The Transfer and Transport of a Passive Scalar Within an Isolated Array of Circular Cylinders in a Uniform Flow

Abstract

The transfer and transport of a passive scalar T from an isolated array of circular cylinders of varying Reynolds number (Re = [100, 333]) and solid fraction (0.0023 < < 0.3) in a uniform steady flow are investigated. This problem is an abstraction of the flow past emergent vegetation or marine aquaculture, in which passive contaminants are continuously generated. The upstream flow (T ∞ = 0) is uniform and incident on an array of N c cylinders whose surfaces are set to T S = 1. Three-dimensional numerical simulations were carried out to investigate the mean and fluctuating Nusselt number of the individual cylinders and the array as a whole. To help interpret the numerical results a mathematical model, partly based on empirical relationships, is developed to predict the transfer. The transfer of the scalar from the array was found to increase when the Reynolds number was increased. As the solid fraction is increased the transfer increases, reaches a maximum, and then decreases. This is due to the collective effect of all the cylinders resulting in (i) a modification of the incident flow and (ii) a reduction in the scalar gradient between the cylinder surface and the locally incident flow on individual cylinders. These effects are highly dependent on the solid fraction. Additional simulations were carried out to decompose the contribution of these two processes on the transfer of individual cylinders.