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ANALYSIS OF A METHOD EOR OPTIMUMDESIGN OF WATERJET PROPULSION

SYSTEMS.

ftDennis Keith Kruse

LIBlttRV

NAVAL POSTGRADUATE SCHOOLXOOTHBY. CALIP. 93940

ANALYSIS OF A METHOD FOR OPTIMUM DESIGN

OF WATERJET PROPULSION SYSTEMS

by

Dennis Keith Kruse

B.S., U. S. Naval Academy

(1965)

SUBMITTED IN

PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE

DEGREE OF OCEAN ENGINEER

AND MASTER OF SCIENCE

at the

MASSACHUSETTS INSTITUTE OF

TECHNOLOGY

^ June, 1973 > y

LIBRARYNAVAL POSTGRADUATE SCHOODMONTEREY, CALIF. 93940

ANALYSIS OF A METHOD FOR OPTIMUM DESIGN

OF WATERJET PROPULSION SYSTEMS

by

Dennis Keith Kruse

Submitted to the Department of Ocean Engineering onMay 11 » 1973. in partial fulfillment of the requirementsfor degrees of Ocean Engineer and Master of Science inMechanical Engineering.

ABSTRACT

An existing computerized method for optimum design ofwaterjet propulsion systems for sub-cavitating hydrofoil craftis analyzed for sensitivity to variations in normally fixedparameters and for sensitivity to variations in. the startingpoints for the search used in the optimization procedure. Acompatible method for off design evaluation of waterjet pro-pulsion systems is developed and incorporated into the opti-mization program in a manner which permits off design evaluationto be performed separately or in conjunction with design. Theevaluation routine requires that system geometry, craft charac-teristics and pump characteristics be specified. System dragand losses are calculated to determine required flow rate andpump head and the corresponding pump speed, efficiency andrequired power are determined. Results of design optimizationfor a series of similar craft are presented and show a strongsensitivity to the input estimate of the take-off drag. Sen-sitivity to starting values of the independent variables wasnoted in some cases and appears to be due to the fact thatjet velocity ratio dominates the other independent variablesas an influence on total system weight. A FORTRAN computerlisting and sample inputs and outputs for both design andevaluation routines are included.

Thesis Supervisor! A. Douglas Carmichael

Title t Professor of Power Engineering

TABLE OF CONTENTS

Title Page 1

Abstract •••••• • •••••• 2

Table of Contents . • 3

List of Figures • ••••• ••••••••• k

List of Symbols Used in Text 5

Chapter 1* Introduction •••••••••• ••• ••• 8

Chapter 2. Methodology Used for Evaluation ••••••••• 11

2.1 Assumed General System Configuration •••• 11

2.2 General Procedure for Evaluation •••••••• 12

2 #3 Specific Evaluation Methodology ••• 13

2,k Cavitation Considerations ••••••••••••••• 2k

Chapter 3 • Design Methodology •• ...•••....... 27

Chapter k* Discussion of Results ••••••••••••••••••• 32

Chapter 5» Conclusions and Recommendations ••••••••• 36

Bibliography 38

Figures •••••••••• •••••••• ........••••. 39

Appendix A. List of Symbols Used in Program .......•• k2

Appendix B • Program Listing • 81

Appendix C. Users' Manual • ..••••. •• 162

LIST OF FIGURES

Figure No. Title Page

1 General Ducting Configuration 39

2 Propulsion Weight Fraction vs. Installed 40Power Propulsive Coefficient at Take-off

3 Cruise Speed Propulsive Coefficient vs. 41Installed Power Propulsive Coefficientat Take-off

4

SYMBOLS USED IN TEXT

Symbol Definition

A area

A nacelle surface area

C nacelle diffuser expansion loss factor

C, nacelle drag coefficient

C . strut drag coefficient

C. spray drag coefficient

C« Schoenherr friction coefficient

C Factor for strut diffuser expansion loss

c strut chord

D diameter

d mean diameterm

f Moody pipe friction factor

g acceleration of gravity

h head loss

H atmospheric headEL

H net positive suction head

K strut diffuser expansion loss coefficient

K. junction mixing loss coefficientj

K.J. form loss coefficient

L nacelle forebody length

L. nacelle diffuser length

N pump RPM

P total pressure

p static pressure

Symbol Definition

pv vapor pressure

Q volume flow rate

q dynamic pressure

RPR ram pressure recovery factor

R bend radius of elbow centerline

RO elbow internal duct radius

s suction specific speed

T thrust

t strut thickness

V velocity

a angle of attack

finozzle depression angle

e diffuser half angle

-*• divergence loss factor

/> density of salt water

<r cavitation number

4>junction angle

Subscript Definition

aux auxiliary inlet

c combined main and auxiliary flow

i main inlet

J jet

n nacelle

t nozzle throat

free stream condition

Subscript Description

1 nacelle inlet

2 nacelle diffuser exit

6 pump inlet

1. INTRODUCTION

Waterjet propulsion has attracted growing interest in

recent years due, in part, to the trend toward the development

of faster and more non-conventional vehicle types such as hydro-

foils and surface-effect ships. These vehicles have made the

potential advantages of waterjet propulsion systems more attrac-

tive, while at the same time lessening some of its disadvantages.

Among the possible advantages are*

a. Reduced vibrations and avoidance of propeller cavita-

tion noise

b. Fewer system components

c. Elimination of underwater appendages

d. Simpler transmission machinery

e. Capable of use in shallow water operations

f

.

