1

29th

Symposium on Naval Hydrodynamics

Gothenburg, Sweden, 26-31 August 2012

Waterjet Thrust Augmentation using

High Void Fraction Air Injection

Xiongjun Wu, Sowmitra Singh, Jin-Keun Choi, and Georges L. Chahine

(DYNAFLOW, INC., U.S.A.)

ABSTRACT

Waterjet thrust can be enhanced by bubble injection in

the exit nozzle as demonstrated with earlier

experiments with void fractions up to 15% (Wu et al.,

2010). Efforts to investigate thrust increases with

higher void fractions are presented here. A four inch

outlet diameter laboratory scale nozzle was used, and

air injections as high as 50% were tested. This was

achieved using improved nozzle geometry with a

carefully designed air injection section. Net thrust

augmentations attaining 70% were measured. The

numerical predictions compared well with the

experimental results. The analysis was further extended

to include compressible shock modeling, and

parametric studies are being conducted to explore the

feasibility of a new design that exploits a choked flow.

INTRODUCTION

Injection of air into a waterjet to augment thrust has

been suggested for decades with the aims to

significantly improve the net thrust and overall

propulsion efficiency of a water jet. Unlike traditional

propulsion devices which are typically limited to less

than 50 knots, this propulsion concept promises thrust

augmentation even at very high vehicle speeds (e.g.

Mor and Gany, 2004)). Analytical, numerical, and

experimental evidence (Tangren et al., 1949, Muir and

Eichhorn, 1963, Ishii et al., 1993, Kameda and

Matsumoto, 1995, Wang and Brennen, 1998, Preston et

al., 2000, Albagli and Gany, 2003, Mor and Gany,

2004, Chahine et al., 2008, Wu et al., 2010, Gany and

Gofer, 2011) showing that bubble injection can

significantly improve the net thrust of a water jet make

the idea of bubble augmented thrust attractive.

Figure 1 illustrates the concept: the liquid

entering the diffuser is first compressed and then it is

mixed with high pressure gas injected via mixing ports.

The resulting multiphase mixture is then accelerated in

the converging nozzle. The resulting pressure drop

makes the injected bubbles increase volume and this

converts the potential energy in the bubbles into liquid

kinetic energy, jet momentum, and this boosts the jet

thrust.

Figure 1: Concept sketch of bubble augmented jet

propulsion.

Various prototypes were developed and tested,

e.g.: Hydroduct by Mottard and Shoemaker (1961),

MARJET by Schell et al. (1965), underwater Ramjet

by Mor and Gany (2004). Anecdotal net thrust increase

due to the injection of the bubbles was reported.

However, the performance appeared strongly related to

the efficiency and proper operation of the bubble

injector and the overall propulsion efficiency was

typically less than that anticipated from the

mathematical models used. Concepts have not been

realized in any operational vessel yet (Gany and Gofer,

2011). The discrepancy between the numerical and

experimental results may be due to poor mixing

efficiency at the injection, possible flow chocking or

weaknesses in the modeling (Varshay, 1994, 1996).

By utilizing more detailed analysis of the two-

phase flow in numerical models that include the

dynamic behavior of bubbles and with better controlled

air injection scheme in experiments, better agreement

between numerical simulation and experiments were

found (Chahine et al., 2008, Wu et al. 2010). These

studies also showed numerically that the geometry of

the BAP nozzle plays a significant role on the

performance and efficiency of a Bubble Augmented

Propulsion (BAP) system, and there was an optimal

geometry that maximized thrust augmentation.

The present study extends previous results to

higher void fractions (up to 50%), and extends the 1D

2

approach to include compressible flow effects to

account for conditions where the speed of sound in the

high void fraction bubbly medium becomes

comparable to the flow speed.

GOVERNING EQUATIONS

The bubbly mixture treated as a continuum satisfies the

following general continuity and momentum equations:

0m

m mt

u , (1)

2

23

mm m m ij m m

Dp

Dt

uu , (2)

where m ,

mu , mp are the mixture density, velocity

and pressure respectively, the subscript m represents

the mixture medium, and ij is the Kronecker delta.

The mixture density and the mixture viscosity

can be expressed as

1m g , (3)

1m g , (4)

where is the local void fraction, defined as the local

volume occupied by the bubbles per unit mixture

volume. The subscript represents the liquid and the

subscript g represents the bubbles. The continuum

flow field has a space and time dependent density,

similar to a compressible liquid problem.

