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Understanding spatial development of a turbulent mixing layer is essential for many engineering applications. However, the flow development is difficult to replicate in physical or numerical experiments. For this reason, the most attractive method for the mixing layer analysis is the direct numerical simulation (DNS), with the most control over the simulation inputs and free from modeling assumptions. On the other hand, the DNS cost often prevents conducting the sensitivity analysis of the simulation results to variations in the numerical procedure and thus, separating numerical and physical effects. In this paper, effects of the computational domain dimensions on statistics collected from DNS of a spatially developing incompressible turbulent mixing layer are analyzed with the focus on determining the domain dimensions suitable for studying the flow asymptotic state. In the simulations, the mixing layer develops between two coflowing laminar boundary layers formed on two sides of a sharp-ended splitter plate of a finite thickness with characteristics close to those of the untripped boundary layers in the experiments by Bell and Mehta, AIAA J., 28(12), 2034 (1990). The simulations were conducted using the spectral-element code Nek5000.

 

Optimal fish array hydrodynamics in accelerating phalanx schools are investigated through a computational framework which combines high fidelity Computational Fluid Dynamics (CFD) simulations with a gradient free surrogate-based optimization algorithm. Critical parameters relevant to a phalanx fish school, such as midline kinematics, separation distance and phase synchronization, are investigated in light of efficient propulsion during an accelerating fish motion. Results show that the optimal midline kinematics in accelerating phalanx schools resemble those of accelerating solitary swimmers. The optimal separation distance in a phalanx school for thunniform biologically-inspired swimmers is shown to be around 2L(whereLis the swimmer’s total length). Furthermore, separation distance is shown to have a stronger effect,ceteris paribus, on the propulsion efficiency of a school when compared to phase synchronization.

 

The wake flow past an axisymmetric body of revolution at a diameter-based Reynolds number$Re=u_{\infty }D/\nu =5000$is investigated via a direct numerical simulation. The study is focused on identification of coherent vortical motions and the dominant frequencies in this flow. Three dominant coherent motions are identified in the wake: the vortex shedding motion with the frequency of$St=fD/u_{\infty }=0.27$, the bubble pumping motion with$St=0.02$, and the very-low-frequency (VLF) motion originated in the very near wake of the body with the frequency$St=0.002$–$0.005$. The vortex shedding pattern is demonstrated to follow a reflectional symmetry breaking mode, whereas the vortex loops are shed alternatingly from each side of the vortex shedding plane, but are subsequently twisted and tangled, giving the resulting wake structure a helical spiraling pattern. The bubble pumping motion is confined to the recirculation region and is a result of a Görtler instability. The VLF motion is related to a stochastic destabilisation of a steady symmetric mode in the near wake and manifests itself as a slow, precessional motion of the wake barycentre. The VLF mode with$St=0.005$is also detectable in the intermediate wake and may be associated with a low-frequency radial flapping of the shear layer.

 

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 of the classical solution.