Steering control directly from the propulsor

Additionally, the low overall system efficiency which causes

waterjet propulsion to compare unfavorably with conventional

propulsion systems at lower speeds is less of a penalty at

higher speeds.

In light of the increasing interest waterjet propulsion,

a number of studies have been made reviewing the important para-

meters involved in the selection of system components; as well

as considerations for overall system design. This led natur-

ally to efforts to computerize the design process and the most

recent, and most comprehensive, of these efforts is the com-

puterized method for design optimization of waterjet propul-

8

sion systems for hydrofoils developed by R.P. Gill, B.T. Conner,

and R.C. Percival(references 1, 2 and 3).

It is desirable to have a compatible method of evaluating

existing or proposed systems which can be used in conjunction

with such a design method. This will enable existing systems,

as well as alternative design proposals, to be evaluated on a

common basis with the computer produced optimum design. It

would also permit the performance of the computer produced

design, or any other design, to be predicted at speeds other

than the design speeds.

This report presents a revision of the computerized design

method developed by Gill, Conner and Percival which permits it

to be used for system evaluation as well as for its original

purpose of design. The inclusion of the evaluation program

within the design program permits common portions of the program

to be used for both evaluation and design and also permits the

off-design performance to be predicted in conjunction with the

design computations. Additionally, it will permit the accuracy

of the program to be analyzed since it can be used to predict

the performance of existing systems and the predicted performance

can then be compared with measured performance. This could lead

ultimately to refinements and improvements in both the design

and evaluation portions of the program.

This report describes the methodology used in the program,

presents an analysis of results obtained by using the program,

and provides a users* manual as an aid in utilizing the program

and interpreting the output obtained from the program. The

methodology used for evaluation is presented in detail, and the

design routine is summarized briefly. The design routine has

been analyzed for sensitivity of a basic design to variations

in normally fixed parameters and to variations in intial values

of the independent variables. The evaluation routine has been

tested by evaluating the performance of a system designed by the

program at design and off-design conditions. The users* manual,

contained in appendices to this report, describes the use of the

program for design as well as for evaluation; and it contains

listings of required and optional inputs, sample controlling

programs, and sample outputs.

10

2. METHODOLOGY USED FOR EVALUATION

2.1 ASSUMED GENERAL SYSTEM CONFIGURATION

The general configuration of the waterjet propulsion

system used for the evaluation routine is the same as that

which is used in the design routine, and is depicted in Figure

1. The components of the system, in order from inlet to out-

put, are i

1. The nacelle or ram inlet, which includes the auxiliary

inlet, if any, and which is assumed to be of a sub-

cavitating type for the calculations.

2. The strut elbow which derects flow from the nacelle

into the strut and which generally contains either

splitter vanes or turning vanes to reduce internal

losses.

3. The strut which supports the foils and carries the

water into the hull, and which is generally used as a

diffuser in order to avoid cavitation in the pump inlet

piping.

4. The hull elbow which directs the flow from the strut to

the pump inlet piping.

5. The pump inlet piping which consists of one or two el-

bows and either a junction, divergence or straight pipe

depending upon the total number of pumps used.

6. The pump which is driven by a gas turbine engine

through a reduction gear.

7. The nozzle or jet which discharges the water through

11

either the transom or the bottom of the hydrofoil at a

high speed thereby producing the required thrust.

The program assumes that the usual two strut configuration is

utilized.

2.2 GENERAL PROCEDURE FOR EVALUATION

The evaluation procedure assumes that the geometry of the

system is defined in its entirety and that a reliable estimate

of ship drag, ie. that portion of total drag not directly at-

tributable to propulsion system components, is available for

the speeds at which the system will be evaluated. Estimated

values of those components of drag due to the propulsion

system; ie. nacelle drag, strut drag and spray drag, are added

to the ship drag to obtain the estimated total drag and, there-

fore, the estimated required thrust. The required flow rate and

jet velocity are related to the required thrust by the equation,

T =/>Q(V. cos(/0 - VQ ) (1)

The required flow rate and required jet velocity, as well as the

required nacelle inlet velocity, can thus be determined by using

equation (1) together with the one-dimensional continuity equa-

tion for an incompressible fluid,

AiVi - Vo = Q (2)

The flow rate and inlet and jet velocities, together with

the system geometry, are sufficient to permit calculation of

all of the head losses in the system ducting. The total system

head loss and the flow rate can then be used to calculate the

required pump speed and shaft horsepower.

12

The required flow rate and inlet velocity, together with

ship speed and system geometry, are also used to calculate

revised estimates of nacelle drag, strut drag and spray drag.

These values are added to ship drag to obtain a new estimate of

total drag. If the revised total drag differs by more than

one per-cent from the previous estimate of the total drag, the

new estimate is used to calculate a new flow rate and new inlet

and jet velocities. The procedure is then repeated until a

total drag estimate is obtained which differs by less than one-

percent from the previous estimate. The calculated system per-

formance is then output by the program.

The evaluation routine also calculates the structural

weight of the system components and the weight of water en-

trained in the system using the same methods as those used in

the design routine. This provides an additional check to en-

sure that the evaluated system is the same as the designed sys-

tem. Additionally, when an existing system is evaluated, the

calculated weights may be compared with actual weights in order

to provide a check of the weight prediction methods used in the

program. This could eventually result in improvements in the

weight estimation models used.

