TWO-ELEMENT AIRFOIL GUST ALLEVIATION USING A PLASMA ACTUATOR
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摘要: 介质阻挡放电等离子体流动控制技术是基于等离子体激励的主动流动控制技术, 具有响应时间短、结构简单、能耗低及不需要额外气源装置等优点, 在飞行器增升减阻、抑振降噪和助燃防冰等方面具有广阔的应用前景. 在延长无人机滞空时间和促进低空无人机发展的背景下, 以GAW-1两段翼型为研究对象, 以正弦交流电压激励下的介质阻挡放电等离子体激励器为控制方式, 采用数值模拟方法开展了基于介质阻挡放电等离子体激励的1-cos型阵风减缓研究, 评估了等离子体控制效果, 揭示了等离子体阵风减缓机理. 在计算时, 将单个非对称布局介质阻挡放电等离子体激励器布置在翼型尾缘处, 激励器诱导的准定常射流的方向与来流相反. 结果表明: (1)施加等离子体激励后, 升力系数的波动量最大减小了51.6%, 自下而上型阵风对翼型的影响大幅减缓; (2)等离子体激励能够增大边界层形状因子、延长分离区长度和增加分离区面积; (3)等离子体诱导射流与诱导涡是实现阵风减缓的关键. 诱导的逆向射流通过阻碍来流发展、引射下翼面流线加速并向上偏转的方式, 减小了上下翼面的压力差, 从而降低了升力系数; 而诱导涡形成的“虚拟凸起”进一步扩大了分离区面积. 研究结果为提升低空无人机气动性能提供了技术支撑.Abstract: Flow control technology using dielectric barrier discharge (DBD) plasma actuators is an active flow control technology based on plasma actuation and has some advantages, such as short response time, simple structure, low consumption power, and no need for additional air source devices. Motivated by the demand of improving the endurance performance and promoting the development of low altitude unmanned aerial vehicles (UAV), the investigations on a two-element airfoil of GAW-1 gust alleviation by using a DBD plasma actuator driven by a sinusoidal alternating current (AC) were carried out with the help of numerical simulation method. The control effect of DBD plasma actuator was evaluated by aerodynamic forces and the gust alleviation mechanism was uncovered by instantaneous flow fields. An asymmetrical DBD plasma actuator was placed at the trailing-edge of airfoil and the direction of the quasi-steady wall jet produced by the plasma actuator was opposite to the incoming flow. The maximum reduction of the fluctuation of lift coefficient was approximately 51.6% after applying the DBD plasma actuation, which indicated that the effect of gust on the airfoil can be weaken effectively by the plasma actuator. In addition, the shape factor of boundary layer was increased, the length and the area of separation zone was prolonged and was extended, respectively, with the help of plasma actuator. Moreover, it is believed that the wall jet and the vortex both created by the plasma actuator play an important role in gust alleviation. The pressure difference between the upper and lower airfoil surfaces was reduced by the induced wall jet which hindered the development of incoming flow, accelerated and deflected the streamline of the lower airfoil surface deflect upwards, leading to reduce the lift coefficient of airfoil. Meanwhile, a virtual hump generated by the induced vortex expanded the area of separation zone. The present results lay a technical foundation for promoting the aerodynamic performance of low altitude UAV.
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Keywords:
- flow control /
- plasma /
- dielectric barrier discharge /
- two-element airfoil /
- unmanned aerial vehicle
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引 言
随着低空空域的逐步开放, 低空经济迅速成为中国经济发展的新热点. 作为低空经济产业的支柱, 低空无人机的研制得到广泛关注. 为了提升低空无人机滞空时间, 研究人员常通过加装襟翼的方式, 提高航时因子$\left(C_L^{1.5}/C_D\right) $. 在低空, 由于地形复杂和气流分布混乱, 阵风效应强烈. 在阵风的强烈作用下, 无人机受到的气动力及力矩会产生剧烈变化, 给安全飞行带来了重大挑战[1]. 为了确保无人机在低空的安全飞行, 常通过加强无人机结构、加装尾缘襟翼和偏转控制舵面等方式来抵抗阵风干扰[2-9], 但结构重量的增加会导致无人机的飞行半径及滞空时间降低.
