WU Xiongjun, CHOI Jin-Keun, SINGH Sowmitra, HSIAO Chao-Tsung, CHAHINE Georges L. DYNAFLOW INC., Jessup, Maryland, USA, E-mail: wxj@dynaflow-inc.com

(Received September 28, 2011, Revised February 7, 2012)

EXPERIMENTAL AND NUMERICAL INVESTIGATION OF BUBBLE AUGMENTED WATERJET PROPULSION*

WU Xiongjun, CHOI Jin-Keun, SINGH Sowmitra, HSIAO Chao-Tsung, CHAHINE Georges L. DYNAFLOW INC., Jessup, Maryland, USA, E-mail: wxj@dynaflow-inc.com

(Received September 28, 2011, Revised February 7, 2012)

This contribution presents experimental and numerical investigations of the concept jet propulsion augmentation using bubble injection. A half-3D (D-shaped cylindrical configuration to enable optimal visualizations) divergent-convergent nozzle was designed, built, and used for extensive experiments under different air injection conditions and thrust measurement schemes. The design, optimization, and analysis were conducted using numerical simulations. The more advanced model was based on a two-way coupling between an Eulerian description of the flow field and a Lagrangian tracking of the injected bubbles using our Surface Averaged Pressure (SAP) model. The numerical results compare very favorably with nozzle experiments and both experiments and simulations validation the thrust augmentation concept. For a properly designed nozzle and air injection system, air injection produces net thrust augmentation, which increases with the rate of bubble injection. Doubling of thrust was measured for a 50% air injection rate. This beneficial effect remains at 50% after account for liquid pump additional work to overcome increased pressure by air injection.

waterjet, propulsion, bubble dynamics, multi-phase flow

Introduction

Bubble injection into a waterjet to augment thrust has received recent revived interest[1-5]. References [1,2] showed interesting results indicating that bubble injection can significantly improve the net thrust and overall self-propulsion efficiency of a water jet system. Several prior studies explored similar ideas, and some of these studies adopted the naming Water Ramjet to such a system by analogy to ramjet aerodynamic propulsion systems[4].

Analytical, numerical, and experimental evidence of the augmentation of jet thrust by bubble expansion in the jet stream, make the idea of bubble augmented thrust attractive. 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[2].

Various prototypes have been developed andtested, e.g., Hydroduct, MARJET, and Underwater Ramjet[3,4,6]. Figure 1 shows how the concept works: fluid enters a diffuser where it is compressed (ram effect). It is then mixed with gas injected via ports at the end of the expansion area. The resulting two-phase mixture is then accelerated through a converging nozzle before exiting the propulsor nozzle. Prototypes of such systems have reported anecdotal net thrust from the injection of the bubbles under poorly controlled conditions. The performance is strongly affected by the efficiency and proper operation of bubble injection and mixing and the overall propulsion efficiency was reported typically to be less than that anticipated from the predictive models used. This may be a result of a poor mixing efficiency at the injection, possible flow chocking, or of weaknesses in the modeling[3].

Previous empirical and numerical studies of bubbly flows have modeled mixtures passing through a nozzle[3-5]. With these models, it was found that expansion of a compressed gas bubble-liquid mixture is an efficient way to generate the momentum necessary for additional thrust[1,2]. However strong approximations and simplifications in these models dictates that we develop a numerical tool which can provide a more detailed analysis of the two-phase flow, andwhich correctly includes the dynamic behavior of the injected bubbles and properly simulate water ramjet propulsion[1].

Fig.1 Concept sketch of bubble augmented jet propulsion

The approach we have developed consists of considering the bubbly mixture flow inside the nozzle from the following two perspectives:

(1) Microscopic level

Individual bubbles are tracked in a Lagrangian fashion, and their dynamics are followed by solving a“surface averaged pressure” Rayleigh-Plesset equation, where the driving pressure is obtained as an average over the bubble surface of the macroscopic solution. The bubble responds to its surrounding medium described by its mixture density, pressure, velocity, etc..

(2) Macroscopic level

Bubbles are considered collectively and the liquid bubble mixture is defined by a time and space void fraction distribution. The two-phase medium has a time and space dependent local density which is related to the local void fraction. The mixture density is provided by the microscale tracking of the bubbles, which provides bubble distribution and size, which determines the local volume fraction.