The flow of the bubbly mixture inside the

nozzle is modeled by coupling Lagrangian tracking of

individual bubbles with Eulerian solution of the

continuum mixture flow. The bubble dynamic

oscillations are in response to the variations of the

mixture flow field variables, and the flow field depends

directly on the bubble density variations. The unsteady

3D modeling is realized by coupling the unsteady

Navier Stokes solver 3DYNAFS_VIS© with the bubble

dynamics and tracking solver 3DYNAFS_DSM©.

Applications of this approach with validations were

presented in Hsiao & Chahine (2001, 2002, 2004a,

2004b, 2005), Chahine et al. (2008), and Wu et al.

(2010).

The bubble dynamics is solved using either a

modified Rayleigh-Plesset equation improved with a

Surface-Averaged Pressure (SAP) scheme:

2

2

3

00

| |3

2 4

42,

enc b

m m

k

mv g enc

RR R

R Rp p P

R R R

u u

(5)

or the following Keller-Herring equation that considers

the effect of liquid compressibility

2

2

3

00

| |31 1

2 3 4

421 .

enc bm m m

m m

k

mv g enc

m m

R RRR R

c c

R RR R dp p P

c c dt R R R

u u

(6)

In the above two equations, R is the bubble

radius at time t, R0 is the initial or reference bubble

radius, is the surface tension parameter, µm is the

medium viscosity, m is the density, pv is the liquid

vapor pressure, pg0 is the initial gas pressure inside the

bubble, and k is the polytropic compression law

constant. uenc is the liquid average velocity vector at the

bubble location, ub is the bubble travel velocity vector,

and Penc is the average ambient pressure “seen” by the

bubble during its travel, and cm is the local speed of

sound in the bubbly mixture. The bubble trajectory is obtained from a

bubble motion equation similar to that derived by

Johnson and Hsieh (1966):

1/2

1/4

3

2

( )1,

2 ( )

m m

b

m

b b bD b b b

m m ijbb

m lk kl

d RF

dt R x

Kv dddg

dt dt R d d

u uu u u u u

uuu u

(7)

The right hand side of Equation (7) is

composed of various forces acting on the bubble. The

first term accounts for the drag force, where the drag

coefficient FD is determined by the empirical equation

of Haberman and Morton (1953). The second and third

term in Equation (7) account for the effect of change in

added mass on the bubble trajectory. The fourth term

accounts for the effect of pressure gradient, and the

fifth term accounts for the effect of gravity. The last

term in Equation (7) is the Saffman (1965) lift force

due to shear as generalized by Li & Ahmadi (1992).

The coefficient K is 2.594, is the kinematic viscosity,

and dij is the deformation tensor.

1-D MODELING

In the present study, a 1D version of the above

approach is used (Chahine et al., 2008, Singh et al.,

2010). When average quantities in a cross section of a

nozzle are considered, 1-D unsteady model can be

reduced from the above governing equations into a

simplified form:

10,m m mu A

t A x

(8)

3

10,m m m m mu u Au p

t A x x

(9)

where A is the local cross-sectional area of the nozzle.

The liquid is assumed incompressible and the dispersed

gas phase contributes to all the compressibility effects

of the mixture. It is also assumed that no bubbles are

created or destroyed other than at the injection location.

In addition, an analytical 0-D model was used

to optimize the nozzle geometry for maximum thrust

enhancement (Singh et al., 2010). This approach

further simplifies the equations and only requires

knowledge of the areas at the inlet, the outlet and the

injection section, as well as the pressure and velocity

jumps at the injection location.

THRUST AUGMENTATION PARAMETERS

Based on the application type, two definitions for thrust

calculations can be used (Chahine et al., 2008, Wu et

al. 2010). For ramjet type propulsion, the thrust of the

nozzle is computed as follows:

2

R m mT p u d AA

, (10)

where mu is the axial component of the mixture

velocity, and the surface integration is taken over a

control surface, A, that encompass both the inlet and

the outlet.

For waterjet type applications, the thrust of the

nozzle is computed from:

2

oW m m

AT u d A , (11)

where oA is the exit surface area of the nozzle.

Under the 1-D assumption, the thrust for the

ramjet and waterjet can be simplified to:

2 2

, , , ,

2

, ,

,

,

R o o i i

m o o m o m i i m i

W m o o m o

T p A p A

A u Au

T A u

(12)

where Ai and um,i are respectively the inlet area and

medium velocity.

