COMPUTATIONAL STUDY OF BOUNDARY LAYER TRANSITION OVER COMPLIANT SURFACES

Abstract

The present work is concerned primarily with the various aspects of flow stability over flexible or compliant surfaces. The flow is assumed to be incompressible. The effects of boundary layer growth on the linear stability of low over single- and multi-layer compliant walls is studied. Correction to the growth rate of parallel-flow theory for boundary-layer non-parallelism are obtained through multiple-scale analysis, applied to the low, the compliant wall and the interface conditions. Results indicate that low noa-parallelism has an overall destabilizing influence on the Tollmien-Schlichting instability (TSI) and the travelling-wave flutter instability (TWF). Flow non-parallelism is also found to have a very strong destabilizing effect on the branch of TWF that stretches to low Reynolds number. The results obtained have important implications for the design and use of compliant layers at low Reynolds numbers. The linear hydrodynamic stability of boundary-layer flow over compliant surfaces subjected to fluid loading is presented. To take into account the interaction between the initial stress and deformation state of the wall (which is in static equilibrium with the mean flow) and the small perturbation, the classical theory of nonlinear elasticity is used, in which the properties of the compliant wall material are prescribed by a linear isotropic law between the second Piola-Kirchhoff stress tensor and the Green strain tensor. Results obtained show that hydrodynamic pressure loading can strongly influence the stability of flow over compliant surfaces, and should be taken into account when evaluating the performance of compliant coatings as transition-delaying or noise-reducing devices in underwater applications. The effects of fluid loading on the stability of non-parallel boundary-layer flow over compliant surfaces is also studied. Results obtained show that the presence of mean shear stress enhances the destabilizing influence of flow non-parallelism on the TSI and TWF instabilities. The last part of the study is to investigate the secondary instabilities of boundary-layer flow over compliant surfaces. A theory for secondary instabilities based on Floquet theory is used. Temporally growing subharmonic mode is being examined. The results show that in the absence of TWF instability modes, suitably designed compliant walls are able to inhibit or suppress the secondary instability associated with the primary TSI waves.