A Functional Relationship for Modeling Laminar to Turbulent Flow Transitions

[+] Author and Article Information
George Papadopoulos

Director for Advanced Programs Innoveering, LLC 100 Remington Blvd Ronkonkoma, New York 11779

1Corresponding author.

ASME doi:10.1115/1.4036594 History: Received August 30, 2015; Revised March 12, 2017


A dimensional analysis that is based on the scaling of the two-dimensional Navier-Stokes equations is presented for correlating bulk flow characteristics arising from a variety of initial conditions. The analysis yields a functional relationship between the characteristic variable of the flow region and the Reynolds number for each of the two independent flow regimes, laminar and turbulent. A linear relationship is realized for the laminar regime, while a non-linear relationship is realized for the turbulent regime. Both relationships incorporate mass-flow profile characteristics to capture the effects of initial conditions (mean flow and turbulence) on the variation of the characteristic variable. The union of these two independent relationships is formed utilizing the concept of flow intermittency to further expand into a generic functional relationship that incorporates transitional flow effects to fully encompass solutions spanning the laminar to turbulent flow regimes. Empirical models of some common flows are formed to demonstrate the engineering potential of the proposed functional relationship.

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