This study makes an attempt to investigate Newtonian/non-Newtonian pipe flows in a laminar-turbulent transition region, which is an extraordinarily complicated process and is not fully understood. The key characteristic of this region is its intermittent nature, i.e., the flow alternates in time between being laminar or turbulent in a certain range of Reynolds numbers. The physical nature of this intermittent flow can be aptly described with the aid of the intermittency factor γ, which is defined as that fraction of time during which the flow at a given position remains turbulent. Spriggs postulated that a weighting factor can be used to calculate the friction factor, applying its values in laminar and turbulent states. Based on these, a model is developed to empirically express the mean velocity and Reynolds shear stress in the transition region. It is found that the intermittency factor can be used as a weighting factor for calculating the flow structures in the transition region. Good agreements can be achieved between the calculations and experimental data available in the literature, indicating that the present model is acceptable to express the flow characteristics in the transition region.
Laminar-turbulent transition of a non-Newtonian fluid flow
