Predicted performance of large water ramjets

ARCHtEF

AIAA Paper

No. 69406

PREDICTED PERFORMANCE OF LARGE WATER RAMJETS

by

JAN H. WITTE

Hydronautics, Inc.

Laurel, Marylaid

/

Lab.

_{v Scheepsbouwkunde}

Iechniche H09

escho

AIAA

2nd Advanced

_{Marine Vehicles}

and Propulsion

_Meeting

SEATTLE, WASHINGTON/MAY 21-23, 1969

I9rs* publication rights reserved by American Institute of Aeronautics and_{Astronautics. 1290 Avenue of the Americas. New York, N. Y. 10019.} Abstracts may be published without permission if credit is given to author and to AIAA. (Price AIAA Member $1.00. Nonmember $1.50)

--NOTES--Abstract

The water ramjet is a low weight con-tender for propelling the high speed Sur-face Effect Ships of the future. This

propulsor which has no moving parts in

contact with the water phase consists of a

simple contoured duct. Compressed air is injected at a high pressure region in the duct, generating a two phase flow. The

ex-panding gas phase accelerates the flow

through a nozzle, thus producing forward thrust. _{The flow is described using the}

Euler and Rayleigh equations, the equation

of movement of the bubbles relative to the water phase and the first law of thermo-dynamics. These equations are used in a computer program for predicting thrust and propulsive efficiency. The effects of scale, forward speed, compression cycle and nozzle length on propulsive efficiency is discussed and tabulated. The basic data and nozzle shape of a water ramjet which generates 0 tons thrust at

80

knots are given and a conceptual design is

dis-cussed. _{Propulsive efficiency is of the}

order of

50-6.

Nomenclature List of Symbols with Dimensions

specific mass, kg/rn3 water velocity, rn/sec gas velocity, rn/sec sectional area, m2 static pressure, N/rn2 force, N force, N temperature, °K bubble radius, rn o gas constant, J/ K kg kinematic viscosity, n'sec water velocity grad1ert, 1/sec heat loss factor, W/rn2 °K time, sec

specific heat at constant pressure, J/°K kg

idem at constant volume, J/°K kg

power, N rn/sec

axial distance, m

bubble production rate, 1/sec tensile strength, N/rn2

List of Symbols Without Dimensions area ratio

local gas concentration mass flow ratio

Poisson constant

Reynolds number for bubble movement

p u

V

S p T t T R R g q y t c p c V N X n a (p a k Re

PREDICTED PERFORMANCE 0F LARGE WATER RAMJETS Jan H. Witte

Senior Research Scientist HYDRONAUTICS, Incorporated

Laurel, Maryland

1

Re Reynolds number for plate Nu Nusselt number

Pr Prandtl number

Cf plate friction factor

compressor efficiency factor diffusor efficiency factor List of Indices

ambient condition

condition at diffusor outlet condition at nozzle entry water

gas

material derivative local derivative acting on intake

acting on nozzle ) combined with T

acting on diffusor

)combined with t acting on air ducting

adiabatic isothermal with friction machinery material Introduction a di o w g D 1 2 i 2 ad is f ma

The development of the high speed captured air bubble (CAB) vessel in the near future, see References i and 2,ieads to the question how these craft will be propelled. The principle contenders in this field are the Supercavitating Propel-ler and the Pump Driven Water Jet. There is no doubt that both propulsors will _offer a reasonable propulsive efficiency and it is thought that using these propulsors the ratio machinery weight to the total weight of the vessel can be kept within accepta-ble limits for speeds up to

₈₀

_knots. Nev-ertheless, increasing the speed of a cer-tain craft will inevitably result in heavier machinery and can become critical for this reason alone.