2.3 SPECIFIC EVALUATION METHODOLOGY

The evaluation routine is begun by inputting the required

parameters to the program and calculating the required flow rate

and jet and inlet velocities in the manner described in the

previous section. The parameters which must be input to the

13

program are*

a. Displacement

b. Prime mover

c. Cross sectional areas and shapes of all systemcomponents

d# Lengths of all system components

e. Bend angles of all elbows in the system

f • Nozzle depression angle

g. Pump type and number of stages

h. Pump blade tip diameter

i. Pump characteristics at design specific speed

j. Depth of submergence of nacelle

k. Height of pump centerline above waterline

1. Craft speeds for which system is to be evaluated

m. Craft drag at evaluation speeds

A more detailed list of both required and optional inputs, in-

cluding the required dimensions and the variable names used in

the program, is contained in Appendix C.

Since it is assumed that the system is of a subcavitating

design, an important consideration in the evaluation of system

performance is a check to determine whether cavitation is occur-

ing within the system at the evaluation speed. Checks for cavi-

tation are made for those points in the system where it is deem-

ed most likely to occur. Within the program, cavitation calcul-

ations are performed concurrently with other calculations; but,

for the sake of clarity and continuity in this report, they

will be described separately in section 2.^«

14

Head loss, drag and estimated weight calculations are per-

formed for each component consecutively in the order in which

the flow passes through them, thus the first component to be

evaluated is the nacelle. Losses in the nacelle are calculated

as three separate components; lip losses, pipe losses and dif-

fuser losses.

When the nacelle subroutine is entered during evaluation,

the first operations performed are the calculation of inlet

velocity ratio, V./V from the input values of V. and V i

and calculation of free stream static pressure, free stream

dynamic pressure, incipient cavitation number, and total pres-

sure for the evaluation speeds.

*o= ^V

o

ôi (po-pv)/qQ

P = p + qo *o Ho

After checking for external cavitation and for cavitation

on the inlet lip, as described in section 2.4, the subroutine

proceeds with the calculation of lip losses. Lip losses are

calculated differently depending on whether or not a positive

indication of inlet lip cavitation was obtained. If cavitation

was indicated, the auxiliary inlet area which must be used to

avoid cavitation is calculated. To accomplish this, the first

step is determining the maximum permissible inlet velocity ratio

by interpolating in the data tables.

The data tables referred to in discussion of ths nacelle eval-

15

uation are the same as those used in the design routine

and are tabulations of the information contained in Tables 1

through 12 and Figures k through 20 of reference 2.

<Wmax = f(L/Dn .<roi .«)

The required auxiliary flow rate is then calculated,

Q = Q - Q.âux c l

Where

"i = Ai

(Wmax Vo

and Q is the required total flow per nacelle.

The ram pressure recovery of the lip is a tabulated

function of the inlet velocity ratio, now limited to (V//V )max.

The total pressure inside the lip is thus

P. = RPR, . q + pi lipHo yo

and the static pressure inside the lip is

Pi = Pt

- i/>vf.

Pressure recovery of the auxiliary inlet was assumed to be

0,8» The total pressure inside the auxiliary is then given by

P = RPR q + paux . auxHo ô

The static pressure inside the auxiliary inlet must be the

same as that previously calculated for inside the main inlet lip.

Therefore, the velocity through the auxiliary inlet can be de-

termined by

Vaux " C2(Paux-Pi>//>]

*•

The auxiliary inlet area required is then

aux "" aux' aux*

If this area is less than the total available auxiliary

16

inlet area, the total pressure of the combined flow is calcul-

ated as the mass weighted average of the combining flows.

Pc - < QauxPaux

+ QiPi>/Qc

The average velocity of the combined flow is calculated

from the dynamic pressure

V£

= [2(PC

- Pi )^]*

and the losses are then obtained directly from the pressure

recovery coefficient to this point, which is

RPRc = (VPo'/lo-

If lip cavitation was not indicated initially, then no

auxiliary inlet area is required to be used, and the ram pres-

sure recovery coefficient of the lip is determined directly as

a tabulated function of V./V •1 o

APd

CKtii .

where C is the diffuser expansion loss factor and K. is the

form loss coefficient.

C 3.19xl0~ 3 e2 + 8.452xl0"

4e

Kt

= (1-A1/A

2)

2

is the diffuser half angle.

6 = tan" 1

[(Dg-D^/aiiJ

Pipe loss in the diffuser is

where f is the Moody pipe friction factor which is calculated

within the routine as a function of Reynold's number.

Total internal losses in the nacelle are then

APn

= (1-Pc)(i/V2) [CK

t+ f(L

d/d

m ) + fLauxli/V2.

17

The nacelle drag coefficient is given by

CD=C

f1 l. 5 (Dm/LN

)3/2 7(DB/L

N)3

where Cf

is the Schoenherr friction coefficient which is cal-

culated as a function of Reynold's number in a seperate sub-

routine.

The total external drag is then

D = CD*/VoA

where A is the external surface area of the nacelle, calcul-

ated in the same way as in the design routine, reference 2.

Calculations for the strut elbow are performed by the

same subroutine that handles all of the elbows in the system

and calculations for all of the elbows are performed in the

same manner as in the design. For purpose of the calculations

an elbow is fully defined by specifying the following parameters:

width, depth, cross sectional area, bend angle, and radius ratio.

