Controversial Issues in Waterjet-Hull Interaction

Deift University of Technology

Ship Hydromechanics Laboratory

Library

Mekelweg 2, 2628 CD Deift The Netherlands Phone: +31 15 2786873 - Fax: +31 15 2781836 CONTROVERSIAL ISSUES IN WATERJET-HULL INTERACTION

Tom van Terwisga _MARIN

The Netherlands

Keith V. Alexander _{Hamilton Jet}

New Zealand ABSTRACT

The paper deals with three issues, being the intake drag of a flush intake, the effect of

interaction in a potential flow and the lift production by the waterjet. Despite several publications

where other opinions have been _{ventilated, it will be shown herethat there is no drag of}

a flush

intake in a non-viscous flow, that _{there is not a potential pressure or velocity effect in the}

powering characteristics due to interaction _{and that there is no net lift production by a waterjet.} The effect on hitherto published efficiency equations will be demonstrated and_{a proper model} accounting for interaction is proposed.

1. _INTRODUCTION

The objective of this work is to contribute in solving misunderstandings in the field of waterjet-hull ìriteraction. Misunderstandings have been observed from publications by several authors on the following issues:

the intake drag of a flush intake,

- _{the contribution of a potential flow disturbance on overall powering characteristics}

the net lìft production by a waterjet system.

These issues are addressed in this paper, using the definitions and powering _{relations that were}

presented by van Terwisga (1993). These relations can be considered _{as an extension of the}

proposed parametric model by the _{ITTC (1987). The extended model breaks interaction}

components down into manageable_{terms, rendering a suitable model for the analysis of above}

issues. The conclusions that are drawn on these issues may lead to changes in design philosophy for intakes and wilt lead to a clearer analysis, and therefore a more reliable

2.1 _{Uterature review}

Many authors refer an intake drag which often makes up for the difference between a particular

definition of gross thrust and some net thrust acting upon the hull1. Although the intake drag is addressed several times, for example by Mossman et al. (1948), Arcand et al. (1968) and Hoshino et al, (1984), little attention is paid to its definition. An _{exception to this rule is the} contribution by Etter et al. (1980).

Mossmari and Randall (1948) determine the intake drag for a number of flush type intakes from

wake survey measurements in a wind tunnel. They implicitly use control volume A for their

definition of gross thrust (CV A in Fig. 1), having the imaginary intake _{area situated infinitely far}

upstream ¡n the free flow. lt can be derived_{however that their definition of intake drag includes} a significant contribution from the tunnel wall in front of the intake.

B

fixed materlal) boundanes

variable (ir1aginary) boundanes n tt* flow

A = intake leading edge ltaginery)

A a ramp tangency point

lec = lower dividing streamline

C - stagnation point

O _{= intake trailing edge or outer i tangency point}

Area f - A1 = intake aree

Area 2 A a dividing atrearn surface Area 4 = A4 Outer lip swfice

Area 6 A6 internal mateiiaj Jet boundary

Area 8 A8 a nozzle discharge area Volume 3 = = pump actutcr volume Sultabti waterjet cctrol volumes: CV k UCFF

CV B: ABC FFA CV C: A5CFF'A

Fig. i _{Definition of jet system's control volume}

4-u,

Gross thrust is associated with the change in momentum flux for a given Control Volume. Net thrust refers to the actu& net force passed through to the hull by the waterjat system.

I,

-- -- -- -- --. --o -- _{-. .. --. .} s, I %t% SI Ii %a%i S,

required to propel the ship, and its bare hull resistance. This intake drag consequently accounts

for a discrepancy between gross and net thrust for the jet system, but also for_{a change in hull} resistance due to the jet action. These authors also implicitly use control volume A (Fig. 1) for the definition of gross thrust, and therefore also include the frictional drag contribution of the hull bounded part of the stream tube.

