文章快速检索 高级检索

1. 北京航空航天大学机械工程及自动化学院, 北京 100083;
2. 沈阳航空航天大学航空航天工程学部, 沈阳 110136

Calculation method of blade element aerodynamic loads based on small perturbation theory
WANG Wei1, LI Dongsheng1, LIU Chun2
1. School of Mechanical Engineering and Automation, Beijing University of Aeronautics and Astronautics, Beijing 100083, China;
2. Faculty of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China
Abstract: A calculation method of blade element aerodynamic loads based on small perturbation theory is established for helicopter flight simulation application. The method synthesizes flap-lag-torsion elastic rotor blade mode, couples rotor dynamic inflow, unsteady aerodynamics model with dynamic stall and rotor trimming model. The entire model is developed in a standard state-space form. To verify this model, the UH-60A helicopter is taken as an example, and the effects of yaw flow on rotor aerodynamic performance are studied at low speed flight and high speed flight. It is shown that yaw flow has a greater effect on rotor aerodynamic performance at high speed flight. Blade induced velocity fields and aerodynamic loads are simulated, and the results are compared with flight test data. It is shown by the results that the method can accurately predict the unsteady aerodynamic rotor loads in steady flight by capturing its variational characteristics along blade azimuthal locations, and it is still applicable for high speed flight.
Key words: helicopter     small disturbance theory     rotor     induced velocity     aerodynamic loads
﻿

1 旋翼叶素气弹模型

1.1 模型概述

 图 1 桨叶基准线和叶素坐标系 Fig. 1 Blade baseline and element coordinate

Pf(s,t)= [xf(s,t)yf(s,t)zf(s,t)Φx(s,t)Φy(s,t)Φz(s,t)]T

1.2 弹性旋翼的惯性模型

1.3 诱导速度

1.4 弹性旋翼的气动载荷

[CNCm]T=CX+D[αq]T(27) 式中:X为状态向量;CN为法向力系数;A、B、C和D为变换矩阵，C和D定义可参见文献[25]

2 挥舞动力学方程

3 旋翼配平模型

 图 2 旋翼系统模型 Fig. 2 Rotor system model

4 偏航流效应

 图 3 偏航角变化曲线 Fig. 3 Yaw angle changing curves
5 算例验证与分析

 参数 μ=0.110 μ=0.368 本文计算 数据/(°) 飞行试验 数据/(°) 本文计算 数据/(°) 飞行试验 数据/(°) θ0 8.69 7.75 13.86 13.21 θ1c 4.79 4.06 7.87 6.56 θ1s -1.84 -2.08 -7.95 -9.07 αs -1.9 -2.3 7.9 7.8 Φs -0.98 -1.22 1.2 1.6
5.1 旋翼诱导速度分布

 图 4 旋翼诱导速度分布图 Fig. 4 Rotor induced velocity graph
5.2 气动力与力矩模拟

 图 5 法向力比较(μ=0.110) Fig. 5 Normal force comparison (μ=0.110)

 图 6 法向力比较(μ=0.368) Fig. 6 Normal force comparison (μ=0.368)

 图 7 俯仰力矩比较(μ=0.110) Fig. 7 Pitching moment comparison (μ=0.110)

 图 8 俯仰力矩比较(μ=0.368) Fig. 8 Pitching moment comparison (μ=0.368)

 图 9 机动飞行仿真画面 Fig. 9 Scene of maneuver flight simulation
6 结 论

1) 采用小扰动原理建立的桨叶系统模型考虑了偏航流效应。低速飞行时,偏航流对旋翼气动性能影响较小;高速飞行时,偏航流对旋翼气动性能影响较大,即偏航角峰值较大,最大达到35°。

2) 建立的旋翼系统模型能够准确预测了UH-60A直升机在低速和高速2种飞行条件下的旋翼诱导速度场，既能较好地反映出随桨盘平面不均匀分布变化,又能体现出随相位变化的规律以及随旋翼气动力变化的滞后效应,能够满足实时飞行仿真的要求。