The radius ratio, R/RO, is the ratio of the radius of the center-

line of the bend to the internal radius of the duct. The inlet

and outlet cross sectional areas are assumed to be equal.

In order to maintain compatibility with the design routine,

the shapes of the elbows are assumed to be the same as the

shapes which are assumed in the design routine. Specifically,

the strut elbow is assumed to be rectangular with the depth

equal to twice the width, the hull elbow is assumed to be

rectangular with the depth equal to one half the width, and the

pump elbow is assumed to be circular in shape. The radius ratios

and bend angles may be specified in the calling program; but.

18

if they are not, they will be assigned the same values as in the

design program. The cross sectional areas must be specified.

The strut subroutine requires that the thickness to chord

ratio, the thickness and chord at the root, the thickness and

chord at the tip, and the inlet and outlet areas be specified.

The shape of the strut internal ducting is assumed to be the

same as that of the strut elbow. The strut length and the dif-

fuser equivalent angle, 20, need not be specified as they are

calculated within the subroutine from other specified para-

meters.

The head losses within the strut diffuser are a combin-

ation of friction losses and expansion losses. The friction

loss coefficient is the Moody friction factor, calculated in

the same manner as in the nacelle subroutine. The expansion

loss coefficient is given by

Ke

= Cs(l-A./A )

2

where C is dependent upon the diffuser equivalent angle, 20,s

and is determined by interpolation in data tables contained in

the subroutine.

Two external drag components, strut drag and spray drag,

are attributable to the strut and are calculated in the strut

subroutine. The drag coefficients for both components are cal-

culated as functions of the thickness to chord ratio. The strut

drag coefficient is given by

Cds

= 2Cfs^ + 2(t/c) + SoCt/c)4]

and the spray drag coefficient is

19

Cdsp= 0.03 (t/c).

The hull elbow losses are determined in the same manner

as previously described for the strut elbow. It may be noted,

however, that the assumed shape for the hull elbow gives it a

more favorable aspect ratio than that of the strut elbow. This,

together with the lower inflow velocity due to diffusion in the

strut, will result in lower losses in the hull elbow than in

the strut elbow.

The pump inlet piping is that portion of the ducting

which connects the hull elbow to the pump inlet. It consists of

a straight pipe, the pump elbow, and a transition piece which

is either a junction, divergence, or another straight pipe de-

pending on whether there are one, four, or two pumps respective-

ly.

The geometry of the pump inlet piping is basically deter-

mined by previous assumptions and previously required inputs

with the only remaining variables being cross sectional area

of the piping and the junction angle, 0. The assumption is

made that the mean velocity is constant throughout the pump

inlet piping, thus the areas of the ducting are fixed by

specifying the area of the hull elbow. The junction angle is

assumed to be zero unless otherwise specified. The divergence

angle need not be specified since it is calculated within the

routine as a function of the distance between the specified

pump location and the specified strut location.

The athwartships pipe makes a transition from a rectangu-

lar shape to a circular shape, but losses due to change of

20

shape are neglected in the calculations. Losses in all straight

pipe sections are calculated using the Moody friction factor in

the manner previously described. Losses for the pump elbow are

calculated in the same manner as for the other elbows in the

system.

The mixing loss coefficient is dependent on the junction

angle, 0, and the divergence loss factor, 7. , and is determined

by

K. 1 +%- 2cos(f(0))J

where

f(0) - 1.40-O.OO58302 .

The divergence loss factor is computed by interpolation

in a data table which is taken from Figure 15 of reference 1.

When a divergence is used, another elbow is required at the

pump entrance. This elbow is treated in the same manner as the

other elbows except that the angle of the bend is equal to the

divergence angle.

The input parameters required for the nozzle calculations

are throat area, jet area, and nozzle depression angle. Nozzle

length is calculated from the pump exit position and the nozzle

depression angle. Nozzle head loss is calculated in the same

manner as in the design routine, where head loss is given by

hn

= [f(Lj/2)/(D

t-D

j) 1-16/(1 + D

t )

lf]Y2/D

j2g

when D. is greater than 1. For D. less than 1, head loss isJ J

assumed to be 1.5% of dynamic head.

With all head losses in the system having thus been deter-

21

mined i they are then summed, the required pump head is calcul-

ated and the pump subroutine is entered for calculation of pump

performance. The required pump head is given by

Hp

= (V2.v2)/2g + heiey+ Ahtotal .

The calculations of pump performance are performed in es-

sentially the same manner as that used by the design routine

for calculating performance at cruise speed. These methods are

described in detail in reference 3 and will only be summarized

here, with emphasis placed on the points where the evaluation

routine differs.

The input parameters to the pump subroutines for evaluation

are pump length, pump type, number of impellers, impeller tip

diameter, and a set of performance characteristics which are

representative of the design condition; ie. a pump speed, pump

head and flow rate which are representative of the design speci-

fic speed of the pump. Additionally, the subroutine utilizes

the required flow rate, required pump head, and various craft

characteristics which are either input or calculated elsewhere

in the evaluation routine.

As in the design routine, the pump characteristic head

and efficiency curves are assumed to be parabolic and off-design

pump speed and efficiency are calculated on that basis. The

off-design pump speed is obtained from the equation

H/HD

- A(Q/QD )

2 + B(Q/QD )(N/ND ) + C(N/ND )

2

where subscript D indicates the design condition. The equation

is solved for N, which is the off-design pump speed. The coef-

22

ficients, A f B and C f are determined for the particular pump

type in the same manner as in the design routine. The off-

design efficiency is calculated in an identical manner after

the design point efficiency has first been determined as a

function of impeller tip diameter in the same way as in the

design routine.