Confusion about external intake drag and internal jet system forces is illustrated_{by statements} in Okamoto et al, (1993) and Kim_{et al. (1994). Okamoto et al. state that 'the intake duct shows}

a thrust generation mechanism' for certain operational _{conditions. Whereas Kim et ai state that}

'the pressure distribution along the intake lip is responsible for additional _{appendage drag'.} Etter et al. (1980) explicitly define the control volume of the waterjet, which corresponds to volume C (Fig. 1). Unlike many other authors, they emphasize a distinction_{between jet system}

net thrust and hull resistance. Their _{inlet drag is defined as the difference between the jet}

system gross thrust and the bare hull resistance. This inlet system drag consequently also incorporates a change in hull resistance due to the jet action.

2.2 _{Definition of intake draq}

We will define the intake drag as the difference between the defined gross thrust and the net

thrust acting upon the hull. A

_{complete definition of}

_{gross thrust should include the}

corresponding control volume. We will define the control volume representing the hydrodynamic

jet model as volume B (Fig. 1), approximately corresponding to the volume considered by Eiter et al. (1980). Because this definition of intake drag does not refer to the bare hull resistance, it does not include a change in hull resistance due to the waterjet action.

The intake area AB is situated perpendicular to the local hull plane at some distance ¡n front of ramp tangency point A'. This distance is arbitrarily chosen to be 10% of the physical intake length A'D. This forward position is favoured over A'B' to avoid major flow _{distortions in the} intake area that might be caused by the intake geometry. In using intake area AB, computed or measured average intake velocities become more reliable.

The gross thrust is now defined as the x-component of _{the force pertinent to the change in} momentum flux over the control volume. lt can be written as2 (see _{also van Terwisga (1993)):}

2

'gJ

J

xJJJPpxav+JJJPxdv

₍₁₎

A1A2+A6#A8 _V

The first term on the right hand _{side of equation (1) represents the forces acting}

on the surfaces 1, 2, 6 and 8 (Fig. 1). The second term represents the force exerted on the fluid by the pump, whereas the third term represents the x-component of the entrained water weight.

As a number of forces act _{on the imaginary surfaces in the flow (area 1,2 and 8), and not}

directly on the material boundary_{of the jet, we can distinguish a net thrust, defined by the force} that is transduced by the material boundaries of the jet system to the hull. This thrust _can subsequently be written as:

Tnetf

_f

xdA+ffFpxdV ₍₂₎

A4 A8 V3

The intake drag D s now obtained from the difference of gross arid net thrust, and can

consequently be written as:

D=I I cydA-IIadA

ç

IJJ

X

jjX

A1+A2 A4 ev &______-....- _,plI4

The change of sign in the contribution _{of area 4 has been accounted}

for, so that all force

contributions are acting upon the combined control volume representing hull and wate rjet. lt

should further be noted that the pressure contribution over the nozzle area A8 and the

contribution to the thrust due to the weight of the entrained water in the jet system (last term

in gross thrust) will be left _{out of consideration here. These terms could appropriately be}

accounted for in a more general thrust _{deduction term.}

2.3 Potential flow consideration

For a better understanding of the concept of intake drag, we will first consider this drag

component for the waterjet operating ¡n free stream conditions. To this end we will consider the

intake drag on control volume A (Fig. 1), where the imaginary intake area ¡s situated infinitely

far upstream. Let us furthermore separate the flow field into a uniform flow field and _a

perturbation field, due to the waterjet action. This latter flow field changes the pressure over the boundaries A2 and A4. lt can easily be seen that only this perturbation pressure may contribute

to a net contribution to the intake drag, as the free stream pressure contribution is cancelled after integration over the entire _{boundary surface (A1+A2+A4). By applying Lagally's}

theorem,

Fig. 2 Geometry of test _{set-up and wake survey plane}

A _I

C

This is an important conclusion, as ¡t implies that the gross thrust for control _{volume A} (designated here as T9j equals the _{net thrust in free stream conditions:}

Tgc,ørjlnet (4)

where subscript O indicates free _{stream conditions.}

While it has been shown that the intake drag for control volume A is zero, it is to be noted that the intake drag for the control volumes B and C is in most cases not equal to zero. This is

caused by the fact that the flow through the intake area AB is already affected by the jet geometry and therefore deviates from the free stream. The intake drag for these control

volumes can be obtained from a relation for the thrust deduction fraction to, as given in van Terwisga (1993).

