Secondary Stability Analysis of Crossflow Vortices using BiGlobal Theory on PIV Base Flows

Abstract

Stability analysis is conventionally applied to highly resolved base flows that are obtained through high-fidelity computational means. Modern experimental methods can capture the flows to higher and higher detail, up to such extent that performing stability analysis thereon has become feasible, at least for specific cases. Secondary instabilities to the primary crossflow vortices in a swept-wing boundary layer are resolved by applying BiGlobal stability theory to the mean flow field measured with tomographic PIV, solving for the high-frequency type I mode dedicatedly. The stability results are found to converge with respect to the mean's ensemble size and are independent of the treatment of the handling of the exterior of the measurement domain. The BiGlobal mode agrees with the instantaneous tomographic PIV and hot-wire anemometry data. This is the first occasion where this approach is applied to this application case. In doing so, one directly avoids problems concerning accounting for the primary vortices' receptivity.

Global Stability Analysis of a Boundary Layer with Surface Indentations

“…The surface deformation embodied by the indentation geometry is enclosed in the Jacobian of the mapping from the physical domain to the computational domain. In addition, we use a bi-quadratic mapping [32] that divides the wall-normal domain into three regions with an equal number of points to optimize the grid distribution in the near-wall region and hence appropriately capture the TS or global mode structures. In the streamwise direction, the grid is clustered around the maximum depth location of the indentations with an interior contraction [33] coupled with the function tan(γπx)/tan(γπ), where γ controls the level of grid clustering.…”