G. F. Wisiicenus showed, Reference

_3,

that by using simple similarity consider-ations, the following expression for the ratio machinery weight to total ship weight may be derived, see list of symbols:

W /W_m constant X

(p

_ma/a ) x (u 2

ma a

The expression is valid for surface effect ships at speeds much higher than hump speed. The formula shows that the weight ratio of the force producing and transmitting machinery increases roughly with the square of the speed. This

illustrates the criticalness of machinery weight with respect to speed. The

numeri-cal value of the constant depends on the type of propulsion system under consider-ation, Supercavitating Propeller System, Pumpjet System, etc. From the equation it follows that if we want to diminish ma-chinery weight for very high speed opera-tion, lighter and tougher materials must

be developed, thus diminishing ma"ma

This subject lies outside the scope of this paper. Secondly, we can try to lower the numerical value of the constant by troducing a propulsion system which is in-herently lighter than the conventional systems. Developments in the aerospace field, where weight is of prime importance, may offer practical solutions. An example

of this philosophy is the water ramjet which is the subject of the present paper. It will be shown that the water ramjet com-bines low weight with excellent high speed

capabilities.

The principle of underwater ramjet pro-pulsion is not generally known. Briefly

this high speed propulsor consists of three parts (see Figure 1). The first

3

Predffusion Diffusion Mixng Air-Water Wake Chamberi Exhaust Nozzle FIGURE 1 - PRINCIPLE SKETCH OF RAMJET

tart is the ram intake which serves to in-crease the static pressure in the water stream entering the propulsor. The static pressure is increased by diffusing the stream internally or externally (pre-diffusion). After leaving the intake sec-tion the water enters the mixing chamber where compressed gas is injected into the water stream. If the speed in the mixing chamber is high enough, turbulence alone is sufficient to generate a mixture of water and finely dispersed gas bubbles, thus decreasing the average density of the working fluid. The mixing chamber is con-nected to the two phase exhaust nozzle where the gas bubbles, which are created during the mixing process, expand to am-bient pressure thereby doing work on the water phase and increasing the mixture velocity. If the ramjet duct has a suit-able shape, the exhaust velocity is higher than the inflow velocity, which results in a forward thrust. Usually this thrust con-sists of the sum of a positive force in-crement acting on the forward part of the

2

j,,'.

Do

30

°o0og

THRUST

000

000

00

FIGURE 2 - RAMJET AT ZERO SPEED

Up until now authors in References ,

5, 6, 7

and 8 have predicted the ramet

thrust and efficiency based on a one di-mensional, isothermal, homogeneous mix-ture theory in the exhaust nozzle. This theory neglects (1) the motion of the air bubbles relative to the water phase; (2) the difference between the gas pressure in the bubbles and the surrounding water phase, which results in oscillating motions of the bubbles in the exhaust nozzle; and

(3)

the fact that the bubbles may be in-jected at a temperature much higher than the water temperature.

In the present theory, which is kept one dimensional, the above described

ef-fects are taken into account. Introduc-tion of suitable factors for diffusor and compressor efficiencies make a detailed prediction of the capabilities of the water ramjet possible. We will first treat the flow in the diffusor, mixing chamber and two phase nozzle separately. The Force Acting on the Outer and Inner Intake Shroud

Kichemann and Weber, Reference _9, have computed the forward force acting on the intake and diffusor of a slender na-celle moving through an ideal fluid. This force, which can be derived from simple momentum considerations, amounts to:

ramjet pod and a negative increment acting

on the inner and outer walls of the

noz-zle. This propulsor has the following merits:

- No rotating machinery in contact with

the water phase; no gearboxes.

- Suitable for very high underwater speeds. - For gas production high RPM, low weight

gas turbine-compressor combinations can be

used. The propulsor itself, which con-sists of a simple contoured duct, also com-bines strong construction with low weight. - Contrary to the popular belief, this

underwater jet engine is self starting. At zero forward speed supersonic air jets can be directed to the rear of the two phase nozzle, entraining the water flow and

pro-ducing thrust (ejector principle). See Figure 2.

Entrained Water

Flow Supersonic Airjets

t1 = PU2S ((mdl - l)2/cpdi) (i)

where

mdl = Sdi/Sa = Ua/Udi (2)

mdl gives the overall velocity ratio be-tween a station far ahead of the propulsor and the diffusor exit. The change of

ve-locity can be produced by decelerating the water flow outside the inlet (pre-diffu-sion) and/or diffusing the flow internally

With the aid of Bernoulli!s theorem we

compute the static pressure in the water flow after leaving the intake:

di = a + ÇJ u

2)

-

(p U

2/sp

2)

₍₃₎

wa

wa

di

The Constant Pressure Mixing Process

For the condition of the gas and the

water phase before mixing and the condi-tion of the gas bubbles after mixing, see. Figures 3 and 24 Isobaric mixing is

as-sumed. It is also assumed that the bub-bles created in the mixing process are big

enough (>l04m) so that the neglection of

the excess pressure in the bubbles due to surface tension is justified.

