An LES study and ... in-line tube-banks 11 increase the wake instabilities further. Large flow structures are lost and broken into small eddies, producing ultimately a fully developed grid turbulence after the final cylinder column. Figure 6a presents time-averaged surface pressure distributions against θ from the front stagna- tion point for the middle circular cylinder, taken from the first column to the fourth column, respectively. The results of Shim[27] are shown for comparison. The surfaces pressures are presented in terms of the coefficient of pressure where 〈 p 〉$_{T}$ denotes an ensemble average across the spanwise direction for all the sampling points on the cylinder surface over the sampling time interval T , though the vortex shedding does not necessarily occur in phase over the whole spanwise direction. The time-averaged boundary layers on either side of each circular cylinder are assumed to be symmetrical. q$_{ref}$ is the dynamic pressure in terms of free stream velocity u$_{o}$ and fluid density ρ , which is given by To make C$_{p}$ equal to unit at the front stagnation point for every cylinder, the corresponding static pressure p$_{ref}$ is calculated according to equation 24 first, C$_{p}$ is hence determined around the cylinder surface. This procedure was also used in the work of Shim[27] for calculating C$_{p}$ . Hence, in view of the transverse pitch ratio S$_{T}$ = 2 . 67 and in terms of the continuity equation u$_{g}$/u$_{o}$ = S$_{T}$ / ( S$_{T}$ − d ), one obtains the corresponding converting factor for the related quantities. Very good agreements for the time-averaged surface pressure distribution around the four cylin- ders are observed between the LES calculations and the experimental measurements of Shim[27] among the four figures of Figure 6. Other quantities, for example, the r.m.s pressure distribution and vortex shedding frequency are also very comparable. They shall be shown in later figures in this paper. For the cylinder from the first column, note that the LES data in figure 6a contain a kink near θ = 85 $^{o}$, which indicates the presence of the laminar boundary layer separating from q$_{ref}$ = 1 2 ρu 2 g (25) C$_{p}$ = 〈 p 〉$_{T}$ − p$_{ref}$ q$_{ref}$ (24) 3.2 Surface pressue characteristics