2.4 Viscous flow consideration

As a second step, let us consider the isolated waterjet operating in a viscous flow. This

condition is less accessible to simple argumentations. To get a proper idea of the viscous intake

drag, a wake survey analysis in an experimental test set-up was considered to be one of the most accurate methods.

Such a test has been conducted in the MARIN large cavitation tunnel, where_{a jet system was} mounted to the wall of the tunnel. The geometry of the test set-up and the plane used for the wake survey (designated VT3) is given in Fig. 2.

velocity ratio in the intake throat lVR., the ratio of ingested flow rate to flow rate ingested from the boundary layer '0bL and Reynolds number of the intake throat Rn1. The test conditions are

specified in Fig. 4. 0.6 0.4 0.2 o o JH cv i for IVRt=0.62 for IVRt=0.94 4 X A CV A - u0

Fig. 3 Control volumes used for derivation of intake drag and lift

Fig. 4 Momentum thickness distribution in plane VT3

Two operational conditions have been tested, representative for modem jet system operations,

viz. lVR values of 0.62 and 0.94. The first value is representative for design speeds, the

second value is representative for heavier jet loading conditions, such as for example may

occur in the hump speed region.

= 2 Rn1 51O lì, 4 IVR=0.62 - ¡VR= 0.94 eo -0.2 -0.4 -0.6

Di193

Di33

-0.8 o 0.5

y / half width intake _[-J

and ingested momentum flux:

pQU0

From a consideration of control volume CV1 of Fig. 3, the following relation can be found in which the intake drag coefficient is related to the displacement thickness _62.

.1 2 2

CDÍ=AIVR J (5-ö)dy

o

where _{= intake throat area (EE' in Fig. 1)}

= -'pacme thickness with active intake

mounted

=

_{pti.urLthickness without intake}

_mounted.

w = width of the wake survey plane.

(6)

lt should be noted that the original_{displacement thickness 62' is set zero over the width of the} intake, as the corresponding part of the stream tube is situated outside of the boundary layer. The difference in displacement _{thickness (62-62') is presented as a function of the transverse} y-coordinate in Fig. 4, which also lists the drag coefficients. It can be concluded from these values and the scatter in displacement thickness, that the intake drag is effectively zero. 3. _{WATERJET-HULL INTERACTION IN POTENTiAL FLOW}

In the relations for both thrust and power delivered by a waterjet system, we find _pressure contributions acting on the protruding _{part of the intake area (Fig 1). It is at first look not} immediately clear whether these pressure contributions have a net effect on thrust and power and thus on efficiency. This section will show that there is again no net effect of the potential flow pressure ccntributon,_{provided the longitudinal}

pressure gradient due to the hull and free

surface, over the intake AD is _{negligibly small, and provided}

the vertical position of the

discharged jet remains at the _{undisturbed water level.}

3.1 _{Literature review}

Although the effects of pressure distortions on jet performance _{are acknowledged in an early} stage (see Kruppa et al. (1 968)), _{much confusion arises}

as to how it should be accounted for in a parametric model, as noticed by Kruppa (1992).

occurs between the undisturbed free_{stream and the intake area of the wate rjet, the introduced}

momentum and energy wake fractions should be corrected for pressure terms. Where a

correction for the energy wake readily follows from Bernoulli's theorem, this ¡s flot so evident

for the momentum wake fraction. The correction for the momentum wake fraction is not

elaborated further in the quoted _{paper however,}

Svensson (1989) includes _{a pressure term in the jet efficiency, accounting for the static} pressure contribution in ingested energy flux. He does however not treat a similar contribution

in the relation for thrust. Static pressure contributions to ingested momentum and energy fluxes

were exphcitly mentioned by Masilge (1991) and van Terwisga (1991).