Pa

o _di

V o

FIGURE 3 - MIXING PROCESS

TO p _{T0,?0 = Pg0}

----2R0 vo

FIGURE 4 - BUBBLE CONDITIONS AFTER MIXING

We then have:

Po = _{go = di} with _di according to

(3)

We also have:

U0 = Ud

U/mdl

(k)

Gas is injected at velocity V0.

The local gas concentration a0 can be derived as follows: 3

aS V p

_{o o o go} M

=t-

_w

_(l-a)SUp

0

00W

where for p we note using the ideal gas go

law:

go = Pdi/RgTo With

(k)

this results in:

(U/CP1V0) wRgTo/'Pdi') a =

(5)

0 1 + i(ua/mdjVo)(pwRgTo/Pdi) where di is given by (3).

The required duct area for isobaric

mixing, S, can be easily computed using

the continuity equation of the water phase:

UdipS

_wdi

=U(l-a)pS

o o

wo

Combined with

(k)

the result is:

S

=cp1S/L -a

o

where a is given by (5).

o

a can also be expressed as:

o

a

=±TnR/\TS

o 3

00

00

For the number of gas bubbles enter-ing the exhaust nozzle we compute:

n0 = 3wUaSaRgTo'l

di R

(8)

where

di is given by (3).

The temperature of the air which is

injected, T, may be an independent given

quantity or may be derived when it is as-sumed that the gas is compressed adia-batically: k-1 T di k (p ) a T

(9)

\ a,

where is given in (3), and k = c/c. When the gas is compressed isotherm-ally we have:

T =T

(io)

o a

The positive force acting on the air duct amounts to:

= di - - dl (11)

Substitution of

(6)

and

₍₃₎

in (11) yields: a

t2 = .P u 2s (c

-(-)

(12)

Addition of t1 and t2 given in (i) and (12) results in the positive thrust on the ramjet nacelle:

T

-

p 112S

_{wa a}

S R0 vo U0 To po go P go 00 10 So X X P = Po

FIGURE 5 - DEFINITION SKETCH FOR NOZZLE FLOW

k

T0 pp

FIGURE 6- DEFINITION SKETCH FOR BUBBLE CONDITIONS

The local gas concentration in a noz-zle section is defined as follows:

a =(k/3)irnR3/VS (1k)

and the entry condition is:

a

= (k/)irnR3/VS

The continuity équation of the liquid

flow in the nozzle is given by:

(1-a) US = (l-a) US

(15)

The saine equation for he gas flow yields: ap VS = a p V S (16)

g

og000

The gas mass in each bubble is also

constant from which it follows:

3 3

Rp =R

p

g o go

The gas law for a perfect gas is given by:

p =pRT

_g

_gg

The first law of thermodynamics

ap-plied on one bubble, where D denotes the

material derivative, may be written as:

_y(T-T)k7R2Dt = cD(- TR3pgT)+ PgD(

(19)

wherein the heat loss factor, y i an

em-pirical function of the Reynolds number based on the relative bubble movement and the Prandtl number of the water phase. For y we use the empirical expression of the heat loss of a sphere in a cross flow:

Nu =

1.3

Pr°'5

+ 0.66

Re°5 Pr°31 (20)

which is valid in the range of relevant

Reynolds numbers based on the bubble

move-ment relative to the liquid phase: 1 < Re

< 10000. Now:

Nu = 2yR,A where X =

0.59

W/m c

Re = 2RIV-Ul/v where y

= l0m2/sec.

w w

The Prandtl number for water is given by

Pr

= 7.7.

+ (mdi -

__

(13)

with a according to (5).