To evaluate the performance of a nozzle

design with air injection, we define a normalized thrust

augmentation parameter, , as following:

,, or ,

i i

i

T Ti R W

T

(13)

in which ,iT and iT are thrusts with and without

bubble injection.

We can also define a normalized thrust

augmentation parameter, m , as the net thrust increase

with bubble injection normalized by the inlet

momentum flux, m inletT

, as following:

, or

i i

m

m inlet

T Ti R W

T

. (14)

OPTIMIZED 3-D NOZZLE GEOMETRY

Numerical simulations have shown that thrust

augmentation can be optimized with geometrical

dimensions selected (Wu et al. 2010). For instance, the

ratio of the exit area to the inlet area or the contraction,

/ ,o inC A A (15)

is an important design parameter. Figure 2 shows the

variation of the normalized thrust augmentation, m ,

with the contraction for an inlet velocity of 2.4 m/s.

The numerical results (Sing et al, 2010) show that the

exit area has to be large enough to satisfy C > 0.6 to

obtain thrust augmentation, i.e. 0m . Figure 2 also

shows that there exists an optimal C value for different

bubble injection void fractions, and that the optimal C

value is around 1.0. Additionally, Figure 2 indicates

that for a given nozzle inlet area, the net thrust increase

is determined only by the exit area and is not controlled

in a major way by nozzle length and cross sectional

variation between the inlet and the outlet, since the 0D-

BAP, which ignores those parameters, provides

answers very close to the more complete simulation.

Figure 2: Variation of the normalized thrust augmentation

with normalized nozzle exit area at inlet velocity 2.4 m/s for

TR, ramjet thrust.

4

Based on these numerical simulations, an

optimized nozzle with equal inlet and exit areas were

designed and built for this study. Figure 3 shows the

dimension of this nozzle used in the experimental study

presented below.

Figure 3: Dimensions of the half 3-D nozzle designed and

built for optimal thrust augmentation.

MODELING OF A CHOKED FLOW

When bubbles are injected continually and steady state

conditions are achieved, the 1-D model described

above reduces to the following form:

( )0,m mu A

x

(16)

( )10.m m mu Au p

A x x

(17)

By neglecting the density of the injected air

relative to the liquid density, m reduces to

1 .m l (18)

The void fraction , , can be connected to the

pressure through an equation of state for the mixture,

which depends on the gas polytropic compression law

constant k, as follows (Brennen, 1995):

1

1

k

ref

ref ref

p

p

, (19)

where ref

p is the reference pressure corresponding to a

reference void fraction of ref

. Here k can be taken to

be 1 (isothermal conditions) since the gas bubbles

execute relatively slow and small amplitude

oscillations. Equation (17) can be integrated accounting for

(18) and (19) to obtain the mixture velocities in the

nozzle as functions of the local gas volume fraction and

the reference quantities ( ,m refu is the mixture velocity

where the pressure is ref

p and the void fraction is ref

)

2 22 1 11

1 1

ref ref ref ref

m m ref

l ref ref ref

kpu u

,

( )ln

( ) ( ) (20)

Of the two solutions in (20), one solution corresponds

to subsonic flow and the other to supersonic flow.

The momentum equation (17) can be

expanded and rewritten in the following form:

2 212m m

m m m m m

d dudA dpu u u

A dx dx dx dx

, (21)

which after use of the continuity equation (16),

simplifies to:

.m

m m

du dpu

dx dx (22)

By combining (21) and (22) and rearranging,

we obtain the following expression:

2

1 1 1 m

mm m

ddA dp

A dx dx dxu

. (23)

Using the expression for the sound speed,

2

1

2

1

2

c

1c , 1

1

1 , 1

1

m

m

k k

ref ref

m kk

lref

ref ref

l ref

dp

d

kpk

pk

,

,

,

(24)

Equation (23) gives the following relation connecting

the area gradient to the pressure gradient within the 1-

D nozzle:

2 2

1 1 1 1

m m m

dA dp

A dx dx u c

. (25)

From Equation (25), one can see that if the

nozzle geometry is such that 0dA dx / at a given

location, then either a zero pressure gradient occurs at

that location, 0,dp dx / or the liquid speed equals the

sound speed of the medium, ,m m

u c (choked flow).

