Computational fluid mechanics

Two papers are included in this progress report. In the first, the compressible Navier-Stokes equations have been used to compute leading edge receptivity of boundary layers over parabolic cylinders. Natural receptivity at the leading edge was simulated and Tollmien-Schlichting waves were observed to develop in response to an acoustic disturbance, applied through the farfield boundary conditions. To facilitate comparison with previous work, all computations were carried out at a free stream Mach number of 0.3. The spatial and temporal behavior of the flowfields are calculated through the use of finite volume algorithms and Runge-Kutta integration. The results are dominated by strong decay of the Tollmien-Schlichting wave due to the presence of the mean flow favorable pressure gradient. The effects of numerical dissipation, forcing frequency, and nose radius are studied. The Strouhal number is shown to have the greatest effect on the unsteady results. In the second paper, a transition model for low-speed flows, previously developed by Young et al., which incorporates first-mode (Tollmien-Schlichting) disturbance information from linear stability theory has been extended to high-speed flow by incorporating the effects of second mode disturbances. The transition model is incorporated into a Reynolds-averaged Navier-Stokes solver with a one-equation turbulence model. Results using a variable turbulent Prandtl number approach demonstrate that the current model accurately reproduces available experimental data for first and second-mode dominated transitional flows. The performance of the present model shows significant improvement over previous transition modeling attempts.