杨超等[10]对阵风减缓技术进行了全面总结, 概述了阵风减缓研究的前沿进展. 主动流动控制技术作为流体力学研究的前沿与热点, 通过激励器诱导产生的扰动, 控制飞行器内外流场, 调整飞行器受力及姿态情况, 从而达到增升减阻及抑振降噪等目的, 为削弱阵风影响提供了新思路. 国内外学者以吹/吸气[11-12]、合成射流[13-14]、喷流[15]和环量控制[16]为激励方式, 以二维翼型及三维机翼为研究对象, 采用数值模拟、风洞实验等研究手段开展了详细研究, 评估了基于流动控制的阵风减缓效果, 获得了激励参数对控制效果的影响规律.
介质阻挡放电等离子体流动控制技术是一种基于等离子激励的主动流动控制技术. 由于等离子体激励器具有控制位置灵活、结构简单和响应时间短等突出优点, 因此, 该技术引起了国内外学者的广泛关注[17-24].
如图1所示, 介质阻挡放电等离子体激励器由上层电极、下层电极、绝缘介质及高压激励电源组成. 上层电极暴露在空气中, 下层电极被绝缘介质覆盖. 两层电极与高压电源的两端相连. 在高电压的激励下, 上层电极周围的空气被电离, 从而形成等离子体. 激励器在工作时会产生准定常的辉光. 目前, 常用的高压激励电源主要有正弦交流[25-27]、纳秒脉冲两种[28-30]. 在不同高压电源的激励下, 激励器会在上层电极周围产生不同的流场. 由于正弦交流电源体积小、重量轻, 正弦交流等离子体激励器产生的电磁干扰小, 因此, 本文主要围绕正弦交流电压激励下的等离子体流动控制开展研究.
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图 1 典型的非对称布局介质阻挡放电等离子体激励器布局示意图Figure 1. Schematic of a traditional asymmetrical DBD plasma actuator目前, 从公开文献来看, 鲜有开展基于等离子体激励的阵风减缓研究. 鉴于等离子体激励器诱导流场与传统吹气[31]、合成射流[32-34]等激励器相比具有独特性, 本文以低空无人机阵风减缓为背景, 以介质阻挡放电等离子体为控制手段, 采用数值模拟方法开展了两段翼型阵风控制研究. 文章段落结构如下: 首先介绍数值计算方法, 其次对计算进行分析, 重点讨论了等离子体流动控制机理.
1. 数值计算
1.1 计算方法
采用GAW-1二维翼型为研究对象[35]. 翼型弦长为100 mm, 襟翼弦长为24 mm, 襟翼偏角为20°. 通过求解基于压力的二维不可压缩雷诺平均Navier-Stokes方程对流场进行数值模拟, 离散化方法为有限体积法, 空间离散格式采用二阶精度迎风格式, 时间推进方法采用LU-SGS (lower-upper symmetric Gauss Seidel)隐式时间推进算法. 采用适用于低雷诺数数值模拟的SST transition四方程转捩模型进行计算. 非定常计算的时间步长为1.0 × 10−4 s, 计算精度为双精度. 来流速度为U∞ = 10 m/s, 基于弦长的雷诺数为Re = 6.6 × 104.
如图2(a)所示, 计算域在流向和法向的长度分别为56倍和50倍翼型弦长. 进口与出口边界条件分别设置为压力远场与压力出口, 两段翼型的壁面设置为无滑移绝热壁面. 如图2(b)所示, 采用结构网格划分计算区域, 对翼型壁面附近的区域进行网格加密. 边界层网格数40, 第一层网格高度为0.001 mm, 增长率为1.2, 确保近壁面网格单元y+ < 1. 网格单元总数为24万.
如图3所示, 通过对比文献中不同迎角下的升力系数(如图3(a))以及12°迎角下的表面压力分布(如图3(b))对计算方法进行验证[36]. 在文献[36]中, 实验模型为0°襟翼偏角的GAW-1翼型, 弦长为101 mm, 基于弦长的雷诺数为Re = 1.6 × 105. 依据文献结果, 对计算条件进行设置, 将翼型弦长设置为101 mm, 基于弦长的雷诺数为Re = 1.6 × 105. 结果表明, 计算结果与文献结果吻合较好, 升力系数的最大误差在7%以内(失速区附近), 说明采用的计算方法能较好反映出GAW-1翼型的气动特性.
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图 3 升力系数及表面压力分布对比Figure 3. Comparison of lift coefficient and surface pressure distribution1.2 阵风模拟
如图4所示, 本文采用1-cos型阵风模型进行阵风模拟. 该模型能较好反映飞行器在极端阵风载荷下的响应情况. 计算时, 通过在远场中添加速度边界条件的方式实现阵风模拟.
