Laboratory investigation of lateral dispersion within dense arrays of randomly distributed cylinders at transitional Reynolds number

Abstract

Relative (effective) lateral dispersion of a passive solute was examined at transitional Reynolds numbers within a two-dimensional array of randomly distributed circular cylinders of uniform diameter d. The present work focuses on dense arrays, for which previously developed theory [Y. Tanino and H. M. Nepf, J. Fluid Mech. 600, 339 (2008)] implies that the asymptotic (long-time/long-distance) dispersion coefficient, when normalized by the mean interstitial fluid velocity, ⟨u¯⟩, and d, will only exhibit a weak dependence on Reynolds number, Red≡⟨u¯⟩d/ν, where ν is the kinematic viscosity. However, the advective distance required to reach asymptotic dispersion is expected to be controlled by pore-scale mixing, which is strongly Red-dependent prior to the onset of full turbulence. Laser-induced fluorescence was used to measure the time-averaged lateral concentration profiles of solute released continuously from a point source in arrays of solid volume fraction ϕ=0.20 and 0.35 at Red=48–120. Results are compared to previous measurements at higher Red. Lateral dispersion reaches the same rate as asymptotic dispersion in fully turbulent flow at x≈154d at (ϕ,Red)=(0.20,110–120) and at x≈87d at (ϕ,Red)=(0.35,300–390). In contrast, dispersion does not reach the fully turbulent flow limit at Red<100 within the range of x considered. Also, concentration profiles deviate further from a Gaussian distribution at ϕ=0.35 than at 0.20 for similar Red and xϕ/d. From these observations, it can be inferred that the pre-asymptotic regime extends farther downstream, in terms of the number of cylinders spanned, at lower Red and at larger ϕ.