The near-wake dynamics of turbulent flow past rigid and flexible cylinders up to ten cylinder diameters downstream is investigated at a range of Reynolds numbers (Re = 100-3900). The very-near-wake (up to three diameters) is dominated by the shear layer dynamics and is very sensitive to disturbances and cylinder aspect ratio. A systematic investigation using spectral direct (DNS) and large-eddy (LES) simulations is performed, using more than 20 three-dimensional simulations, with varying spanwise length and number of degrees of freedom ranging from 200,000 to 100,000,000. The investigation concentrated on the dynamics of the shear layer and its effect on the very-near-wake mean velocity states, the effect of the eddy-viscosity subfilter model on the flow properties, the existence of an inertial range in the turbulent near-wake, and the dimensionality of the near-wake are investigated.
Shown below, is a flow visualisation of pressure iso-contours at Reynolds number Re=3900 for a rigid cylinder. It represents a 3-dimensional simulation with 100,000,000 degrees of freedom at a computational domain spanning 40 by 18 by 6.28 in the streamwise, flow-normal and spanwise directions.
Flexible circular cylinder simulations are also performed at Reynolds numbers ranging from 100-1000, subject to forced vibrations or vortex-induced vibrations(VIV). Resolution up to 60,000,000 degrees of freedom, using 64 processors was performed in order to analyse structural responses as well as hydrodynamic forces and their relation to the near-wake flow structures examined in the transitional (200-300) and turbulent (1000) Reynolds number range. Both linear and non-linear sets of equations for the finite amplitude vibrations of a string are investigated, combined with an Arbitrary Lagrangian-Eulerian (ALE) flow solver. This has been applied to low Reynolds number simulations (100) past flexible cylinder with pinned ends.
Shearing and flat inflow simulations are additionally performed, both for free and pinned ends, for aspect ratios up to 570. The investigation concentrates on the dynamics of vortex-dislocation in flexible vibrating cylinders. For the VIV case, analytical models are developed for the drag coefficient spanwise distribution and the Strouhal number spanwise distribution, with respect to the root-mean-square of the crossflow displacement of the cable.
Pressure iso-contours at -0.09: Flow visualisation of vortex-dislocation in flow past flexible vibrating cylinders. DNS of forced vibration of a flexible cable with pinned ends, with an aspect ratio of 567. The inflow varies linearly along the span, with the Reynolds number increasing from 60 to 100 (right to left).
Iso-contours of spanwise vorticity (blue color: -0.18, yellow color: +0.18). View normal to the (x,z) horizontal plane. The shear flow past the cylinder is going upward. Presence of two vortex dislocations and evidence of vortex links between the cells of different frequency. Visualization of vortex division whereby a vortex (here blue vortex at the bottom center of the picture) from the cell of low frequency (second cell from the left) is connected with two other vortices of the same sign from the cell of high frequency (first cell from the left). Note the considerable spanwise spreading of the first dislocation between the first and second cell. Simulations by Didier Lucor and Constantinos Evangelinos.
A modification of a phase averaging technique used in experimental studies was utilized in order to systematically quantify the contribution from the coherent motion to the mean flow and the Reynolds stresses in the rigid cylinder simulations. The most energetic modes were analysed using the proper orthogonal decomposition (POD) approach, indicating that the turbulent near-wake behaves as a dynamical system of relatively low dimensionality.
The results of the POD analysis was utilized to reduce the computation cost of simulations by using the 10 to 20 most energetic modes extracted, in Navier-Stokes simulations, in order to reduce the computational expense associated with DNS. The principle is shown below, where a flow field is calculated using tradition DNS techniques (left column). With 8 POD modes extracted from the original field, the flow field may be reproduced (middle column), and Navier-Stokes simulations may be performed, at considerably lower cost, using these extracted POD modes (right column). This is currently extended to non-linear Galerkin POD and incorporated within the NekTar. suite.
