Research Papers: Multiphase Flows

Thrust Enhancement Through Bubble Injection Into an Expanding-Contracting Nozzle With a Throat

[+] Author and Article Information
Sowmitra Singh

Dynaflow, Inc.,
10621-J Iron Bridge Road,
Jessup, MD 20794
e-mail: sowmitra@dynaflow-inc.com

Tiffany Fourmeau

Dynaflow, Inc.,
10621-J Iron Bridge Road,
Jessup, MD 20794
e-mail: tiffany@dynaflow-inc.com

Jin-Keun Choi

Dynaflow, Inc.,
10621-J Iron Bridge Road,
Jessup, MD 20794
e-mail: jkchoi@dynaflow-inc.com

Georges L. Chahine

Dynaflow, Inc.,
10621-J Iron Bridge Road,
Jessup, MD 20794
e-mail: glchahine@dynaflow-inc.com

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received December 5, 2012; final manuscript received January 21, 2014; published online May 6, 2014. Assoc. Editor: Ali Beskok.

J. Fluids Eng 136(7), 071301 (May 06, 2014) (7 pages) Paper No: FE-12-1607; doi: 10.1115/1.4026855 History: Received December 05, 2012; Revised January 21, 2014

This paper addresses the concept of thrust augmentation through bubble injection into an expanding-contracting nozzle with a throat. The presence of a throat in an expanding-contracting nozzle can result in flow transition from the subsonic regime to the supersonic regime (choked conditions) for a bubbly mixture flow, which may result in a substantial increase in jet thrust. This increase would primarily arise from the fact that the injected gas bubbles expand drastically in the supersonic region of the flow. In the current work, an analytical 1D model is developed to capture choked bubbly flow in an expanding-contracting nozzle with a throat. The study provides analytical and numerical support to analytical observations and serves as a design tool for nozzle geometries that can achieve efficient choked bubbly flows through nozzles. Starting from the 1D mixture continuity and momentum equations, along with an equation of state for the bubbly mixture, expressions for mixture velocity and gas volume fraction were derived. Starting with a fixed geometry and an imposed upstream pressure for a choked flow in the nozzle, the derived expressions were iteratively solved to obtain the exit pressures and velocities for different injected gas volume fractions. The variation of thrust enhancement with the injected gas volume fraction was also studied. Additionally, the geometric parameters were varied (area of the exit, area of the throat) to understand the influence of the nozzle geometry on the thrust enhancement and on the flow conditions at the inlet. This parametric study provides a performance map that can be used to design a bubble augmented waterjet propulsor, which can achieve and exploit supersonic flow. It was found that the optimum geometry for choked flows, unlike the optimum geometry under purely subsonic flows, had a dependence on the injected gas volume fraction. Furthermore, for the same injected gas volume fraction the optimum geometry for choked flows resulted in greater thrust enhancement compared to the optimum geometry for purely subsonic flows.

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Fig. 1

Expanding-contracting nozzles: absence of throat implies purely subsonic flow (top), presence of throat allows for the possibility of choked flow (bottom)

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Fig. 2

Typical nozzle design for thrust enhancement by bubble injection

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Fig. 3

Geometry of an expanding-contracting nozzle incorporating a throat

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Fig. 4

Axial distribution of the pressure p from the inlet to the exit. Curves for choked flow versus purely subsonic flow are shown.

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Fig. 5

Axial distribution of mixture velocity from the inlet to the exit for the choked flow versus the purely subsonic flow

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Fig. 6

Axial distribution of gas volume fraction α from the inlet to the exit. The void fraction of the supposed subsonic flow near the throat results in phase separation in the segment (1.5 < x < 1.65) of the BAP nozzle.

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Fig. 9

Performance map of ξm with varying Athroat/Ainlet and Aexit/Ainlet (α0=0.4, pinlet = 5 atm)

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Fig. 8

Performance map of ξm with varying Athroat/Ainlet and Aexit/Ainlet (α0=0.2, pinlet = 5 atm)

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Fig. 10

Performance map of ξm with varying Athroat/Ainlet and Aexit/Ainlet (α0=0.6, pinlet = 5 atm)

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Fig. 7

Contour plots of axial distribution of flow quantities in the BAP nozzle: pressure (top), velocity (middle), void fraction (bottom)

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Fig. 13

Optimum ξm versus α0 for different ratios of Ainjection/Ainlet

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Fig. 12

Optimum ξm versus α0 for different inlet/upstream pressures

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Fig. 11

Inlet velocity map with varying Athroat/Ainlet and Aexit/Ainlet (α0=0.4, pinlet = 5 atm)




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