A generalized hydraulic calculation model for non-newtonian fluid pipe flow and its application evaluation

Abstract

A generalized hydraulic model that is independent of the rheological model is presented for non-Newtonian fluids flow in pipes. The generalized model was developed without assuming that the generalized flow index (n') remains constant over all shear rates. Based on the pipe flow control equation, the explicit equations between the wall shear stress and volumetric flow of all common rheological models flowing in pipe were obtained, such as the Casson model, HerschelBulkley model and the Robertson-Stiff model, and they all can be solved numerically to obtain the accurate wall shear rate and shear stress. We give the theoretic calculation method of n' for all time-independent non-Newtonian fluids. This method is applicable to all common rheological models without the assumption that n' is constant. Moreover, we derived the general expression of generalized Reynolds number and then gave a utility pressure loss calculation model. A set of measured hydraulic data were utilized to evaluate this model. The results show that it can precisely calculate pipe flow parameters for all types of different non-Newtonian fluid. The proposed model will lay a foundation for the application and more extensive use of complex but more precise rheological models in engineering.