# Flow past cylinder

## Best Practice Advice for the UFR

### Key Physics

The most important feature of the flow past a long, square cylinder is the unsteady, alternate shedding of vortices from the cylinder which are swept downstream forming a Karman vortex street that dominates the wake. The fluctuations due to the shed vortices have a dominant frequency and cause a strong momentum exchange. The first advice is that this unsteady vortex-shedding flow cannot be calculated by steady RANS calculations, but as a minimum unsteady 2D RANS must be used. The shed vortices are mainly two-dimensional, but large-scale 3D structures modulate the shedding frequency and the amplitude of fluctuations. The approach flow is largely inviscid with very thin laminar layers on the front side. The flow separates at the front corners and thin flapping separated shear layers form along the sides with a thin reverse flow region having large gradients. These shear layers are first laminar, but then undergo transition to turbulence after about 15% of the side length. In the experiment, the oncoming flow had a uniform velocity and 2-3% turbulence of an unknown length scale.

### Numerical issues

As mentioned already, an unsteady calculation procedure must be used also for RANS calculations. First order upwind schemes for the convection terms cannot be used as they introduce too much numerical diffusion, damping out the unsteady vortex motion. Even higher order upwind schemes were found to be problematic in LES calculations and hence central differencing should be used. the minimum grids in the cross sectional plane (see Fig.1) are as follows:

• RANS with wall-functions ≈ 100 x 70
• Two-layer RANS ≈ 170 x 170
• LES ≈ 150 x 150

For LES this is probably still not fine enough near the side-walls where the gradients are particularly large. In the 3D LES calculations at least 20 grid-points should be used in the spanwise direction. Grid stretching in the wake should be avoided as this was found to have an adverse effect in some LES calculations (but was not confirmed by all).

### Computational domain and boundary conditions

The lateral boundaries should be placed at the location of the walls of the water tunnel, so that the blockage is the same as in the experiment. This means that the lateral width of the domain should be 14 cylinder widths D, as shown in Fig. 1. At the lateral boundaries, slip conditions (symmetry conditions) can be used. The inflow plane, where uniform conditions are applied, should be placed about 10 D upstream of the cylinder as it was found that at x/D ≈ -5 used in many calculations there is already an influence of the cylinder on the oncoming flow. In RANS calculations the turbulence level at inflow should be equal to the experimental level of 3% and the turbulence length scale should be chosen such that the ratio of eddy-viscosity to molecular viscosity is about 10 rather than a significantly higher value. In all LES carried out so far, turbulence at the inflow was neglected. The outflow plane should be placed at least 15 D downstream of the cylinder and here zero gradient conditions can be used in RANS calculations and the convective conditions should be used in LES calculations. The wall boundary conditions are discussed in the section on physical modelling. In LES calculations the spanwise extent of the domain should be at least 4 D and periodicity conditions should be applied at the boundaries.

### Physical modelling

The standard k - ε RANS model with wall-functions should not be used for this flow as it produces rather poor results because the periodic motion is strongly underpredicted. This is to a large extent due to the excessive turbulence production in the stagnation flow resulting from the use of this model. The Kato-Launder modification removes this problem and yields improved results, but together with wall-functions these are still not very good and hence wall functions should be avoided in RANS calculations. The excessive turbulence production problem is also absent when a RSM model used, but this overpredicts the periodic motion — however more testing with this model is really needed. When combined with the two-layer approach resolving the near-wall region, the Kato-Launder version of the k - ε model yields reasonable results for engineering parameters such as the Strouhal number, the mean drag coefficient and the size of the mean recirculation zone. The fluctuating quantities are not reliably predicted by this model. In particular, the turbulent stochastic fluctuations are severely underpredicted in the RANS calculations. The fairly high values of these fluctuations in the experiment (see Rodi, 1997, 2002) most likely stem from low frequency variations of the shedding motion due to 3D effects which cannot be accounted for in 2D RANS calculations. LES allows to pick up these motions and in general gives a better simulation of the details of the flow and is hence more suitable. In fact, the more successful of the LES predictions are better than any of the RANS calculations reported. Hence, if the details of the flow are of interest, LES should be used rather than RANS. However, the price to be paid is a large increase in computing time, roughly 10 fold if one goes from a RANS calculation with two-layer approach to a LES calculation and 36 fold if one goes from a RANS calculation with wall-functions to an LES (Rodi, 2002).

The subgrid-scale model used in LES was found not to be crucial for this flow; the standard Smagorinsky model, with wall-damping functions, is adequate for this application. Also, there was no significant influence of the near-wall treatment detected, i.e. whether a no-slip condition or wall-functions were used, but the advice is to use a no-slip condition if a sufficiently fine near-wall resolution can be afforded. The quality of an LES calculation depends in the end mainly on the calculation domain, which needs to be chosen sufficiently large, and on a sufficiently fine resolution.

### Application uncertainties

The main uncertainty concerns the turbulence of the oncoming flow. The intensity was measured 3D upstream of the cylinder, but no information is available from the experiment on the length scale and hence considerable uncertainties exist about the characteristics of the turbulence at the inflow boundary when this is placed 10 D upstream of the cylinder as recommended. If the inflow boundary is moved closer to the cylinder, then uncertainties are introduced concerning the mean velocity and pressure at this boundary.

### Recommendations for future work

The unsteady RANS calculations have all been done with fairly dated turbulence models and it would be interesting to learn about the performance of modern models like the Spalart-Allmaras model, the Menter SST model or Durbin's V2F model for this flow. It was further found that even the most successful LES simulations are not entirely satisfactory as they had difficulties to get both the near-wake region and the recovery in the further downstream region predicted correctly. Hence, also further LES test calculations are recommended. Of particular interest would be calculations with a spanwise extent of the calculation domain larger than 4D. Also, the inflow boundary should be placed further upstream of the cylinder, at about 10D (so far the inflow boundary was placed around 5D upstream). Further, an even better numerical resolution should be attempted, especially near the side walls. Finally, the turbulence in the oncoming free stream was neglected so far and should be included in the inflow conditions. Additional experiments would also be helpful in which the turbulence at inflow is carefully measured and for different Reynolds numbers and free stream turbulence levels to allow a wider testing of the calculation procedures.