3) 本文计算的桨叶叶素气动载荷分布趋势与飞行试验数据吻合,既能较好地反映载荷的幅值变化,又能体现出相位变化的规律,其计算精度能够满足旋翼设计的要求,计算速度满足实时飞行模拟。

4) 高速飞行时,由于前行桨叶遇到较大扰动非线性气流以及尾涡流场畸变效应,使得桨叶气动载荷变化剧烈并在方位角90°/270°附近产生了相位偏移,俯仰力矩存在较大非线性扰动性。

 [1] 栗英杰. 直升机飞行模拟器关键技术研究[D].长春:吉林大学,2012:1-2. LI Y J.Research on key technologies of helicopter flight simulator[D].Changchun:Jilin University,2012:1-2(in Chinese). Cited By in Cnki (6) [2] 王芳. 机动飞行状态下的旋翼入流和响应分析[D].南京:南京航空航天大学,2007:4-5. WANG F.Investigation on the inflow and aerodynamic response of rotors in maneuvering flight[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2007:4-5(in Chinese). Cited By in Cnki (1) [3] PITT D M,PETERS D A.Theoretical prediction of dynamic inflow derivatives[J].Vertica,1981,5(1):21-34. [4] PETERS D A,BOYD D D,HE C J.Finite-state induced-flow model for rotors in hover and forward flight[J].Journal of the American Helicopter Society,1989,34(4):5-17. Click to display the text [5] KELLER J D. An investigation of helicopter dynamic coupling using an analytical model[J].Journal of the American Helicopter Society,1996,41(4):322-330. Click to display the text [6] ZHAO J G. Dynamic wake distortion model for helicopter maneuvering flight[D].Atlanta,Georgia:Georgia Institute of Technology,2005:35-36. Click to display the text [7] DUMONT A,LE PAPE A,PETER J.Aerodynamic shape optimization of hovering rotors using a discrete adjoint of the reynolds-averaged navier-stokes equations[J].Journal of the American Helicopter Society,2011,56(3):256-258. Click to display the text [8] 徐广,王博,徐国华.基于CFD的直升机旋翼流场及气动力计算[J].南京航空航天大学学报,2011,43(3):369-374. XU G,WANG B,XU G H.Computation on flow field and aerodynamic load of helicopter rotors based on CFD[J].Journal of Nanjing University of Aeronautics & Astronautics,2011,43(3):369-374(in Chinese). Cited By in Cnki (1) [9] 李攀. 旋翼非定常自由尾迹及高置信度直升机飞行力学建模研究[D].南京:南京航空航天大学,2010:6-7. LI P.Rotor unsteady free-vortex wake model and investigation on high-fidelity modeling of helicopter flight dynamics[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2010:6-7(in Chinese). Cited By in Cnki (8) [10] CURTISS H C. Stability and control modeling[J].Vertica,1988,12(4):381-394. [11] TISCHLER M B. System identification requirements for high-bandwidth rotorcraft flight control system design[J].Journal of Guidance,Control,Dynamics,1990,13(5):835-841. Click to display the text [12] HOWLETT J J. UH-60 black hawk engineering simulation program:Volume I-mathematical model:NASA CR-166309[R].Reston:AIAA,1981:27-58. [13] BHAGWAT M J.Mathematical modeling of the transient dynamics of helicopter rotor wakes using a time-accurate free-vortex methods[D].College Park,Maryland:University of Maryland,2001:97-121. [14] RIBERA M. Helicopter flight dynamics simulation with with a time-accurate free-vortex wake model[D].College Park,Mary-land:University of Maryland,2007:104-150. [15] 赵景根,徐国华,招启军.基于自由尾迹分析的直升机旋翼下洗流场计算方法[J].