In the design routine , the flow coefficient, head coef-

ficient and suction specific speed are determined and output

for the design condition only. In the evaluation routine these

parameters are determined and output for the evaluated conditions

in order to more fully describe the pump performance at these

conditions.

During design, the pump subroutine calls the gear and fuel

subroutines which are used to calculate reduction gear weight

and weight of fuel required for specified endurance at cruise

speed. These subroutines are also called during evaluation,

but their use is somewhat different than in design. For eval-

uation the gear ratio must be specified whereas in design it is

calculated as the ratio of prime mover design speed to pump

design speed. The type of reduction gear may be either speci-

fied, or selected on the basis of gear ratio and number of in-

puts and outputs in both design and evaluation routines. The

fuel subroutine does not calculate a fuel weight during eval-

uation, but instead, it calculates the fuel consumption rate at

the evaluated speed, assuming the craft is at specified dis-

placement. If the fuel weight is desired to be included in the

23

total system weight output at the end of evaluation, it must

be specified in the inputs.

2.4 CAVITATION CONSIDERATIONS

There are six points, two external and four internal, where

cavitation is most likely to occur, and an important part of the

evaluation of a system is a determination of whether cavitation

is expected to occur at any of these points at the evaluated

speeds. The six points which must be checked for cavitation aret

It The exterior surface of the nacelle.

2. The exterior surface of the strut.

3. Inside the nacelle inlet lip.

4. Inside the strut elbow.

5. At the pump inlet.

6. On the pump impeller.

The check for cavitation on the exterior of the nacelle is

accomplished by interpolating in a data table to obtain the

forebody length to maximum diameter ratio, L/D » for a nacelle

having an external pressure coefficient equal to the negative

of the free stream incipient cavitation number. The inlet to

maximum diameter ratio, D./D , corresponding to this L/D_ isl m ° m

determined by interpolating in another data table. This value

is compared with the actual D./D and if the actual value isi m

greater cavitation can be expected to occur and an indication

to that effect is printed in the output data.

The cavitation number for flow around a strut can be ap-

proximated by

^= [1.15(t/c) + 1]2-1.

24

The incipient cavitation number for flow around the strut is

crjL

= (Ha-p

v)g/|(1.137V

o )

2,

If <ri< <r at the evaluated speed, then cavitation is likely and

is so indicated in the output data.

The check for cavitation on the inside of the nacelle in-

let lip is accomplished by interpolating in a data table to de-

termine the limiting inlet velocity ratio beyond which cavitation

will occur inside the lip#

(V./V ) . f(L/D ,cr . ,<*)i' o max ' m 01'

If V./V at the evaluated condition is greater than (V./V )V o 1 o max

cavitation will occur unless sufficient auxiliary flow is pro-

vided to reduce the effective inlet velocity to that correspond-

ing to (VV,^.The auxiliary inlet area required to provide sufficient

auxiliary flow to avoid cavitation is calculated in the manner

described in Section 2.3« If the required auxiliary inlet area

is greater than the available auxiliary inlet area, then cavita-

tion can not be avoided and the output of the program will indi-

cate that inlet lip cavitation will occur at the evaluated speed.

If cavitation can be avoided only by using some portion of the

auxiliary inlet area, then the output will indicate the aux-

iliary inlet area which is required.

The incipient cavitation number on the turning vanes in

the strut elbow is given by

where subscript 2 indicates conditions at the exit of the nacelle

25

diffuser. The incipient cavitation number, <r, . , is a character-xvi

istic number which has been determined experimentally, thus the

critical velocity at the diffuser exit can be determined.

Vcrit "&ii + 1 -p

1o8S/<ô >3*CV /(1 +9jTl )*l

These two values are compared. If V2max is greater than

V rit cavitation is likely to occur and will be indicated in the

program output.

Cavitation is assumed to occur in the pump inlet if the

local static pressure, p^, is less than vapor pressure, pi or

more precisely, if local dynamic head is less than local total

head minus vapor head, ie. (P^-P*) < ^ p6"^v^'

where P6-p

6= (Q/A

6 )

2/2g

and P/;-P,r= V^/2g + H -P, -P,,.x-v o a loss v

If this condition exists at the evaluated speed, an indication

to that effect is printed in the program output.

Cavitation on the pump impeller is not intrinsically deter-

mined by the program, but the suction specific speed, S, at

which the pump is operating at the evaluated speed is determined

and printed out. The suction specific speed at which cavitation

occurs may vary depending upon the pump design; but, by knowing

the suction specific speed at which the pump is required to

operate, the user can readily determine if the limiting value is

exceeded. The suction specific speed at the evaluated condition

is determined by

s = nqVh°;75

where H - the net positive suction head, is given by

Hsv = V

o/2§+ H

a * Pv " Ploss-

26

3. DESIGN METHODOLOGY

The design methodology used in the design portion of the

program is described in detail in references 1, 2, and 3i and

is summarized here to lend continuity and completeness to this

report.

