Quantifying the influence of vortex instability on mean velocity field statistics of wingtip vortex  

涡不稳定性对翼尖涡平均速度场统计量影响的量化分析

作　　者：Zepeng Cheng Chong Pan Jiangsheng Wang 程泽鹏;潘翀;王将升

机构地区：[1]Key Laboratory of Fluid Mechanics of Ministry of Education,Beihang University,Beijing 100191,China [2]Tianmushan Laboratory,Hangzhou 310023,China

出　　处：《Acta Mechanica Sinica》2024年第11期13-21,共9页力学学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12202031,12225202,and 12102024);Tianmushan Laboratory Foundation(Grant No.TK2023-B-004).

摘　　要：During its evolution to the far field,the wingtip vortex exhibits complex instability behaviors such as long-wave/short-wave instability and vortex wandering.However,the quantification influence of vortex instability on its velocity field statistics has not been well investigated.To this end,experimental measurements of a canonical wingtip vortex generated by an elliptical wing under various angles of attack and Reynolds numbers were conducted using particle image velocimetry.It is found that the streamwise variation of wandering amplitude presents an exponential growth within the middle-to-far wake region and asymptotically saturates to 10−1b in the far wake,which differs from the previous report of a linear growth trend in the nearwake region.Further,two average methods,i.e.,time average(TA)and ensemble average(EA),were adopted to compare the velocity field statistics.In both TA-and EA-obtained flow fields,the vortex radius rc,peak vorticity x p,and vortex circulationΓall demonstrate a power-law scaling with respect to the streamwise location,rc∝x^(kr),Ω_(x)^(p) ∝x^(-kω) and Г∝x^(kГ),respectively.For a full rolling-up wingtip vortex in the middle-to-far wake region,the fact that kГ=k_(ω)-2k_(r) demonstrates that the vortex circulation can be scaled Г=Ω_(x)^(p)(r_(c))^(2).On the other hand,TA overestimates the decay rate of peak vorticity k and the growth rate of vortex radius kr.Furthermore,the TA-introduced bias level of the peak vorticity and vortex radius is found to be scaled with an empirical scaling between the wandering amplitude by a power law,respectively.These findings provide significant practical value for detecting wake vortex in wake vortex spacing systems.在向远场演化过程中,翼尖涡表现出如长波/短波不稳定性和涡摇摆运动等复杂的不稳定行为.然而,涡不稳定性对其流场统计量的量化影响尚未得到很好的研究.为此,本文采用粒子图像测速技术对椭圆机翼在不同迎角和雷诺数下产生的翼尖涡进行了实验测量.研究发现,在中、远场的尾迹区域,翼尖涡摇摆运动的幅值沿流向呈指数增长并在远尾迹区域逐渐饱和至10^(−1)b.该发现与前人所报道的近场区域时的线性增长趋势不同.进一步地,采用时间平均和系综平均等两种平均方法比较分析各自的速度场统计量.在时间平均和系综平均获得的平均流场中,翼尖涡的涡核半径rc,峰值涡量Ω_(x)^(p)和环量Γ的沿程变化均可以用幂次律关系式来描述,即rc∝x^(kr),Ω_(x)^(p) ∝x^(-kω)和Г∝x^(kГ).对于中、远场已完全卷起的翼尖涡,三者的幂因子满足kГ=k_(ω)-2k_(r),表明此时的翼尖涡环量可用Г=Ω_(x)^(p)(r_(c))^(2)近似表述.研究还发现时间平均高估了峰值涡量的衰减速率和涡核半径的增长速率,而两种平均方式引起的峰值涡量与涡核半径的估计误差均可用摇摆幅值的幂次律来预测.以上发现对民航运输中尾流间隔系统的尾涡探测和识别具有重要意义和实用价值.

关 键 词：Vortex flow Vortex instability Wingtip vortex PIV 

分 类 号：O35[理学—流体力学]