Numerical study of leading-edge receptivity on the infinite-thin flat-plat boundary layer

Abstract

The laminar-turbulent transition has always been one of the most concerned and significant research topics. Receptivity is the first stage of the laminar-turbulent transition process in the boundary layer, and also plays a key role in the laminar-turbulent transition. However, previous studies for leading-edge receptivity mostly focused on the external sound disturbances, while it is seldom to see the relevant research on the leading-edge receptivity to free-stream turbulence in the boundary layer which is universal in the free stream. In view of this, direct numerical simulation is utilized in this paper to study the leading-edge receptivity to free-stream turbulence exciting the Tollmien-Schlichting (T-S) wave in the boundary layer. The high-order high-resolution compact finite difference schemes based on non-uniform meshes and fast Fourier transform are used in spatial discretization, and the fourth order modified Runge-Kutta scheme is used in temporal discretization to solve Navier-Stokes equations for direct numerical simulation. Perturbation waves with short wavelengths, whose wavelengths are approximately one-third of the disturbance wavelengths of free-stream turbulence, are excited in the boundary layer under the free-stream turbulence; and our numerical results show that the dispersion relations, growth rates and neutral stability curve of the group of the excited perturbation waves with different frequencies are in line with the solutions obtained from the linear stability theory. These obtained numerical results confirm that the group of the excited perturbation waves with different frequencies are a group of T-S waves with different frequencies and the interaction between leading-edge of flat plate and free-stream turbulence to excite unstable waves in the boundary layer is one of the receptivity mechanisms. Furthermore, it is found that the amplitudes of the excited T-S waves in the boundary layer increase linearly with increasing the amplitude of the free-stream turbulence; while the normal wave number and incident angle of free-stream turbulence are approximately 60 and 20, the leading-edge receptivity coefficient KI reaches a maximum; and the values of leading-edge receptivity coefficient KI