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It is well known that drag created by turbulent flow over a surface can be reduced by oscillating the surface in the direction transverse to the mean flow. Efforts to understand the mechanism by which this occurs often apply the solution for laminar flow in the infinite half-space over a planar, oscillating wall (Stokes’ second problem) through the viscous and buffer layer of the streamwise turbulent flow. This approach is used for flows having planar surfaces, such as channel flow, and flows over curved surfaces, such as the interior of round pipes. However, surface curvature introduces an additional effect that can be significant, especially when the viscous region is not small compared to the pipe radius. The exact solutions for flow over transversely oscillating walls in a laminar pipe and planar channel flow are compared to the solution of Stokes’ second problem to determine the effects of wall curvature and/or finite domain size. It is shown that a single non-dimensional parameter, the Womersley number, can be used to scale these effects and that both effects become small at a Womersley number of greater than about 6.51, which is the Womersley number based on the thickness of the Stokes’ layer ofmore »the classical solution.« less

The turbulent wake flow past a sphere at ReD= 3700 is investigated via Direct Numerical Simulation (DNS). The characteristic motions in the wake flow, such as vortex shedding and bubble pumping are identified by the probes placed in the near wake with a dominating frequency of St= fu∞/D= 0.22 and 0.004, respectively. The modal analysis is conducted in the wake area using Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). The vortex shedding and bubble pumping motions are also captured by the modal analysis. The results from POD and DMD show comparable patterns of both characteristic motions. For the bubble pumping motion, the dominating frequency of the corresponding POD mode is St= 0.004, while the DMD mode that is directly related to the separation bubble has the frequency of St= 0.009.

A high-order in space spectral-element methodology for the solution of a strongly coupled fluid-structure interaction (FSI) problem is developed. A methodology is based on a partitioned solution of incompressible fluid equations on body-fitted grids, and nonlinearly-elastic solid deformation equations coupled via a fixed-point iteration approach with Aitken relaxation. A comprehensive verification strategy of the developed methodology is presented, including h-, p-and temporal refinement studies. An expected order of convergence is demonstrated first separately for the corresponding fluid and solid solvers, followed by a self-convergence study on a coupled FSI problem (self-convergence refers to a convergence to a reference solution obtained with the same solver at higher resolution). To this end, a new three-dimensional fluid-structure interaction benchmark is proposed for a verification of the FSI codes, which consists of a fluid flow in a channel with one rigid and one flexible wall. It is shown that, due to a consistent problem formulation, including initial and boundary conditions, a high-order spatial convergence on a fully coupled FSI problem can be demonstrated. Finally, a developed framework is applied successfully to a Direct Numerical Simulation of a turbulent flow in a channel interacting with a compliant wall, where the fluid-structure interface is fully resolved.