Boundary-Layer Receptivity Analysis Of A Naca-0012 Airfoil Withwall Suction.

Abstract

In this work, a receptivity analysis of the boundary layer evolving along a NACA-0012 wing
profile with suction at wall surface is considered. The environmental perturbations that arrive from the
free stream and enter the boundary layer, such as acoustic or vortical waves, do not have the correct
wave parameters (i.e., the frequency and the wavelength) to excite the instability wave. Thus, a wavemodulation
mechanism is needed in order to create the modal instability. The interaction between the
external disturbance and the perturbation induced in the boundary layer by suction at the wing surface can
activate this mechanism. In the model proposed here, the Navier-Stokes equations that govern the problem
are linearized around a basic flow which is determined by the boundary-layer equations. Besides,
considering that the boundary layer evolves with two different length scales, the theory of multiple scales
is employed to solve the receptivity problem. A solvability condition, given by the orthogonality relation
between the adjoint eigenfunction (solution of the adjoint eigenvalue problem) and the non-homogeneous
term of the receptivity differential equation, allows the solution of the non-homogeneous problem. After
imposing the solvability condition, a first-order differential equation with variable coefficients is
obtained. The analytical expression of this equation gives the solution of the complex multiplicative
coefficient that allows the wave-amplitude estimation as well as the obtention of the here-denominated
receptivity function which gives an estimation of how receptive is the airfoil boundary layer to the considered
disturbances.