系数的峰值越高。飞行高度越高、速度越小,前机初始尾涡的危险区域越大;随着纵向距离的增加,危险区域不断减小,并随涡核的下沉不断下降。侧风使危险区域发生偏离,侧风越大,偏离程度越大。顺风会增加危险区域的纵向距离,顶风则与之相反。两架B737-800飞机在12000 m高度以0.78马赫数进行编队飞行时,前、后机纵向距离3000 m处,无风情况下后机最优位置为横向距离30 m或-30 m、垂直距离29 m,此时燃油流量减少率为7.01%。相较于无风,左侧风20 m·s^(-1)下,燃油流量减少率和垂直距离不变,横向距离增加;顺风20 m·s^(-1)下,燃油流量减少率增加,横向距离不变,垂直距离减少;顶风20 m·s^(-1)下,燃油流量减少率减小,横向距离不变,垂直距离增加。

Formation flight is one of the important measures to realize the green development of civil aviation.Based on the analysis of the hazard area of the tail vortex of the lead aircraft,determining the optimal position of the trailing aircraft is the key to formation flight.Firstly,based on the Probabilistic Two-Phase Wake Vortex Decay,the evolution of the induced roll moment coefficient of the trailing aircraft was analyzed by using the Hallock-Burnham vortex model and the induced roll moment coefficient model.Then,based on the safety threshold,the wake vortex hazard area of the lead aircraft was calculated with considering the influence of flight altitude,speed,and wind on the hazard area.Finally,based on the fuel flow reduction rate at different positions of the trailing aircraft,the optimal position of the trailing aircraft in formation flight was obtained.The results show that the induced rolling moment coefficient is first increased,then decreased,and again increased with the increase of the transverse distance between the leading and trailing aircraft.With the increase of longitudinal distance,it decreased slowly first and then rapidly.The higher altitude leads to a lower speed and a higher peak value of the induced rolling moment coefficient,and thus the larger wake vortex hazard area of the lead aircraft.With the increase of the longitudinal distance,the hazard area is decreased continuously,and the altitude is decreased continuously with the sinking of the vortex core.The crosswind diverges the hazard area,and the greater crosswind leads to the greater deviation.A tailwind increases the longitudinal distance of the hazard area,while a headwind does the opposite.When two B737-800 aircraft fly in formation at 12000 m altitude at Mach 0.78,if the longitudinal spacing between lead and trailing aircraft is 3000 m,the optimal position of the trailing aircraft in no wind condition is the transverse spacing of 30 m or negative 30 meters and vertical spacing of29 m,and the fuel flow reduction rate is 7.01%.Compared with the no wind condition,the fuel flow reduction rate and vertical distance remain the same under the left wind of 20 meters per second,while the lateral distance increases.At the downwind condition of 20 meters per second,the reduction rate of the fuel flow increases,the lateral distance remains unchanged,and the vertical distance decreases.At the headwind condition of 20 meters per second,the reduction rate of the fuel flow decreases,the lateral distance remains the same,and the vertical distance increases.