上海交通大学学报

上海交通大学学报, 2023, 57(6): 747-756 doi: 10.16183/j.cnki.jsjtu.2021.380

航空航天

考虑阶跃型地面的翼型前飞气动特性影响研究

徐晓刚1, 张扬,1, 昌敏2, 陈刚1

1.西安交通大学 机械结构强度与振动国家重点实验室,西安 710049

2.西北工业大学 无人系统技术研究院,西安 710072

Influence of Aerodynamic Characteristics of Airfoil Forward Flight Considering Step-Type Ground

XU Xiaogang1, ZHANG Yang,1, CHANG Min2, CHEN Gang1

1. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an 710049, China

2. Unmanned System Research Institute, Northwestern Polytechnical University, Xi’an 710072, China

通讯作者: 张 扬,博士生导师;E-mail:youngz@xjtu.edu.cn.

责任编辑: 李博文

收稿日期: 2021-09-26   修回日期: 2021-11-23   接受日期: 2021-12-16  

基金资助: 国家自然科学基金青年项目(11602199)

Received: 2021-09-26   Revised: 2021-11-23   Accepted: 2021-12-16  

作者简介 About authors

徐晓刚(1996-),硕士生,主要从事飞行器设计研究.

摘要

翼型前飞过程中,地面效应带来的气动力影响难以忽略,尤其在地面结构产生突变时翼型的气动性能必然产生较大变化.通过NACA4412翼型算例,研究了翼型前飞过程中阶跃型地面引起的气动性能影响,分析高度和迎角两种因素与翼型气动性能的相关性.结果表明:在阶跃型地面作用下,翼型前飞在地面效应缺失时会引起翼型升阻比陡降,且与离地高度存在线性关系.离地攻角则与气动性能突变之间存在相反关系,即翼型脱离地面时需维持较大迎角才能减弱气动性能陡变效应,舰载机的起降过程属于典型的阶跃型地面.基于上述结果,为地面效应影响下翼型的气动设计提供参考.

关键词： 阶跃型地面; 地面效应; 气动特性; 前飞

Abstract

The aerodynamic influence of ground effects during forward flight is difficult to ignore, especially when there is a sudden change in the ground structure. The aerodynamic performance of the airfoil during forward flight is investigated using the NACA4412 airfoil, the correlation between two factors, i.e., height and angle of attack, and the aerodynamic performance of the airfoil are analyzed. The results show that under the effect of step-type ground, the wing forward flight causes a steep drop in lift-to-drag ratio when the ground effect is absent, and there is a linear relationship with the height above the ground. The angle of attack from the ground has an inverse relationship with the sudden change in aerodynamic performance, i.e., the airfoil needs to maintain a large angle of attack when it leaves the ground in order to reduce the steep change in aerodynamic performance. The take-off and landing process of a shipboard aircraft is typical of a step-type ground. This paper provides a reference for the aerodynamic design of an airfoil under the influence of ground effects.

Keywords： step-type ground; ground effect; pneumatic characteristics; forward flight

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本文引用格式

徐晓刚, 张扬, 昌敏, 陈刚. 考虑阶跃型地面的翼型前飞气动特性影响研究[J]. 上海交通大学学报, 2023, 57(6): 747-756 doi:10.16183/j.cnki.jsjtu.2021.380

XU Xiaogang, ZHANG Yang, CHANG Min, CHEN Gang. Influence of Aerodynamic Characteristics of Airfoil Forward Flight Considering Step-Type Ground[J]. Journal of Shanghai Jiaotong University, 2023, 57(6): 747-756 doi:10.16183/j.cnki.jsjtu.2021.380

飞行器在近地飞行时,地面的阻滞效应使得下洗流的动压转换成静压,从而引起飞行器升阻比提升[1-2].地面类型变化会影响机翼下表面的压力分布,使机翼的气动特性发生较大改变.国内外围绕静态和动态地面效应开展了大量研究[3⇓⇓⇓⇓⇓⇓-10],但关于阶跃型地面效应的研究并不多,而阶跃型地面在飞行器飞行场景中十分常见,例如在舰载机起飞和着陆过程,航母甲板与海平面就是典型的阶跃地面,为实现尺度有限甲板的安全起降,要求舰载机具有优良的低速性能,较高的飞行品质和设计技术.因此,研究飞行器在阶跃型地面的气动特性十分必要.

