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参考文献 1
CHENEYJ R M C. The ABC helicopter [C]// AIAA/AHS VTOL Research Design, and Operations Meeting. Atlanta, GA: Georgia Institute of Technology, 1969.
参考文献 2
LEISHMANJ G, ANANTHANS. Aerodynamic optimization of a coaxial prorotor[C]//Proceedings of the 62nd Annual Forum of the American Helicopter Society. Phoenix, America: American Helicopter Society, 2006: 64⁃85.
参考文献 3
JUN S, YEE K, LEE J. Robust design optimization of unmanned aerial vehicle coaxial rotor considering operational uncertainty[J]. Journal of Aircraft, 2011, 48(2): 353⁃367.
参考文献 4
RANDO, KHROMOVV. Aerodynamic optimization of coaxial rotor in hover and axial flight [C]//27th Congress of the International Council of the Aeronautical Sciences 2010. Nice, France: ICAS Secretariat, 2010: 893⁃905.
参考文献 5
GIOVANETTIE B, HALLK C. Minimum loss load and twist distributions for coaxial helicopter rotors in hover[C]//Proceedings of the 71st Annual Forum of the American Helicopter Society. Virginia Beach, VA: American Helicopter Society, 2015: 648⁃657.
参考文献 6
GIOVANETTIE B, HALLK C. A variational approach to multipoint aerodynamic optimization of conventional and coaxial helicopter rotors[C]// Proceedings of the 71st Annual Forum of the American Helicopter Society. Virginia Beach, VA: American Helicopter Society, 2015: 752⁃764.
参考文献 7
BAGAIA. Aerodynamic design of the X2 technology demonstrator™ main rotor blade[C]//Proceedings of the 64th Annual Forum of the American Helicopter Society. Montreal, Canada: American Helicopter Society, 2008: 29⁃44.
参考文献 8
LAKSHMINARAYANV K, BAEDERJ D. High⁃resolution computational investigation of trimmed coaxial rotor aerodynamics in hover [J]. Journal of the American Helicopter Society, 2009, 54(4): 42008.
参考文献 9
KIM H W, BROWNR E. A comparison of coaxial and conventional rotor performance [J]. Journal of the American Helicopter Society, 2010, 55(1): 12004.
参考文献 10
WACHSPRESSD A, QUACKENBUSHT R. Impact of rotor design on coaxial rotor performance, wake geometry and noise[C]//Proceedings of the 62nd Annual Forum of the American Helicopter Society. Phoenix: American Helicopter Society, 2006: 41⁃63.
参考文献 11
QUEIPON V, HAFTKAR T, SHYYW. Surrogate⁃based analysis and optimization[J]. Progress in Aerospace Sciences, 2005, 41(1): 1⁃28.
参考文献 12
ZHUZheng, ZHAOQijun. Optimization for rotor blade⁃tip planform with low HSI noise characteristics in forward flight[J]. Journal of Aerospace Enginering, 2016, 231(7): 1312⁃1324.
参考文献 13
招启军, 朱正, 原昕. 桨叶外形对共轴刚性旋翼悬停性能影响的CFD分析[J]. 南京航空航天大学学报, 2017, 49(5): 653⁃661.
ZHAOQijun, ZHUZheng, YUANXin. CFD Analyses on effects of blade shape on hover performance of coaxial rigid rotors[J]. Journal of Nanjing University of Aeronautics & Aeronautics, 2017, 49(5): 653⁃661.
目录 contents

    摘要

    采用前行桨叶概念(Advancing blade concept, ABC)的共轴刚性旋翼构型的直升机具有高速前飞的能力,然而大前飞速度带来的强桨尖压缩性等影响对桨叶气动外形提出了更高的要求。鉴于此,本文针对共轴刚性旋翼的气动布局进行了优化设计通过改进桨叶平面外形提升旋翼前飞性能。基于雷诺平均NS(Reynolds⁃averaged Navier⁃Stokes, RANS)方程对共轴旋翼流场进行了气动性能数值模拟,在此基础上建立了代理模型结合遗传算法(Genetic algorithm, GA)的高效共轴旋翼气动布局优化方法,以前飞升阻比为目标函数进行优化,得到约束外形下的具有非线性弦长分布、尖削及后掠特征的桨叶外形。试验结果表明优化桨叶相比基准矩形桨叶升阻比得到明显的提升(前进比为0.6状态下升阻比提升约30%),证明了优化的有效性。

