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Technical Briefs

The Effect of Nonuniform Viscosity on Stagnation Point Pressure

[+] Author and Article Information
Stuart E. Norris

Department of Mechanical Engineering,  University of Auckland, Private Bag 92019, Auckland, New Zealand e-mail: s.norris@auckland.ac.nz

J. Fluids Eng 133(4), 044501 (May 03, 2011) (4 pages) doi:10.1115/1.4003875 History: Received November 07, 2010; Revised March 25, 2011; Published May 03, 2011; Online May 03, 2011

For high Reynolds number flows the total pressure remains constant along stream lines. At low Reynolds numbers the total pressure decreases in a global sense due to the actions of viscosity, but it may increase locally in regions such as stagnation points. Previous studies have considered the case of constant viscosity flow. However, gradients in the effective viscosity can occur normal to the wall for the flow of lubricating oils, and for turbulent flows calculated using an eddy viscosity model. In this paper the effect of these viscosity gradients on the stagnation point pressure are examined.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

The geometry at the stagnation point

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Figure 2

The variation of eddy viscosity along the stagnation stream line for the three cases shown in Fig. 3

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Figure 3

The total pressure coefficient cpt along the stagnation stream line for a cylinder at a free-stream Reynolds number of 100 and constant eddy viscosity (γ=1), and for the eddy viscosity at the wall being higher (γ=2) and lower (γ=0.1) than in the free stream

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Figure 4

The stagnation point pressure coefficient cp0 for the flow around a cylinder flow with a free-stream Reynolds number of 100 and 0<γ≤2

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Figure 5

The stagnation point pressure coefficient cp0 for the flow around a cylinder flow with a free-stream Reynolds number of 1000 and 0<γ≤2

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