Three-dimensionality of flow through an array of cylinders

Using direct numerical simulations, this paper presents the first comprehensive investigation of the three-dimensional flow characteristics for a large array of cylinders in steady current, by systematically varying the array arrangement through the number of cylinders in the range N = 1–109, gap ratio G/d (1.2–14.7, G is the center-to-center distance between two adjacent cylinders, d is the cylinder diameter), array-to-element diameter ratio D/d (7.3–48.6, D is the array diameter), incident flow angle θ (0°, 90°), and the uniformity of the array. The three-dimensional flow field both within and behind the array is shown varying widely with gap ratio, array-to-element diameter ratio, incident flow angle, and the uniformity of the array, which demonstrates the influence of array arrangement. Physical mechanisms for the effects of G/d, D/d, θ and non-uniformity are interpreted. The arrangement effects become most critical in the intermediate range of flow blockage parameter ΓD= 0.8–3 (ΓD=aD/1−ϕ, where a is the frontal area per unit volume, and ϕ is the solid volume fraction). The flow three-dimensionality arises from the wakes of individual cylinders (element wake) and the array wake behind the array at low and high values of ΓD, respectively, and from both wakes at the intermediate range of ΓD. A transition from element-wake into array-wake three-dimensionality occurs as array shear layers are susceptible to shear layer instability while quasi-two-dimensional spanwise vortices form within the array. Across arrangements modeled, it is confirmed that the extent of flow three-dimensionality is, to first order, controlled by flow blockage parameter as this parameter controls the bleeding velocity that largely determines the extent of three-dimensionality.