    Abstract

    Coaxial rigid rotor helicopter using advancing blade concept (ABC) is capable of high speed forward flight. However large area of reverse flow region and intense blade tip compressibility brought by high forward speed put forward higher requirements for blade planform. In light of this, optimization design of coaxial rotor planform is conducted to impove forward performance by changing blade planform. Coaxial rotor flow⁃field is simulated by solving Reynolds⁃averaged Navier⁃Stokes (RANS) equations. An optimization method combining surrogated model and genetic algorithm (GA) is established based on aerodynamic simulations. The optimized blade features nonlinear chord distribution and tapered sweptback blade tip under geometry constraints when lift⁃drag⁃ratio is set as objective function. Compared with baseline rectangular blade, the optimized blade has a higher lift⁃drag⁃ratio (When the advance ratio is 0.6, the lift⁃to⁃drag ratio is increased about 30%), which proves the optimization is valid.

    共轴刚性旋翼由于采用了前行桨叶概念——升力主要由每副旋翼的前行侧提供,对后行侧桨叶卸载,通过上下两幅旋翼反转平衡反扭矩,从而相比常规单旋翼获得了高速前飞的能[1]。旋翼桨叶的气动布局是影响其气动性能的关键。常规单旋翼构型的直升机由于前飞速度较小,大多数情况下单一翼型配置与简单弦长变化即可满足需求。而共轴刚性旋翼的典型工作状态为大前进比的高速前飞状态,前飞速度的增加导致桨叶所处的流场环境复杂程度大大增加。因此,为获得表现更优秀的共轴刚性旋翼需要对桨叶气动布局进行详细优化设计。气动外形设计主要有试验和理论两类方法。理论设计可以节省时间和精力,但是需要试验进行验证。在理论分析方法方面,以前的直升机旋翼桨叶优化方法中主要采用一些近似理论或者分析模型进行旋翼模拟,这些方法计算效率高,比较依赖经验参数。随着CFD技术的快速发展,以CFD方法为代表的数值模拟方法逐步成为桨叶气动外形设计中的重要研究手段。

    国外的一些专家学者对共轴旋翼气动布局进行了相关的优化设计工作。Leishman[2]使用自由尾迹法对共轴旋翼的气动性能进行了优化设计。Jun[3]采用了动量/叶素理论以悬停状态气动性能为目标,进行了多变量的优化设计。Rand[4]和Giovanetti[5]均基于动量/叶素理论对悬停状态的共轴旋翼桨叶的平面外形和扭转分布进行了优化设计。Giovanetti[6]应用类似方法对共轴旋翼前飞状态性能进行了优化,得到了与悬停优化桨叶完全不同的气动外形,弦长从桨根到桨尖先是逐渐增大、然后逐渐减小。Bagai[7]采用入流模型对X2验证机主旋翼气动布局设计进行了详细的分析。Lakshminarayan[8]采用可压RANS方程深入研究了悬停状态共轴旋翼的气动特性。Kim[9]则使用涡输运模型详细比较了共轴旋翼与单旋翼之间的性能差别。Wachspress[10]研究了桨叶设计参数对共轴旋翼性能、尾迹形状和噪声的影响。上述性能计算方法虽然大多速度较快,但是无法准确模拟共轴旋翼流场复杂的干扰现象,而且主要以计算悬停状态的气动性能为主,无法发挥现今共轴刚性旋翼高速前飞的性能潜在优势。