The two levels are fully coupled: the bubble dynamics are in response to the variations of the mixture flow field characteristics, and the flow field depends directly on the bubble position and size variations. This is achieved through two-way coupling between the unsteady Navier Stokes solver 3DynaFS-Vis? and the bubble dynamics and tracking code 3DynaFSDsm?. A quasi-steady version of the code was also developed, and was extensively used to conduct parametric studies useful for fast estimation of the overall performance of selected geometric design[3-5].

1. Numerical model

1.1 Governing equations

The two-phase mixture density and viscosity can be related to the void volume fraction, α, by:

where the subscript l represents the liquid and the subscriptg represents the gas bubbles.

The two-phase mixture satisfies the following general continuity and momentum equations:

where, the subscript m represents the mixture medium, and δijis the Kronecker delta.

The flowfield has a variable density because the voidfraction varies in space and in time. This makes the overall flow field problem similar to a compressible flow problem.

1.2 Lagrangian bu bble tracking

Lagrangian bubble trackingis accomplishedby 3DynaFS-Dsm?[7](or a corresponding FluentUser Defined Function called Discrete Bubble Model (DBM)). It is a multi-bubble dynamics code for tracking the motion and describing the dynamics of bubble nuclei released in a flow field. The user can select a bubble dynamics model, either the incompressible Rayleigh-Plesset equation or the compressible Keller-Herring equation[8,9]. In the first option, the bubble dynamics is solved by using a modified Rayleigh-Plesset equation improved with a Surface Averaged Pressure (SAP) scheme

If the second option is adopted, the effect of liqui d compressibility is accounted for by using the following Keller-Herring equation.

In the above equations, R is the spherical bubble radius, dots representtime derivatives, and cmis thesound speed in the liquid at the bubble surface. Equations (5) and (6) are commonly used and describe nonlinear bubble oscillations in an incompressible or slightly compressible liquid valid when the bubble wall speed is small compared to the sound speed in the liquid. In this paper, for all cases considered the bubble growth rate (radial bubble wall speed) is very much smaller than the water sound speed, which justifies the use of either of the above two equations. These equations also assume a balance of normal stresses at the bubble wall

wherepgis the bubble gas pressure, pvis the liquidvapor pressure,γ is the surface tension parameter and μis the dynamic viscosity of the liquid. Since gas diffusion is very slow, we assumethat the mass of gas inside each bubble does not change and that the bubble follows a polytropic compression law

where k is the polytropic gas constant, pg0is the initial bubble gas pressure, andR0is thecorresponding initia l bubble radius.Pencisthe ambient pressure “seen” by the bubble during its travel. With the SAP model, Pencand uencare the average of the pressure over the surface of the bubble.

The bubbletrajectory is obtained from the bubble motion equation[10]

The first term in Eq.(9) accounts for the drag force effect on the bubble trajectory. The drag coefficient FD is determined empirically as used in our previous studies[11-13]. The second and third term in Eq.(9) 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 Eq.(9) is the Saffman lift force due to shear. The coefficient K is 2.594, ν is the kinematic viscosity, andijd is the deformation tensor.

1.3 0-Dand 1-D modelling

To study conditions where the flow can be considered one-dimensional with cross section averaged quantities, the governing equations for unsteady 1-D flowthrough a nozzle of varying cross-section, A(x), can be written as

where ρm,um,pare the mixture density, velocity and pressure, all dep endent on x and t.

Aone dimensional code,1-D BAP, was developed for this study[3].The liquid was assumed to beincompressible so that all compressibilityeffects of the mixture arose from the disperse gas phase only. The void fraction, α, is determined by the volume occupied by the bubbles per unit mixture volume, additionally, it is assumed that other than at the injection locations, no bubbles are created or destroyed. If we are interested in the steady solutions, the time derivatives terms in Eq.(10) can be ignored. In addition, if we assume that the bubbles remain spherical, the local bubble dynamics in the nozzle is governed by either of the two Eqs.(5) or (6) or by assuming that the bubbles are readily in static equilibrium with the local pressure. This quasi-steady approximation can be written by removing all dynamics components from the Rayleigh-Plesset equation. This method is further described in Ref.[5].

In addition to the 1-D model, an analytical 0-D model to predict thrust enhancement due to bubble injectionwas developed[5]starting from the mixture continuity and momentum equations in the expandingcontacting nozzle. The model takes into account the areas of the inlet section, the outlet section and the injection section. It also accounts for the pressure and velocity jumps at the injection location.