阵风表达式为
$$ w_g = \frac{1}{2} w_{g 0}\left[1-\cos \left(\frac{2 \text{π} x_g}{H_g}\right)\right], \quad 0 \leqslant x_g \leqslant H_g $$ (1) 其中, wg0为阵风速度幅值, 单位m/s; xg为阵风坐标系下的x轴坐标, 单位m; Hg为阵风场的长度, 单位m.
通过与文献[15]结果对比的方式考核阵风模拟情况. 在文献[15]中, 翼型为NACA0012翼型, 弦长为1 m, 初始迎角为0°, 来流马赫数0.2, 阵风的速度幅值wg0/U∞ = tan2° =
0.0349 , 阵风长度Hg = 25c. 图5给出了升力系数CL随无量纲时间s (s = 2U∞t/c)的变化情况. 从图中可以看出, 本文的计算结果与文献结果吻合较好, 表明本文采用的计算方法及阵风模型能较好模拟出阵风效应.在本文计算时, 首先对无阵风情况下的GAW-1两段翼型绕流流场进行数值模拟, 当计算结果收敛后, 在来流的法向方向上添加阵风模型, 开展阵风影响下的数值计算. 阵风速度幅值取wg0/U∞ = tan2° =
0.0349 , 阵风场长度取Hg = 25c.1.3 等离子体激励器模拟
采用Suzen等[37]提出的体积力模型模拟等离子体激励效果. 该模型通过将等离子体方程产生的洛伦兹力添加到N-S方程的体积力源项中, 实现等离子体方程与流动方程的耦合求解.
图6给出了静止空气下等离子体激励器的诱导流场. 从图中可以看出, 本文计算得到的流线分布与实验结果吻合良好, 表明该计算模型能够较好地模拟出等离子体激励效果.
如图7所示, 在本文研究中, 将非对称布局等离子体激励器布置在翼型上翼面的尾缘处. 上下两层电极的宽度为2 mm, 厚度为0.05 mm. 两层电极的搭接处距离翼型后缘2 mm. 绝缘介质覆盖了整个翼面, 其厚度为0.1 mm. 依据实验结果, 激励器诱导射流的速度为6 m/s, 射流方向与来流方向相反. 关于等离子体流动控制的数值模拟细节可参考文献[38].
1.4 网格无关性验证
网格数量对数值模拟结果影响较大, 直接决定着计算的时间、成本以及计算结果的准确性[39]. 本文采用12万 (coarse grid)、24万 (fine grid)和36万 (dense grid) 3套网格开展网格无关性研究. 如图8所示, 当采用12万网格(coarse grid)开展计算时, 0°迎角下的压力分布与采用其余两套网格的计算结果稍有差异, 而采用24万 (fine grid)和36万 (dense grid)两套网格的计算结果基本相同, 因此, 本文均采用24万网格(fine grid)开展计算.
2. 计算结果与分析
本节从气动力及流场两个方面分析基于等离子体激励的自下而上型阵风减缓结果, 探索等离子体阵风减缓的流动控制机理.
2.1 气动力结果
图9给出了阵风影响下, 施加等离子体激励前后升力系数随时间变化情况. 图中黑色实线代表阵风速度幅值wg随时间变化曲线, 红色实线为施加激励前的升力系数, 蓝色实线表示施加激励后的升力系数. 纵坐标分别为升力系数增量和阵风速度幅值, 横坐标为无量纲时间s. 本文采用开环控制. 由于等离子体激励器的放电频率一般在kHz以上, 等离子体激励器诱导流场的变化频率与放电频率一致, 并且诱导流场的变化幅值在1 m/s左右, 因此, 对于流场响应时间而言, 等离子体激励器诱导的高频流场近似于恒定值, 即等离子体施加的扰动近似为定值. 等离子体激励器工作的无量纲时间为s = 0 ~ 50. 当s = 0时, 等离子体激励器开启; 当s = 50时, 等离子体激励器关闭. 施加激励前, 随着阵风扰动的增强, 翼型的有效迎角逐渐增大, 升力系数不断增加. 当阵风扰动达到最大时(s = 25), 升力系数尚未达到峰值, 说明升力系数与阵风速度幅值之间存在响应延迟. 随后阵风扰动逐渐减弱, 升力系数逐渐降低, 在s = 50时阵风扰动消失, 翼型升力系数比初始时刻略大. 由于等离子体激励器在s = 50时关闭, 因此, 当s > 50, 施加前后的升力系数变化较小. 总的来看, 施加等离子体激励后, 升力系数的变化量显著降低. 当s = 28时, 升力波动量降低了51.6%, 表明等离子体激励能够有效减缓自下而上型阵风的影响.
