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.

References

References
1.
Albagli
,
D.
, and
Gany
,
A.
,
2003
, “
High Speed Bubbly Nozzle Flow With Heat, Mass, and Momentum Interactions
,”
Int. J. Heat Mass Transf.
,
46
, pp.
1993
2003
.10.1016/S0017-9310(02)00476-3
2.
Mor
,
M.
, and
Gany
,
A.
,
2004
, “
Analysis of Two-Phase Homogeneous Bubbly Flows Including Friction and Mass Addition
,”
ASME J. Fluids Eng.
,
126
, pp.
102
109
.10.1115/1.1637628
3.
Chahine
,
G. L.
,
Hsiao
,
C.-T.
,
Choi
,
J.-K.
, and
Wu
,
X.
,
2008
, “
Bubble Augmented Waterjet Propulsion: Two-Phase Model Development and Experimental Validation
,”
Proc. 27th Symposium on Naval Hydrodynamics
, Seoul, Korea.
4.
Wu
,
X.
,
Choi
,
J.-K.
,
Hsiao
,
C.-T.
, and
Chahine
,
G. L.
,
2010
, “
Bubble Augmented Waterjet Propulsion: Numerical and Experimental Studies
,”
Proc. 28th Symposium on Naval Hydrodynamics
, Pasadena, CA.
5.
Mottard
,
E. J.
, and
Shoemaker
,
C. J.
,
1961
, “
Preliminary Investigation of an Underwater Ramjet Powered by Compressed Air
,” NASA Technical Note D-991, NASA, Washington, DC.
6.
Schell
,
C. J.
, Jr.
, Harold, O.,
1965
, “
The Hydro-Pneumatic Ram-Jet
,” U.S. Patent No. 3,171,379.
7.
Wang
,
Y.-C.
, and
Brennen
,
C. E.
,
1998
, “
One-Dimensional Bubbly Cavitating Flows Through a Converging-Diverging Nozzle
,”
ASME J. Fluids Eng.
,
120
, pp.
166
170
.10.1115/1.2819642
8.
Van Wijngaarden
,
L.
,
1966
, “
Linear and Non-linear Dispersion of Pressure Pulses in Liquid Bubble Mixtures
,”
Proc. 6th Symposium on Naval Hydrodynamics
, Washington, DC.
9.
Van Wijngaarden
,
L.
,
1968
, “
On the Equations of Motion for Mixtures of Liquid and Gas Bubbles
,”
J. Fluid Mech.
,
33
, pp.
465
474
.10.1017/S002211206800145X
10.
Van Wijngaarden
,
L.
,
1972
, “
One-Dimensional Flow of Liquids Containing Small Gas Bubbles
,”
Ann. Rev. Fluid Mech.
,
4
, pp.
369
396
.10.1146/annurev.fl.04.010172.002101
11.
Noordzij
,
L.
, and
van Wijngaarden
,
L.
,
1974
, “
Relaxation Effects Caused by Relative Motion on Shock Waves in Gas-Bubble/Liquid Mixtures
,”
J. Fluid Mech.
,
66
, pp.
15
143
.10.1017/S0022112074000103
12.
Wu
,
X.
,
Singh
,
S.
,
Choi
,
J.-K.
, and
Chahine
,
G. L.
,
2012
, “
Waterjet Thrust Augmentation Using High Void Fraction Air Injection
,”
Proc. 29th Symposium on Naval Hydrodynamics
, Gothenburg, Sweden.
13.
Wu
,
X.
,
Choi
,
J.-K.
,
Singh
,
S.
,
Chao
,
C.-T.
, and
Chahine
,
G. L.
,
2012
, “
Experimental and Numerical Investigation of Bubble Augmented Waterjet Propulsion
,”
J. Hydrodynamics
,
24
(
5
), pp.
635
647
.10.1016/S1001-6058(11)60287-4
14.
Singh
,
S.
,
Choi
,
J.-K.
, and
Chahine
,
G. L.
,
2012
, “
Optimum Configuration of an Expanding-Contracting-Nozzle for Thrust Enhancement by Bubble Injection
,”
ASME J. Fluids Eng.
,
134
, p.
011301
.10.1115/1.4005687
15.
Tillman
,
T. G.
, and
Presz
,
W. M.
, Jr.
,
1995
, “
Thrust Characteristics of a Supersonic Mixer Ejector
,”
J. Propulsion Power
,
11
(
5
), pp.
931
937
.10.2514/3.23919
16.
Presz
,
W.
, Jr.
,
Reynolds
,
G.
, and
Hunter
,
C.
,
2002
, “
Thrust Augmentation With Mixer/Ejector Systems
,”
Proc. 40th AIAA Aerospace Sciences Meeting & Exhibit
, Reno, NV.
17.
Dijkstra
,
F.
,
Maree
,
A. G. M.
,
Caporicci
,
M.
, and
Immich
,
H.
,
1997
, “
Experimental Investigation of the Thrust Enhancement Potential of Ejector Rockets
,”
Proc. 33rd Joint Propulsion Conference and Exhibit
, Seattle, WA.
18.
Mor
,
M.
, and
Gany
,
A.
,
2007
, “
Performance mapping of Bubbly Water Ramjet
,”
Int. J. Maritime Eng.
,
149
, pp.
45
50
.10.3940/rina.ijme.2007.a1.8107
19.
Brennen
,
C. E.
,
1995
,
Cavitation and Bubble Dynamics
,
Oxford University Press
, New York.
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