Non-local sub-characteristic zones of influence in unsteady interactive boundary-layers

The properties of incompressible, unsteady, interactive, boundary layers are examined for a model hypersonic boundary layer and internal flow past humps or, equivalently, external flow past short-scaled humps. Using a linear high frequency analysis, it is shown that the domains of dependence within the viscous sublayer may be a strong function of position within the sublayer and may be strongly influenced by the pressure displacement interaction, or the prescribed displacement condition. Detailed calculations are presented for the hypersonic boundary layer. This effect is found to carry over directly to the fully viscous problem as well as the nonlinear problem. In the fully viscous problem, the non-local character of the domains of dependence manifests itself in the sub-characteristics. Potential implications of the domain of dependence structure on finite difference computations of unsteady boundary layers are briefly discussed

Departure solutions of the unsteady thin-layer and full Navier-Stokes equations solved using streamline curvature based iteration techniques

The development of a thorough understanding of the mechanisms for vortex eruptions from viscous layers, which are believed to be associated with phenomena such as dynamic stall onset and transition, is crucial if accurate models of such phenomena are to be formulated. The development of such models may, in turn, allow for the possibility that such effects could be accounted for during the design of various aerodynamic devices such as wings, helicopter rotors, and turbomachinery blading and thus lead to designs which are stall free or stall resistant and which have better stall-recovery properties. The present investigation is being conducted as part of an effort to develop analytical and numerical tools which can be used to help improve our understanding of the vortex-eruption mechanism at high Reynolds numbers. The addition of the normal-momentum equation to the classical unsteady boundary-layer equations is crucial according to recent asymptotic analyses of the vortex-eruption problem and is a key feature of the analyses being developed by the present authors. The purpose of this paper is as follows: to describe departure solution behavior observed when using unsteady, streamline-curvature based solution procedures in which nontrivial transverse pressure gradient effects are included; and to show that special treatment of the time-derivative of the normal velocity is needed to eliminate the ill-posed solution behavior, which is observed when small spatial and temporal step sizes are used

The impact of dynamic roughness elements on marginally separated boundary layers

It has been shown experimentally that dynamic roughness elements – small bumps embedded within a boundary layer, oscillating at a fixed frequency – are able to increase the angle of attack at which a laminar boundary layer will separate from the leading edge of an airfoil (Grager et al., in 6th AIAA Flow Control Conference, 2012, pp. 25–28). In this paper, we attempt to verify that such an increase is possible by considering a two-dimensional dynamic roughness element in the context of marginal separation theory, and suggest the mechanisms through which any increase may come about. We will show that a dynamic roughness element can increase the value of Γ_{c} as compared to the clean airfoil case; Γ_{c} represents, mathematically, the critical value of the parameter Γ below which a solution exists in the governing equations and, physically, the maximum angle of attack possible below which a laminar boundary layer will remain predominantly attached to the surface. Furthermore, we find that the dynamic roughness element impacts on the perturbation pressure gradient in two possible ways: either by decreasing the magnitude of the adverse pressure peak or by increasing the streamwise extent in which favourable pressure perturbations exist. Finally, we discover that the marginal separation bubble does not necessarily have to exist at Γ = Γ_{c} in the time-averaged flow and that full breakaway separation can therefore occur as a result of the bursting of transient bubbles existing within the length scale of marginal separation theory