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图 9 阵风影响下施加激励前后升力系数随时间变化情况Figure 9. The variation of lift coefficients over time before and after plasma actuation under the influence of gusts图10给出了不同时刻施加激励前后翼型表面压力分布情况. 如图10(a)所示, 刚施加激励时, 翼型表面压力变化较小; 如图10(b) ~ 图10(d)所示, 随着时间的推移, 翼型上翼面的负压显著减小、下翼面的正压略有降低, 使得翼型升力系数降低; 值得一提的是, 在激励器位置附近, 由于等离子体诱导射流引起的局部气流加速, 使得局部负压增大.
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图 10 不同时刻下施加激励前后翼型表面压力系数分布情况Figure 10. The distributions of pressure coefficient on airfoil surface at different times before and after plasma actuation under the influence of gusts2.2 流场结果
图11给出了施加激励前后, 翼型速度场分布情况. 如图11(a) ~ 图11(d)所示, 随着阵风扰动幅值的增加, 翼型有效迎角逐渐增大, 翼型上翼面的分离点逐渐往翼型前缘移动, 分离区的面积逐渐增大.
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图 11 不同时刻下施加激励前后的翼型速度场Figure 11. The velocity field around the airfoil at different times before and after plasma actuation under the influence of gusts如图11(e)所示, 刚施加激励时, 翼型绕流流场变化较小. 有趣的是, 在等离子体诱导流场与来流相互作用下, 等离子体激励器在分离区内诱导产生一个小尺度诱导涡. 如图11(f) ~ 图11(g)所示, 随着时间的推移, 等离子体诱导涡向上游移动. 诱导涡在逆向运动的过程中, 在表面形成了“虚拟凸起”, 扩大了分离区面积. 当达到襟翼前缘时, 诱导涡停止运动. 如图11(h)所示, 当s = 40时, 诱导涡融入到大尺度分离泡中, 耗散消失. 此外, 等离子体诱导射流使得上翼面的气流受阻, 气流流速降低; 另外, 在等离子体诱导射流的引射作用下, 上翼面的负压增大, 使得下翼面的气流加速, 并向上偏转. 等离子体诱导射流减小了上下翼面的压力差, 从而降低了升力系数, 减缓了阵风影响. 笔者认为, 在等离子体诱导涡与逆向射流的共同作用下, 翼型上翼面的分离点逐渐往翼型前缘移动, 分离区逐渐增大.
为了进一步定量评估等离子体激励器的控制效果, 基于参考文献[40], 引入了分离区长度Ls和分离区面积As. 分离区长度Ls定义为尾缘弦向坐标与上翼面分离点弦向坐标之差, 分离区面积As定义为Ux≤0的区域. 图12和图13分别给出了分离区长度Ls和分离区面积As随时间变化情况. 施加激励前, Ls和As的变化形态与阵风扰动的变化规律类似. 施加激励后, 分离区长度Ls增加, 分离区面积As增大. 分离区长度Ls最大增加了8.6%, 分离区面积As最大增大了40%.
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图 12 施加激励前后无量纲分离区长度随时间变化情况Figure 12. The non-dimensional length of separation zone versus time before and after plasma actuation under the influence of gusts![]()
图 13 施加激励前后无量纲分离区面积随时间变化情况Figure 13. The non-dimensional area of separation zone versus time before and after plasma actuation under the influence of gusts上述研究结果表明, 等离子体控制效果的好坏主要由流动分离决定. 而流动分离与边界层速度剖面密切相关. 边界层形状因子H12 (H12 = δ*/θ)表征速度剖面的形状, 用来衡量边界层的饱满程度[40]. H12越大, 边界层越不饱满, 越容易发生流动分离. 边界层形状因子H12通过式(2) ~ 式(4)进行计算. 其中δ*表示位移厚度, θ表示动量厚度, Uxy为当地速度, U∞为来流速度. 积分从上翼面yw开始, 到达来流速度99%的位置yref结束. 如图14所示, 施加激励前, 形状因子H12沿着弦向逐渐增大. 施加激励后, 形状因子H12的变化形态与施加激励前类似, 但数值增大, 表明在相同时刻下, 施加激励后, 流场更容易发生分离
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图 14 施加激励前后边界层形状因子随弦向变化情况Figure 14. The shape factor of boundary layer in a chordwise direction before and after plasma actuation under the influence of gusts$$ \mathit{H} _{ \mathrm{12}} \mathit{ = \delta } ^{ \mathit{*} } \mathrm{/} \mathit{\theta } $$ (2) $$ \delta^* = \int_{y_{\mathrm{w}}}^{y_{{\mathrm{r e f}}}}\left(1-\frac{U_{x y}}{U_{\infty}}\right) {\mathrm{d}} y $$ (3) $$ \theta = \int_{y_{\mathrm{w}}}^{y_{{\mathrm{r e f}}}} \frac{U_{x y}}{U_{\infty}}\left(1-\frac{U_{x y}}{U_{\infty}}\right) {\mathrm{d}} y $$ (4) 图15给出了s = 20时刻, 施加激励前后, 流场湍动能(turbulence kinetic energy, TKE)的分布情况. 由图可知, 湍动能主要集中在翼型尾缘. 施加激励后, 等离子体诱导流场与来流相互作用, 增强了边界层与外流的掺混, 扩大了高湍动能区域的面积[41-45].
