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Technical Briefs

# Development-Length Requirements for Fully Developed Laminar Flow in Concentric Annuli

[+] Author and Article Information
R. J. Poole

Department of Engineering, University of Liverpool, Brownlow Street, Liverpool L69 3GH, UKrobpoole@liv.ac.uk

J. Fluids Eng 132(6), 064501 (Jun 11, 2010) (4 pages) doi:10.1115/1.4001694 History: Received June 10, 2009; Revised April 28, 2010; Published June 11, 2010; Online June 11, 2010

## Abstract

In this technical brief we report the results of a systematic numerical investigation of developing laminar flow in axisymmetric concentric annuli over a wide range of radius ratio $(0.01 and Reynolds number $(0.001. When the annular gap is used as the characteristic length scale we find that for radius ratios greater than 0.5 the development length collapses to the channel-flow correlation. For lower values of radius ratio the wall curvature plays an increasingly important role and the development length remains a function of both radius ratio and Reynolds number. Finally we show that the use of an empirical modified length scale to normalize both the development length and the characteristic length scale in the Reynolds number collapses all of the data onto the channel-flow correlation regardless of the radius ratio.

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## Figures

Figure 2

Effect of radius ratio on normalized development length variation with Reynolds number (a) using Ro as the length scale, (b) using h as the length scale and (c) using h∗ (Eq. 6) as the length scale

Figure 1

Schematic of coordinate system, computational domain, and definitions including radius ratios studied (the inner solid line on the right hand side diagram corresponds to N=0.5 while the other radius ratios are indicated by dashed lines)

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