The Flow in the Two Phase chaust Nozzle Compared with the theories expounded in References

6,

7 and

8,

the present

theory shows the following similarities: Quasi one-dimensional flow in the nozzle. This means that changes in the flow proper-ties perpendicular to the flow axis are small compared with changes in the direc-tion of the flow; fricdirec-tionless flow along the nozzle walls is assumed; the surface

tension influence is neglected (R > l04m);

the water temperature is constant; the gas

mass flow rate is very small compared with

the liquid mass flow rate (.i « 1); the gas phase follows the perfect gas law.

The most important differences are: The velocity of the gas phase (bubbles) is not equal to the local velocity (V u);

the gas pressure in the bubbles is not equal to the local static water pressure

(p p); the temperature in a bubble is

different from the surrounding water(TgTa). It is assumed that the gas flow consists of spherical bubbles with a constant value of their radius R at a certain nozzle section; the bubbles have a constant drag coeffi-cient see Reference 10.

Figures 5 and 6 define the relevant quantities.

----____---

o---

-

0---

-o--4'

0

---o

_t-'

Substitution of these quantities into (20)results in: i 1.11

[v_011v

R j (21)

For practical cases y is a large number, which accounts for the fact that the hot

air bubbles cool very rapidly.

Neglecting the mass of the gas phase compared with the mass of the liquid phase, we may apply Euler's law on a section of the nozzle:

- _{(la)P + OPg}

_{= (l_a)pU}

₍₂₂₎

For the equation of motion of one bub-ble we may write:

k k

10V

DU\

-TR

+ CD2pR(V_U)IV_UI = o

(23)

The first term gives the driving force on the bubble due to the pressure gradient; the second term describes the inertia caused by the virtual mass of the bubble; the third term denotes the drag force act-ing on the bubble when it moves relative to the surrounding liquid. The absolute signs assure that the drag force will al-ways act contrary to the bubble movement. The equation of motion of the bubble wall is described by the well-known Rayleigh equation:

R fDR\

P - Pg

(2k)

- Dt2

2Dt)

We now have nine equations

(1k)

-

(18),

(19)

combined with (21), and (22) - (2k)

given, but we have ten unknowns, viz., a,

n, R, V, U, S, p, T, Pg and i. For the tenth equation a linear increase of the

liquid velocity in the nozzle is pre-scribed:

U = U where = q = constant (25)

Hence, the system can now be solved in principle.

Outline of the Numerical Solution Method In order to rearrange the differen-tial equations, the material derivatives are expressed in local derivatives using the following transformations:

D/Dt = V(/x)

, DU/Dt = Vq

D2R/Dt2 = v(aV/x)(R/ax) + V2 (2R/bt2)

For rearranging the algebraic equa-tions we immediately see from combining

(1k), (16) and (17):

= n = constant (26)

o

5

Similarly we compute from the alge-braic equations

(1k)

through (18)

a = R3u/(R3u + CV) where

c=(vs

₀₀

3

00/03

00

S =(k/3)rn[(R3/V) + (C/U))

T = T0(PgR3/PgORQ3)

Using these stepping stones we can

compute aa/x and S/x and after some

algebraic manipulations we can reduce the problem to a system of differential

equa-tions of the following general foriii:

= w

Pg/òx = F1 (R, V, _Pg w)

= F2 (R, V, Pg w) (30)

= F3(R, V, Pg ' w)

= F4(R, V, Pg '

We now have evolved 5 equations (30) with 5 unknowns, R, V, p , p, W. This sys

tern can be solved using Runge-Kutta method.

The boundary conditions are as

fol-lows:

At the nozzle entrance: R ,V ,p p and

o o o go

At the nozzle exit: p =- p

Here the water phase reaches ambient

pres-sure. The force acting on the inner noz-zle contour can now be computed.

Thrust and Efficiency Neglecting Internal and External Friction Losses

After solving the equations given in the last section, the force on the inner nozzle contour can be computed numerically

using: X a

-

dx

₍₃₁₎

T2 =

1H

-

a(_g)

_{- Pa]}

s

o

where S/x is derived from (28). Usually

this force is negative. The positive force acting on the ramjet nacelle was given by (13). Hence the ramjet thrust computed by integrating the pressures along the ramjet duct is given by

T = T

+ T2 ₍₃₂₎

T, given by (13) and T2 by (31).