As a sequel to their 1968 paper, Kruppa (1992) presents a relation for_{overall efficiency based} ori thrust (thrust power efficiency), in which he _{incorporates the potenVal flow and viscous flow} interaction effects separately. He _{notes the lack of a pressure term in}

the momentum equation for thrust and consequently _{observes that the equations for thrust power efficiency for ram type} inlets on the one hands and flush type inlets on the other hand are not compatible. Based on this observation, Kruppa queries a conclusion by Svensson (1989), where the positive effect of a retarded potential flow wake on thrust power efficiency is noted.

Another relation for the jet efficiency_{¡s presented by Dyne et aI. (1994).}

These authors do not explicitly use a potential flow_{pressure contribution, but implicitly do, through the use of a wake} fraction including potential flow effects.

3.2 _{Study of efficiency relations}

In his search for _{a better physical understanding of waterjet-hull interaction, Jon Hamiltcn}

(1994) put the following thought _{experiment forward. 'Imagine}

an infinitesimal waterjetnear the

stagnation point of the hull. How will this affect the interaction efficiency?'.

This limiting case is consìdered a good test case for the aforementioned _{parametric models} governing the overall efficiency. To keep_{the comparison as pure as possible, we wilt consider} the et-hull operating in a potential flow. As a consequence, the ducting losses are zero. It is furthermore assumed that the _{pump efficiency equals unity, that the nozzle centreline remains} at the free stream water surface and that the resistance increment of the hull equals _zero. The overall efficiency 10A by Svensson (1989) now reduces to the following relation:

IGypI.L)

i

where t _{= hull speed / nozzle velocity ratio; U0/u}

= potential flow velocity coefficient u/U0

The wake fraction w, used by

_{many authors, relates for a potential flow to the velocity}

coefficient c in the following way:

CVp=t W ₍₈₎

A relation between the pressure coefficient _{used by Svensson and the velocitycoefficient} can be found using Bernoulli's theorem:

cp=1-.cjp

Similarly, the relation for overall _{efficiency TIOA by Dyne (1994) reduces to:}

'lOA

+cvplt

2p.

From the breakdown of the overall efficiency as proposed by van Terwisga (1993), the following terms remain:

lei

l0AflI

11ml where:

(2

_1+NVR (12)

NVR =

_{nozzle velqcity ratio u/LJ0 or 1/p.}

lei

= _{energy interaction efticiency}

HjsdHjs This efficiency equals i in a potential flow

provided the nozzle centretine coincides with the free water surface

H5

= _{total head over complete jet system}

subscript O indicates free stream conditions

and

(7)

i

CrnCvp

imi

NVR1

(13)

-

----.- ---'

netu' net

Cm = _{momentum velocity coefficient due to boundary layer velocity distribution}

1VR10 = _{intake velocity ratio in free stream conditions; u1gU0}

Because we consider a potential flow, the momentum velocity coefficient 0m equals unity. A representative value for lVR0 pertinent to control volume B of 1.03 has been used.

The results of the above efficiency relations are plotted in Fig. 5 for a range of jet operating

conditions (expressed in NVR value) and _{a strong flow retardation (c=O.1). ltcan be seen that}

all of the above efficiency relations predict values for the overall efficiency in excess of 1.0,

which is unrealistic. This would imply that we had found an original realization of the perpetuum mobile. We will therefore consider the momentum interaction efficiency

TmI in some more detail,

as this is the responsible source for the excessive_efficiency.

o

Cvp=O.1, wQ.9

nozzle elevation, intake, pump and nozzle losses equal zero

Fig. 5 Computed overall efficiencies for an infinitesimal watorjet near the stagnation point