1.4 3-D unsteady fully coupled modeling

Fig.2 Sketch of the test setup for the bubble augmented jet propulsion experiment

The 3-D coupling between the mixture flow field and the bubble dynamics and tracking is realized by coupling the viscous Eulerian code, 3DynaFS_Vis?, withthe Lagrangian multi-bubble dynamics code 3Dy naF S_Dsm?. Th e unstead y tw o-way inte rac tion canbedescribedasfollows.Thedynamicsofthe bubbles in the flow field are determined by the local densities, velocities, pressures, and pressure gradients of the mixture medium as described in Eqs.(5) to (9). The mixture flow field is influenced by the presence of the bubbles. The local void fraction, and accordingly the local mixture density, is modified by the migration and size change of the bubbles, i.e., the bubble population and size. The flow field is adjusted according to the modified mixture density distribution in such a way that the continuity and momentum are conserved through Eqs.(3) and (4).

The two-way interaction described above is very strong as the void fraction can ch ange significantly (from near zero in the water inlet to as high as 70% at the nozzle exit) in Bubble Augmented jet Propulsion (BAP) applications. Void fractions based on the αcell (cells where the local α?s are computed) concept were introduced in the 3-D space to compute the void fraction[3].

1.5 Thrust d efinitions

We use two definitions for the thrust based on the application type. Forramjet type propulsion, where bothinlet and outlet conditions are results of the engineering solution, the thrust of the nozzle can be computed by integrating the pressure and the momentum flux over the surface of a control volume that contains both the inlet and outlet of the nozzle.

where umis the axialcomponent of the mixture velocity.

For waterjet type applications, where the inlet conditionsare provided by the available pump, the exitwater jet momentum flux is the relevant quantity and the thrust of the nozzle can be defined as the integral only the momentum flux over the exit surface of the nozzle.

where Aois the exit surface area of the nozzle.

Under the 1-D assumption, the expression for the thrust of the ramjet can be expanded as follows

where the subscripts i and o represent theinlet and the outlet of the ramjet respectively. The component of the thrust described in the first parenthesis in Eq.(13) is the contribution from the pressure variation between the inlet and the outlet. The terms in the second parenthesis represent the thrust due to the momentum change between the inlet and the outlet.

The thrust for a waterjet with the 1-D assumption can be simply written as

We can define two normalized thrust augmentation, the first one, ξ, is define d as the net thrust increase with bubble injection normalized by the thrust without bubble injection as follows (the*indicatesWorR)

inwhich T*,αand T*,0are thrusts with and without bubble injection, and can be applied to either ramjet or water jet thrust.

The second one,ξm, is defined as the net thrust increase with bubble injection normalized by the inlet momentum flux as follows

where Tm-inletis inlet momentumflux.

2. Experiment al study

2.1 Set-up

The test setup used in this study is shown in Fig.2. The tests were conducted in Dynaflow?s 72 ft windwave tank. The flow wasdriven by two 15 HP pumps (Goulds Model 3656), each of which is capable of producing a maximum flow rate of 550 gpm at a pressure head of 25 psi. 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 in a tank below the free surface. The wind wave tank is used as a very large water reservoir, so that the possible accumulation of air bubbles generated from the testing is minimized. A flow adaptor is used to convert the flow from a circular cross section to a matching cross section with the shape of the test section geometry. A flow straightening section is inserted between the flow adaptor and the nozzle inlet.

2.2 Pressure and velocity measurements

Variable reluctance type pressure transducer arrays are arranged in the nozzle walls to measure the pressures at different locations along the test section. Pressure signals are sent to the data acquisition system for data logging.

Various methods were used for velocity measurement depending on the experimental conditions:

(1) A planar PIV system was used to characterize the flow field without air injection or in the region before air injection.

(2) An optical bubble tracking method was used for velocity measurement for flows with low void fraction air injections when individual bubbles could be tracked to characterize the flow field.

(3) For flows with high void fraction which posed difficulties for optical method, Pitot tubes and Kiel probes were used for velocity measurement. Void fraction effects are corrected for using the following formula[14]

2.3 Void fraction meas urements

The void fractionwas measured or estimated using several methods:

(1) A nominal void fraction was obtained by dividing the air flow rate by the liquid flow rate.

