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Re [231], but, contrary to what happens within plane channels, smaller entrance effects at higher Re [189, 229, 231, 309]. This behaviour can be explained by the convective motions perpendicular to the active walls (membranes) induced by the obstacles, which, in flow conditions intermediate between full turbulence and creeping, accelerate the development of the concentration field. 4.4.5 Correlations for pressure drop and influence of pumping power on energy consumptions Data on pressure drops in ED systems can be found in several references [39, 177, 178, 195, 221, 228, 234, 279]. The energy consumption for feed solutions pumping is strongly dependent on pressure drops, which can be simply characterized by the correlation between the friction factor (f) and the Reynolds number, often reported in the literature as a power law: f=ARe-B (25) Actually, the exponent B tends to 1 at very low Re (Figure 14 (a)), but decreases as Re increases (Figure 14 (b)) due to higher inertial effects [281]. Therefore, we stress that correlations as those in eq. (25) are more suitable for fitting narrow Re ranges, similarly to the case of Sh. For larger ranges or ranges starting from low Re values, the trend of the friction coefficient normalized by that of the spacerless plane channel as a function of Re may be fitted by polynomial laws [6]. Figure 14. Darcy friction factor in spacer-filled channels. (a) Lower Reynolds numbers: results from CFD simulations of fully developed flow within woven spacers with different pitch-to-height ratios (Δl/h) and flow attack angles (γ) (adapted from [281]). Higher Reynolds numbers: experimental data concerning floating eddy promoters with different pitch-to-height ratios (Δl/h) [195]. Note that the equivalent diameter to calculate Re and f is equal to the channel thickness h, according to the definitions in [195]. 44PDF Image | Electrodialysis for water desalination
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