3.3 _{Consideration of interaction on momentum balance}

By definition, the momentum interaction efficiency relates the net thrust in free stream

conditions to that in operational conditions. Operational conditions refer here to the _situation where the waterjet system is mounted _{in the vessel,}

Because the net thrust Tnet cannot be directly obtained from flow rate_{considerations, as in the}

case of the gross thrust T9, it could be obtained from:

* Svenason [1989) * Dyne [19943 * Terwlsga [1993] e- modifiedmodel 0.5 _{15 2 2.5 3} 35 NVR [-]

and

'net'g'

'ji

where t = jet system's thrust deduction _fraction

As a consequence, the momentum interaction efficiency can be written as:

1lmlmlmI

with T_gO TI

mI-'g

(l-t)

TI - (1 -t1)

subscript O indicates free stream _conditions,

The above parametric relation for_{the momentum interaction efficiency (eq. (13)) could be found}

with the assumption that the jet _{system's thrust deduction fraction t would primarily be} a function of the operational condition_{of the jet system, and only to a negligible extent by the flow} about the hull. This assumption_{appeared to be wrong however. lt will be shown in the following}

that, in a potential flow, the

_{net thrust in free stream conditions equals the net thrust in}

operational conditions, for the _{same flow rate. As a result, the}

momentum interaction efficiency equals unity in a potential flow. This result is also incorporated _{in Fig. 5 where it is referred to} as 'modified model'.

We will now concentrate on a relation for the thrust deduction _{fraction Ç in operational}

conditions. To this end., let us first consider a two dimensional _{double model (mirrored about} the free surface) of _{a waterjet-hull system in a potential flow (Fig. 6). This}

condition leaves free

surface effects out of _{consideration. Depending on the hull shape, the jet}

system may be operating in an accelerated or a decelerated flow,

B

Ftow about isoated body

+

4-

_u0

4 X

Fig. 6 Flow field decomposition for a waterjet-hull configuration

From its definition, the following expression for the thrust deduction fraction t can be derived (see also van Terwisga (1993)):

I,

t

4 u0

/

J________ A (18)

If the integral term over the streamline ASt in the right hand side of this equation would be

where FXABCD _{= external force acting in x-direction on protruding part of intake (see Fig. 6)}

An expression for FXABCD can be obtained from a consideration ofthe force Th x-direction acting

upon the streamline f'BCDJ and a momentum consideration on the control volume ll'BASI forward of the imaginary intake _{area AB.}

The force FBcD, acting _{on the control volume, can subsequently be written as:}

FBCD=-PQ(U -U0) +fpn ds

(19)

where p _{= mass density of fluid}

Q = flow rate through jet system

u1 _{= mean ingested momentum velocity in intake area AB} U0 = free stream velocity

'V z

Walerjet n free stream

Th\,

P.

the character of this integral term, we decompose the total flow field into a free stream field for the jet system mounted on a flat plate, and the flow field about the hull_{without jet (see Fig. 6).} The total pressure p Is now linearized as the sum of the _{pressure p0, occurring when the half} body is positioned in the free stream, and a perturbation pressure p', caused by the intake

action

p=pc,.p/ (20)

The integral term over ASt can now be written as:

JSA ds =JsAponxds _JSA

'n ds

(21)

With Lagally's theorem, it can again be shown that the first integral term on the right hand side of this equation equals zero if the body contour part AJ ¡s oriented parallel to the x-coordinate. This condition is usually fulfilled for hull forms fitted with wateilets.

The second integral term on the right hand side, or perturbation term due to the jet action, can be neglected whenever either the perturbation pressure p' is negligibly small, _{or whenever the} normal in x-direction is negligibly _{small in the area where p'}

cannot be neglected. The first condition is a condition imposed on the flow induced by the intake, and ¡s an argument _to position the imaginary intake_{area AB slightly ahead of the ramp tangency point A'. The second} condition imposes a geometrical constraint on the body containing the jet.