Therefore, if a throat is present in the nozzle, the

mixture speed can reach there the sound speed and the

flow can transition from a subsonic regime (upstream

of the throat) to a supersonic regime (downstream of

the throat).

5

Under choked conditions, the void fraction at

the throat,* , can be computed by equating the

mixture speed, m

u (20), to the sound speed, m

c , (24):

2

* ,

2

* **

(1 ) (1 )1 1 1ln

(1 ) 22

ref m ref l ref

ref ref ref ref

u

p

.

(26)

For a typical nozzle designed for thrust

enhancement by bubble injection sketched in Figure 4,

if choked flow occurs then the problem may be broken

down into three regions:

Liquid flow through a diverging nozzle,

Flow across the injection section ,

Bubbly choked flow after the injection section.

Equations (16), (17), (18), (19), (20) and (26) can

be solved for flow quantities in the nozzle after the

injection section. The velocity and the pressure

immediately after the injection, inj

V and

injp

can be

related to the injected void fraction, 0 , by the

following relationships (Singh et al., 2010):

2

2 2

1

1

2 2

oinj inj

l o oinj inj inj

inlet inlet injection inj

l linlet inlet inj inj

V V

p p V

A V A V

p V p V

. (27)

In the above relations, inj

V is the mixture velocity just

before injection, inj

p is the pressure just before

injection, injectionA is the area of the injection section, and

inletA is the area of the inlet section. Given the geometry

of the nozzle and the injected void fraction, the above

system of equations can be solved (with specified

inlet/upstream pressure) to compute the exit pressure,

the exit velocity and the inlet velocity under choked

conditions.

Once the throat void fraction is obtained by

solving equation (26), the velocity and void fraction at

any location after the injection section can be obtained

by simultaneously solving the continuity equation (16)

along with the equation for mixture velocity (20). Two

solutions result each for the mixture velocity and the

void fraction. The solution pair with a void fraction

greater than the throat void fraction apply for the

region downstream of the throat and the solution pair

with a void fraction less than the throat void fraction

apply for the region upstream of the throat. Once the

void fraction at a given location is known, the pressure

at that location is obtained using the equation of state

(19). Once these flow quantities are known, the thrust

for the geometry under choked conditions can be

computed.

Figure 4: Typical Nozzle Design for thrust enhancement by

bubble injection.

CHOKED NOZZLE DESIGN STUDY

The BAP geometry with a throat shown in Figure 5 is

used to demonstrate a choked flow computation, using

the 0-D BAP model. The geometrical conditions

Athroat/Ainlet=1.06, Aexit/Ainlet=2.4, an upstream pressure,

pinlet= 5 atm, and 0 0.2 are used for the computations.

Figure 6 through Figure 8 show the axial

distributions of flow quantities downstream of the

injection section. Under choked conditions, the flow

makes a transition from the subsonic regime to the

supersonic regime across the throat where the mixture

velocity becomes equal to the mixture sound speed at

the throat (about 30 m/s for these conditions). This can

be seen clearly in Figure 7. Because of this transition,

in the section after the throat, the void fraction and the

mixture velocity continue to increase (contrary to the

subsonic case) and the pressure continues to decrease

even though the cross-sectional area of the nozzle

increases. This, in turn, results in very high exit

velocities and thereby very high momentum thrust.

Would the flow have remained subsonic (as

illustrated in the figures), the presence of a throat

merely increases the flow velocity and decreases the

pressure in the converging section and then bring them

back to the previous state in the expansion section. In

subsonic flow, the throat does not provide any gain in

thrust.

Figure 5: Geometry of an expanding-contracting nozzle

incorporating a throat.

6

Figure 6: Axial distribution of the pressure, p, downstream

of the injection section. Curves for choked flow versus purely

subsonic flow are shown.

Figure 7: Axial distribution of mixture velocity,

mu ,

downstream of the injection section for the choked flow

versus the purely subsonic flow.

Figure 8: Axial distribution of gas volume fraction, , from

the injection section to the exit. The void fraction of the

supposed subsonic flow near the throat (even though

shocking conditions are considered) result in phase separation

in the segment (1.5<x<1.65) of the BAP nozzle.