Another method to compute the rarnjet thrust can be found by subtracting the mo-mentum of the flow at the nozzle outlet from the momentum of the flow far upstream

of the intake (station-a). Then the fol-lowing expression can be derived:

T=pUS /u

_aal

-U

X a

\ a

+0

(p-p)S

X g a X (33)

The second term allows for the fact

that when the water phase in the nozzle

attains the pressure

= a at the nozzle

exit, the gas pressure in the bubbles may

be p.

The theory given in the preceding sections can be checked by comparing the thrust calculated by integrating the wall pressures (32) with the thrust calculated from the in- and outgoing momentum of the

flow (33). These two figures should be ex-actly equal in the frictionless case.

The compressor power for driving the

system in the adiabatic case is given by: k-1 k

'k' 'di\

N =P.p S U R T

¡-i (-I

-

1 (3k) ad w a a g a\k_lJ \ i

Idem in the isothermal case: N

=ipSURT

is w a a g a

di"a

The confoxiriing propulsive efficien-cies are:

'ad = ru/Nd

(36)

is = 'ais

(37)

Thrust and Efficiencies Allowing for

External Friction Losses

The various losses in the system can be approximated by introducing the

follow-ing factors:

- The diffusor efficiency

This quantity is defined by the re-lation

dif = didi

(38)

where

di is given by (3).

The entry condition in two phase noz-zle now becomes

= go = dif - The compressor efficiency TIC.

The fact that the compression process is not without losses can be incorporated

in (31+) and (35) as follows: Nadf = (1,/rl) Nd

()

6 with N according to (3k). ad

Nif = (l/r) Ni

(1+0) with Ni according to (35).

- The frictional drag force Df acting on

the outer side of the nozzle. . This drag

force is computed by assuming that it is

equal to the drag of a flat plate with the

length of the ramjet nacelle. The width of the plate is taken to be equal to irD. The length of the nacelle is the

diffu-sor length Ldi plus the length of the noz-zle L A reasonable estimate for

X

a

Ldi is given by

Ldj = D/2

The expression for D, is:

Df ₌

_CfPU

_{IrD(Ldi + L} (1+2)

where cf is the plate friction coefficient

in turbulent flow.

For Cf the following empirical formula is

used: Cf (Log Re )2.58 Re p p (1+3) with

U(Ldi + L

) Re -p w water

As has been discussed already, the intro-duction of wall friction results in

dif-ferent answers when Equations. (32) and (33) are used. Of these two expressicns, only the thrust calculated with (33)

re-mains true when friction is incorporated. The system efficiencies with frictional

effects become:

adf = (T - Df)/Ndf in the adiabatic case

and rl = (i - Df)/Ni in the isothermal

case. (1+1+)

Discussion of the Computed Results

The computer program which was

ini-tiated was too small for performing a real

optimization study. Nevertheless the

re-sults can be used for indicating several

tendencies. For every efficiency point the entire nozzle shape must be calculaten

which takes about 15 minutes on a fast corn-puter. The effect of different air

is very important. In particular we will study the results of two processes; an adiabatic process followed by hot air in-jection in the mixing tube and an iso-thermal process which supplies compressed air of ambient temperature. Beforehand, we cannot judge which of the two processes will result in the best propulsive effi-ciency. A good feature of the isothermal process is its low installed SHP. In

gen-eral the adiabatic process will be penal-ized, because the compression heat in the bubbles is lost to the surrounding water phase inside the nozzle. However we may visualize a system using a very short

noz-zle in which the residence time of the

bubbles is small compared with the time

which is needed for the gas bubbles to cool to ambient temperature. We will study the feasibility of such a system.

Another important consideration is the effect of scale on rarnjet nozzle shape aod

propulsive efficiency on which depends the

practicality of model testing. Two sys-tems will be compared in which the length dimension is changed by a factor of 10. The thrust levels of the systems are of the order of 100 to 10,000 pounds respec-tively; the initial bubble diameter i and

10 mm. The water velocity gradient along the nozzle of the large scale system is 1/lo of the small scale gradient. The bub-ble diameter at the injection point is chosen to be very small compared with the duct diameter. The bubble drag coefficient amounts to CD = 2.5 which is valid for the range of Reynolds numbers for the relative bubble movement, see Reference lo.