    鉴于此,本文在吸取国内外共轴刚性旋翼平面外形的先进设计经验的基础上,给出了共轴刚性旋翼平面外形优化设计思路。将代理模型方法和遗传算法相结合建立了一套组合优化方法。基于建立的高效的组合优化方法,开展了共轴刚性旋翼桨叶气动布局优化设计工作,获得了高性能的共轴刚性旋翼桨叶气动布局设计方案。

  • 1 共轴刚性旋翼桨叶优化设计方法

  • 1.1 共轴刚性旋翼流场数值模拟

    对于共轴刚性旋翼的前飞非定常流场,建立以绝对物理量为参数的守恒积分形式的可压非定常RANS方程,方程如下

    tΩWdΩ+Ω(Fc-Fv)dS=0
    (1)

    守恒变量W,对流通量Fc和黏性通量Fv分别为

    W=ρρuρvρwρEFc=ρVρuV+nxpρvV+nypρwV+nzpρHV+V'pFv=0nxτxx+nyτxy+nzτxznxτyx+nyτyy+nzτyznxτzx+nyτzy+nzτzznxΘx+nyΘy+nzΘz
    (2)

    式中:V=(V-Vω)·n=(u-ue)nx+(v-ve)ny+(w-we)nzΩ为控制体体积,S为控制体表面积;Vω=(ue,ve,we)为牵连速度;V=(u,v,w)为气流速度;n=(nx,ny,nz)为单元表面法矢量;ρpEH分别为密度,压力,总能和总焓;τ(·)Θ(·)为黏性应力张量项和热通量项,其中各分量定义为

    τxx=2μux-23μ·Vτxy=τyx=μ(uy+vx)τyy=2μuy-23μ·Vτzy=τyz=μ(vz+wy)τzz=2μuz-23μ·Vτxz=τzx=μ(uz+wx)
    (3)
    Θx=uτxx+vτxy+wτxz+κTxΘy=uτyx+vτyy+wτyz+κTyΘz=uτzx+vτzy+wτzz+κTz
    (4)

    式中:μ,κ,T分别为黏性系数;热传导系数和绝对温度;u(·),v(·),w(·)下标表示对该方向的偏导数。

    通过求解上述可压非定常RANS方程,建立起基于运动嵌套网格的共轴刚性旋翼的前飞流场的数值模拟方法。所采用的网格如图1所示,背景网格与桨叶网格均采用结构网格,对桨叶所处的XY方向位置以及桨尖所处的Z方向位置的背景网格进行加密以更好地捕捉流场细节。空间离散上采用精度较高的Roe⁃MUSCL格式,时间推进采用高效的隐式LU⁃SGS算法,湍流模型为Spalart⁃Allmara模型。共轴旋翼系统中操纵量配平采用Newton⁃Rhapson迭代法。

    图1
                            共轴旋翼前飞流场网格

    图1 共轴旋翼前飞流场网格

    Fig.1 Coaxial rotor grid used in forward flight

  • 1.2 优化方法

    代理模型方法可以在保证一定精度的情况下减少计算量,但是在处理气动外形优化这种多维变量问题时必须付出较大的计算[11]。而遗传算法适用于多变量、多目标的复杂问题,拥有广阔的空间搜索能力。在优化过程中需要多次计算目标函数值,但是基于CFD方法的流场求解时间相比于遗传算法本身所耗时间较长。因此,为了提高优化设计的计算效率,基于遗传算法改进的拉丁超立方方法(PermGA LHS)和径向基函数建立了代理模型优化方法,将代理模型方法和遗传算法相结合建立了一套组合优化方[12]。优化过程如图2所示,具体步骤如下:

