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 (1.6 h) 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.

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