Propulsive efficiency ad = 38. Nozzle Data: x U V S R

iO3m

m/s m/s iO3m2

103m

TABLE 1 Given Data

Sa = 0.002m2, Ua = 50m/sec 100 knots, Ta = 293°K, R = 290 J/°K kg,p=l.O3xiG5N/m2,

= 1026 kg/rn3, 9 = 600(sec1 ), R= O.00lrn,1J = 25 rn/see,

di = 2, i = 0.0015, = 0.85,

di = 0.95, CD 2.5

Ramjet Data: Compressor power Nad = 545 W 7k hp, Thrust Tad = 1+23.1 N 96 lb.

The propulsive efficiency of the fol-lowing systems will be computed for dif-ferent speeds and thermodynamic cycles: - An exposed installation which consists of a simple contoured shroud which is fixed to the sidewall of the CAB vehicle.

- A buried installation which has the same characteristics as the above mentioned one but is mounted inside the side wall and draws sea water through a flush intake, thus eliminating external nacelle friction. - An ideal installation which gives an in-dication of the maximum propulsive effi-ciency which can be achieved using an ideal compressor = i and diffusor

Il = 1 and

no wall friction. The influence of the slip between the water phase and the air bubbles is taken into account.

In order to give a view of the be-havior of the gas and liquid phase in the nozzle, we have calculated the case of a

mail 96 pound thrust water ramjet opera-ting at 100 knots using an adiabatic cy-cle with hot air injection. The given data and the trend of the relevant quantities U, V, S, R, a, Pg) and Tg as a function

of the nozzle length coordinate x are shown in Table i. The following trends are visible: The slip between the air and the water phase V-U increases downstream of the nozzle. The nozzle cross sectional area S decreases downstream, passes a min-imum and increases again (con-di nozzle). The local gas concentration a and bubble radius R show the same behavior but their

Entrano e a, R Minimum Throat Ex i t 0 25.0 25.0 5.49 1.0 19.9 10.1 10.1 563 2 26.2 28.1 5.02 0.9k 17.5 9.97 9.8 1+67 1+ _27.1+ 30.1 4.6 0.89 13.7 9.52 _{9.59 371} 6 28.6 31.9 4.39 0.86 12.4 9.21+ 9.29 327 8 29.8 33.1+ 4.19 0.85 11.9 9.07 8.95 309 12 32.2 36.0 _3.90 0.86 12.1+ 8.23 _8.30 292 16 3k.6 38.6 3.67 0.88 13.3 7.55 7.58 289 20 _37.0 41.2 3.48 0.92 14.5 6.81 6.82 287 28 1+1.8 46.1+ 3.21 0.99 18.1 5.20 5.18 285 36 1+6.6 _51.5 3.12 1.13 2k.1+ 3.52 3.1+5 ₂₈₂ 1+4 51.4 56.8 3.38 1.37 36.7 1.95 1.68 280 1+6.9 _{53.1 58.7 3.67 1.51 43.5 1.46} 1.03 279 a Pg p T % iO N/rn2 i 0 N/rn2 K

minimum value lies far upstream of the

nozzle throat. The difference in pressure between the air in the bubbles and the surrounding water phase, Pg - p may be either positive or negative near the noz-zle entrance. Further downstream Pg - P becomes positive and increases with in-creasing x. This means that at the

noz-zle exit plane where p = p, Pg >

resulting in an under-expanded two phase

jet. We observe that the temperature

in-side the bubbles, T, drops very rapidly

and in fact drops below ambient half way through the nozzle. Consequently, near the nozzle entrance the air bubbles are losing heat which goes to the water phase; near the nozzle exit heat is conducted from the water to the air bubbles.

In Tables 2a and 2b the propulsive efficiency of the different systems is shown for the two thermodnaraic cycles.

TABLE 2a

Small Scale Ramjet - Given Data as in Table 1.

TABLE 2b

Given Data - Large Scale Ramjet.

Sa = O.2B m2 q = 60(sec1 ) R = 0.01 m. Other Data Similar to Table 1.

