Laminar, transitional and turbulent flow of Herschel-Bulkley fluids in concentric annulus

An integrated approach is presented for the flow of Herschel-Bulkley fluids in a concentric annulus, modelled as a slot, covering the full range of flow types, laminar, transitional, and turbulent flows. Prior analytical solutions for laminar flow are utilized. Turbulent flow solutions are developed using the Metzner-Reed Reynolds number after determining the local power law parameters as functions of flow geometry and the Herschel-Bulkley rheological parameters. The friction factor is estimated by modifying the pipe flow equation. Transitional flow is solved introducing transitional Reynolds numbers which are functions of the local power law index. Thus, an integrated, complete and consistent set, combining analytical, semi-analytical and empirical equations, is provided which describe fully the flow of Herschel-Bulkley fluids in concentric annuli, modelled as a slot. The comparison with experimental and simulator data from various sources shows very good agreement over the entire range of flow types.