Transition Criteria for Laminar to Turbulent Flow for Yield Power Law (YPL) Fluids Based on Stability Analysis

Abstract

It is well known that a Newtonian fluid with the presence of solid particles in suspension behaves non-Newtonian. Higher the solid content, more significant the yield stress of the fluid. Determination of the hydraulic behavior of fluids having a significant yield stress is a challenging task. For engineering purposes, pressure drop within the system, during pipeline transportation, has to be estimated carefully and accurately. Flow regime plays a vital role during hydraulic calculations. The inaccurate determination of flow regime can lead us to large errors in frictional pressure drop calculations and ultimately leads to error in designing and flow assurance point of view, since hydraulic calculations are including a friction factor term, which is a direct function of flow regime. In general, Reynolds number is the main parameter used by the industry for determining the flow regime, and the friction factor. This approach works reasonably accurate for Newtonian fluids. However, as the yield stress of the fluid increases, this conventional technique for determining the flow regime is not as accurate. Although many approaches have been introduced for estimating the flow regime for non-Newtonian fluids, there exists a lack of information and confidence of such predictions for fluids having high yield stress, such as Yield Power Law (YPL) fluids (i.e., Herchel-Bulkley). (1)τ=τy+Kγm This study presents an analytical solution for predicting the transition from laminar to non-laminar flow regime based on Ryan & Johnson’s approach using the stability analysis and equation of motion for YPL fluids. Comparing with the experimental results for YPL fluids under different flow conditions, including laminar and non-laminar flow regimes, show that presented approach gives a better estimation of the transition from laminar to non-laminar flow regime than conventional Reynolds number approach. In some cases, it is observed that although the Reynolds number is high, flow is still laminar, which is predicted accurately using the presented model. This study provides a higher accuracy in estimating the flow regime, which leads to a higher confidence in hydraulic designs and determining limitations of the system in concern.