A model to determine the drag coefficient of aggregated nonspherical flocs in the ballasted flocculation

The ballasted flocs exhibit distinct transition characteristics due to their hybrid internal structure (porous coagulated suspended particles and solid ballast proportions) and compact aggregation. The drag force exerted on a ballasted floc in fluid medium is distinct from conventional flocs due to less internal resistances, partially impermeable structure, and compact aggregation. Incorporating properties of ballasted floc (shape, porosity, permeability, ballasted proportion, transition regime condition) can lead to precise determination of drag coefficient (CD). In previous ballasted flocculation (BF) studies, researchers adopted CD = 24/Re, which is a generalized equation and is limited to spherical objects in laminar regime. However, because of the non-spherical shape, hybrid floc structure having porous and solid proportions, and the non-laminar transition of ballasted flocs, the drag coefficient can be underestimated. In this study, a deterministic drag model is proposed for ballasted flocs, which corresponds to the real time regime condition and the ballasted floc characteristics. The equation incorporates the floc shape characteristics (degree of sphericity) and the floc composition characteristics (porosity, permeability, ballast embedment ratio) that influence the drag force applied during floc transition. The evaluation of model predictions with real time CCD Camera based floc size and settling velocity observations from previous studies revealed that the proposed model is most suitable approach (R2 = 0.83) to determine drag coefficient of ballasted flocs. This can lead to efficient designing of ballasted flocculation facilities.