(2) A photographic method was used to measure the void fraction with image analysis. This was applicable only to low void fraction media where the bubbles did not overlap too much in the images.

(3) The attenuation of laser light through the bubbly medium due to light scattering on the bubble surfaces.

(4) An acoustic method that utilizes DYNAFLOW?s Acoustic bubble Spectrometer? (ABS) was used to measure bubble size distribution and integrate it to obtain the void fraction[15-17].

(5) Conductivity probes were used to measure conductivity and convert this to void fraction information. This method can be applied to a wide range of void fraction, but appears more accurate for the higher void fractions.

Fig.3 Experiment setup for exit momentum force measurement using a load cell

2.4 Thrust measurements

Additionally, a force load setup, as shown in Fig.3, was used to efficiently measure real time the exit momentum force directly using a force measurement plate. The plate hada dimension of 0.305 m × 0.152 m and was placed in front of the BAP nozzle exit at a prescribed distance. Flow of the mixture coming out from the BAP impinged on the plate and the force applied on the plate was measured by a load cell (PCB Load and Torque Model 1102-115-03A with full scale of 200 lbf.). In order to capture as much as possible of the exit momentum 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 from one direction which from the side was in a direction perpendicular to the force load plate.

The air source for air injections was provided by a 5 hp air compressor (Compbell Hausfeld DP5810-Q) which has a rating of 25.4 CFM at 90 PSI.

Fig.4 Cut-through plane dimensions of original nozzle design with an expansion exit

Fig.5(a)CAD rendered drawing of the 3-D nozzle with an expansion without the side plate

Fig.5(b) CAD drawing of the complete nozzle with a flow adaptor and a flow straightener sections

Fig.6 Area changes of the half-circle cross section along the nozzle for different parametrically examined throatareas

Fig.7 The change of thrust normalized with inlet momentum flux with nominal void fraction at injection. The different colors correspond to the colors of the examinedprofiles shown in Fig.6

2.5 Propulsor/nozzle geometry design

In the study reported here, the nozzle was fully madeof transparent Plexiglas to enable visualization. The geometry washalf of a fully 3-D cylindrical axisymmetric divergent convergent nozzle with a vertical cut through a center plane. This set up represents the flow of the full 3-D nozzle and enables good flow visualization of the bubbles away from the cylindrical wall through the flat transparent plate in the symmetry plane. The initial design featured an expansion exit as well, as shown in Fig.4 in the cut-through plane as previously reported[3,4]. Figure 5 shows CAD drawings of the half 3-D nozzle with the expansion exit.

1D-BAP was used to evaluate the effects of the throat on the performance of the nozzle with an expansion exit. Figure 6 shows, for a parametric study, variations of the cross section outline along the nozzle for different throat geometries. Notice that the only vary ing parameter in these profiles is the diameter of the throat.

Figure 7 shows the predicted normalized thrusts for different nominal void fractions at injection for the different geometry profiles. The color of the thrust curve corresponds to the color of the nozzle geometry in Fig.6 Th e thrust is normalized by the inlet momentum flux defined as

As indicated in Fig.7,the expansion exit actually causes a thrust decrease with bubble injection, this prompted themodification of the base nozzle design to a nozzle without the expansion exit section.Figure 8shows the dimensions of the half 3-D nozzle, which has the same dimensions as those shown in Fig.4 without the expansion exit.

Fig.8 Dimensions of the half 3-D nozzle selected for test ing

Fig.9 CAD drawing of the air injector positioned in the outer boundary of the nozzle. On the left is the injector assemblyand on the right is an exploded view of the air chamber and porous membrane

2.6 Air injection scheme

In order to achieve as uniform bubble injection as possible, a porous medium air injector covering the outerhalf circular boundary ofthe nozzle was used. Figure 9 shows a CAD drawing of the outer air injector. A half circular air chamber was covered by a fle-xible porous plate that was curved to match the nozzle wall profile and was used as the nozzle boundary wall. Compressed air was forced through the porous plate to inject bubble streams in the propulsor flow. As shown on the right picture of Fig.9, the air chamber was partitioned into six separate small chambers and each chamber had its own air supply line such that more uniform air injection could be achieved by adjusting the pressured applied to each chamber and compensate for differences in porous plate properties and hydrostatic head.