地面效应在二维翼型增升作用研究较为广泛.早期Zerihan等[7]使用风洞进行大量的地面效应实验,翼型为Tyrrell方程式赛车的前翼LS(1)-0413,发现随着高度的减小,升力系数会增大,但在极近地面时升力系数会逐渐下降;Ahmed等[8]在风洞中对NACA0012翼型进行了地面效应测试,发现翼型上表面的压力分布随离地高度的变化很小,而升力增加来源于下表面压力分布的改变;Yang等[9]通过数值模拟研究了地面效应下NACA0012翼型气动特性受空气压缩性的影响,发现失速攻角(α)会随着高度的降低而减小;Ahmed等[10]在低湍流风洞研究了翼型的地面效应,并得出了相同的结论;Qu等[11]对比了NACA4412翼型定常和非定常地面效应的差异,根据升力增量将迎角和高度分成了3个区域,分析了不同范围攻角的流场;秦绪国等[12]进行了非定常的水面波浪模拟,用流体体积(VOF)方法模拟波浪水面,比较NACA2410翼型在固定波浪地面和水面波浪流场的差异,发现固定地面波浪升力和力矩系数的结果更接近余弦曲线分布;张海潮等[13]在拖曳水槽中模拟机翼在低雷诺数条件下的地面效应,水槽底部铺有硬质的波浪形曲面,同时使用粒子图像测速(PIV)测量机翼位于曲面地形的波峰和波节等不同相位下翼尖涡的速度场规律,发现离地高度较低时,曲面地形会使翼尖涡提前发生耗散并产生明显的展向位移,大攻角下周期性曲面具有更高的增升减阻效率;Zhu等[14]研究了柔性仿生翼振动和滑翔时的地面效应特性,独特之处在于通过双向流固耦合分析柔性翼的受力和变形以及柔性翼周围流场的变化;Nuhait等[15]对定常和非定常地面效应进行了参数分析,发现展弦比的增大会增强矩形和三角形平面的定常和非定常效应;乐挺等[16]基于理论分析,主要对地效飞机的纵向稳定特性进行了研究,得到了保证动稳定性时飞机重心与迎角焦点、高度焦点的位置关系.近几年随着数值模拟的不断发展,动网格技术逐渐成熟;Qu等[17]使用滑移网格模拟地面,研究了某型地效飞行器波浪状海面上的气动性能,详细分析了波浪面、飞行高度和攻角对气动特性和流场的影响,之后使用动态分层网格技术,研究了不同的地面边界条件起飞过程[18],发现在相同高度和攻角条件下,相对于静态地面效应的升力增量受到流动滞后和真空效应共同的影响,动态地面效应的流动滞后增加动态过程的有效攻角,但真空效应降低了翼型下表面地面处的压力,使升力减小;Roozitalab等[19]研究了阶跃地面效应对翼型起飞和降落气动特性的影响,通过对比NACA4412翼型在有无Gurney襟翼的升力和阻力系数,说明Gurney襟翼在起飞和着陆过程都会导致升力和阻力系数产生更大变化,着陆下的升力衰减量和阻力增加量均明显高于起飞过程对应的变化量.

以NACA4412翼型为例,通过重叠动网格方法研究在阶跃型地面的影响下,从涡量、流线、驻点等方面详细介绍整个过程翼型周围流场的变化,深入分析地面与翼型之间的相互作用机理,探讨地面形状变化与翼型气动特性的关联性与阶跃型地面效应对翼型气动性能的影响.

1 数值模拟方法

直角坐标系下偏微分形式的二维不可压非定常Navier-Stokes方程[20]为

∂u∂x+∂v∂y=0
∂u∂t+u ∂u∂x+v ∂u∂y=- 1ρ∂p∂x+ μρ∂2u∂x2+∂2u∂y2
∂v∂t+u ∂v∂x+v ∂v∂y=- 1ρ∂p∂y+ μρ∂2v∂x2+∂2v∂y2

式中:u、v为x、y方向的速度分量;ρ为流体密度;p为流体压力;μ为流体黏性系数.

k-ω SST湍流模型是一个两方程湍流模型,适合求解低速流动问题,方程[21]为

$\begin{aligned}\frac{(\rho k)}t+u_j&\frac{(\rho k)}{x_j}=\\\\P-\beta^*\rho k\omega+\frac{x_j}{x_j}&\bigg[(\mu+\sigma_k\mu_t)\frac k{x_j}\bigg]\end{aligned}$
$\begin{gathered}\frac{(\rho\omega)}{t}+u_{j}\frac{(\rho\omega)}{x_{j}}= \\\frac\gamma{v_t}P-\beta\rho\omega^2+\frac1{x_j}\bigg[(\mu+\sigma_w\mu_t)\frac\omega{x_j}\bigg]+ \\2\rho(1-F_{1})\frac{\sigma_{\omega2}}{\omega}\frac{k}{x_{j}}\frac{\omega}{x_{j}} \end{gathered}$

式中:ω为比耗散率;k为湍动能;ε为湍动能耗散率;uj(j=1, 2, 3)为速度分量;F1为加权函数;P为混合函数;μt为湍流动力黏性;vt为湍流运动黏性;β*、β、σk、σω、σω2、γ和a1均为封闭常数[22].

