Boundary layer leading-edge receptivity to sound at incidence angles

Abstract

The leading-edge receptivity to acoustic waves of two-dimensional parabolic bodies was investigated using a spatial solution of the Navier–Stokes equations in vorticity/streamfunction form in parabolic coordinates. The free stream is composed of a uniform flow with a superposed periodic velocity fluctuation of small amplitude. The method follows that of Haddad & Corke (1998) in which the solution for the basic flow and linearized perturbation flow are solved separately. We primarily investigated the effect of frequency and angle of incidence (−180° [les ] α2 [les ] 180°) of the acoustic waves on the leading-edge receptivity. The results at α2 = 0° were found to be in quantitative agreement with those of Haddad & Corke (1998), and substantiated the Strouhal number scaling based on the nose radius. The results with sound waves at angles of incidence agreed qualitatively with the analysis of Hammerton & Kerschen (1996). These included a maximum receptivity at α2 = 90°, and an asymmetric variation in the receptivity with sound incidence angle, with minima at angles which were slightly less than α2 = 0° and α2 = 180°.

Discussions on driven cavity flow

“…Since the perturbation quantities are assumed to be small compared to the basic flow quantities, any negligible numerical errors or oscillations in the basic flow solutions, will greatly affect the solution of the perturbation equation (Haddad & Corke [25], Erturk & Corke [16], Erturk et. al.…”

Tollmien-schlichting wave amplitudes on a semi-infinite flat plate and a parabolic body: comparison of a parabolized stability equation method and direct numerical simulations

“…Therefore, in this paper a grid size of Z × Y = 2000 × 100 is used, as this produces results which are practically grid independent, but the simulations do not use up all the available computer memory, which greatly increases the computation time. (18) and (35). The horizontal dotted line is the value λ = 0.4696 which is the skin friction coefficient for the Blasius boundary layer, and this figure shows that all the results tend to this solution far downstream, which is a good check on the numerical scheme.…”

“…Haddad & Corke (18) developed their code for a parabolic body so as to eliminate the discontinuous curvature issue of the elliptical body studied by Reed et al (31), see (10) for a more detailed discussion. This DNS method was extended to parabolic bodies at non-zero angles of attack by Ertuck & Corke (35) and Haddad et al (36), and to the MSE by Wanderley & Corke (37). The results of (37) were compared to the DNS results of Fuciarelli et al (38) and the experiments of Saric & White (39).…”

Asymptotic receptivity analysis and the parabolized stability equation: a combined approach to boundary layer transition

“…An alternative approach taken by Corke and co-workers is based on linearisation about the base flow, that leads to decoupling of the base and unsteady flows which can then be solved separately. Haddad & Corke (1998) considered parabolic bodies with axis of symmetry parallel to the mean flow, Erturk & Corke (2001) and Haddad et al (2005) extended the analysis to parabolic bodies at an angle-of-attack to the mean flow, while Wanderley & Corke (2001) considered bodies with elliptical leading edges in order to compare with the results of Fuciarelli et al (1998).…”