Fig. 10 Experimental setup for characterizing the bubbles generated from the porous plate

The flexible porous plate was 1/8 inch thick and has pores of 7 μm diameter. To characterize the bubble sizes generated from the flexible porous plate, an experiment as sketched in Fig.10, was used to measure the bubble size distributio n obtained under different pressure and flow conditions. A 1 inch square porous plate was glued at one end of square Plexiglas tube and compressed air was applied to the other end of the tube and forced through the porous plate to generate bubbles.

Fig.11 Variation of bubble generation with differentair injection rate

Figure 11 shows bubbles generated atdifferent air flowrate, both the number of bubbles and the bubble sizes increase with increased air flow rate. The mean bubble radius was 860 μm, 1 100 μm, and 1300 μm for air flow rates at 1 l/min, 2 l/min, and 3 l/min respectively in absence of shear or liquid flow.

Figure 12 shows a picture of bubbles generated from the outer air injector. Most of the bubbles were concentrated on the outer boundary, and the bubble concentration was significantly lower in the central region. In order to achieve a more uniform distribution, an in ner air injection scheme, as show in Fig.13, was also designed to fit in the nozzle. The inner air injection consisted of a flat injector and a half circular injector with a total of three air injection faces, one on the flat injector and two on both sides of the circular injector.

Fig.12 Air injection from the outer air injectorin the half 3-D BAPnozzle.

Fig.13 A sketch of the inner air injector

Fig.14 The simulation domain of the nozzle used to study the effects of the inner injector on the flow fieldof the nozzle

To study how the flow field in the nozzle was affected by the inner injector, we conducted preliminary liquid only CFD simulations. Figure 14 shows the simulation domain of the nozzle with the inner injector. A vertical symmetry plane was used to speed up the computation (Fig.15). Figure 16 shows comparisons of the pressure and velocity distributions with and without the inner air injector when the inlet velocity was 4.67 m/s (300 gpm). As shown in the figures, the effects of the inner injector on the flow field are not significant from both the pressures and the velocities. The differences of thrust in this case with and without the inner air injector were 0.3 N and 1.9 N forwaterjet and ramjet thrusts respectively.

Fig.15 Close up of the inner injector grid

Fig.16 Comparison of the pressure distributions and velocity distributions along the nozzle with andwithout the inner injector

Fig.17 A snapshot of the 3-D nozzle set up with air inje ction

To achieve better control over the injected bubbles distribution, the inner air injector also has independent air chambers such that air supply to each air chamber can be adjusted to achieve overall uniform bubble injection. Combined with the outer air injecto r, a more uniform bubble injection can be achieved compared to using just a single air injector. Figure 17 shows a picture of the 3-D nozzle set up in the tank. As shown in the picture, multiple air hoses are connected to the chambers of the air injectors to control the air supply independently.

3. Numerical study

3.1 Nozzle geometry optimization

To study the effects of nozzle geometry on the thrust augmentation, a series of numerical studies were conducted to provide guidance for nozzle geometry optimization.

Fig.18Variation of the normalized thrust augmentation (Eq.(16)) with normalized nozzle exit area at 2.4 m/s

Figure 18 shows the variation of the normalized ramj et thrust augmentation,ξm(Eq.(16)), with the normalized nozzle outlet area, C for inlet velocity 2.4m/s. C is defined as the ratio of the exit area to the inlet area,

As indicated in the figure, both 0-D BAP (a simplified analytic approach[4,5]) and 1-D BAP results show thatin order to obtain a positive thrust augmentation gain, i.e.,ξm＞0, the exit area has to be large enough such that C is greater than about 0.6. Figure 18 also shows that there is an optimal C value for different bubble injection void fractions, which is around 1.0. Notice that the base design shown in Fig.8 before has a C value of 0.27 that is well below the minimum C value for positive net thrust increase. This is consistent with the measurements[3].

Additionally, Fig.18 indicates that for a given nozzle inlet area, the net thrust increase is determined only by the exit area and is not controlled by the nozzle length and the cross sections variation in between. Therefore the easiest optimization to ourexperimental base nozzle was to cut short the e xit contract ion section such that C became close to the optimal value for thrust augmentation. Figure 19 shows the corresponding variation of ξ as defined in Eq.(15) with C. ξ indicates that there is a region with 0.75＜C＜1.0, where the bubble injection is detrimental.