With the neglect of the pressure integral over ASI, we have obtained a simple expression _in terms of _{U0 and NVR for the thrust}

deduction fraction t in operational conditions without free surface effects:

i -IVR

t=

NVR-lVR

A similar relation was found for the thrust deduction _{fraction in free stream conditions t}

(van Terwisga (1993)).

We will now add free surface effects while considering the flow in the _{protruding part of the.} stream tube configuring the jet _{system with intake AB. Free}

surface effects_{may be interpreted}

as a change in the relation _{between the velocity field}

and the static pressure, due to the

variable contribution of the watet column above the point considered (Bernoulli). _{However, as} the pressure integral over part ABCD is not affected by a uniform change _{in static pressure,} such free surface effects do not affect the thrust deduction t.. Only if_{a pressure gradient over} (22)

Substituting eq. (22) in eq. (17) learns that the contributions of r' _{and T1"ml counteract each} other, leading to a momentum interaction efficiency equalling unity in a potential flow.

3.4 _{Implications for net-qross thrust relaton}

The interpretation of the above discussion is that, as long as the pressure integral over ASI is negligible, the net thrust in operational conditions equals the net thrust of the jet system in free stream conditions for equal NVR value. The integral temi is either negligible for an imaginary intake of the jet that is sufficiently far upstream of the ramp tangency point, or for a hull form ¡n front of the intake area AB with a negligible component of the normal in thrust (x) direction. In case this integral temi is not negligible, part of the hull's resistance is found back in thejet

system's thrust or vice versa. This will lead to mutual changes in the values of the momentum interaction efficiency and the hull's _{resistance increment.}

The implication for the computation of not thrust in a potential flow is, _{that the net thrust equals}

the gross thrust pertinent to control volume A (Fig. 1):

Tnet 'Tgo (23)

For a viscous flow, the ingested _{momentum should be corrected for}

a momentum deficit ¡n the

intake area AB, due to the viscous stresses acting on the hull bounded part of stream tube ll'BAI. The net thrust in a viscous flow can consequently be obtained_from:

TnetpQUo(NVRCm) (24)

The proper parametric relation for the momentum interaction efficiency now reads:

i

lC

NVR-1 (25)

This im proved relation for the momentum interaction efficiency3, which may be contrasted with the original one given in eq. (13), causes the overall efficiency_{to adopt realistic values, smaller}

or equal than unity. The effect of the _{above conclusion on the interaction efficiency for} a representative flow retardation

_{(c=O.95) is shown in Fig. 7 for the}

efficiency equations

discussed before. The above improved relation for interaction efficiency is designated 'modified

model' in the Figure.

When using the relations for interaction efficiency as given in van Terwisga (1993), care should be takenthat the improved relation for Tj _{Is taken, as presented here.}

1.2

1.15

1.05

0.95

Cvp = 095, w = 0.05

nozzle alavation, Intake, pump arid nozzie_{Iose equal zero}

Sverisson [1989] -. Dyne [1994]

- Terwisga [1993] modified modal

Fig. 7 Computed interaction efficiencies for a waterjet in a retarded potential flow Although not explicitly given _{in the efficiency relations ofother authors, the interaction}

efficiency

mnt could be computed from the following relation:

TlINT

fl OA

(26)

Realizing that representative

NVR values range from approx. 1 .5 to 3, errors in interaction (and

thus in overall efficiency) _{occur from 1 .5 to 2.5% (Dyne (1994)) to 2.5 to 10% (Svensson (1989)} and van Terwisga (1993)).

4. _{WATERJET LIFT PRODUCTION}

A net lifting force on the stern of the vessel with _{an active waterjet has been suggested by}

Svensson (1989). This conclusion was obtained from pressure measurements _{in the intake and}

on the hull in the vicinity of the _{intake. According to}

Svensson, this lifting force, generated by the inlets, can be in excess of 5% of the displacement of a high speed craft.