Considering a Athroat/Ainlet=1.06 and pinlet=5

atm, a parametric study was performed to understand

the effect of the influence of the contraction area ratio,

Aexit/Ainlet, on the normalized thrust augmentation

parameter, m . Figure 9 shows the resulting thrust

augmentation curves. This shows that under choked

conditions, the optimum Aexit/Ainlet is found to be about

2.4 for an injected void fraction of 0.2 and about 2.0

for an injected void fraction of 0.4, while the optimum

Aexit/Ainlet was 1.0 under subsonic conditions.

Figure 9: Variation of the normalized thrust augmentation

parameter with variation of Aexit/Ainlet: choked flow versus

purely subsonic flow.

It appears that for choked flows the optimal

contraction ratio is a function of the injected void

fraction. It is also clear from the figure that the values

of the normalized thrust augmentation parameter are

overall much higher for choked flows that for subsonic

flows. Studies are being conducted to understand the

individual and collective influences of parameters such

as Aexit/Ainlet, Athroat/Ainlet and pinlet on m .

SETUP FOR EXPERIMENTAL STUDY

The test setup used in this study is shown in Figure 10.

The flow can be driven by two 15 HP pumps (Goulds

Model 3656) with each pump capable of a flow rate of

2.1 m3/min (550 gpm) at 170 kPa (25 psi) pressure

head. The two pumps can work in parallel to boost the

flow rate and a bypass line is used to adjust the flow

rate. The nozzle test section is placed below the free

surface in DYNAFLOW’s wind wave tank, which is used

here as a very large water reservoir, so that

accumulation of air bubbles generated from the testing

is minimized. A flow adaptor is used to convert the

flow from the inlet pipes circular cross section to match

the cross section shape of the nozzle assembly

7

geometry. A flow straightening section is inserted

between the flow adaptor and the nozzle inlet.

We used a 3-dimensional set up, which was half

of the full three dimensional axisymmetric nozzle with

a vertical cut through a center plane. This set up

represents the flow of the full three dimensional nozzle

more closely and enables good flow visualization

through the flat transparent center-plane.

Instrumentation was provided for flow rate,

pressures, velocities, and void fractions measurements

as in (Chahine et al., 2008, Wu et al. 2010).

Additionally, a direct momentum force measurement

scheme was designed using a submerged PCB load

cell. A high capacity air compressor was used to

achieve high void fractions. This 5 HP air compressor

(Compbell Hausfeld DP5810-Q) had a rating of 0.72

m3/min (25.4 CFM) at 620 kPa (90 psi).

Figure 10: Sketch of the test setup for the Bubble

Augmented Jet Propulsion experiment.

In order to achieve a bubble distribution as

uniform as possible, a half circular air injector made

from a flexible porous membrane was used to cover the

inner half circular boundary of the nozzle (Figure 11).

In order to achieve higher void fraction and better air

distribution near the centerline of the nozzle, a center-

body was inserted in the nozzle (Figure 12). This

center-body air injector consisted of a flat plate with a

porous face and a half cylinder with porous surfaces on

both sides.

Figure 11: 3D rendering of the air injector positioned in the

outer boundary of the nozzle. On the left is the injector

assembly and on the right is an exploded view of the air

chamber and porous membrane.

Figure 12: A sketch of the inner air injector.

Figure 13: Picture of the nozzle with direct force

measurement.

Figure 13 shows a picture of the 3D nozzle at

low air injection rates for an incoming water flow rate

of 0.76 m3/min (200 gpm). Figure 14 shows a close up

of the contraction section at 0.87 m3/min (230 gpm)

inlet water flow and 16% void fraction.

FLOW STRUCTURING OF EXIT FLOW

Flow visualizations were conducted using high speed

motion pictures. These showed clear large scale flow

structures of the mixture once the two-phase medium

exited the BAP nozzle. Figure 15 shows an example of

such flow structuring at the exit.

To quantify the flow structuring, the video

images were analyzed to extract the frequency of the

main flow structures. Figure 16 shows the variation of

the average flow structure frequency with the void

fraction at different flow rates. This indicates that the

flow structure frequency increases with the flow rate

and decreases with the void fraction. The frequency, f,

can be normalized as a Strouhal number:

,fD

SV

(28)

where D is the nozzle exit diameter, and V is the mean

exit velocity. As show in Figure 17, normalization

brings the different flow rate curves almost on top of

each other, and the Strouhal number decreased with the

void fraction regardless of the water flow rate.