Fig.19 Variation of the normalized thrust augmentation with normalized nozzle exit area at 2.4 m/s

Fig.20 Variation of net thrust increase with nominal void fraction for different lengths of the half 3-D nozzle, anda nominal inlet velocity of 2.4 m/s

Fig.21 Variation of net thrust increase with nominal void fraction for different lengths of the half 3-D nozzle anda nominal inlet velocity of 3.57 m/s

Figure 20 and Fig.21 show 1-D BAP simulations of the net thrust increase if the nozzle contraction section was shortened differently from the base nozzle for nominal inlet flows of 2.4 m/s and 3.57 m/s. The resulting total BAP length is measured from the nozzleinlet. As shown in the figures, the best nozzle length for maximum net thrust increase falls between nozzle length of 0.9 m and 1.02 m, which correspond to C values of 1.46 and 0.78. Therefore, for the optimized nozzle used in this study, the converging section of the nozzle was cut down to 0.3153 m which gives a C value of 1.0 and a nozzle length of 0.9775 m. Figure 22 shows the dimension of the modified nozzle with a shortened converging section.

Fig.22 Dimensions of the modified half 3-D nozzle cutshort from the base nozzle for optimal thrust augmentation

3.2Numerical thrust predictions

Both 1-D and 3-D two-way coupled numerical simulations were conducted to evaluate the performanceof the selected half 3-D nozzle geometry.

Fig.23 Pressure contours (a) and axial velocity contours (b) from 3-D computations at a nominal inlet velocityof 3.11 m/s without air injection

Figure 23 shows the pressures and flow velocities along the axial direction for a nominal inlet flow velocityof 3.11 m/s (200 GPM) without air injection. Thepressure contours indicate that the pressure varies significantly along the axial direction but is quite uniform vertically. The velocity contours show that there are re-circulating zones near the ai r injection area.

Fig.24 Bubble size distribution for the bubble injection used in the 3-D two-way coupling simulation

In or?der to estimate the nozzle performance, 3DYNAFS 3D two-way coupled simulations were conducted for different bubble injection rates at nominal inlet flow velocity of 3.11 m/s. Figure 24 shows the selected size distribution of the bubbles injected at a base line void fraction of 4.43%. Bubble distributions for higher void fractions have si milar distributionshapes but the number of bubbles is multiplied by the ratio of the needed void fraction to the base line void fraction, the bubbles are injected into the flow through the inner and outer injectors.

Fig.25 Exit velocity profile from 3DynaFS_Vis? predictions for different void fractions of bubble injection at a nominal inlet velocity of 3.11 m/s.

Figure 25 shows the exit velocity profile for different void fractions. As the curves show, the profiles have similar shapes but the velocity magnitudes increase significantly with increased bubble injection. The average pressure and velocity distributions along the nozzle are shown in Fig.26 and Fig.27, and, as expected, higher bubble injectionrates cause higher pressure increases at the inlet, and significantly higher exit velocity enhancements.

Fig.26 3DynaFS_Vis? results showing average pressure distributions along the nozzle for different nominal void fractions at a nominal inlet velocity of 3.11 m/s

Fig.27 3DynaFS_Vis? results showing average velocity variations along the nozzle for different nominal void fractions at a nominal inlet velocity of 3.11 m/s

Fig.28 Comparison of the normalized thrust augmentationcomputed from the 1-D and 3-D models for different nominal void fractions at a nominal inlet velocity of 3.11 m/s (needs to be reconciled with later comparison)

Figure 28 shows the predicted normalized net thrustincrease,ξm, as a function of the void fraction obtained by the 0-D, 1-D-BAP, as well as the 3-D simulations. All simulations show positive net thrust for the 3-D nozzle. 0-D and 1-D results match closely. Thepredictions from the 1-D and 3-D codes match pretty well at low void fractions and start to deviate atvoid fractions higher than 20%, 3DynaFS_Vis? predicts higher thrust increase than what 1-D BAP predicts, the difference is due to the fact that 1-D BAP does not fully consider bubble dynamics as 3DynaFS_Vis? does. These effects become stronger as the void frac tion increases.

4. Results

4.1 Effects of air injection on inlet flow

To examine the effects of air injection on the inlet flow condition, the fluctuations of the inlet flow rate with and without air injection were examined systematically with the pump and valve settings being maintainedthe same. Figure 29 shows the inlet flow rate fluctuations (defined as the ratio of the flow rates, (Qmax-Qmin)/Qave, where Qmax, Qmin, andQaveare the measured maximum, minimum, and average flow rates) with and without air injection at different flow conditions, the fluctuations were less than 4% in any test conditions, and air injection did not have any noticeable effects on the inlet flow rate. Therefore, no flow rate adjustment was performed 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.

