Absorption of a passive scalar by a random sphere pack beneath a turbulent channel flow

Using pore-resolved direct numerical simulation (DNS), we investigate passive scalar transport at a unit Schmidt number in a turbulent flow over a randomly packed bed of spheres. The scalar is introduced at the domain’s free-slip top boundary and absorbed by the bed, which maintains a constant and uniform scalar value on the sphere surfaces. Eight cases are analysed, which are characterised by friction Reynolds numbers of ${\textit{Re}}_\tau \in [150, 500]$ and permeability Reynolds numbers of ${\textit{Re}}_{{\kern-1pt}K} \in [0.4, 2.8]$ , while flow depth-to-sphere-diameter ratios vary within $h/D \in \{ 3, 5, 10 \}$ and the roughness Reynolds numbers lie within $k_s^+ \in [20,200]$ . For cases with comparable ${\textit{Re}}_\tau$ , the permeable wall behaviour enhances scalar absorption, as indicated by increases in the Sherwood number and the scalar roughness function $\Delta c^+$ over ${\textit{Re}}_{{\kern-1pt}K}$ . At progressively higher ${\textit{Re}}_{{\kern-1pt}K}$ , the scalar absorption diverges increasingly from the momentum absorption, as its distribution peaks deeper below the crests of the sphere pack and spreads over a wider vertical region. The fixed-value scalar boundary condition emphasises certain similarities between the scalar and velocity fields. Near-interface scalar fluctuations are correlated with streamwise velocity fluctuations, and the turbulent Schmidt number remains close to its value in the free-flow region. Compared with zero-flux scalar boundary conditions, prescribing a uniform scalar value on the sphere surfaces reduces spatial heterogeneity within the pore space, thereby limiting both dispersive transport and the form-induced production of temporal scalar fluctuations.