A Critical Review of the Correlations Used for Predicting the Onset of the Transition Flow Regime in Pipe Flow of Yield Stress Fluids

Abstract In this paper, we present a critical review of the models used for predicting onset of the transition flow regime in pipe flow of yield stress fluids. Using the experimental data obtained by the Particle Image Velocimetry (PIV) technique, we developed a new methodology to identify the beginning of the transition flow regime in pipe flow of yield stress fluids. The new method was then used to evaluate the accuracy of the existing transition flow regime model predictions. The proposed approach relies on the boundary layer theory to classify flow into laminar and turbulent. The boundary layer theory enables microscopic characterization of the flow transition that translates into a more in-depth fundamental understanding of the transition phenomena. The corresponding literature, experimental validation, and proof of the concept are presented. We investigated 36 possible permutations of Reynolds number (Re) and critical Reynolds number (Recrit.) definitions (i.e., six Re definitions combined with six critical Re definitions), and in none of these cases, the onset of the transition regime was accurately and consistently predicted. It was noted that the percentage difference between the maximum and minimum values of Re, for the same flow rate and fluid properties, ranged between 27% to 58%, based on fluid properties and flow rate combination, mainly because of the subjectivity of the Re definitions. In order to ensure an accurate prediction of the transition zone, test fluids were designed to have a wide range of generalized Reynolds numbers (i.e., 20 to 9000, as defined by the API-RP:13D) within the physical capacity of the experimental facility (i.e. for a given pipe diameter, maximum pressure capacity of the flow loop and maximum available pump flow rate). The yield stress of the test fluids varied from 0.10 to 0.95 Pa (determined by using the nonlinear curve fitting technique recommended by the API RP:13-D). Results indicated that most of the current transition criteria for the pipe flow of yield power law (YPL) fluids have low accuracy and lack of consistency to predict the onset of the actual transition regime as compared to the data measured by using the PIV technique. This was regardless of the Reynolds number definition used. The proposed PIV measurement-based criterion provides an objective measure that can be used to develop more accurate future transition models or improve the accuracy of existing transition criteria.

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