    图2
                            优化方法流程图

    图2 优化方法流程图

    Fig.2 Optimization process

    (1) 产生N个初始父代种群样本点,然后采用高精度的数值方法计算目标函数值。

    (2) 以父代种群作为样本点建立代理模型。

    (3) 将父代种群带入到遗传算法中进行各种遗传操作,产生子代种群,目标函数值均采用第(2)步中建立的代理模型来计算。

    (4) 对第(3)步中产生的子代种群设置约束条件进行筛选,筛选出m个优秀个体数目并利用高精度的数值方法来重新计算目标函数值。

    (5) 若满足收敛准则,则输出优化结果,否则继续。

    (6) 将第(4)步中筛选出来的m个优秀个体加入到父代种群中,从而更新和充实父代种群,即N=N+m。返回步骤(2),继续迭代,直至收敛为止。

  • 1.3 桨叶平面外形的函数表示

    根据文献[7,13]中的参数研究可知,相对于矩形桨叶,后掠桨叶更适合以高速前飞为主要设计点的共轴旋翼。此外,具有桨叶尖削而中段弦长增大特点的弦长分布也有助于改善激波分离现象,从而提高共轴刚性旋翼大前飞速度气动性能的目的,综合考虑后掠、尖削和非线性弦长分布等特点以及桨叶实际加工的要求,进行桨叶先进气动外形优化设计。

    3给出了桨尖平面形状参数化示意图,R表示旋翼半径,c表示基准弦长,x表示展向位置,y表示弦向位置。P1~P8分别为桨叶前缘和后缘上的设计点。P7P8的展向位置为0.25R处,从桨叶根部到展向0.25R处的剖面弦长均为基准弦长。var1,var2,var3,var4,var5,var6,var7var8为8个设计变量(图示位置均为正值)。首先通过数学函数构建特征点之间的外形。P7点和P1点之间的前缘外形曲线为三次函数曲线;P1P3之间的前缘外形曲线为抛物线;后缘P8P2之间的曲线、P2P4之间的曲线连接均为三次函数;桨尖部位采用直线后掠尖削的外形。采用如图所示的三次函数和抛物线的优点在于连接处均相切,可以实现光滑过渡的效果。

    图3
                            桨叶平面外形参数

    图3 桨叶平面外形参数

    Fig.3 Blade planform parameterization

    桨叶平面外形的数学函数构建具体如下:

  • (1)0.25<xvar1时的前缘部分

    y=a1(x-0.25R)3+b1(x-0.25R)2
    (5)

    式中a1=2×-var2(var1-0.25)3,b1=3×var2(var1-0.25)2

  • (2)var1<xvar4时的前缘部分

    y=-k1(x-var1)2+var2
    (6)

    式中k1=var2+var3(var4-var1)2

  • (3)var4<x1.0时的前缘部分

    y=-(x-var4)k2-var3
    (7)

    式中k2=var5-var31.0-var4

  • (4)0.25<xvar1时的后缘部分

    y=-a2(x-0.25)3+b2(x-0.25)2-1.0
    (8)

    式中a2=2×-var6(var1-0.25)3,b2=3×-var6(var1-0.25)2

  • (5)var1<xvar4时的后缘部分

    y=-a3(x-var4)3+b3(x-var4)2-1.0-var7
    (9)

    式中a3=2×-var6+var7(var1-var4)3,b3=3×-var6+var7(var1-var4)2

  • (6)var4<x1.0时的后缘部分

    y=-(x-var4)k3-(1.0+var7)
    (10)

    式中k3=var5+var8-var7-1.01.0-var4

    为了在变量空间中能够实现设定的桨尖外形构建,即后掠、尖削以及桨叶中段大弦长的平面外形特点,对各个变量施加一定的数值约束,桨尖弦长下限被设定为0.3倍基准弦长。除此之外,为了保持旋翼实度基本一致,桨叶面积与矩形桨叶相比变化不得超过10%。8个设计变量的范围定义限定如下

    0.6<var1<0.70<var2<0.20<var3<0.20.85<var4<0.95var3<var5<0.8var2<var6<0.30<var7<var60.3<var8<var7+1.0-var3
  • 2 桨叶外形优化设计流程

