Boundary Layer Receptivity to Sound: Navier-Stokes Computations

Abstract

Here we discuss the computational modeling of the receptivity of the laminar boundary layer on a semi-infinite flat plate with an elliptic leading edge. The incompressible flow is computed in a spatial simulation using the full Navier-Stokes equations in general curvilinear coordinates. Finite differences are used in both space directions and in time. First, the steady basic state is obtained in a transient approach using spatially varying time steps. Then, small-amplitude acoustic disturbances of the freestream velocity are applied as unsteady boundary conditions, and the governing equations are solved time-accurately to evaluate the spatial and temporal developments of instability waves (Tollmien-Schlichting waves) in the boundary layer. A sharper leading edge is found to be less receptive to freestream disturbances.

Acoustic Receptivity Measurements Using Modal Decomposition of a Modified Orr–Sommerfeld Equation

“…Previous acoustic receptivity experiments 7-10 attempted to provide validation for computational studies. [11][12][13][14] So far, the experimental evidence has been inconclusive due to sparse data and uncertainty in the Stokes and TS wave separation technique. To provide quality acoustic receptivity measurements, an improved experimental technique must be developed.…”

“…The receptivity of planar, two-dimensional sound has been addressed by theory, [2][3][4][5][6] experiments, [7][8][9][10] and direct numerical simulation (DNS). [11][12][13][14] Theoretical studies utilizing triple deck theory and the unsteady-boundary-layer equations showed that the interaction of freestream disturbances with surface features generate Tollmien-Schlichting (TS) waves. These surface features include the leading edge, 2 localized (e.g., 2D discrete roughness) 4 and non-localized roughness, 5 and strong streamwise gradients.…”

“…Experiments at Arizona State University (ASU), [7][8][9][10] coupled with matching DNS studies, [11][12][13][14] investigated acoustic receptivity by introducing planar freestream sound into the test environment and measuring the amplitude of TS waves near branch II. Early experiments used continuous acoustic forcing, 7 while later experiments used pulsed-sound forcing.…”

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

“…Early DNS studies which investigated the evolution of T-S waves, solved the nonlinear time dependent Navier-Stokes equations, such as in Reed et al (31). These simulations were conducted to model the experiments of Saric & Rasmussen (32) and Saric et al (33) who studied an elliptical leading edge attached to a finite thickness flat plate.…”

“…Hence (18) developed a more efficient spatial code which linearised about the base flow and solved for the steady base flow and the unsteady perturbation flow separately. 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).…”