Fig.29 Air injection had no noticeable effects on inlet flow rate fluctuations. The dimensionless fluctuation is defined as the ratio (Qmax-Qmin)/Qave

4.2Performance of force measurement plate

As expected, the placement of the force measurement plate has noticeable effects on the force measured. Figure 30 shows the force measured by the load cell under different void fractions and inlet flow rate conditions when the force measurement plate was placed at three different standoff distances from the nozzle exit. It is clear from the tests that at the largest tested standoff distance of 5.338 inch, the force measurement plate captures the most of the exit momentum force. Therefore all the force measurement results reported afterward were obtained with the force measurement plate position at that 5.338 inch distance from the nozzle exit.

Fig.30 Load cell force measurement versus void-fractionfor different water flow rates and different stand-offdistances of the measurement plate from the exit

Fig.31 Fraction of the total exit momentum force captured by the force measurement plate at different exit mixture flow rate (with and without air injection)

The efficiency of the force measurement platein capturing the exit momentum force was also examined at different inlet flow rare and air injection conditions. Figure 31 shows the variation of ratio of the force captured by the force measurement plate, F/ρlQlVl, with the exit mixture flow rate, Ql/(1-α), in which,Qlisthe liquid flow rate and Vlis the liquid velo- city at the exit which is assumed to be the same as the mixture velocity. As shown in the figure, the fraction of the exit momentum force decreases when the exit mixture flow rate increases and reaches to a plateau. A fourth order polynomial curve fitting given by the following,

captures the trend pretty well, in which Qmis the exit mixtureflow rate andy is the corresponding capture efficiency of the exit momentumforce of the forcemeasurement plate. When compared with the numerical simulations, the measured thrust force, T*, was corrected by the capture efficiency, y, from the

force directly measured by the load cell as follows

4.3 Effects of air injection on net thrust

From the 0-D BAP theory, the normalized thrust increase can be expressed as follows

Since for the nozzle geometry under consideration,therefore

From the mixture continuity equation, we know that

T herefore,

Extensive experiments were conducted to study the effects of air injection on the nozzle thrust. In addition to the direct force measurements using the load cell, pressure and velocity measurements were also conducted at the nozzle inlet and exit. Figure 32 shows the test matrix of void fraction and inlet liquid flow rate in the experimental study, void fraction ranged from 0 up to 50% and the inlet velocity range from 3.1 m/s (200 GPM) to 9.3 m/s (600 GPM).

Figure 33 shows the variations of the normalized net thrust increase with void fraction, obtained from both numerical simulations and experiments. The numerical and experimental results agree very well with each other and follow the theoretic prediction of α(1-α), which proves that the nozzle become more efficient in net thrust increase with increased void fraction.

The thrust in Fig.33 is the waterjet thrust. In the discussion below, we evaluate the nozzle performance using a ramjet thrust by including the loss from inlet pressure changes. The air injection causes inlet pressure increase, which means that the water jet pump needs to work harder to overcome this additional resistance from the air injection. To examine this effect, the v ariation of the normalized inlet pressure increase with the void fraction is plotted in Fig.34. This figure shows that the normalized inlet pressure increases almost linearly with the void fraction.

Fig.32 Experimental conditions showing the coverage range of air injection and liquid flow rate

Fig.33 Variation of normalized net thrust with void fraction

Fig.34 Normalized pressure increase at inlet versus void fraction

This effect does not however cancel outthe thrust gain observed in Fig.33. As shown in Fig.35, withincreasing void fraction, the normalizedthrust gain, obtained by subtracting the normalized inlet pressure force from the normalized thrust increase, increases. As a result, the net total thrust becomes larger and larger indicating increased thrust gain with higher voidfraction even after factoring in the inlet pressure force increase.

Fig.35 The net thrust increase vs. void fraction, obtainedfrom subtracting the inlet pressure force in Fig.34 from the thrust gain in Fig.33

5. Conclusions

This contribution described experimental and numerical investigations of waterjet nozzle propulsor thrust enhancement thorough bubble injection. Numericalmodeling was based on two-way coupling between a model ofthe mixture flow field and Lagrangian tracking of the injected bubbles. The experimental studies were performed on a laboratory largescale nozzle to validate and compare with the numerical results.

