On the Influence of Reynolds Shear Stress Upon the Velocity Patterns Generated in Turbulent Starting Pipe Flow

Abstract

[Abstract] Experimental evidence yields a wide variety of starting turbulent pipe flows, usually with greatly deformed mean velocity profiles. Some experimental tests attain profiles with maximum values in the near-wall region, while some others report well-defined local concavities within globally convex mean velocity profiles. To the authors’ knowledge, no available explanation yet exists for such a kind of behavior. This theoretical research studies the specific effects that certain patterns of Reynolds shear stress cause on the mean velocity field obtained in unsteady turbulent flows. A simple model of transient Reynolds shear stress is devised, and this model is used to calculate the mean velocity field of starting turbulent flow. Those mean flow patterns are related to the actual velocity profiles reported in the experimental literature on starting flow. We learn how the different Reynolds shear stress patterns contribute to create the resulting mean velocity patterns and which particular configuration of Reynolds shear stress is responsible for each one of the reported experimental velocity profiles. We explain why, how, where, and when each particular deformation in the unsteady mean velocity profile is caused, and the relationship between each type of deformation and the Reynolds shear stress that brings it forth. We issue some predictions identifying types of flow that, to our knowledge, have not yet been reported in the experimental literature, and we offer clues for those experimental researchers willing to discover the predicted flow patterns. This research continues the exposition of the theory of underlying laminar flow initiated in previous papers.