涡黏性系数由下式确定:

μt=min ρkω,a1ρkΩF2

式中:Ω为旋度幅度.

空间离散采用二阶迎风格式,压力速度耦合采用压力耦合方程组的半隐式算法(SIMPLE),通过编写用户自定义函数(UDF)设置网格区域运动,流场网格静止,翼型相对流场前飞,翼型表面满足无滑移物面,流场入口和出口均为压力远场.

不同于网格重构[19]的方法,每次改变几何都会重新生成一次网格,计算效率较低.本文使用的重叠网格可以在翼型近壁面处充分加密边界层,而远场的网格量并不发生较大改变,移动前景网格或者背景网格都不引起全局网格的变化,通过软件内置算法对前景网格和背景网格交界面处修改节点,在提高计算效率的同时实现翼型表面气动特性的精确模拟.

数值模拟使用的翼型为NACA4412,弦长c=1 m,翼型运动速度v0=40 m/s,雷诺数Re=2.8×106,数值模拟翼型在阶跃型地面运动的示意图如图1(a)所示,边界条件设定方法与计算区域网格如图1(b)和图1(c)所示,对翼型周围网格进行加密.

图1

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图1   几何和网格示意图

Fig.1   Geometry and grid schematics


为证明重叠网格的可靠性,在相同条件下,使用重叠网格在Fluent软件中进行数值模拟,并与实验数据[23]对比,定常计算结果如图2所示,其中C1为升力系数.数值模拟和风洞实验结果吻合较好,证明重叠网格的计算结果可信.

图2

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图2   重叠网格验证

Fig.2   Verification of overlapping grids


研究非定常流动的阶跃地面效应时,翼型到达台阶端面之前,应保证流场中各个变量得到充分发展.在没有台阶面的大范围远场下,测试翼型从右向左移动,测得相同条件下需移动15 m才能实现流场收敛,此处设置翼型前缘距断面处的距离为25 m.计算过程所设置的参数:v0=40 m/s,ρ=1.225 kg/m3, p=101 325 Pa, 温度T=288.15 K, Re=2.8×106,网格第一层高度为6×10-6m,为了详细观察后缘处涡的产生和脱落,采用较小时间步长,大小为速度倒数的1%,即Δt=0.000 25 s.按照上述条件分别对3种不同数量的网格进行无关性验证,近场网格为贴体生成,按照增长率1.05外推260层,近场网格规模为 100 000 网格单元.对于重叠网格,背景网格严重影响翼型尾迹的模拟精度,因此对3种不同背景网格进行测试,网格规模分别为 95 000、270 000 和 490 000 网格单元,分别命名为粗网格(Coarse),中等网格(Medium)和密网格(Fine).不同背景网格计算所得的升力与阻力系数(Cd)如图3所示.结果表明3种背景网格对结果影响不大,后文统一采用Medium网格进行分析研究.

图3

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图3   网格无关性验证

Fig.3   Grid-independence verification


2 结果分析

2.1 高度对气动特性影响

以攻角α=10° 为例,研究NACA4412分别在不同离地高度h/c=0.2, 0.3, 0.4, 0.5, 1.0下的流动情况,如图4所示.图4(a)结果显示整个升力系数曲线均呈现先减小后增大的变化趋势,在无地面效应时,α=10°对应的升力系数Cl=1.42,而在距地高度h/c=0.3时的Cl=1.4,h/c=0.2时的Cl=1.51,说明该计算状态下NACA4412翼型地面效应的增升作用在0.2c以下较为明显.未脱离地面对应时刻为t=0.6 s(区域I),随着离地高度增加,升力系数依次减小,在远离地面之后(区域 II),均恢复至无地面下的升力系数值1.42.在区域I内,h/c在0.2和0.3的阻力系数呈一定曲线变化,地效作用明显,翼型后缘涡的附着和脱落使升力系数发生变化,而升致阻力与升力系数的平方成正比,因此阻力系数表现为小范围波动,如图4(c)所示.整个过程阻力系数曲线均表现为先增大后减小,最终在远离地面对应时间1 s处,阻力系数均趋于无地面下的阻力系数值0.018.攻角一定时,离地间隙增大,阶跃型地面效应影响会减弱,具体表现为升力和阻力系数变化量减小,且在0.6 s飞越台阶面时,数值振荡的现象也减弱.