Porous

membrane

Air chamber

Chamber partitions

8

Figure 14: View of the contraction section of the BAP

nozzle. Higher void fraction are seen in the top section as

bubbles rise under gravity. Nominal inlet velocity is 3.57 m/s

and nominal void fraction at injection is 16%.

Figure 15: Visualization of the large flow structures in front

of the BAP nozzle exit.

Figure 16: Variation of the flow structuring frequency with

the void fraction at different water flow rates.

Figure 17: Normalized flow structure frequency variation

with void fraction at different flow rate.

FORCE MEASUREMENTS

In our previous studies, the thrust augmentation was

computed from velocity and pressure measurements. In

the present study, force was measured by using a setup

as sketched in Figure 18. The part of the exit

momentum force impacting directly on a force

measurement plate was recorded.

Figure 19 shows a picture of the plate mounted

in front of the BAP exit. The plate had the dimensions

of 30.5 cm (12 in.) by 15.2 cm (6 in.) and was placed

downstream of the nozzle exit at prescribed distances.

Flow of the mixture coming out from the nozzle

impinged on the plate, and the force applied on the

plate was measured by a load cell (PCB Load &

Torque Model 1102-115-03A with full scale of 890 N

(200 lbf)).

In order to capture as much of the exit

momentum as possible with the force measurement

plate, enclosure plates (side, top, bottom, and front

plates) were used together with the force measurement

plate such that the diverted flow could only exit in one

direction which was parallel to the impact plate. The

influence of the distance between the plate and the

nozzle exit was examined and was found, as expected,

to have a noticeable effect on the measured force.

Figure 20 shows the force measured by the load

cell at different void fraction and inlet flow rate

conditions for three different standoff distances of the

measurement plate from the nozzle exit. It is clear from

the tests that at the largest standoff distance of 13.6 cm

(5.34 in.), the force measurement plate captures the

most of the exit momentum force. When the plate was

closer, the interaction between the plate and the exit

flow reduced the force acting on the plate. Therefore

all the force measurements results reported below were

obtained at this location.

Flow

Flow

9

Figure 18: Experimental setup for exit momentum force

measurements using a load cell.

Figure 19: Picture of the instrumented force measurement

plate.

The efficiency of the force measurement plate

in capturing the exit momentum force was also

examined. Figure 21 shows the variations of the

normalized force captured by the plate, / l l mF QV ,

versus the exit mixture flow rate, / (1 )lQ . Here lQ

is the liquid flow rate and mV is the medium velocity at

the nozzle exit assumed to be the same as the liquid

velocity. As shown in the figure, the fraction of the

captured exit momentum force decreases with the

increased exit mixture flow rate and reaches a plateau.

This may be attributed to the flow interaction between

the nozzle flow and the flow deflected by the plate,

which increases with the nozzle flow rate.

In order to obtain the momentum thrust of the

nozzle, T, the force F, directly measured by load cell is

corrected by the above measured capture efficiency, e,

using:

FT

e . (29)

Figure 20: Load cell force measurement versus void-fraction

for different water flow rates and different stand-off distances

of the measurement plate from the exit

Figure 21: Fraction of the total exit momentum force

captured by the force measurement plate at different exit

mixture flow rates (with and without air injection).

10

EFFECTS OF AIR INJECTION ON INLET

FLOW

The effects of air injection on the inlet flow behavior

were examined systematically with the pump and valve

settings being maintained untouched. Figure 22 shows

the signal output of the flow meter that measures the

inlet flow rate. Very little effect of the air injection can

be seen.

Figure 23 shows the inlet flow rate

fluctuations with and without air injection at different

flow conditions. The fluctuations in the flow rate were

less than 4% of the flow rate for all test conditions, and

air injection did not have any noticeable effects on the

inlet flow rate or its fluctuations. Therefore, no flow

rate adjustment was made in the thrust measurement

tests, and the inlet velocity profile was assumed to be

the same for the same flow rate regardless of air

injection condition.

However, there was a noticeable pressure

increase in the upstream of the nozzle when air was

injected. This was accepted by the pump without any

noticeable change of flow rate. This change in the

upstream pressure is examined below.

Figure 22: Signal output of flow meter measuring the inlet

flow rate with and without air injection.