The design routine uses a directed pattern search to select

a system which is optimized from the standpoint of having the

lowest overall system weight of any satisfactory system. The

system weight includes all structural and machinery weight at-

tributable to the propulsion system, as well as the weight of

all water entrained in the system above the waterline and the

weight of fuel required to provide the specified endurance at

cruise speed. The craft displacement is held constant during

the optimization routine, thus the selection of a minimum

weight propulsion system maximizes the payload for that part-

icular craft.

The variable parameters used in the design optimization

are jet velocity ratio, V ./V , inlet velocity ratio, V./V ,

and nacelle inlet to maximum diameter ratio, D./D • The pat-

tern search subroutine selects different values of these para-

meters for each design iteration and retains the values which

produced the minimum weight system. When the search pattern

has been completed! V ./V . V./V . and D./D are reset to thej o I o l m

values corresponding to the minimum weight system and the

design routine is entered for a final time in order to re-

produce that system.

2?

In addition to V./VQ

, Vi/V ()t and D

i/D

m ; the design

routine requires that at least the following information be

specified to define the craft for which the propulsion system

is being designed!

a* Displacement

b. Range

c. Prime mover

d. Craft speed at take-off and cruise

e. Craft drag at take-off and cruise

f • Depth of submergence of foil

g. Distance of strut from transom

h. Distance of pump exit from transom

i. Height of pump centerline above waterline

The design routine begins by using the inlet and jet

velocity ratios chosen by the pattern search subroutine, to- .

gether with the specified craft speed, to calculate the required

inlet and jet velocities at the cruise condition. The optimum

nozzle depression angle is then determined by

fi -tW-1(Dtatal/A).

These values are then used to calculate the required flow rate

and the required inlet and jet areas.

The design routine then proceeds to size the components

of the system in the same sequence as previously described for

the evaluation routine; and , after each component has been

sized, losses and drags are determined in the same manner as in

the evaluation routine.

28

The nacelle inlet to maximum diameter ratio, as selected

by the pattern search subroutine, determines the amount of dif-

fusion possible prior to the strut elbow. Since the inlet dia-

meter has already been determined, the maximum diameter is

therefore fixed by the diameter ratio. The length of the

nacelle forebody is determined by selecting the length to max-

imum diameter ratio which is just at incipient cavitation on

the external surface at cruise speed. The ratio of inlet to

maximum diameter which corresponds to the forebody shape thus

chosen is compared with that ratio previously specified. If

the previously specified ratio exceeds the maximum ratio allow-

ed by cavitation, the forebody is resized using the maximum

allowable ratio. An iteration is then performed to determine

the overall nacelle length which will result in the least total

power loss due to external drag and diffusion in the ducting.

The inlet area of the strut elbow is set equal to the exit

area of the nacelle diffuser. The elbow shape, radius ratio

and bend angle are determined according to assumptions pre-

viously described for the evaluation routine. The number of

splitters or guide vanes is then determined to minimize losses

in the elbow.

The strut diffuser inlet area and shape is set equal to

the exit of the strut elbow, and the diffuser area ratio is

chosen to avoid cavitation in the pump inlet piping. The ex-

ternal surface of the strut is sized as necessary to enclose

the ducting, and the shape is chosen to avoid external cavi-

29

tation.

The nacelle, strut and spray drags which have been calcul-

ated during this iteration are compared with previous estimates

of these drags. If a significant difference exists, the drag

estimates are revised and calculations begin anewi otherwise the

rest of the system is then designed.

The hull elbow is designed in the same manner as the strut

elbow, and the configuration of the pump inlet piping is select-

ed according to the number of pumps. The pump inlet piping be-

gins with a transition from the shape of the hull elbow to a

circular shape, and the rest of the piping is circular is shape.

The size of the pump inlet piping is chosen to maintain a con-

stant velocity throughout its length.

The nozzle is assumed to have an inlet area equal to the

pump outlet area. This and the jet area which has been previous-

ly determined are used to calculate losses in the nozzle.

The ducting losses prior to the pump are used to deter-

mine net positive suction head, and nozzle losses are added to

determine the required pump head. Two basic pump designs are

considered i axial with an inducer impeller, and centrifugal

with double suction impellers. The alternative pumps are sized

by using assumed specific speeds, flow coefficients and impeller

diameter ratios for each alternative. The number of axial stages

is determined by cavitation criteria, while the number of stages

in the centrifugal pump is chosen to minimize combined pump,

gear and fuel weight. The required gear ratio is determined

30

as the ratio of prime mover normal operating speed to required

pump speed at take-off and this ratio, together with the re-

quired shaft horsepower at take-off, determines the type and

size of gear to be used. The fuel weight required to provide

the specified endurance at cruise speed is calculated for each

alternative design, and that pump design which requires the

lowest combined weight of pump, gear and fuel is then chosen

as the pump to be used by the design.

31

k. DISCUSSION OP RESULTS

Sample outputs for both the evaluation and the design

routine are contained in Appendix C. The format used for output

from the evaluation routine is essentially the same as that used

for design. This permits maximum compatibility within the out-

put subroutine; and, additionally, facilitates comparison of

data produced by. the design routine with that produced by the

evaluation routine for the same or any other system.

The design routine was analyzed for sensitivity of a basic

design to variations in initial values of the independent vari-

ables and to variations in normally fixed parameters. The basic

design used in the analysis was for a 750 ton hydrofoil with a

take-off speed of 30 knots, a cruise speed of 45 knots, and an

endurance of 2000 miles at cruise speed. Two LM2500 gas tur-

bines were the specified prime movers, and the specified number

of pumps was two.