图4

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图4   α=10°不同高度下的升阻力系数对比

Fig.4   Comparison of lift and drag coefficients at different heights and a 10° angle of attack


脱离台阶面时,升力和阻力系数均出现振荡的情况,这是由于流场的非定常效应,在翼型后缘处涡不断地附着与脱落,且受台阶影响较大,下表面的压力分布出现较大改变,如当α=10°、t=0.6 s、h/c=0.2时,下翼面长度在0.8c~c区间内,台阶面处产生的涡导致下表面压力系数变号.

Roozitalab等[19]在对比不同高度下流场的研究中采用观察流线数量的偏转方法说明下洗程度的大小,流线数量受主观因素影响较大,不同高度翼型周围流线数量不容易控制,影响机理的分析较为简单.本研究使用驻点的位置变化进一步解释有效攻角的变化,驻点位置变化如图5所示,其中S1~S5对应区域I的t=0.5 s经过水平地面,S'1~S'5对应区域 II 的 t=0.63 s经过阶跃地面,离地高度h/c为 0.2~0.5.随着离地间隙增加,相同时刻下的驻点逐渐向翼型前缘靠近,有效攻角减小,升力减小.

图5

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图5   不同时刻和高度的驻点位置

Fig.5   Stagnation positions at different moments and altitudes


图6为不同高度下的压力(Cp)分布曲线.结果显示,随高度增加,虽然吸力峰峰值变化不大,但上下表面压差减小.表1所示曲线所围面积也依次减小,升力降低,与分析结论一致.

图6

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图6   不同高度的压力分布曲线

Fig.6   Pressure coefficient distribution curves at different heights


表1   压力曲线所围面积

Tab.1  Area enclosed by pressure curve

h/c面积系数
0.21.5268
0.31.4207
0.41.3838
0.51.3624
1.01.3501

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在研究阶跃地效下的非定常运动时,以高度h/c=0.2为例进行具体分析.在h/c=0.2,α=10°条件下,非定常过程中流场和涡量的变化如图7和图8所示.结果表明,α=10°时,翼型后缘并未发生显著流动分离,翼型在从右向左运动经过台阶面时,因为边界层的不稳定性,剪切层失稳,边界层的形态发生变化,当量翼型随之改变,经过台阶面时,驻点迅速向前缘点靠近,如表2所示,有效攻角减小,升力系数减小.台阶面的存在使得在翼型弦长方向上存在截面不同的两段流管区域,气流在流过翼型下表面时,流管面积缩小,面积的变化引起速度增加,翼型上下表面压力差值减小,最终反映为升力降低.图8的涡量云图也表明翼型下方存在阻滞作用,台阶面存在使翼型下方的动态气垫作用减弱,被压缩的气流得到释放,增升作用降低,但翼型上表面和后缘处涡量并没有大的改变.翼型在飞越台阶面时,台阶处产生一个随时间变化的涡,翼型下表面的压力分布随时间而变化,导致翼型从t=0.6 s开始,升力和阻力系数曲线都出现小幅度的振荡.

图7

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图7   不同时刻下h/c=0.2,α=10°的流场变化

Fig.7   Flow field at different moments at h/c=0.2 and a 10° angle of attack


图8

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图8   不同时刻下h/c=0.2,α=10°的涡量云图

Fig.8   Vorticity at different moments at h/c=0.2 and a 10° angle of attack


表2   h/c=0.2驻点位置和升力系数变化

Tab.2  Variation in stationary position and lift coefficient at h/c=0.2

t/s驻点与前缘点的距离占弦长比例/%Cl
0.503.861.508
0.631.661.036
0.640.870.892
0.650.760.925
1.001.661.400

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不同时刻的压力分布曲线如图9所示,结合表2结果得出,在t=0.63 s和t=1.00 s时,两个时刻下的驻点均在距前缘点1.66%处,有效攻角相同,但t=1.00 s时,上表面具有更大的负压,两个时刻下表面的压力分布相差不大,因此t=1.00 s产生了较大的升力系数.t=0.63, 0.64, 0.65 s对应曲线的面积系数分别为 1.0492、0.9042、0.9371,t=0.65 s时翼型即将远离台阶面, x/c在0.8~1的范围之内,翼型周围流场发生下洗,下表面压力由正值变为负值,在翼型前缘处向上的合力增大,会产生较大的抬头力矩,不利于飞机的纵向静稳定性,在飞越台阶面的整个过程中,上表面的吸力峰在台阶面附近均有损失,导致升力降低.

