Rheological model influence on pipe flow predictions for homogeneous non-Newtonian fluids

Abstract

The reliable prediction of pressure drop versus flow rate for non-Newtonian pipe flow is important in many industrial processes. In laminar flow scale up is straightforward, but transitional velocity and turbulent flow predictions remain a practical problem. Various theoretical models exist, but nothing in literature shows conclusively which of these is the most reliable and consistent, nor is it evident what effect the choice of rheological model has on the predictions. The aim of this work was to i) evaluate the influence of different rheological models when used in existing prediction techniques for non-Newtonian flow ii) characterise each material type using selected (commonly used) rheological models and iii) predict laminar, transitional and turbulent pipe flow characteristics for each material type using existing prediction techniques, for comparison with experimental results. Only time-independent, homogeneous, non-Newtonian fluids in pipe sizes from 13mm to 200mm were investigated. Rheological models and laminar flow predictions used only the power law, Bingham plastic, Herschel-Bulkley, Casson and Hallbom yield plastic models. The techniques used to predict transitional velocity were Ryan & Johnson, Metzner-Reed, Hedström intersection method, Slatter and Hallbom. For turbulent flow the Newtonian approximation, Dodge & Metzner, Wilson & Thomas, Slatter, Hallbom modified Wilson & Thomas and the Bowen correlation methods were used. The study documents the relevant theory and presents an assessment of the influence of rheology on pipe flow predictions, summarised in terms of the practical performance of the various rheological model/prediction method combinations for the different materials. In laminar flow at practical pseudo shear rates (8V/D; taken as 40s-1) the choice of rheological model does not significantly influence pressure drop predictions. For yield-pseudoplastic materials (eg. kaolin) the Hedström intersection and the Slatter Reynolds number method with Bingham plastic or Casson rheology predicted transitional velocity most accurately. For Bingham plastic materials (eg. bentonite) the best predictions were obtained using the Metzner & Reed Reynolds number with Bingham plastic rheology, although similar results were observed for this technique with all rheologies. The transitional velocity for pseudoplastic materials (eg. CMC) was best predicted by the Slatter and Metzner & Reed Reynolds number methods, using power law or Casson rheology. For turbulent flow of yield pseudoplastic materials the Slatter method using the Casson rheology gave the most accurate predictions overall. Turbulent flow of Bingham plastic materials was best predicted by the Slatter, Hallbom pseudo fluid Nikuradse and Dodge & Metzner methods, using Bingham plastic, Casson or yield plastic rheology. For pseudoplastic materials the Slatter and Wilson & Thomas methods were the most accurate, when used with yield plastic or power law rheology. Transitionalal velocity and turbulent flow predictions for materials with a yield stress vary significantly with rheological model. Laminar data should therefore be examined thoroughly and rheological models fitted with care. For pseudoplastic fluids there is little difference in predictions between the various techniques as long as power law rheology is used.