Research Papers: Fundamental Issues and Canonical Flows

A Functional Relationship for Modeling Laminar to Turbulent Flow Transitions

[+] Author and Article Information
George Papadopoulos

Fellow ASME
Innoveering, LLC,
100 Remington Boulevard,
Ronkonkoma, NY 11779
e-mail: George.Papadopoulos@innoveering.net

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received August 30, 2015; final manuscript received March 12, 2017; published online June 20, 2017. Assoc. Editor: D. Keith Walters.

J. Fluids Eng 139(9), 091202 (Jun 20, 2017) (10 pages) Paper No: FE-15-1606; doi: 10.1115/1.4036594 History: Received August 30, 2015; Revised March 12, 2017

A dimensional analysis which 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 nonlinear 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 leveraging the concept of flow intermittency to yield a generic functional relationship that incorporates transitional flow effects and fully encompasses solutions spanning the laminar to turbulent flow regimes. Empirical models to several common flows are formed to demonstrate the engineering potential of the proposed functional relationship.

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Fig. 1

Velocity-distribution coefficients and coefficient of nonuniformity as functions of radial extent of plug flow (laminar regime)

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Fig. 2

Velocity-distribution coefficients for fully developed turbulent pipe flow

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Fig. 3

Normalized bulk velocity versus Reynolds number for fully developed pipe flow

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Fig. 4

Reynolds number effect on Clauser’s shape parameter

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Fig. 5

Centerline velocity decay data for a variety of axisymmetric jets

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Fig. 6

Application of coefficient of profile uniformity to jet decay data for laminar axisymmetric jets issuing from short pipes

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Fig. 7

Jet decay data plotted using the effective diameter term along with fitted distributions (dashed lines) based on proposed relationship

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Fig. 8

Variation of the separation bubble length with Reynolds number for the flow over a blunt rectangular plate

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Fig. 9

Reattachment length versus Reynolds number for axisymmetric sudden expansion flow: low Re range

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Fig. 10

Reattachment length versus Reynolds number for axisymmetric sudden expansion flow: moderate to high Re range

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Fig. 11

Reattachment length normalized by the effective step height for axisymmetric sudden expansion flow: low Re range

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Fig. 12

Reattachment length data fitted using the functional relationship of Eq. (29)




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