This section aims to explain that there is no net lift contribution from the _{pressure field about} the intakes, as long as the bottom plating about the intake is sufficiently_wide.

To study the net lift production of a waterjet unit, we wilt mount the unit _{on an infinitely large}

horizontal plate and let it operate in a potential flow. A potential flow_{assures a proper modelling} of the flow, provided the boundary layer about the real hull ¡s thin. This is_{a realistic assumption}

for most hull forms fitted_{with waterjets. Because}

we focus on the induced lift_{production by the} intake, we consider the jet to be discharged horizontally.

I

-u

05 15 2 25 3 35

3.0 0.04 o C 0.02 V o + -002 L) -0.04 s -0.06 o ₂ width plane width intake

Aftward distance from intake trailing edge / intake length - 4.3

3

H

Fig. 8 Waterjet induced lift force as a function of plane area behind intake

4

*' IV0.94

thrust vector), we consider the momentum balance for the control volumes indicated in Fig. _3. Because there is no change in the vertical momentum flux for Control Volume A, the sum of

the vertical forces acting upon this volume equals zero:

F2 1t-F2 _{i ic'O} (27)

where subscript mt indicates a direct force on the jet plate system.

A similar momentum balance can be worked out for Control Volume 1, In contrast to Control Volume A, there is exchange of vertical momentum through the lower boundary l'J°, caused by the flow rate Q that is ingested by the intake. The momentum balance subsequently reads:

F2_{CDJ +} F2 _{= 4mz i "J" (28)}

Figure 3 indicates that a flow rate through boundary l"J' occurs with a magnitude equal to the flow rate Q through the jet system. This flow rate causes a velocity component u2 through the boundary 'J', which in turn causesa momentum flux

mz lt can be demonstrated however1

that this vertical momentum flux becomes negligibly small for the situation where the boundary

l"J" is sufficiently wide, relative to the intake throat _{area (EE' in Fig. 1). This implies that the net}

vertical force ori jet system and plating is effectively equal to zero.

Deviations from this zero vertical force can occur for finite dimensions of the mounting plate of the waterjet. This is demonstrated in Figure 8. The presented net lift force has been obtained

from integration of potential flow pressures obtained from computations with the MARIN

There is no intake drag for

_{a flush type intake operating in a potential flow. From the} experimental results of a flush type intake in representative operating conditions, it appears that

the intake drag in a viscous flow _{is negligibly small.}

There ¡s no interaction effect of the _{potential flow distortion by the hull on the jet performance,}

unless a longitudinal _{pressure gradient due to the hull, over the intake area AD exists (Fig. 1).}

A suitable control volume for the computation of the gross and net thrust is control volume A

(Fig. 1). This volume has its intake _{situated well ahead of the intake in the free stream. A}

correction on the gross thrust is necessary to account for the viscous stresses exerted by the hull on part of the stream tube.

There is no net contribution of the intake induced flow on the total lift force on jet-hull system, provided the area around the flush intake opening s sufficiently large. _{If the area aft of the} intake opening is sufficiently reduced, a net lift force occurs, its orientation depending on the operating condition of the intake.

ACKNOWLEDGEMENT

The work that is presented here could only be accomplished through numerous discussions, both with people from the HAMILTON Jet and the MARIN staff. The authors are much obliged for the contributions of these people

REFERENCES

Arcand, L. and C.R. ComoDi; 'Waterjet propulsion for high speed ships', Proceedings of the

AIAA'SNAME Advance Marine Vehicles Meeting, paper No. 67-350, Norfolk, Virginia Dyne, G. and P. Lindell; 'Waterjet testing in the SSPA towing tank', International _symposium

on Waterjet Propulsion - Latest Developments, Dec. 1-2 1994, London

Etter, R.J., Krishnamoorthy, V. and Scherer, J.O.; 'Model testing of waterjet propelled_craft', Proceedings of the 19th ATTC, 1980

Hamilton, J.O.F.; verbal communications, June 1994

Hoshino, T. and Baba, E.; 'Self _{propulsion test of a semi-displacement craft model with a}

waterjet propulsor', Journal of the Society of Naval Architects of Japan, Vol 155, _June

. _{... II} I 1Ç41 I TTU I II".