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图 15 施加激励前后湍动能分布情况Figure 15. The distributions of TKE before and after plasma actuation under the influence of gusts2.3 流动控制机理讨论
结合图16, 对等离子体自下而上型阵风减缓机理进行讨论总结. 总的来看, 等离子体诱导射流与诱导涡在阵风减缓中起到了较为重要的作用. 笔者认为, 减缓机理主要有3种: 一是逆向诱导射流阻碍了来流的发展, 增大了分离区面积, 这是等离子体诱导射流的直接作用; 二是诱导射流的引射作用, 使得下翼面的气流加速, 并向上偏转, 减小了上下翼面的压力差, 从而降低了升力系数; 三是诱导涡形成的“虚拟凸起”进一步扩大了分离区面积.
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图 16 等离子体阵风减缓机理示意图Figure 16. Schematic of gust alleviation mechanism of plasma actuators3. 结 论
本文以GAW-1两段翼型为研究对象, 以非对称布局等离子体激励器为控制方式, 采用数值模拟方法, 开展了基于等离子体激励的自下而上型阵风减缓研究, 通过气动力评估了等离子体控制效果, 厘清了等离子体激励下翼型绕流流场的时空演化过程, 讨论了等离子体阵风减缓机理, 得到了以下结论.
(1)施加等离子体激励后, 升力系数的波动量最大减小了51.6%, 表明等离子体激励能够有效减缓阵风影响.
(2)在等离子体激励下, 边界层形状因子增大、分离区长度增加、分离面积扩大; 结果表明, 分离区长度Ls最大增加了8.6%, 分离区面积As最大增大了40%.
(3)等离子体诱导射流与诱导涡是实现阵风减缓的关键. 诱导射流通过阻碍来流发展、引射下翼面流线加速并向上偏转的方式, 减小了上下翼面的压力差, 从而降低了升力系数; 而诱导涡形成的“虚拟凸起”进一步增大了分离区面积.
本文仅是等离子体自下而上型阵风减缓研究的初步探索. 下一步将通过辨析非定常等离子体激励参数与阵风参数的耦合关系, 提出最优参数组合, 进一步降低等离子体激励器消耗功率、提升控制效果, 为开展三维机翼等离子体阵风减缓控制研究提供技术支撑.
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图 1 典型的非对称布局介质阻挡放电等离子体激励器布局示意图
Figure 1. Schematic of a traditional asymmetrical DBD plasma actuator
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图 3 升力系数及表面压力分布对比
Figure 3. Comparison of lift coefficient and surface pressure distribution
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图 9 阵风影响下施加激励前后升力系数随时间变化情况
Figure 9. The variation of lift coefficients over time before and after plasma actuation under the influence of gusts
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图 10 不同时刻下施加激励前后翼型表面压力系数分布情况
Figure 10. The distributions of pressure coefficient on airfoil surface at different times before and after plasma actuation under the influence of gusts
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图 11 不同时刻下施加激励前后的翼型速度场
Figure 11. The velocity field around the airfoil at different times before and after plasma actuation under the influence of gusts
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图 12 施加激励前后无量纲分离区长度随时间变化情况
Figure 12. The non-dimensional length of separation zone versus time before and after plasma actuation under the influence of gusts
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图 13 施加激励前后无量纲分离区面积随时间变化情况
Figure 13. The non-dimensional area of separation zone versus time before and after plasma actuation under the influence of gusts
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图 14 施加激励前后边界层形状因子随弦向变化情况
Figure 14. The shape factor of boundary layer in a chordwise direction before and after plasma actuation under the influence of gusts
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图 15 施加激励前后湍动能分布情况
Figure 15. The distributions of TKE before and after plasma actuation under the influence of gusts
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