图9

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图9   不同时刻的压力系数曲线

Fig.9   Pressure coefficient curves at different moments


2.2 攻角对气动特性影响

为了更好地说明在阶跃地效下该翼型的非定常特性,分别取升力线的线性段一个小攻角5°和失速点附近发生流动分离的大攻角15°进行研究,离地间隙h/c=0.3.图10对应了不同攻角下升力和阻力系数的变化规律,在离地间隙h/c一定时,攻角越大,在0.6 s飞越台阶面,受到阶跃地面的影响也更大,升力系数变化量也会增加.因此在无法改变离地间隙时,经过阶跃地面应采用小攻角飞行,以减弱升力系数变化,以防发生失速.阻力系数的变化与升力系数变化类似,区别是台阶面的存在使得升力系数减小,阻力系数增大.

图10

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图10   不同攻角下力系数变化曲线

Fig.10   Force coefficients at different angles of attack


当攻角改变时,相同离地高度翼型的压力变化更加明显,取非定常运动中t=0.63 s时刻研究攻角变化影响.图11和图12是不同参数下t=0.63 s的流场和涡量云图.图11表明不同条件下的压力云图均会在台阶拐点处出现一个3/4圆形的低压区域,图12较为明显地展示了该点涡量变化情况,相同高度大攻角会产生更大的涡量区域.

图11

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图11   不同条件下t=0.63 s的流场分布

Fig.11   Distribution of flow field in different conditions at t=0.63 s


图12

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图12   不同攻角下t=0.63 s的涡量云图

Fig.12   Vorticity for different angles of attack at t=0.63 s


离地间隙的改变会影响大攻角翼型后缘处的分离情况,在水平和阶跃地面会产生相同的影响.图13展示了15°攻角下不同离地间隙阶跃地面对翼型后缘分离的影响,分别对应h/c=0.3,0.5,1.0, 相同攻角下高度的增加,会减小后缘的分离涡,在经过台阶面时,大攻角飞行应保持较大的离地间隙,以防飞机提前发生失速.

图13

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图13   t=0.63 s,α=15°不同高度翼型后缘处的分离

Fig.13   Separation at trailing edge of airfoils of different heights at an angle of attack of 15° and t=0.63 s


为研究阶跃地效对翼型有效攻角的影响,构造以下表达式:

Δx=xT-xUFF

式中:xT为不同时刻驻点的位置;xUFF为无边界流场驻点的位置;用二者的差值说明地面效应变化对驻点位置的影响.

图14(a)为t=0.50 s在阶跃地面驻点位置的变化,相同离地间隙攻角增大,驻点位置变化量增大,向翼型后缘移动,有效攻角增大,地面效应的增升作用明显.图14(b)表明15°攻角在离地间隙h/c为0.3时,驻点位置比无地面效应更靠近后缘,但高度的降低也加剧了后缘处的流动分离,涡的脱落也带走一部分升力,导致翼型在近地面飞行时,升力系数反而降低.在离地间隙h/c分别为0.5、1.0时,地面的增升作用减弱,同时台阶面的存在使翼型下方压力得到释放,攻角越大,驻点的位置越靠近前缘,有效攻角减小,升力系数减小更快,结果与图10不同攻角下升力系数变化曲线相符.

图14

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图14   不同时刻攻角和高度对驻点位置的影响曲线

Fig.14   Effect of angle of attack and height on stationary position at different moments


3 结论

以NACA4412翼型为例,在阶跃型地面效应影响下进行不同参数的非定常计算,通过数值仿真分析,研究不同参数下流场的变化和翼型驻点的位置,得出以下结论:

(1) 在以一定的离地间隙和攻角飞越阶跃台阶面时,翼型后缘处存在涡的不断脱落和附着,而且台阶拐点处会产生一个随时间变化的涡,由于流场的非定常效应,翼型下表面压力分布时刻发生变化,升力和阻力系数变化均会出现小幅度振荡.在离开台阶面时,翼型后缘处下表面压力会发生方向变化,产生较大的抬头力矩,影响飞行的纵向稳定性.

(2) 离地间隙相同时,大攻角受到突变地面效应的影响较大,驻点位置向前缘移动,有效攻角减小,升力系数衰减更多,在离地间隙一定时应采用小攻角飞行,以减弱升力系数的变化,以防提前发生失速.

(3) 攻角相同时,离地间隙减小,驻点位置向后缘移动,有效攻角增大,在飞越台阶面处,升力和阻力系数的振荡加剧,而且会增大翼型后缘的分离涡,较大攻角如15°的升力系数会下降,大攻角飞行应保持较大的离地间隙,延缓翼型上表面的流动分离.

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