基于三阶显式格式的旋翼时间步进自由尾迹计算与验证  

Prediction and Validation of Rotor Time-marching Free Wake Based on 3rd-order Explicit Numerical Scheme

作　　者：辛冀[1] 李攀[1] 陈仁良[1] 

机构地区：[1]南京航空航天大学直升机旋翼动力学国家级重点实验室,江苏南京210016

出　　处：《航空学报》2013年第11期2452-2463,共12页Acta Aeronautica et Astronautica Sinica

基　　金：江苏省普通高校研究生科研创新计划(CXLX12_0166);中央高校基本科研业务费专项资金(NN2012031)

摘　　要：以已有的二阶显式时间步进自由尾迹计算格式CB2D(Center difference and Backward difference 2nd-order scheme with numerical Dissipation term)为基础,根据其修正方程中误差项的特有形式,通过在格式中加入速度离散多项式,构建了一种三阶显式格式CB3D(Center difference and Backward difference 3rd-order scheme with numerical Dissipation term)。该格式在消去二阶误差项的同时也消除了二阶的数值反耗散效应,使计算格式更加稳定。利用该计算格式对悬停状态下的旋翼尾迹进行了迭代计算,结果表明,新格式的精度达到了3阶,收敛速度较之前也有较大的提高。数值试验表明,将会引起数值反耗散效应的二阶误差项单独加入CB3D格式后,格式稳定性出现了下降,验证了CB3D格式对其进行消除的必要性。选取了悬停总距突增和前飞总距突增两种非定常状态作为算例,使用新格式对其进行了数值模拟,给出了不同时刻的尾迹结构图,分析了尾迹变化与气动力之间的关系。将非定常状态下计算得到的拉力随时间变化情况与试验值进行了对比,取得了较好的一致性。A new explicit time-marching free wake scheme named CB3D （Center difference and Backward difference 3rd-or- der scheme with numerical Dissipation term） is presented on the basis of the former CB2D （Center difference and Backward difference 2nd-order scheme with numerical Dissipation term） scheme. The 2nd-order error terms in the modified equation of the CB2D scheme are eliminated with discrete velocity polynomials. The 2rid-order anti-dissipation terms are also eliminated at the same time and the stability of the new scheme is enhanced. The free wake of a hovering rotor is predicted iteratively with the two schemes and the results show that the CB3D scheme reaches a 3rd-order accuracy, its convergence rate is im- proved considerably. When adding an artificial numerical error into the initial wake geometry, CB3D yields a more realistic resultant wake geometry than the CB2D scheme and so it is more stable. Two unsteady flying states, namely, collective pitch ramping up of the rotor in hovering and forward flying, are chosen to validate the CB3D scheme. Wake geometries in the unsteady process are plotted and the influence of wake geometry upon rotor airload is analyzed. The predicted time-var- ying rotor thrust is compared with the corresponding experimental results, which shows there is good agreement between them.

关 键 词：旋翼 时间步进 自由尾迹 三阶精度 显式格式 

分 类 号：V211.52[航空宇航科学与技术—航空宇航推进理论与工程]