CFD verification and weak compressibility correction of unsteady aerodynamic force models applied to high-amplitude oscillating incoming flows
-
摘要: 针对大振幅振荡来流条件下薄翼受到的非定常气动力，Isaccs和Greenberg分别发展了非定常气动力模型。这两种模型可以用于直升飞机桨叶与风力发电叶片的气动力分析，模型在不可压缩无黏来流条件下建立，但实际流动不可避免粘性和弱可压缩性的影响，需要检验两种模型的适用性。针对粘性效应的影响，2014年Strangfeld对于NACA0018翼型，通过风洞实验验证了在Reynolds数25万时，Isaccs和Greenberg的模型仍适用，实验的Mach数为0.0326，流动近似不可压缩流动。针对可压缩性的影响，通过数值模拟方法进行了研究。首先重复了实验在Mach数为0.0326时的结果，并进一步考察了当Mach数提高为0.1、0.2和0.3时非定常气动力的变化。结果表明随着Mach数的提高，升力系数的最高点逐渐高于模型，并且相位逐渐落后，在Mach数为0.3时差别最明显，非定常升力系数最高点计算与模型相差50%。此即表明弱可压缩性对模型的预测结果影响不可忽略。为了扩展模型在Mach数变化时的适用范围，对模型进行了弱可压缩性修正。通过考虑速度变化引起均匀来流中密度的变化，修正了翼型附近流体密度，使其跟随来流Mach数变化。采用此方法，将计算与模型的幅值差别减小到5%左右。
-
关键词:
- Isaacs模型 /
- Greenberg模型 /
- 非定常气动力 /
- 低马赫数 /
- 弱可压缩性修正
Abstract: The two-dimensional airfoil theories of Isaacs and Greenberg for unsteady aerodynamic forces are widely adopted to estimate the aerodynamic performance of wind-turban blades and helicopter blade loads. The models are established under the assumption that the incoming flow is incompressible and without viscosity. However, the viscosity and compressibility are inevitable and the applicability of the model to predict the aerodynamic force in real flows needs to be checked. For the viscous effects, Strangfeld et al. verified the models experimentally using the data of NACA 0018 from wind tunnel at Reynolds number 0.25 million in 2014. The Mach number of the experiment is near 0.0326, which makes the flow almost incompressible. To check the effects of compressibility, a numerical simulation of NACA 0018 is conducted. For verification, the result of Strangfeld et al. at Mach number 0.0326 is repeated using CFD. The simulation further extends to the Mach number 0.1, 0.2 and 0.3 cases to investigate performance of the model at higher Mach numbers. The results show that maximum lift coefficient increases and the phase lags with Mach number increasing. Maximum overshot is at Mach number 0.3, which is over 50% more than the prediction of the models. The results show that the compressibility is non-negligible and the Mach number is needed to be taken into account as a sensitive factor. To extend the application range of Mach number, a correction is added to the models to account the influence of weak compressibility. The correction relates the variation of density of the incoming flow to the Mach number changing, which changes the density near the airfoil. As the aerodynamic force are proportional to the density, the correction would increase the aerodynamic force as Mach number increases. Using the correction, the differences of the models and simulation is within 5%. -
图 1 Isaacs模型与Greenberg模型比较
Figure 1. The comparison of Isaacs' model and Greenberg's model
图 3 Mach为0.0326时翼型表面压力系数与实验对比
Figure 3. Comparison of CFD calculation and the experiment of Strangfeld on the pressure coefficient
图 8 定常流动不同马赫数升力系数、力矩系数与马赫数0.0326时各个系数之比
Figure 8. The rate of steady moment and lift coefficients at Mach number 0.1, 0.2, 0.3 over those at Mach number 0.0326
图 9 升力系数可压缩性修正
Figure 9. Compressibility correction of the Isaacs' and Greenberg's model
-
[1] Theodorsen T. General theory of aerodynamic instability and the mechanism of flutter[R]. NACA Rep No. 496, 1935:413-433. [2] Isaacs R. Airfoil theory for flows of variable velocity[J]. Journal of the Aeronautical Sciences, 1945, 12(1):113-117. doi: 10.2514/8.11202 [3] Isaacs R. Airfoil theory for rotary wing aircraft[J]. Journal of the Aeronautical Sciences, 1946, 13(4):218-220. doi: 10.2514/8.11351 [4] Greenberg J M. Airfoil in sinusoidal motion in a pulsating stream[R]. NACA TN1326, 1947. [5] Mateescu D, Neculita S. Low frequency oscillations of thin airfoils in subsonic compressible flows[C]//44th AIAA Aerospace Sciences Meeting and Exhibit, Reno, Nevada, 2006. [6] William P Walker, Mayuresh J Patil. Unsteady aerodynamics of deformable thin airfoils[J]. Journal of Aircraft, 2014, 51(6):1673-1680. doi: 10.2514/1.C031434 [7] Ramesh K, Gopalarathnam A, Edwards J R, et al. Theoretical analysis of perching and hovering maneuvers[R]. AIAA 2013-3194. [8] Cho S H, Kim T, Song S J. Freestream Pulsation Effects on the Aeroelastic Response of a Finite Wing[J]. AIAA Journal, 2008, 46(11):2723-2729. doi: 10.2514/1.33731 [9] 刘启宽, 李亮, 张志军, 等.风力机叶片大挠度挥舞振动特性分析[J].动力学与控制学报, 2012, 10(2):171-177. http://www.cnki.com.cn/Article/CJFDTOTAL-DLXK201202015.htmLiu Q, Li L, Zhang Z, et al. Flapwise characteristics of a wind turbine blade with large deflection[J]. Journal of Dynamics and Control, 2012, 10(2):171-177. http://www.cnki.com.cn/Article/CJFDTOTAL-DLXK201202015.htm [10] Williams D, Quach V, Kerstens W, et al. Low-Reynolds number wing response to an oscillating freestream with and without feed forward control[R]. AIAA 2009-143. [11] Jose A I, Baeder J D. Steady and unsteady aerodynamic modeling of trailing edge flaps with overhang and gap using CFD and lower order models[R]. AIAA 2009-1071. [12] Strangfeld C, Müller-Vahl H, Greenblatt D, et al. Airfoil subjected to high-amplitude free-stream oscillations:theory and experiments[C]//7th AIAA Theoretical Fluid Mechanics Conference, Atlanta, GA, 2014. [13] Mian H H, Gang Wang, Raza M A. Application and validation of HUNS3D flow solver for aerodynamic drag prediction cases[C]//Proceedings of 201310th International Bhurban Conference on Applied Sciences and Technology, Islamabad, Pakistan, 2013:209-218. [14] Liou Meng Sing. A sequel to AUSM, Part Ⅱ:AUSM+-up for all speeds[J]. Journal of Computational Physics, 2006, 214:137-170. doi: 10.1016/j.jcp.2005.09.020 [15] Spalart P R, Allmaras S R. A one-equation turbulence model for Aerodynamic flows[J]. Le Recherche Aerospatiale, 1994, 1:5-21. https://www.researchgate.net/publication/236888804_A_One-Equation_Turbulence_Model_for_Aerodynamic_Flows [16] Katz J, Plotkin A. Low-speed aerodynamics[M]. Cambridge, Cambridge University Press, 2001. -
下载:
点击查看大图
图(10)
计量
- 文章访问数: 229
- HTML全文浏览量: 39
- PDF下载量: 578
- 被引次数: 0
