Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem
Viscous extension of potential-flow unsteady aerodynamics: the lift frequency response problem
复制标题
势流非定常空气动力学的粘性扩展：升力频率响应问题
DOI：
10.1017/jfm.2019.159
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发表时间：
2019
影响因子：
3.7
通讯作者：
Rezaei, Amir S.
中科院分区：
文献类型：
--
作者：
Taha, Haithem;Rezaei, Amir S.
多年来，库塔条件在非定常流中的应用一直存在争议，20世纪70年代和80年代的研究活动有所增加。这种对库塔条件的不满，最近随着人们对低雷诺数、高频率生物激发飞行的兴趣的增加而重新焕发了活力。然而，没有令人信服的替代库塔条件，即使它不是数学推导。考虑到升力和涡量的产生本质上是粘性过程，我们通过放松库塔条件，给出了非定常空气动力学经典理论的粘性扩展。我们在压力分布中引入了后缘奇异项，并利用三层粘性边界层理论确定了其强度。基于扩展的理论，我们开发（第一次）的理论粘性的（与雷诺数相关）扩展的Theodorsen升力频率响应函数。研究发现，粘性引起更多的相位滞后的Theodorsen功能，特别是在高频率和低雷诺数。通过对NACA 0012在低雷诺数下正弦俯仰时的Navier-Stokes方程和在相对高雷诺数下的雷诺平均Navier-Stokes方程的层流数值模拟，验证了所得理论结果的正确性。所观察到的粘性引起的滞后背后的物理关系，尾流粘性阻尼，循环发展和库塔条件进行了讨论。此外，粘性贡献的升力显着降低虚拟质量，特别是在高频率和雷诺数。
The application of the Kutta condition to unsteady flows has been controversial over the years, with increased research activities over the 1970s and 1980s. This dissatisfaction with the Kutta condition has been recently rejuvenated with the increased interest in low-Reynolds-number, high-frequency bio-inspired flight. However, there is no convincing alternative to the Kutta condition, even though it is not mathematically derived. Realizing that the lift generation and vorticity production are essentially viscous processes, we provide a viscous extension of the classical theory of unsteady aerodynamics by relaxing the Kutta condition. We introduce a trailing-edge singularity term in the pressure distribution and determine its strength by using the triple-deck viscous boundary layer theory. Based on the extended theory, we develop (for the first time) a theoretical viscous (Reynolds-number-dependent) extension of the Theodorsen lift frequency response function. It is found that viscosity induces more phase lag to the Theodorsen function particularly at high frequencies and low Reynolds numbers. The obtained theoretical results are validated against numerical laminar simulations of Navier–Stokes equations over a sinusoidally pitching NACA 0012 at low Reynolds numbers and using Reynolds-averaged Navier–Stokes equations at relatively high Reynolds numbers. The physics behind the observed viscosity-induced lag is discussed in relation to wake viscous damping, circulation development and the Kutta condition. Also, the viscous contribution to the lift is shown to significantly decrease the virtual mass, particularly at high frequencies and Reynolds numbers.