Numerical investigation on evolution of T-S wave on a two-dimensional compliant wall with finite length

Inspired by the flexible characteristics of bird feathers, numerical simulations are used to study the influence of the compliant wall on the evolution of T-S wave in the subsonic boundary layer flow. First, the numerical results on the rigid wall are in good agreement with the linear stability theory, which verifies the reliability of the adopted numerical methods. On this basis, part of the rigid wall is replaced with a compliant wall, and the results show that the compliant wall can suppress the spatial growth of T-S wave, thus delaying the flow transition. Furthermore, the deformation of the compliant wall not only follows the waveform of T-S wave, but also includes larger-scale vibrations with the same frequency as the disturbance source, which are caused by the leading edge and trailing edge of the compliant section. The actual deformation of the compliant wall is a superposition of these waves. Later parameter study shows that increasing the surface mass density has almost no effect on the compliant wall in terms of attenuating disturbance. Increasing the surface tension or increasing the elastic coefficient of the foundation can increase the stiffness of the compliant wall and thus reduce the amplitude of wall deformation. Increasing the damping can suppress the propagation of large-scale wall vibrations generated at the leading edge and trailing edge of the compliant section, while having little effect on the deformation directly corresponding to T-S wave. The overall trend is that when the amplitude of wall deformation decreases, the attenuation effect of the compliant wall on T-S wave decreases.