The Reynolds and Prandtl number dependence of weak fountains

Lin, W., and Armfield, S.W. (2003) The Reynolds and Prandtl number dependence of weak fountains. Computational Mechanics, 31 (5). pp. 379-389.

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Abstract

The effect of the Prandtl number (Pr) and the Reynolds number (Re) on the behaviour of weak laminar axisymmetric and plane fountains has been studied using dimensional and scaling analyses and direct numerical simulation. For Fr ~ 1.0 and assuming viscous effects are important, the analysis shows that for both the axisymmetric and plane fountains, ym ~ FrRe^(-1/2), where Fr is the Froude number defined at the fountain source and ym is the non-dimensionalized fountain height. These scalings are also valid for the non-dimensionalized fountain width. The analyses also shows tms ~ Fr^2, where tms is the non-dimensionalized time scale for the fountain flow in the fountain core to reach steady state, and using this time scale DyT ~ Fr(RePr)^(-1/2), where DyT is the non-dimensionalized thickness of the temperature layer on the symmetry axis over which the fountain fluid temperature changes from the inlet value to that of the ambient fluid. All these scalings have been quantified by the direct numerical simulations, hence confirming in certain ranges the phenomenological scaling obtained in this paper.

Item ID: 9517
Item Type: Article (Refereed Research - C1)
Keywords: weak fountain flow; Prandtl number; Reynolds number; direct numerical simulation; scaling analysis
ISSN: 1432-0924
Funders: National Natural Science Foundation of China, Australian Research Council, Yunnan Provincial Science Foundation, China
Date Deposited: 23 Mar 2010 05:49
FoR Codes: 09 ENGINEERING > 0915 Interdisciplinary Engineering > 091504 Fluidisation and Fluid Mechanics @ 100%
SEO Codes: 97 EXPANDING KNOWLEDGE > 970109 Expanding Knowledge in Engineering @ 70%
97 EXPANDING KNOWLEDGE > 970102 Expanding Knowledge in the Physical Sciences @ 30%
Citation Count from Web of Science Web of Science 18
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