Tables 2a and 2b show that for the given data,isothermal compression is better than adiabatic compression.

The effect of scale on efficiency is smaller than 2 percent for the exposed and buried installation. The scale

ef-fect can be explained by noting that a factor 10 increase in bubble diameter

8

means a factor 1000 increase in heat capac-ity resulting in different therrrodynamic behavior of the bubbles at both scales; it

is seen that for constant water velocity

gradient, q, in the nozzle, the propulsive

efficiency decreases slowly with increasing forward speed at both scales. The computed values of Pg show that the higher the forward speed, the more under-expanded the two phase jet becomes; this lowers propul-sive efficiency. By increasing q with in-creasing forward speed a longer nozzle shape with a larger expansion ratio can be obtained resulting in a more efficient propulsor.

In order to illustrate the influence

of scale on the shape of the ramjet nozzle

we will give the results computed for the conditions denoted by an asterisk in Table

2b, forward speed 90 knots, isothermal com-pression. The nozzle coordinates are given

in Table 3 for both scales. It is seen that the largest discrepancy between the sectional areas occur at the nozzle exit.

Here the relative difference between the scales is smaller than 3 percent based on

area and 1.5 percent based on diameter. This result, which is typical for the gases

given in Tables 2a and 2b illustrates the

fact that the influence of scale on nozzle shape is small.

TABIF 3

Nozzle Shape of Small and Large Scale

Rami et

U = 90 knots, isothermal compression

condition in Tables 2a and 2b.

Tables ka and kb show the effect of

increasing q by a factor k, hence reducing the nozzle length by a factor 1/k. It is seen that the propulsive efficiency drops for all cases. The reason for this is that

by shortening the nozzle the pressure

gra-dient along the nozzle axis increases. This

means higher slip losses and a more

U Exposed Inst. Buried Inst. Ideal Inst. knots

j%

is 6o kk.2 53.3 k7.9 57.6 6k.o 80.0 70 kl.3 51.6 45.5 56.6 62.0 78.0 80 38.5 k9.3 k3.2 55.1 60.0 77.6 90 35.6 k6.k* _ko.9 53.1* 58.1 76.8 100 32.9 k3.l 38.8 50.8 56.6 75.9

Small Scale Large Scale

xxlO3m SXlO3m2 xXlO2m SX1Om2

0 5.018 0 5.018 k k.5k8 k 8 k.l88 8 k.l82 12 3.896 12 3.866 16 3.660 16 3.6k5 20 3.k7l 20 3.k51 2k 3.330 2k 3.302 28 3.237 28 3.205 32 3.202 32 3.157 36 3.2k8 36 3.191 ko 3.kl9 ko 3.3kk k2.6 3.637 k2.6 3.517 a Exposed Inst. Buried Inst. Ideal Inst. knots is is 'a 'is 60 kk.o 52.24 k6.9 55.7 62.8 75.7 70 241.24 50.3 2424.7 54.2 60.9 75.0 80 38.7 247.6 242.3 52.0 59.0 73.9 90 36..l 24424* 40.2 495* 57.2 72.5 lOO 33.7 kl.9 38.k k8.5 6.i 71.0

under-expanded two phase jet, thus lower propulsive efficiency. From these results it may be concluded that the combination of an adiabatic cycle with hot air injection and a very short two phase nozzle gives an

efficiency which is too low to be practical. TABLE ka

Given Data - Small Scale Ramjet Same as in Table 2a except p = 0.003

13 = 100 knots

a

TABLE kb

Given Data - Large Scale Rarnjet Same as in Table 2b except = 0.003 U = 100 knots

a

Conceptual Design of a Large

Water Rarnjet

In the previous section we concluded that the water ramjet should be driven using an isotherzial compression cycle. Un-fortunately such a process can only be realized by using a very large number of adiabatic air compression stages inter-connected by intercoolers. For simplicity we have restricted the number of compres-sor stages to three with two intercoolers which form an integral part of the ramjet nacelle. These intercoolers can be

de-signed with a low internal friction lass. Trial calculations have shown that the penalty may be smaller than 0.1 percent in tenis of propulsive efficiency. Figure 7 shows a general arrangement drawing of an installation which delivers a thrust of the order of )4Q tons at a forward speed of 80

knots. The following input data were used:

S = 2 rn2, U ko rn/sec 80 knots, T = 293°K, a = 1.03 X

lN/rn2,

Rg = 290 J/kg°K, = 1026 kg/rn3, = 0.01 m, V = ko rn/sec, Pdi = 2, 9 p = 0.0015, c = 0.85, di = 0.95, CD= 2.5

The nozzle shape is shown in Figure 7.