兵工学报,2006,27(1):63-68. ZHAO J G,XU G H,ZHAO Q J.A calculating method of helicopter rotor downwash flowfield based on free wake analysis[J].Acta Armamentarii,2006,27(1):63-68(in Chinese). Cited By in Cnki (6) [16] LI P,CHEN R L.Rotor unsteady aerodynamics model using an efficient free-vortex method[J].Aircraft Engineering and Aerospace Technology,2012,84(5):311-320. Click to display the text [17] 刘勇,邵松,朱清华,等.基于时间精确自由尾迹方法的旋翼非定常气动特性分析[J].航空学报,2012,33(4):607-616. LIU Y,SHAO S,ZHU Q H,et al.Analysis of rotor unsteady aerodynamic characteristics based on time accurate free wake formulation[J].Acta Aeronautica et Astronautica Sinica,2012,33(4):607-616(in Chinese). Cited By in Cnki (2) [18] 吕维梁,史勇杰,魏鹏,等.旋翼非定常气动载荷及瞬态气动响应计算[J].南京航空航天大学学报,2013,45(1):21-27. LV W L,SHI Y J,WEI P,et al.Computation of rotor unsteady aerodynamic loads and transient aerodynamic response[J].Journal of Nanjing University of Aeronautics & Astronautics,2013,45(1):21-27(in Chinese). Cited By in Cnki (7) [19] 曹义华. 直升机机动飞行旋翼的气动力模拟[J].航空学报,1999,20(1):39-42. CAO Y H.Modeling the aerodynamic forces of a maneuvering helicopter rotor[J].Acta Aeronautica et Astronautica Sinica,1999,20(1):39-42(in Chinese). Cited By in Cnki (8) [20] CAO Y H. A new inverse solution technique for studying helicopter maneuvering flight[J].Journal of the American Helicopter society,2000,45(1):43-53. Click to display the text [21] 苏媛,曹栋,曹义华.计及大迎角失速的直升机旋翼的气动力模拟[J].北京航空航天大学学报,2010,36(2):168-171. SU Y,CAO D,CAO Y H.Simulation of helicopter rotor aerody-namic force in conditions of high angle of attack and dynamic stall[J].Journal of Beijing University of Aeronautics and Astronautics,2010,36(2):168-171(in Chinese). Cited By in Cnki (3) [22] DREIER M E. Introduction to helicopter and tiltrotor flight simulation[M].Reston:AIAA,2007:190-194. [23] HOUSEN S S,BROWN R E.Rotor-wake modeling for simulation of helicopter flight mechanics in autorotation[J].Journal of Aircraft,2003,40(5):938-945. Click to display the text [24] LI P,CHEN R L.A mathematical model for helicopter comprehensive analysis[J].Chinese Journal of Aeronautics,2010,23(3):320-326. Click to display the text [25] Leishman J G,Crouse G L.State-space model for unsteady airfoil behavior and dynamic stall:AIAA-1989-1219[R].Reston:AIAA,1989:36-38. [26] 徐进. 直升机大机动飞行中旋翼非定常空气动力研究[D].南京:南京航空航天大学,2007:47-48. XU J.Unsteady aerodynamics investigation for the isolated rotor in large amplitude maneuvering flight[D].Nanjing:Nanjing University of Aeronautics and Astronautics,2007:47-48(in Chinese). Cited By in Cnki (5) [27] PURSER P E,SPEARMAN M L.Wind-tunnel tests at low speed of swept and yawed wings having various plan forms:NACA Technical Note 2445[R].Reston:NACA,1951:86-87. [28] SITARAMAN J. CFD based unsteady aerodynamic modeling for rotor aeroelastic analysis[D].Maryland:University of Maryland,2003:119,152.

#### 文章信息

WANG Wei, LI Dongsheng, LIU Chun

Calculation method of blade element aerodynamic loads based on small perturbation theory

Journal of Beijing University of Aeronautics and Astronsutics, 2016, 42(2): 294-302.
http://dx.doi.org/10.13700/j.bh.1001-5965.2015.0087