The present study presents a new nonlinear unsteady aerodynamic model to investigate the aeroelastic behavior of a self-sustained oscillating rigid airfoil. Here the unsteady Euler equations are considered simulating inviscid compressible transonic flow over an oscillating airfoil. In regard to providing boundedness criteria, a high-order technique based on a normalized variable diagram scheme has been presented. Since using dynamic mesh for simulating flow over a dynamic airfoil is too complex and requires many computational efforts, the current paper proposes a nonorthogonal and static mesh with oscillation of flow boundary. The results are compared with both well-validated numerical methods and experimental data. A time-marching method is employed to determine system responses. The predicted flutter boundary for NACA0012 airfoil at different free-stream Mach numbers is in fair agreement with direct flutter tools of the Hopf bifurcation points. Finally, the influences of the center of mass and elastic axis position on the system aeroelastic behavior are examined.

中文翻译：

---

使用边界振荡方法模拟自持振荡刚性翼型的气动弹性响应

本研究提出了一种新的非线性非定常空气动力学模型来研究自持振荡刚性翼型的气动弹性行为。在这里，非定常欧拉方程被认为是模拟振动翼型上的无粘性可压缩跨音速流动。关于提供有界标准，已经提出了基于归一化变量图方案的高阶技术。由于使用动态网格模拟动态翼型上的流动过于复杂且需要大量计算工作，因此本文提出了一种具有流动边界振荡的非正交静态网格。结果与经过充分验证的数值方法和实验数据进行了比较。采用时间推进方法来确定系统响应。NACA0012 翼型在不同自由流马赫数下的预测颤振边界与 Hopf 分岔点的直接颤振工具相当一致。最后，研究了质心和弹性轴位置对系统气动弹性行为的影响。