Conference 1987, pp 304-313, ca

Kim, K.S., S.Y. Hong and H.S. Choi; 'Analysis of the wateret-propeUed ship flow by a higher

order boundary &ement method, NAV 94, tnt. Conference on Ship and Manne research, Rome, 1994

Kruppa, C.; 'Aspects of High-Speed Propulsion', Proceedings of International _{Symposium on} Propulsors and Cavitation, STG - Nr. 3007, Hamburg, June 22-25 1992

Kruppa, _{C., Brandt, H. and Östergaard, C.;}

'Wasserstrahlantriebe

fur

Hochgeschwindigkeitsfahrzeuge', Jahrbuch der STG 62, Band 1968, Nov., pp 228-258

Masilge, C.;

_{'Konzeption und Analyse eines}

_{integrierten Strahiantriebes}

mit einem

rotationssymmetrischen G renzschichteinlauf', thesis, Berlin 1991

Mossman, E.A. and Randall, L.M.; 'An experimental investigation of the design variables for NACA RM No. A7130, Jan. 1948

Okamoto, Y., H. Sugioka and Y. Kitamura; 'On the pressure distribution of a wateqet intake duct in self propulsion conditions', FAST'93 Conference, Yokohama, Dec. 1993

Svensson, R.; 'Experience with the KaMeWa Waterjet Propulsion system',_{AIM Conference,} Paper No. 89-1440-CP, Arlington, June 1989.

Terwisga, T. van; 'The effect of _{waterjet-hull interaction on thrust and propulsive efficiency',} Proceedings of the FAST'91 Conference, Vol. 2, Trondheim, June 1991

Terwisga, T. van; 'A theoretical model for the powering characteristics of waterjet-hull systems',

FAST'93 Conference, Yokohama, Dec. 1993

8. _{LIST OF SYMBOLS}

A1 intake throat area

0D intake drag coefficient: CD = D1/pQU0

c _{momentum velocity coefficient due to boundary layer velocity distribution}

c, _{potential flow velocity coefficient; c=U/U0} D _{intake drag}

F _{pressure force per unit mass}

g1 _{gravity acceleration component in i-direction}

s waterjet system head

JVR1 _{Intake Velocity Ratìo in imaginary intake}

area; IVR1=u./U0

n1 _{unit normal vector component in i-direction}

PD delivered power to pump impeller

E effective power; PE=RBHVS

p _{static pressure (time averaged)}

Q flow rate

maximum flow rate that can be obtained from the boundary layer r _{resistance increment fraction;}

r=l-Tflet/RBR

T9 _{gross thrust, equal to the change in momentum flux through a given control}

volume

Tnet net thrust, passed through to the hull

t _{jet system thrust deduction fraction;}

_{t=1 -T/T9}

U0 _{free stream velocity in x-direction}

u _{mean intake velocity}

u _{mean nozzle velocity}

w

_{water fraction (1-c)}

r

_{energy interaction efficiency; Hs0/H5}

ideal jet system efficiency; _{11TgoU O'JSE0}

ThNT interaction efficiency;

_{=S((' +r)lm:)}

momentum interaction efficiency;

m1=Tfl1Tfl9t

OA overall efficiency;

_1oA=E'D

p specific mass of fluid

component of total mean stress in _i-direction

subscripts:

i _intake

ij,k

_{tensor indices denoting the ordinate (xy,z)}

n _nozzle

O free stream conditions

intake area situated infinitely far upstream