EFFECTS OF AIR INJECTION ON NET

THRUST

The nozzle geometry under consideration has the same

inlet and outlet area ( ,o iA A ). If we account for

2 2 2

, ,0 , ,0 , ,L outlet L inlet L inletu u u the thrust augmentation

expression, (13) ,can be simplified to

2 20

, , , ,

0

(1 ) / 1.L outlet L inlet

T Tu u

T

(30)

From the mixture continuity equation, we know that

2 2

, , , ,(1 ) .l L outlet l L inletu u

(31)

Therefore,

, ,0

2

,0

(1 )1 .

1(1 )

p p

p

T T

T

(32)

Extensive experiments were conducted to

study the effects of air injection on the nozzle thrust. In

addition to the direct force measurement using the load

cell, pressure measurements at the nozzle inlet were

also conducted. Figure 24 shows the range of tested

void fraction (0 to 50%) and the inlet liquid flow rate

0.76 m3/min (200 gpm, inlet velocity = 3.1 m/s) to 2.27

m3/min (600 gpm, inlet velocity = 9.3 m/s).

Figure 23: Pump flow rate percent fluctuations versus flow

rate. Air injection appears to have no noticeable effects on

these fluctuations.

Figure 24: Nominal void fraction coverage range for

different air injection rates (in standard gallon per minute

(SGPM), 1 SGPM = 0.00379 m3/min of air at 1 atm) at

different liquid inlet flow rates.

11

Figure 25 shows the normalized net thrust

increase vs. the exit void fraction. Results from

numerical simulations and experiments shown in the

figure agree well with each other. The results also

follow the simplified theoretical curve, / 1 ,

which shows that air injection becomes more efficient

and produces further net thrust increase with increased

void fraction.

Figure 25: Variation of normalized (water jet) net thrust

enhancement with void fraction.

Figure 26: Normalized pressure increase at the inlet versus

void fraction

The air injection causes an increase in the inlet

pressure, which means that the water jet pump needs to

work harder to overcome this negative effect from the

air injection. To examine the effect of the void fraction

on the inlet pressure, the normalized inlet pressure

increase is plotted in Figure 26. As shown in the figure,

this effect increases almost linearly with the exit void

fraction.

Figure 27 compares the thrust gain due to air

injection and the thrust loss due to inlet pressure rise as

functions of the void fraction at the exit. As the void

fraction increases, the difference between the thrust

increase and the inlet pressure force rise becomes

larger. Figure 28 shows the net thrust gain obtained by

subtracting the pressure force loss from the thrust gain.

This illustrates again that injection of higher void

fractions results in significant thrust gains, with

measured 70% increase at 50% void fraction.

Figure 27: Comparison between momentum thrust increase

due to air injection and thrust decrease due to inlet pressure

increase.

Figure 28: Variation of normalized (Ramjet) net thrust gain

with void fraction. 70% net thrust enhancements are seen

with 50% air fraction at the nozzle exit.

CONCLUSIONS

Experimental and numerical studies of the influence of

bubble injection on the thrust of waterjet propulsion

were presented. The numerical model was based on a

1D version of the two-way coupled Eulerian-

Lagrangian method, which models the bubbly flow and

tracks bubbles. Optimum nozzle geometry was

obtained using the numerical prediction method.

The 1-D model was extended to include

supersonic flow modeling to be applied experimentally

in future efforts. This new extension of the method can

provide a useful design tool to study the choked flow in

the BAP. Further studies are underway to examine the

12

feasibility of taking advantage of a supersonic exit flow

to achieve higher thrust augmentation.

With a 4 in. outlet diameter laboratory scale

nozzle and carefully designed air injection,

significantly high void fractions (~ 50%) injections

were achieved. The exit momentum was measured

using an impact plate based thrust measurement

scheme. The experiments showed good nozzle

performance and significant net thrust increases with

increasing void fractions, even after accounting for

inlet pressure increases due to the bubble injection.

Net thrust augmentation was as high as 70% for an exit

void fraction of 50%. This study indicated that a well-

designed nozzle with a proper air injection scheme can

provide significant performance improvement with

high void fraction air injection.

ACKNOWLEDGEMENT

This work was supported by the Office of Naval

Research under the contracts N00014-09-C-0676,

N00014-11-C-0482 monitored by Dr. Ki-Han Kim. We

gratefully acknowledge this support. The authors also

acknowledge Ms. Tiffany Fourmeau of DYNAFLOW,

INC. for her effort in carrying out some of the

parametric studies presented in this paper.

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