Three-Stage Air Gas Turbine Engine A Compressor

i..1.L

ii

-Iii Il i

J11

uJ

UI

..s-uuu-1

lin iiinini11111 Water A

/

i-

_45ff.

- i m.

FIGURE 7 - CONCEPTUAL DESIGN OF LARGE WATER RAMJET

For this case we compute a propulsive efficiency of 52.2% and a thrust of

3.36 X

_{lcN- 77,000 lb.}

For a buried installation the corres-ponding results are 58.6% and 86,000 lb. respectively.

The air mass flow rate for both con-figurations is 12k kg/sec, the SHP of the compressor system amounts to 35,000 hp.

Concluding Remarks

In conclusion it is stated that large water ramjets for propelling the high speed surface effect ships of the future can be built with propulsive efficiencies of 50-60 percent depending on the degree of sophis-tication. The maximal attainable forward speed of the propulsor seems only limited by the bursting strength of the nacelle. The weight of this propulsor is extremely low since all flow passages are filled with air, the heat exchangers are part of the nacelle structure and the air compressors can be directly connected to the power tur-bine of the engine. The last feature elim-inates gear boxes and assures low compres-sor weight by virtue of very high RPM operation. Ingestion of air through the ramjet inlet will produce no problems as

long as the ingested air volume rate is small compared with the water volume going through the propulsor. Since the engine has no moving parts in contact with the water phase the damage hazard caused by foreign object ingestion is minimal. For military applications the sound absorbing wake of bubbles behind the propulsor may be advantageous. Cab Sidewall q Exposed Inst. Buried Inst. Ideal Inst. 1/sec is' is is'° 600 39.5 53.1 k2.k 57.2 55.3 7k.5 1200 36.7 k6.8 39.6 5o.k 51.3 66.5 1800 3k.3 kl.7 37.0 k5.o k8.l 60.2 2k00 32.0 37.9 3k.6 kl.o k6.2 55.6 q Exposed Inst. Buried Inst. Ideal Inst. 1/sec

_1is%

is 6o kl.o k8.5 k2.o 52.5 5k.6 69.5 120 38.5 k3.6 ko.8 k6.9 52.k 61.9 180 37.6 38.7 39.7 kl.8 5l.k 56.5 2kO 37.5 36.0 39.6 38.4 50.1 52.7

Acknowledgement

The writer is indebted to Ir. F. Van

Der Walle and Dr. L. Van Wyngaarden at

the N.S .M.B., Wageningen, Netherlands, for many constructive remarks.

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(CAB) Vehicle Progress Report,' Journal of I-Iydronautics, Vol. 20, No.

2, April

1968.

Ford, Allen G., "Progress in Air

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October

1966.

Wislicenus, George F., "Hydrodynamics and Propulsion of Submerged Bodies," A.R.S. Journal, Vol.

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1960.

Anderson, R. G., Rush, C. W., and McClellan, T. R., "Development of a

Hydroduct," CALTECH Thesis

l9k7.

Muir, J. F., Eichhorn, R., "Compres-sible Flow of an Air-Water Mixture Through a Vertical Two Dimensional Converging-Diverging Nozzle," Pro-ceedings of the

1963

Heat Transfer and Fluid Dynamics Institute,

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196k.

Gadd, G. E., "A Note on Air Blown Water RamJets," NFL Ship T.M.

51,

April

_195k.

Van der Walle, F., "Theoretical

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8.

Witte, J. H., "An application of Homogeneous Mixture Theory for Pre-dicting the Performance of a Water-Air Ramjet. N.S.M.B. Lab. Memo Nr 11.

Kchemann, D. and Weber, J., "Aero-dynamics of Propulsion," McGraw Hill,

1953,

page

62.

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