  • 2.1 桨叶参数设置

    优化设计采用的共轴刚性模型旋翼由上下两副同轴反转的旋翼构成,每副旋翼有4片外形完全相同的桨叶组成。以桨叶根部起始位置的翼型弦长为基准弦长,记为c。采用半径相同、弦长均为基准弦长c的矩形桨叶作为气动性能对比的基准桨叶。设置上旋翼为右旋,下旋翼为左旋。上旋翼4片桨叶初始方位角设置为45°,135°,225°和315°,下旋翼4片桨叶初始方位角设置为0°,90°,180°和270°。基准模型桨叶的半径为2.0 m,基准弦长0.2 m。桨叶根切为0.2倍旋翼半径。上旋翼和下旋翼之间的轴间距定为0.15倍的桨叶半径。桨叶无下反,扭转角采用正负扭转分布,从桨根到0.4R为2.8°正扭转线性分布、从0.4R到桨尖为4.8°负扭转分布。翼型配置采用椭圆翼型和OA系列翼型,详见表1

    表1 桨叶翼型配置

    Tab.1 Blade airfoil distribution

    0.2R~0.25R0.25R~0.3R

    0.25R~

    (var1-.1)∙R

    (var1-0.1)R~var1R

    var1R~

    1.0R

    DBLN⁃526

    DBLN⁃526~

    OA212

    OA212~

    OA209

    OA209~

    OA206

    OA206

    选定与高速直升机巡航速度相近的0.6前进比为设计状态前飞速度。前飞时桨尖旋转马赫数为0.528,即桨尖旋转速度为179.55 m/s。为了使优化结果更具可靠性,不同桨叶外形的共轴刚性旋翼的总拉力和偏置量保持一致,即总拉力系数为0.013、偏置量为0.35。通过配平策略改变总距和横向周期变距保证总拉力和偏置量不变。

    目标函数为前飞当量升阻比。因此,本文优化工作的变量参数和目标响应函数如下

    Designvariables:x1,x2,x3,x4,x5,x6,x7,x8Objectivefunctions:MaximumLD
    (11)
  • 2.2 优化进程

    采用PermGA LHS试验设计方法获得的初始样本点分布。变量个数为8,样本点数量为100,标准化后变量范围均为0~1。将实际的八维变量空间降维成三维,三维空间中的样本点及其二维投影如图4所示,实际空间点分布均匀。

    图4
                            三维空间中的样本点及其二维投影

    图4 三维空间中的样本点及其二维投影

    Fig.4 Sample points in 3D space and their projections

    优化过程总共经历了4代,将每代种群中的样本点按照目标函数从小到大排列,从而给出了优化过程中所有种群的目标值比较,如图5所示。从图中可以看出,随着优化的进行,样本点目标值朝着高升阻比的有利方向推进。比较第三代和第四代样本点可知,第四代的最优点的升阻比高于第三代的最优点,此时接近收敛条件。

    图5
                            优化进程中样本点目标值对比

    图5 优化进程中样本点目标值对比

    Fig.5 Objective value comparison during optimization process

    2给出了迭代过程中近似模型的误差比较,评价函数采用均方根差函数(Root mean square error, RMSE)和平均相对误差(Mean relative error, MRE)。可见两种评价函数下,误差值都随着优化迭代的进行而逐渐减小,达到了相对较高的拟合精度。

    表2 近似模型的误差分析

    Tab.2 Error analyses

    GenerationRMSEMRE
    2nd1.981.360
    3rd0.7990.614
    4th0.6170.427
  • 3 优化桨叶气动性能分析

    6给出了优化桨叶平面外形,图7给出了优化桨叶的展向弦长分布。该优化桨叶具有明显的尖削、后掠和非线性弦长特征,满足设计变量范围对外形的约束。

    图6
                            优化桨叶外形

    图6 优化桨叶外形

    Fig.6 Planform of optimized blade

    图7
                            优化桨叶展向弦长分布

    图7 优化桨叶展向弦长分布

    Fig.7 Spanwise chord distribution of optimized blade

    计算了前进比为0.4,0.5,0.6和0.7时的采用优化桨叶的共轴刚性旋翼和基准矩形桨叶旋翼的前飞升阻比,结果如图8所示。两种旋翼均在0.6前进比时达到最大升阻比,原始共轴旋翼的最大升阻比为8.06,而采用优化桨叶的共轴刚性旋翼的最大升阻比为10.45,提高了约30%。虽然优化只针对0.6前进比状态,但是不同前飞速度时的性能均有所提升。

