Laminar to turbulent transition of yield power law fluids in annuli

Abstract

Abstract An analysis of laminar to turbulent transition of yield power law (YPL) fluids in concentric and eccentric annuli is presented. Both theoretical and experimental approaches are followed to better understand the onset of transitional flow. The objective of this study is to investigate the stability of the flow in concentric and eccentric annuli. Theoretical analysis of the inner and outer shear regions, to clarify the earlier transition observed with experimental studies, are within the scope of this study. A stability criterion based on the ratio of turbulent energy production and rate of work done by viscous stresses is used to determine the end of laminar flow. Experiments are conducted for laminar, transition and turbulent regions of flow in a fully eccentric annulus. Eight distinct YPL fluids are tested and the results are compared with a proposed model and models available in the literature. The proposed stability parameter shows an earlier transition near the outer wall for a wide range of non-Newtonian fluids, which is in agreement with measurements in the literature. The proposed modification is extended to eccentric annuli and showed good agreement with experiments. To the authors’ knowledge, this is the first theoretical study to locally predict the onset of transition in eccentric annuli of YPL fluids. Transition from laminar to turbulent significantly depends on eccentricity, diameter ratio and fluid properties, especially to the shear thinning ability of a fluid. The proposed modification allows a fair prediction of the transition from laminar to turbulent regions in eccentric annuli. With the proposed approach, the percentage of laminar and non-laminar regions for a cross section of an eccentric annulus can be predicted.