Inviscid blocking effects in multibody flows

The same processes occur in three-dimensional flows. For a random array of fixed rigid spheres (see Koch and Brady, 1985 [340]), the axisymmetric velocity disturbance in the far wake of a test sphere tends to 

The kinematic constraint imposed by a rigid body ensures that the flow goes around each body and this flow (on the upstream portion of the body) is strongly determined by the body shape. This blocking effect is not a feature of distributed drag models - its importance is illustrated here using inviscid models (see Eames, Hunt Belcher [163] for a more comprehensive description). We show in Section 7.4 how inviscid blocking may be included into future computational models. 

Consider a group of bodies lying within a perimeter/surface S, denoted by a dashed curve (see Fig. 7.3), in a steady uniform flow, U. The total volume bounded by S and the volume of the bodies, are V and W respectively. The average voidage of the bodies within V is a = Vb/V. The cross-sectional area (or width) of the streamline tube, which just passes around V, tends to far upstream of the cloud. 

---