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Research Papers

Analytical Solutions for a Family of Gaussian Impinging Jets

[+] Author and Article Information
Zhuyun Xu

The Boundary Layer Wind Tunnel Laboratory, University of Western Ontario, Ontario N6A 5B9, Canadazxu@blwtl.uwo.ca

Horia Hangan

The Boundary Layer Wind Tunnel Laboratory, University of Western Ontario, Ontario N6A 5B9, Canadahmh@blwtl.uwo.ca

Pei Yu

Department of Applied Mathematics, University of Western Ontario, Ontario N6A 5B7 Canadapyu@uwo.ca

J. Appl. Mech 75(2), 021019 (Feb 27, 2008) (12 pages) doi:10.1115/1.2775502 History: Received February 19, 2007; Revised July 19, 2007; Published February 27, 2008

Various types of impinging jet flows are analytically modeled using inviscid free Gaussian jet solutions superimposed with experimentally fitted boundary layer models. Improved (more robust) and simplified solutions to existing models are defined. Velocity profiles, surface pressure distributions, and streamline plots are calculated for circular, plane, and annular impinging jets. The models show excellent agreement with existing experimental results in both laminar and turbulent conditions and for different Reynolds numbers.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Comparison of front n term average value series

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Figure 2

Comparison of the impinging jet boundary layer depths between empirical models and roughness test data (Δ is the roughness height of the sandpaper)

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Figure 3

Streamlines of a plane impinging jet model: (a) present model (−ψ corresponds to Rubel’s ψ value); (b) calculated by Rubel and Phares , cited from Ref. 5

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Figure 4

Comparison of surface pressure distribution (the error bar is for the experiments)

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Figure 5

Laminar circular impinging jet streamlines (−ψ is used)

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Figure 6

An axis symmetric impinging jet combined model with updraft and downdraft: (a) influx profile; (b) contours of stream function

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Figure 7

Velocity comparison (model: k=2.05; test: H*∕D*=4, cited from Ref. 17): (a) radial velocity profiles; (b) axial velocity profiles

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Figure 8

Radial velocity comparisons for turbulent circular impinging jets: (a) Rej=23000, H*∕D*=2; (b) Rej=190000, H*∕D*=2.

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Figure 9

Comparison of the plate surface pressure distribution

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Figure 10

Particular influx velocity profile of an annular jet

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Figure 11

Annular impinging jet (rm=0.35, δw=0.16): (a) streamlines by present model (−ψ is used); (b) numerical solution by Rubel (16)

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Figure 12

Streamlines for an annular impinging jet with the influx profile shown in Fig. 1 (rm=0.65, δw=0.8)

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Figure 13

An annular impinging jet with a large recirculation ring: (a) influx velocity profile estimated from the surface pressure values of Ref. 8; (b) Streamlines (−ψ is used)

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