Flow in arteries, arterial bypass grafts and larger bronchial airways can influence local biology/pathology, and conduit geometry may be non-planar (Caro et al. 1996, 2002; Sherwin et al. 2002). Characteristics of non-planar flows include swirling, bulk mixing and a relatively uniform distribution of wall shear. We report model studies undertaken to clarify the determinants and implications of these flows.
The model comprised effectively two sequential planar bends. γ defined the relative rotation of the planes of curvature of the upstream and downstream bends (γ = 0 deg co-planar). u{special}1 and u{special}2 defined the angles subtending the upstream and downstream bends, respectively. We employed a 2-generation bifurcating-tube model (Fig. 1) where the time course of reddening of a litmus coating represented local relative wall shear rate (Caro et al. 2002) or a T-tube model with upstream bend (Fig. 2) and CFD (Sherwin et al. 1996). The flows were steady, laminar (Reynolds number >> 1) and developed at the inlet.
With γ = 90 deg, flow at the downstream bend was swirling with pitch, l{special}. l{special} increased downstream of the downstream bend, requiring its measurement at a consistent location. Increase of Re reduced l{special}, implying Re-dependent biasing of the flow at the upstream bend (e.g. McConalogue & Srivastra, 1968). Change of bend curvature also changes flow biasing (e.g. Agrawal et al. 1978). Swirling (and associated phenomena) at the downstream bend largely depend therefore on a Dean-like number at the upstream bend (Dean number (De) = Re (a/R)1/2 where a and R are respectively tube radius and radius of curvature). Biasing will attenuate downstream of the upstream bend.
γ and u{special}2 also influence downstream bend flow. Where γ = 0 deg, there is no swirl and increase of Re increases wall shear non-uniformity. Where γ > 0 deg, increase of Re increases wall shear uniformity. Where γ = 90 deg, l{special} is minimal and swirl rate, v{special}, is maximal (since l{special} = U/v{special}, where U is mean velocity). Increase of u{special}2 reduces l{special}; where u{special}2 = 90 deg, l{special} is least (v{special} maximal).
Atherosclerosis and intimal hyperplasia at arterial bypass grafts develop preferentially where wall shear is low. The findings may be relevant to inhibition of atherosclerosis by exercise and the better prognosis for arterial bypass grafts where ‘run off’ is high. Swirl will influence inhaled particle/aerosol distribution and flow/airway wall interaction (Lazarowski & Boucher, 2001). Reynolds number dependent l{special} is consistent with movement of stagnation regions during breathing and cardiac cycles.