    图8
                            优化桨叶和基准桨叶共轴旋翼前飞性能比较

    图8 优化桨叶和基准桨叶共轴旋翼前飞性能比较

    Fig.8 Performance comparison of baseline blade and optimized blade in forward flight

    优化桨叶的气动外形特征有利于改善共轴旋翼的前飞性能。桨叶的大部分面积集中在展向位置中部段,这部分翼段避开了反流区和强压缩性的不利影响,升力潜能得到充分挖掘,从而使得升力分布更加合理。后掠尖削桨尖使得垂直于尖部前缘的相对气流速度减小,有利于减轻桨尖高马赫数来流的强压缩性;同时桨尖面积小,产生的负升力也低。因此综合起来在大前进比时的气动性能比基准矩形桨叶得到大幅提升。

    共轴刚性旋翼的桨叶载荷非定常特性非常显著,其气动力波动次数与桨叶片数紧密相关。图9给出了旋转一周的瞬时桨叶拉力系数变化。可知,上下旋翼旋转一周各自均产生了4次周期性变化,由于上下旋翼桨叶存在相位差,导致共轴旋翼总拉力产生了9次明显波动。如果忽略上、下旋翼气动力差别,那么共轴旋翼一个旋转周期包含了8个载荷周期。

    图9
                            优化桨叶旋翼拉力系数

    图9 优化桨叶旋翼拉力系数

    Fig.9 Thrust coefficient of optimized rotor

  • 4 结论

    本文基于共轴刚性旋翼气动特性数值模拟方法和桨叶气动外形混合优化方法设计得到一副高性能的共轴刚性旋翼桨叶外形,通过研究可以得到以下结论:

    (1) 本文建立的代理模型与遗传算法组合的优化方法能够对共轴刚性旋翼气动外形进行高效优化。

    (2) 优化的共轴桨叶外形的升阻比相比基准矩形桨叶有明显提高,证明非线性弦长分布、尖削和后掠的特征组合有利于高速前飞状态。

    (3) 优化的外形带来的性能改进主要由于:桨叶中部段的升力潜能得到充分挖掘,升力分布更加合理;后掠尖削桨尖使得垂直于尖部前缘的相对气流速度减小,有利于减轻桨尖高马赫数来流的强压缩性;桨尖面积小,产生的负升力也低。

  • 参考文献

    • 1

      CHENEY J R M C. The ABC helicopter [C]// AIAA/AHS VTOL Research Design, and Operations Meeting. Atlanta, GA: Georgia Institute of Technology, 1969.

    • 2

      LEISHMAN J G, ANANTHAN S. Aerodynamic optimization of a coaxial prorotor[C]//Proceedings of the 62nd Annual Forum of the American Helicopter Society. Phoenix, America: American Helicopter Society, 2006: 64⁃85.

    • 3

      JUN S, YEE K, LEE J. Robust design optimization of unmanned aerial vehicle coaxial rotor considering operational uncertainty[J]. Journal of Aircraft, 2011, 48(2): 353⁃367.

    • 4

      RAND O, KHROMOV V. Aerodynamic optimization of coaxial rotor in hover and axial flight [C]//27th Congress of the International Council of the Aeronautical Sciences 2010. Nice, France: ICAS Secretariat, 2010: 893⁃905.

    • 5

      GIOVANETTI E B, HALL K C. Minimum loss load and twist distributions for coaxial helicopter rotors in hover[C]//Proceedings of the 71st Annual Forum of the American Helicopter Society. Virginia Beach, VA: American Helicopter Society, 2015: 648⁃657.

    • 6

      GIOVANETTI E B, HALL K C. A variational approach to multipoint aerodynamic optimization of conventional and coaxial helicopter rotors[C]// Proceedings of the 71st Annual Forum of the American Helicopter Society. Virginia Beach, VA: American Helicopter Society, 2015: 752⁃764.

