The impact of cylinder diameter distribution on longitudinal and transverse dispersion within random cylinder arrays

Numerous studies focus on flow and mixing within cylinder arrays because of their similarity to vegetated flows. Randomly distributed cylinders are considered to be a closer representation of the natural distribution of vegetation stems compared with regularly distributed arrays. This study builds on previous work based on a single, fixed, cylinder diameter to consider non-uniform cylinder diameter distributions. The flow fields associated with arrays of randomly distributed cylinders are modeled in two dimensions using the ANSYS Fluent Computational Fluid Dynamics software with Reynolds Stress Model turbulence closure. A transient scalar transport model is used to characterize longitudinal and transverse mixing (Dx and Dy) within each geometry. The modeling approach is validated against independent laboratory data, and the dispersion coefficients are shown to be comparable with previous experimental studies. Eight different cylinder diameter configurations (six uniform and two non-uniform) are considered, each at 20 different solid volume fractions and with seven different transverse positions for the injection location. The new dispersion data cover a broad range of solid volume fractions, for which simultaneous estimates of Dx and Dy have not been available previously. There are no systematic differences in non-dimensional Dx and Dy between uniform and non-uniform cylinder diameter distributions. When non-dimensionalized by cylinder diameter, both dispersion coefficients are independent of solid volume fraction. When non-dimensionalized by cylinder spacing, both longitudinal and transverse dispersion can be described as linear functions of the ratio of cylinder diameter to cylinder spacing.