Effect of Compliant Walls on Three-Dimensional Primary and Secondary Instabilities in Boundary Layer Transition.

摘要

The use of passive devices to obtain drag and noise reduction or transition delays in boundary layers is highly desirable. One such device that show promise for hydrodynamic applications is the compliant coating. The present study extends the mechanical model to allow for three-dimensional waves. This study also looks at the effect of compliant walls on three-dimensional secondary instabilities. For the primary and secondary instability analysis, spectral and shooting approximations are used to obtain solutions of the governing equations and boundary conditions. The spectral approximation consists of local and global methods of solution while the shooting approach is local. The global method is used to determine the discrete spectrum of eigenvalue without any initial guess. The local method requires a sufficiently accurate initial guess to converge to the eigenvalue. Eigenvectors may be obtained with either local approach. For the initial stage of this analysis, two- and three-dimensional primary instabilities propagate over compliant coatings. Results over the compliant walls are compared with the rigid wall case. Three-dimensional instabilities are found to dominate transition over the compliant walls considered. However, transition delays are still obtained compared with transition delay predictions for rigid walls. The angles of wave propagation are plotted with Reynolds number and frequency. Low frequency waves are found to be highly three-dimensional.