To better study the physics of a real BAP while maintaining good accessibilities for experimental measurements, half 3-D nozzles were built and studied. Numerical studies were used to obtain an optimal nozzle geometry to produce the best net thrust increase. An efficient thrust measured scheme was implemented to directly measure the exit momentum force. Comprehensive experiments were conducted to cover a wide range of air injection condition. Results from numerical simulation and experiment agree very well and proved that a well designed nozzle can obtain net thrust increase with air injection, and the nozzle performance of net thrust increase improves with increase void fraction. Thrust increases as high as～100% were measured with a void fraction of ～50%. Corrections with pump output pressure increases reduce the enhancement to about 70%, still a very significant improvement.

Acknowledgement

This work was supported by the Office of Naval Research under the contract N00014-09-C-0676, monitored by Dr. Kim Ki-Han. We gratefully acknowledge this support.

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[4]WU X., CHOI J.-K. and HSIAO C.-T. et al. Bubble augmented waterjet propulsion: Numerical and experimental studies[C]. 28th Symposium on Naval Hydrodynamics. Pasadena, California, USA, 2010.

[5]SINGH S., CHOI J.-K. and CHAHINE G. L. Optimum configuration of an expanding-contracting-nozzle for thrust enhancement by bubble injection[J]. Journal of Fluids Engineering, 2012, 134(1): 011302.

[6] GANY A., GOFER A. Study of a novel air augmented waterjet boost concept[C]. 11th International Conference on Fast Sea Transportation FAST 2011. Honolulu, Hawaii, USA, 2011.

[7] CHAHINE G. L., HSIAO C.-T. 3DynaFS? a three-dimensional free surface and bubble dynamics code com Version 6.0[M]. Jessup, MD, USA, DYNAFLOW, Inc. User Manual, 2012.

[8] BRENNEN C. Cavitation and bubble dynamics[M]. New York: Oxford University Press, 1995.

[9] VOKURKA K. Comparison of Rayleigh?s, Herring?s, and Gilmore?s models of gas bubbles[J]. Acustica, 1986, 59(3): 214-219.

[10]JOHNSON V. E., HSIEH T. The influence of the trajectories of gas nuclei on cavitation inception[C]. Proceedings Sixth Symposium on Naval Hydrodynamics. Washington D. C., 1966, 163-179.

[11] HSIAO C.-T., JAIN A. and CHAHINE G. L. Effects of gas diffusion on bubble entrainment and dynamics around a propeller[C]. 26th Symposium on Naval Hydrodynamics. Rome, Italy, 2006.

[12] CHOI J.-K., CHAHINE G. L. Modeling of bubble generated noise in tip vortex cavitation inception[J]. Acta Acustica united with Acustica, 2007, 93(4): 555-565.

[13] HSIAO C.-T., CHAHINE G. L. Scaling of tip vortex cavitation inception for a marine propeller[C]. 27th Symposium on Naval Hydrodynamics. Seoul, Korea, 2008.

[14] DESHPANDE S. S., TRUJILLO M. F. and WU X. et al. Computational and experimental characterization of a liquid jet plunging into a quiescent pool at shallow inclination[J]. International Journal of Heat and Fluid Flow, 2012, 34: 1-14.

[15]WU X., CHAHINE G. L. Development of an acoustic instrument for bubble sizing distribution measurement[C]. Proceedings of the 9th International Conference on Hydrodynamics. Shanghai, 2010, 330-336.

[16]CHAHINE G. L., KALUMUCK K. M. and CHENG J.-Y. et al. Validation of bubble distribution measurement s of the ABS Acoustic Bubble Spectrometer? with highspeed video photography[C]. Proceedings Fourth International Symposium on Cavitation CAV2001. Pasadena, CA, USA, 2001.

[17]CHAHINE G. L., WU X. and LU X. Development of an acoustics-based instrument for bubble measurement in liquids[J]. The Journal of the Acoustical Society of America, 2008, 123(5): 3559.

10.1016/S1001-6058(11)60287-4

* Biography: WU Xiongjun (1969-), Male, Ph. D., Senior Research Scientist

CHAHINE Georges L.,

E-mail: glchahine@dynaflow-inc.com