[论文解读] Evaluation of Aerodynamic Characteristics in Oscillatory Coning Motion Using CFD Methods

Mohamed Sereez, Mikhail Goman|arXiv (Cornell University)|Jan 1, 2022

Aerospace and Aviation Technology被引用 1

一句话总结

本论文提出一种基于CFD的仿真方法，利用OpenFOAM对NASA通用研究模型在Re=1×10⁶、M=0.2条件下的旋停平衡流和振荡锥流进行模拟。该方法能够准确预测非定常气动力力和力矩，通过傅里叶分析周期性响应提取动态导数，与参考CFD数据具有强一致性，展现出在大迎角飞行器动力学建模中的广阔应用前景。

ABSTRACT

Adequate modelling of aerodynamic autorotation in the stall region is critical for a more realistic loss-of-control in-flight (LOC-I) pilot training [1]. Wind tunnel rotary-balance testing of scaled aircraft models with measurements of aerodynamic forces and moments are commonly used to collect data for static conditions to investigate aircraft departures in stall region and spin regimes at high angles of attack [2, 3]. These data for steady conditions with constant angle of attack ?, sideslip ?, and constant conical rotation rate ? are helpful but not sufficient [4]. Rotary balance oscillatory coning tests, in which the axis of rotation is misaligned with the tunnel flow on some angle ?, creates a periodic variation in angle of attack and sideslip with amplitude ?. The balance reading time histories have periodic variation of aerodynamic characteristics with periodic time defined by conical rotation rate ? so that the mean values of aerodynamic characteristics are representing the rotary-balance data, while the amplitudes of unsteady periodical components inform about unsteady aerodynamic derivatives which are required for evaluation of dynamic stability in stall lateral departures and unsteady spins. The rotary-balance tests are carried out at different angles of attack ?, sideslip ? and rotation with angular velocity ? which coincides with the flow velocity V in the wind tunnel at ?=0 as shown in Fig. 1. In such pure conical motion, the angle of attack and sideslip remain constant, which provides kinematic conditions as in standard static tests at given ?,?, but with a steady conical rotation ?. When the axis of rotation is misaligned with the tunnel flow on some angle ? the unsteady aerodynamic derivatives in pitch and yaw can be extracted using the Fourier approximation of periodical variation of aerodynamic coefficients. Stall aerodynamics largely depends on the Reynolds number, but when tested in a wind tunnel, the values of the Reynolds number that can be achieved are usually much lower than in real flight conditions. The CFD methods to predict stall aerodynamics based on CFD methods, as shown in [1], can be effectively used for extrapolating results to higher Reynolds numbers, as well as for eliminating interference effects produced by a support system in wind tunnel. In this paper, we use open-source CFD software OpenFOAM to develop and validate the methodology of predicting stall aerodynamics in rotary-balance and oscillatory coning testing conditions [6]. An inverse quaternion transformation is applied to present projections of aerodynamic forces and moments in the body-fixed axes, which allows comparison of simulated results with experimental data and their direct use in aerodynamic modelling. The dual time stepping method is implemented in OpenFOAM to speed up the simulation. The OpenFOAM simulation results for the NASA Common Research Model (CRM) rolling moment coefficient C_l (?) at Re=10^6 have been validated via comparison with the NLR ENFLOW CFD code results [1,5] (see Fig. 2). This comparison confirms the reliability of the implemented rotary-balance procedure in OpenFOAM with reasonably high accuracy. Additionally, the oscillatory conning data with ?=3^o and Fourier approximation of the unsteady aerodynamic derivatives in pitch and yaw will be also presented. The effect of the top sting supporting a scaled model in wind tunnel rotary-balance tests allowed to evaluate the level of interference and make important corrections to improve the fidelity of the aerodynamic model. We also present CFD simulation results showing the transformation of the aerodynamic autorotation zone with the increase of the Reynolds number typical for real flight conditions.

研究动机与目标

• 开发并验证一种CFD框架，用于模拟后 stall 区域的旋停平衡流和振荡锥流。
• 实现在非定常旋转流条件下对非定常气动力和力矩的精确预测。
• 从振荡锥流仿真中提取非定常气动导数（如$C_{i\dot{\alpha}}^{oc}$、$C_{i\dot{\beta}}^{oc}$），用于动态稳定性建模。
• 展示OpenFOAM在正确边界条件设置下模拟复杂动态网格运动（包括锥形旋转和振荡锥流）的能力。
• 提供一种经过验证的开源CFD方法，以补充风洞试验，将数据扩展至更高雷诺数和更清洁的流动条件。

提出的方法

• 在OpenFOAM中实现自定义的“锥形运动”动态网格函数，采用基于四元数的网格旋转方法，以模拟任意轴向旋转。
• 应用非定常雷诺平均Navier-Stokes（URANS）方程，并采用剪切应力传输（SST）湍流模型进行流场求解。
• 采用“movingWallVelocity”边界条件，通过确保法向速度通量为零，实现对旋转表面的无滑移边界条件。
• 模拟稳态旋停平衡运动和非稳态振荡锥流，设定旋转轴偏移量（$\delta$）和无量纲旋转速率（$\omega$）。
• 对周期性气动力响应（$C_i(t) = C_{i0} + C_{is}\sin(\Omega t) + C_{ic}\cos(\Omega t)$）进行傅里叶级数逼近，以提取非定常导数。
• 将结果与参考CFD数据（ENFLOW代码）进行对比，并分析力/力矩轨迹的收敛性与环路形状。

实验结果

研究问题

• RQ1 OpenFOAM能否在中等雷诺数和低马赫数条件下，准确模拟NASA CRM的旋停平衡流和振荡锥流？
• RQ2 振荡锥流中的非定常气动响应与稳态旋停平衡结果相比如何？能否通过动态导数实现线性近似？
• RQ3 模拟得到的气动环路（如$C_Z$-$\alpha$、$C_m$-$\alpha$、$C_l$-$\alpha$）在失速区域能否反映预期的行为特征？
• RQ4 基于傅里叶的提取方法在从周期性响应中恢复非定常气动导数（$C_{i\dot{\alpha}}^{oc}$、$C_{i\dot{\beta}}^{oc}$）方面表现如何？
• RQ5 流场可视化（如流线、壁面摩擦、压力分布）为振荡锥流期间的非定常流动物理机制提供了哪些见解？

主要发现

• OpenFOAM对旋停平衡流的仿真结果与参考CFD数据（ENFLOW代码）高度一致，验证了计算框架的可靠性。
• 在振荡锥流中，法向力和滚转力矩系数表现出闭合环路轨迹，且可通过椭圆拟合良好逼近，表明其具有可线性化的非定常行为特征。
• 对周期性响应的傅里叶级数逼近成功提取了静态分量（$C_{i0}$）和动态分量（$C_{is}$、$C_{ic}$），从而实现了非定常气动导数的推导。
• 线性近似形式$C_i = C_{irb}(\alpha,\beta,\omega) + C_{i\dot{\alpha}}^{oc} \frac{\dot{\alpha}}{2V} + C_{i\dot{\beta}}^{oc} \frac{\dot{\beta}}{2V}$在大部分区域有效，但在迎角$\theta=11^\circ$的失速区存在偏差。
• 在$\alpha(t)=13.3^\circ$、$\beta=1.96^\circ$、$\omega=0.1$条件下，流场可视化揭示了复杂的分离模式和压力梯度，支持了力/力矩系数中观察到的非定常行为。