翼型风洞试验中不确定性分析的自动微分方法
收稿日期: 2013-10-14
修回日期: 2013-12-20
网络出版日期: 2014-03-20
基金资助
国家自然科学基金（11272264）
Uncertainty Analysis of Airfoil Wind Tunnel Tests with Automatic Differentiation
Received date: 2013-10-14
Revised date: 2013-12-20
Online published: 2014-03-20
Supported by
National Natural Science Foundation of China (11272264)
为了深入分析风洞试验中来流参数的扰动对翼型气动试验结果的影响，基于雷诺平均Navier-Stokes方程有限体积方法，采用Spalart-Allmaras湍流模型，发展了一套二维计算流体力学（CFD）程序，应用自动微分方法对CFD程序进行改造，建立了对应过程的敏感性导数计算方法和程序，可以一次性获得翼型各处压力系数和所有气动力系数对迎角、马赫数和雷诺数的敏感性导数。研究结果表明：在亚声速和跨声速中，翼型压力分布对马赫数最敏感，比对雷诺数的敏感性至少高8个量级，但是，在亚声速来流中，翼型压力系数的不确定性由迎角摄动引起的部分比马赫数摄动引起的部分高1个量级，迎角控制精度很大程度上决定了风洞试验结果的精度；在跨声速来流中，迎角摄动引起的不确定性比马赫数摄动引起的要低1个量级，同时，对马赫数敏感性的增强使得翼型压力分布的不确定性在跨声速范围比在亚声速范围高1个量级，此时马赫数的控制精度很大程度上决定了风洞试验结果的精度。
徐林程 , 王刚 , 武洁 , 叶正寅 . 翼型风洞试验中不确定性分析的自动微分方法[J]. 航空学报, 2014 , 35(8) : 2102 -2111 . DOI: 10.7527/S1000-6893.2013.0503
In order to obtain a deep understanding of the way that the perturbations from free stream influence the test results, based on finite volume algorithm, solving the Reynolds-averaged Navier-Stokes equations with Spalart-Allmaras turbulence model, we develop a set of computational fluid dynamics (CFD) program for 2 dimension problems and then build the corresponding process to compute sensitive derivatives with the method of automatic differentiation. With the transformed program, one computational course yields derivatives of all aerodynamic coefficients with respect to angle of attack, Mach number and Reynolds number. As the computational results show, in subsonic flow and transonic flow, surface pressure coefficients of the airfoil are the most sensitive to Mach number, to which the sensitivities are at least 8 order higher than that to Reynolds number. However, in subsonic flow, uncertainties caused by angle of attack perturbations is one order higher than that caused by Mach number perturbations, which means that wind tunnel accuracy of angle of attack would determine the accuracy of experimental results to a great extent, while transonic flow reverses the above results and conclusion. Furthermore, increased sensitivities to Mach number lead to the fact that uncertainties of pressure coefficients of the airfoil in transonic flow are one order higher than that in subsonic flow, which means, in transonic flow, wind tunnel accuracy of Mach number should be raised to guarantee the accuracy of the experimental results.
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