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Research Papers: Fundamental Issues and Canonical Flows

Optimization of Piecewise Conical Nozzles: Theory and Application

[+] Author and Article Information
Karsten Hasselmann

Department of Mechanical Engineering,
Muenster University of Applied Sciences,
Steinfurt 48565, Germany
e-mail: hasselmann@fh-muenster.de

Stefan aus der Wiesche

Department of Mechanical Engineering,
Muenster University of Applied Sciences,
Steinfurt 48565, Germany

Eugeny Y. Kenig

Chair of Fluid Process Engineering,
Paderborn University,
Paderborn 33098, Germany

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 29, 2018; final manuscript received May 2, 2019; published online June 7, 2019. Assoc. Editor: Philipp Epple.

J. Fluids Eng 141(12), 121202 (Jun 07, 2019) (11 pages) Paper No: FE-18-1718; doi: 10.1115/1.4043707 History: Received October 29, 2018; Revised May 02, 2019

An optimization study based on computational fluid dynamics (CFD) in combination with Stratford's analytical separation criterion was developed for the design of piecewise conical contraction zones and nozzles. The risk of flow separation was formally covered by a newly introduced dimensionless separation number. The use of this separation number can be interpreted as an adaption of Stratford's separation criterion to piecewise conical nozzles. In the nozzle design optimization process, the risk of flow separation was reduced by minimizing the separation number. It was found that the flow-optimized piecewise conical nozzle did not correspond to a direct geometric approximation of an ideal polynomial profile. In fact, it was beneficial to reduce the flow deflection in the outlet region for a piecewise conical nozzle to increase the nozzle performance. In order to validate the novel design method, extensive tests for different nozzle designs were conducted by means of wind tunnel tests. The measured velocity profiles and wall pressure distributions agreed well with the CFD predictions.

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References

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Figures

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Fig. 1

Typical velocity curves along the contraction zone calculated by a potential flow analysis [1]: (a) geometry and (b) velocity profiles

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Fig. 2

Comparison of an ideal smooth shape, a geometrically optimized shape, and a flow-optimized shape of a typical contraction zone

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Fig. 3

Potential flow analysis along a typical piecewise conical contraction zone with four segments

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Fig. 4

Numerically obtained pressure coefficient along a typical piecewise conical contraction zone

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Fig. 5

Illustration of the computational domain

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Fig. 6

Grid independence study: (a) pressure coefficient at the most critical pressure rise and (b) outlet flow nonuniformity

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Fig. 7

Turbulence model assessment: (a) pressure coefficient at the most critical pressure rise and (b) outlet flow nonuniformity

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Fig. 8

Streamwise velocity analysis with the critical zone at Re = 2.3 × 105: (a) streamwise velocity of the geometrically optimized shape and (b) streamwise velocity of the flow-optimized shape

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Fig. 9

Stratford number distribution of both optimized nozzles at Re = 2.3 × 105: (a) geometrically optimized shape and (b) flow-optimized shape

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Fig. 10

Outlet velocity profile of both optimized shapes in comparison to the ideal shape

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Fig. 11

Experimental setting

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Fig. 12

Experimental validation of the CFD results at Re = 2.3 × 105: (a) static pressure distribution of the geometrically optimized nozzle, (b) outlet velocity profile of the geometrically optimized nozzle, (c) static pressure distribution of the flow-optimized nozzle, and (d) outlet velocity profile of the flow-optimized nozzle

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Fig. 13

Axial acceleration of the flow inside the nozzles: (a) experimental validation at Re = 2.3 × 105 and (b) experimental comparison at different Reynolds numbers

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Fig. 14

Velocity profiles and turbulence intensity distribution of the experimental data: (a) radial velocity profile at Re = 1.4 × 105, (b) radial turbulence intensity distribution at Re = 1.4 × 105, (c) radial velocity profile at Re = 2.3 × 105, (d) radial turbulence intensity distribution at Re = 2.3 × 105, (e) radial velocity profile at Re = 4.4 × 105, and (f) radial turbulence intensity distribution at Re = 4.4 × 105

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