后掠角对后掠机翼边界层稳定性及转捩的影响

后掠机翼边界层流动稳定性及转捩对翼型的设计及优化有着重要的参考价值,而机翼后掠角是引起后掠机翼边界层横流失稳的关键参数之一.以NACA0012翼型为研究对象,通过求解三维可压缩Navier-Stokes方程计算了展向无限长后掠机翼的基本流场;通过求解Orr-Sommerfeld方程得到了扰动Tollmien-Schishting波演化的中性曲线及幅值曲线,研究了后掠角对后掠机翼边界层流动稳定性的影响;最后采用e N方法进行了转捩预测.研究发现,随后掠角的增大,横流强度和扰动幅值放大指数n均先增加后减小,且后掠角在40°~50°之间横流强度达到最大值.当后掠角在50°左右时,用转捩预测e N方法计算的幅值增长指数N值最大,导致转捩发生所需的初始扰动幅值最小,转捩最易发生.

Effect of sweep angle on stability and transition in a swept-wing boundary layer

The stability and transition of swept-wing boundary layers have important reference value to the design and optimization of airfoil. The sweep angle is one of the key parameters to the cross-flow instability of swept-wing boundary layers. Based on the NACA0012 airfoil profile, the mean flow of a swept-wing boundary layer was calculated by numerically solving the three-dimensional compressible Navier-Stokes equation, then the neutral curve and the growth curve of unstable Toumien-Schlisting wave were obtained by solving the Orr-Sommerfeld equation to study the effect of the sweep angle, and the transition position was predicted by applying eN method. Study shows that with the increase of sweep angle, both the strength of the cross-flow and the amplification factor n of the disturbance amplitude increase firstly and then decrease, and the strength of the cross-flow reaches its peak value when the sweep angle is in the range of 40° to 50°. The N factor predicted by eN method is the largest one when the sweep angle is about 50°, implying that with which angle, the induce disturbance with a smaller amplitude can easily lead to the occurrence of transition.