Best Practice Advice

Key Physics

The flow past finite height circular cylinders mounted on a flat plate is very complex as described in some detail in the Introduction and as illustrated in Fig. 1. The flow is highly three-dimensional with an interaction of various vortex systems. There is generally unsteady vortex shedding behind the cylinder unless the cylinder height is rather small (h/D below 2). The vortex shedding that occurs in the test cases considered (h/D = 2.5 and 5) is strongly influenced by the end effects, and in particular the effects of the free-end at the cylinder top.

Numerical Issues

The LES presented and discussed were carried out with a finite-volume code that uses a Cartesian grid and an immersed boundary method. 45 and 27 Million grid points were used for the h/D = 2.5 and 5 cases respectively, and an even finer resolution near the ground plate and in vertical direction at mid-height would have been desirable. The mesh sizes ∆x and Δy around the cylinder were 0.004D and 0.008D for h/D = 2.5 and 5 respectively. For the h/D = 2.5 case the mesh sizes Δz in vertical direction vary from 0.0085D near the ground plate to 0.0625D at mid-height and 0.0014D at the free-end increasing again towards the frictionless upper boundary. For the h/D = 5 case, the corresponding values are 0.00175D, 0.125D and 0.0028D. The calculations could of course also be performed with methods using wall- conforming grids, but the mesh sizes should be similar to the ones just given, or in vertical direction even better near the ground and at mid-height of the cylinder. As discussed in some detail in Palau-Salvador et al (2010), LES of the h/D = 2.5 case have been obtained with coarser meshes (e.g. 6.4 Million grid points by Fröhlich and Rodi 2004) and these calculations could also capture most of the main features of the complex flow, including the vortex shedding near the ground and the development of tip vortices, but some of the details like the complex flow behaviour on the top of the cylinder could not be resolved.

Computational Domain and Boundary Conditions

A computational domain similar to the one sketched in Fig. 3 should be used. The extent of the domain upstream of the cylinder (1.6h) is the minimum for the h/D = 2.5 case and should actually be chosen larger if possible. For wall-resolving LES, no-slip conditions should be used at the cylinder and ground plate walls while the top wall and side walls can be treated as frictionless rigid lid. At the outflow, the convective boundary condition should be used. At the inflow boundary the mean velocity profile taken from the measurements should be specified. In the LES presented, fluctuations at the inflow were set to zero and developed then in the boundary layer approaching the cylinder. By prescribing fluctuations corresponding to the turbulent boundary layer, a more realistic boundary layer approaching the cylinder could probably be achieved.

Physical Modelling

As was discussed in Palau-Salvador et al (2010), steady RANS methods can get some of the mean-flow features like separation on the sides and on the top, horseshoe vortex and tip vortices, but none of the many details discussed above and of course no features that are due to the unsteady nature of the flow which includes the mean pressure in the separation region. Hence, an eddy-resolving method is necessary to do justice to this complex flow. The wall- resolving LES presented have shown good results using the dynamic Smagorinsky model approach. However, with the fine grids as used in the LES presented, the subgrid-scale model is not very influential and probably a standard Smagorinsky model with near-wall damping could also be used.

Application Uncertainties

One of the main uncertainties is the oncoming boundary layer developing on the ground plate when the flow approaches the cylinder. Also, in the experiments the free-stream turbulence above the boundary layer was 2% which was not accounted for at all in the calculations. Further, the top and side walls were treated as frictionless rigid lids in the LES presented, but the boundary layers at these walls may have had some influence.

Recommendations for Future Work

LES with an even finer grid, particularly with better resolution near the ground plate and in vertical direction at mid-height of the cylinder would be of interest. Also a study on the influence of specifying more realistic boundary-layer characteristics at the inflow would be of interest. Further it would be intriguing to see how hybrid RANS/LES methods, e.g. the DES method, would perform for this flow.

Contributed by: Guillermo Palau-Salvador, Wolfgang Rodi, — Universidad Politecnica de Valencia, Karlsruhe Institute of Technology