    • 7

      BAGAI A. Aerodynamic design of the X2 technology demonstrator™ main rotor blade[C]//Proceedings of the 64th Annual Forum of the American Helicopter Society. Montreal, Canada: American Helicopter Society, 2008: 29⁃44.

    • 8

      LAKSHMINARAYAN V K, BAEDER J D. High⁃resolution computational investigation of trimmed coaxial rotor aerodynamics in hover [J]. Journal of the American Helicopter Society, 2009, 54(4): 42008.

    • 9

      KIM H W, BROWN R E. A comparison of coaxial and conventional rotor performance [J]. Journal of the American Helicopter Society, 2010, 55(1): 12004.

    • 10

      WACHSPRESS D A, QUACKENBUSH T R. Impact of rotor design on coaxial rotor performance, wake geometry and noise[C]//Proceedings of the 62nd Annual Forum of the American Helicopter Society. Phoenix: American Helicopter Society, 2006: 41⁃63.

    • 11

      QUEIPO N V, HAFTKA R T, SHYY W. Surrogate⁃based analysis and optimization[J]. Progress in Aerospace Sciences, 2005, 41(1): 1⁃28.

    • 12

      ZHU Zheng, ZHAO Qijun. Optimization for rotor blade⁃tip planform with low HSI noise characteristics in forward flight[J]. Journal of Aerospace Enginering, 2016, 231(7): 1312⁃1324.

    • 13

      招启军, 朱正, 原昕. 桨叶外形对共轴刚性旋翼悬停性能影响的CFD分析[J]. 南京航空航天大学学报, 2017, 49(5): 653⁃661.

      ZHAO Qijun, ZHU Zheng, YUAN Xin. CFD Analyses on effects of blade shape on hover performance of coaxial rigid rotors[J]. Journal of Nanjing University of Aeronautics & Aeronautics, 2017, 49(5): 653⁃661.

招启军

机 构:南京航空航天大学直升机旋翼动力学国家级重点实验室,南京,210016

Affiliation:National Key Laboratory of Rotorcraft Aerodynamics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

角 色:通讯作者

Role:Corresponding author

邮 箱:zhaoqijun@nuaa.edu.cn

作者简介:招启军,E⁃mail:zhaoqijun@nuaa.edu.cn。

张威

机 构:

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,南京,210016

2. 中国直升机设计研究所,景德镇,333001

Affiliation:

1. National Key Laboratory of Rotorcraft Aerodynamics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

2. China Helicopter Research and Development Institute, Jingdezhen, 333001, China

原昕

机 构:南京航空航天大学直升机旋翼动力学国家级重点实验室,南京,210016

Affiliation:National Key Laboratory of Rotorcraft Aerodynamics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

朱正

机 构:南京航空航天大学直升机旋翼动力学国家级重点实验室,南京,210016

Affiliation:National Key Laboratory of Rotorcraft Aerodynamics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

王博

机 构:南京航空航天大学直升机旋翼动力学国家级重点实验室,南京,210016

Affiliation:National Key Laboratory of Rotorcraft Aerodynamics, Nanjing University of Aeronautics & Astronautics, Nanjing, 210016, China

孙静

角 色:中文编辑

Role:Editor

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0.2R~0.25R0.25R~0.3R

0.25R~

(var1-.1)∙R

(var1-0.1)R~var1R

var1R~

1.0R

DBLN⁃526

DBLN⁃526~

OA212

OA212~

OA209

OA209~

OA206

OA206
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GenerationRMSEMRE
2nd1.981.360
3rd0.7990.614
4th0.6170.427
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图1 共轴旋翼前飞流场网格