In most cases there was little or no variation in the result-

ing system design when the starting values of the independent

system parameters were varied. In some cases, however, signifi-

cant variations occured with total system weight varying by as

much as 3.5$. In those cases where results did vary, the jet

velocity ratio of the resulting design deviated very little from

that of the basic design. The inlet velocity ratio and nacelle

diameter ratio both varied over a considerable range, however,

consequently the changes in system weight resulted primarily

from changes in the nacelle and strut designs. This suggests

32

that the optimum design is primarily defined by the jet velocity

ratio and that the inlet velocity ratio and nacelle diameter

ratio become important only after the optimum jet velocity ratio

has been determined. This may also explain the apparent lack of

correlation between inlet velocity ratio and other parameters

in designs produced by the program. Further study of this

problem is needed and it may be necessary to revise the design

routine so that once an initial solution is obtained, the jet

velocity ratio is fixed at the resulting value while further

variations in the other two system parameters are explored.

The results showed a considerable sensitivity to varia-

tions in craft drag; particularly that component of drag which

is not directly attributable to the propulsion system, referred

to here as ship drag. Ship drag is a craft characteristic which

is independent of the propulsion system design and it is held

constant at the input value throughout the design calculations.

Relatively small variations in ship drag produced comparatively

large changes in total system weight. This sensitivity is ap-

parently due to the fact that the cases studied for this report

fall in a region where the selection of a system design is con-

strained by a power limitation imposed by the specified prime

movers. If there were no power limitation * the optimum system

would have a very high jet velocity ratio and consequently a

low volume flow rate thereby reducing both ducting weight and

the weight of entrained water. If take-off drag, and therefore

the required take-off thrust, is so high that a power limita-

33

tion is imposed; then the jet velocity must be reduced in order

to reduce the required pump head sufficiently to bring required

power back within limits. The reduction in thrust due to the

lowered jet velocity must then be compensated for by increasing

the flow rate. This requires larger and heavier ducting and

results in a larger volume of entrained water. This suggests

that the optimum combination of craft and propulsion system

would be one in which the propulsion system design selected by

the design routine just bordered on being power limited.

In view of the above discussion, it appears that the pro-

pulsion coefficient based upon installed horsepower is an impor-

tant system parameter since it is basically a measure of the

fraction of installed horsepower required to overcome drag.

PCi = (Dtotal

V)/(55 ° SHPi»

The propulsion weight fraction and the propulsive coefficient

based on used horsepower at cruise speed are plotted against the

installed power propulsive coefficient at take-off in Figures 2

and 3 respectively. The curves are plotted for designs in which

ship drag was the only parameter varied. The other points plot-

ted represent designs in which other parameters were varied.

The results also showed some sensitivity to variations in

the strut length. This was to be expected since reducing the

strut length would reduce the required pump head as well as

reducing the amount of ducting and entrained water in the

system. The sensitivity was not nearly as pronounced as the

sensitivity to ship drag.

3^

The evaluation routine was tested by evaluating systems

designed by the design routine at both design and off design

speeds. The results were satisfactory and, when the evaluation

conditions were the same as design conditions, the operational

characteristics of the system as determined by the evaluation

routine were nearly identical to those calculated by the design

routine.

35

5. CONCLUSIONS AND RECOMMENDATIONS

A computer program to evaluate the performance of a

waterjet propulsion system has been developed and incorporated

into the program for design optimization of waterjet propulsion

systems. The evaluation routine can be used successfully to

evaluate a wide array of possible system configurations. A

lack of available data on the configuration and performance of

existing systems precluded the use of the evaluation routine to

analyze the performance of an actual system for this report*

When such information is available, it is recommended that this

be done. The results obtained from the evaluation routine could

then be compared with actual performance data to further eval-

uate the accuracy of the methods used in the program.

The sensitivity of the design routine to initial values of

the independent variables requires further study. The use of

either a random search or an additional pattern search is sug-

gested to explore further variations in inlet velocity ratio

and nacelle diameter ratio once the best jet velocity ratio has

been determined in the manner currently used in the program.

The results of the design routine are highly sensitive to

variations in ship drag when the available power is barely

adequate for the design conditions. This indicates that the

total hydrofoil design should be carefully tailored to the prime

mover so that the total power required at design conditions is

somewhat less than the total available power in order to allow

for growth. If the hydrofoil is designed so that maximum

36

available horsepower is required at either take-off or cruise

condition, the specified craft conditions must include an ade-

quate margin for growth. If not, a serious degradation of per-

formance would occur when the inevitable growth took place

because, if maximum power is already being used, there would be

no way of increasing available thrust to compensate for increased

drag without exceeding the power limitations of the prime mover.

37

BIBLIOGRAPHY

1. Gill, R.P., Design Optimization of Waterjet PropulsionSystems for Hydrofoils, Ocean Engineer Thesis, M.I.T.,May 1972.

2. Conner, B.T., A Study of Ram Type Intake Parameters,Ocean Engineer Thesis, M.I.T., June 1972.

3. Percival, R.C., Optimization of Waterjet Propulsion Pumpsfor Hydrofoil Applications, Ocean Engineer Thesis, M.I.T.,May 1972.

4. Brandau, J.H., Performance of Waterjet Propulsion Systems -

A Review of the State of the Art, Journal of Hydronautics,vol, 2, no. 2, pp. 6l-73t April 1968.