Fig.1 Coaxial rotor grid used in forward flight

图2 优化方法流程图

Fig.2 Optimization process

图3 桨叶平面外形参数

Fig.3 Blade planform parameterization

表1 桨叶翼型配置

Tab.1 Blade airfoil distribution

图4 三维空间中的样本点及其二维投影

Fig.4 Sample points in 3D space and their projections

图5 优化进程中样本点目标值对比

Fig.5 Objective value comparison during optimization process

表2 近似模型的误差分析

Tab.2 Error analyses

图6 优化桨叶外形

Fig.6 Planform of optimized blade

图7 优化桨叶展向弦长分布

Fig.7 Spanwise chord distribution of optimized blade

图8 优化桨叶和基准桨叶共轴旋翼前飞性能比较

Fig.8 Performance comparison of baseline blade and optimized blade in forward flight

图9 优化桨叶旋翼拉力系数

Fig.9 Thrust coefficient of optimized rotor

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  • 参考文献

    • 1

      CHENEY J R M C. The ABC helicopter [C]// AIAA/AHS VTOL Research Design, and Operations Meeting. Atlanta, GA: Georgia Institute of Technology, 1969.

    • 2

      LEISHMAN J G, ANANTHAN S. Aerodynamic optimization of a coaxial prorotor[C]//Proceedings of the 62nd Annual Forum of the American Helicopter Society. Phoenix, America: American Helicopter Society, 2006: 64⁃85.

    • 3

      JUN S, YEE K, LEE J. Robust design optimization of unmanned aerial vehicle coaxial rotor considering operational uncertainty[J]. Journal of Aircraft, 2011, 48(2): 353⁃367.

    • 4

      RAND O, KHROMOV V. Aerodynamic optimization of coaxial rotor in hover and axial flight [C]//27th Congress of the International Council of the Aeronautical Sciences 2010. Nice, France: ICAS Secretariat, 2010: 893⁃905.

    • 5

      GIOVANETTI E B, HALL K C. Minimum loss load and twist distributions for coaxial helicopter rotors in hover[C]//Proceedings of the 71st Annual Forum of the American Helicopter Society. Virginia Beach, VA: American Helicopter Society, 2015: 648⁃657.

    • 6

      GIOVANETTI E B, HALL K C. A variational approach to multipoint aerodynamic optimization of conventional and coaxial helicopter rotors[C]// Proceedings of the 71st Annual Forum of the American Helicopter Society. Virginia Beach, VA: American Helicopter Society, 2015: 752⁃764.

    • 7

      BAGAI A. Aerodynamic design of the X2 technology demonstrator™ main rotor blade[C]//Proceedings of the 64th Annual Forum of the American Helicopter Society. Montreal, Canada: American Helicopter Society, 2008: 29⁃44.

    • 8

      LAKSHMINARAYAN V K, BAEDER J D. High⁃resolution computational investigation of trimmed coaxial rotor aerodynamics in hover [J]. Journal of the American Helicopter Society, 2009, 54(4): 42008.

    • 9

      KIM H W, BROWN R E. A comparison of coaxial and conventional rotor performance [J]. Journal of the American Helicopter Society, 2010, 55(1): 12004.

    • 10

      WACHSPRESS D A, QUACKENBUSH T R. Impact of rotor design on coaxial rotor performance, wake geometry and noise[C]//Proceedings of the 62nd Annual Forum of the American Helicopter Society. Phoenix: American Helicopter Society, 2006: 41⁃63.

    • 11

      QUEIPO N V, HAFTKA R T, SHYY W. Surrogate⁃based analysis and optimization[J]. Progress in Aerospace Sciences, 2005, 41(1): 1⁃28.

    • 12

      ZHU Zheng, ZHAO Qijun. Optimization for rotor blade⁃tip planform with low HSI noise characteristics in forward flight[J]. Journal of Aerospace Enginering, 2016, 231(7): 1312⁃1324.

    • 13

      招启军, 朱正, 原昕. 桨叶外形对共轴刚性旋翼悬停性能影响的CFD分析[J]. 南京航空航天大学学报, 2017, 49(5): 653⁃661.

      ZHAO Qijun, ZHU Zheng, YUAN Xin. CFD Analyses on effects of blade shape on hover performance of coaxial rigid rotors[J]. Journal of Nanjing University of Aeronautics & Aeronautics, 2017, 49(5): 653⁃661.

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