5. Arcand, L. and Comolli, C, Optimization of Waterjet Pro-pulsion for High Speed Ships, Journal of Hydronautics, vol.2, no. 1, pp. 2-8, 1968.

6. Chironis, E.P. ed., Gear Design and Application* McGraw-HillBook Co., New York, 1967.

7. Hatte, R. and Davis, H. , Selection of Hydrofoil WaterjetPropulsion Systems, AIAA Paper 66-732, August I966.

8. Hoerner, S.F., Fluid Dynamic Drag, published by author,1965.

9. Johnson, V.E., Waterjet Propulsion for High Speed Hydro-foil Craft, AIAA Paper 64-306, June 1964.

10. Levy, J., The Design of Waterjet Propulsion Systems forHydrofoil Craft, Journal of Marine Technology, vol. 2,no. 1, pp. 15-26, January 1965*

11. Traskel, J. and Beck, W.E., Waterjet Propulsion for MarineVehicles, AIAA Paper 65-2^5, March I965.

38

}

TOP VIEW

-*- V

FIGURE 1 : GENERAL DUCTING CONFIGURATION

39

o

&4

0.7

0.6

5 0-5

0.4

ow

a °- 3

w

0.2

0.1

0.0

TWO LM 2500 f s

TWO PUMPS

750 TON DISP.

2000 MILE RANGE

30 KNOT TAKE-OFF

45 KNOT CRUISE

_i_ j_

WITH FUEL

A WITHOUT FUEL

0.0 0.1 0.2 0.3

INSTALLED POWER PROPULSIVE COEFFICIENT AT TAKE-OFF

FIGURE 2: PROPULSION SYSTEM WEIGHT FRACTION VS. INSTALLED

POWER PROPULSIVE COEFFICIENT AT TAKE-OFF

40

0.7

0,6

0.5

0.4

0.3-

wMOH&,

&Oow>MWE3OhOos

QWwOh

wa 0.2

OSo

0.1 -

0.0

TWO LM 2500'

s

TWO PUMPS

750 TON DISP.

2000 MILE RANGE

30 KNOT TAKE-OFF

45 KNOT CRUISE

© ONLY DRAG VARIED

A OTHER PARAMETERS VARIED

0.0 0.1 0.2 0.3

INSTALLED POWER PROPULSIVE COEFFICIENT AT TAKE-OFF

FIGURE It CRUISE SPEED PROPULSIVE COEFFICIENT VS. INSTALLED

POWER PROPULSIVE COEFFICIENT AT TAKE-OFF

41

APPENDIX A

LIST OF SYMBOLS USED IN PROGRAM

SYMBOLS USED IN COMMON Jj-3

SYMBOLS USED IN H20JT NOT IN COMMON 56

SYMBOLS USED IN FCT NOT IN COMMON 58

SYMBOLS USED IN NACEL NOT IN COMMON 60

SYMBOLS USED IN ELBOW NOT IN COMMON 65

SYMBOLS USED IN STRUT NOT IN COMMON 6?

SYMBOLS USED IN JUNCT NOT IN COMMON 69

SYMBOLS USED IN PIPE NOT IN COMMON 70

SYMBOLS USED IN DIVRG NOT IN COMMON 71

SYMBOLS USED IN NOZZL NOT IN COMMON 73

SYMBOLS USED IN PUMP NOT IN COMMON 7^

SYMBOLS USED IN FUEL NOT IN COMMON 77

SYMBOLS USED IN PTTRN NOT IN COMMON 78

SYMBOLS USED IN OUTPUT NOT IN COMMON 79

kZ

Label

PARMS

DRAG

FLOW

LIST OF SYMBOLS

USED IN COMMON

VariableName Subscript

VJVO

VIVO

DIDM

TDRAG(I) I

1

2

3-5

STRTD(I)

POD(I)

SPRAY ( I

)

REST(I)*

VO(I)

TRIM(I)

Q(I)

De script ion/U sage

System parameters

Jet velocity ratio

Inlet velocity ratio

Inlet diameter tomaximum nacelle diameterratio

Drag estimates

Total craft drag atcondition I, pound force

Cruise condition

Take-off condition

Evaluation conditions

Strut drag at conditionI, pound force

Nacelle drag at conditionI v pound force

Spray drag at conditionI, pound force

TDRAG ( I ) -SPRAY ( I ) -STRTD ( I

)

-POD(I),pound force

Craft velocity at conditionIt foot per second

Craft trim angle at con-dition I, degree

Flow characteristics

Volume flow rate at con-dition I, cubic foot persecond

*3

Label

ELBW

CHARS

VariableName

AIN

AJET

AREA(ICOMP)

VJ(I)

VI(I)

Subscript Description/Usage

Inlet area, square foot

Jet area, square foot

Ducting cross-sectionalarea at station ICOMP,square foot

Jet velocity at conditionI, foot per second

Inlet velocity at con-dition I, foot per second

Elbow data

XK(IELB) IELB Radius ratio of elbowIELB

1 Strut elbow

2 Hull elbow

3 Pump elbow

4 Divergence elbow

RO(IELB) Duct radius at elbowIELB, degree

THATA ( IELB

)

Angle of bend of elbo

WIDTH

DEPTH

TYPE(3»ITYPE)

WGTS(LS,LC)

IELB, foot

Width of duct at elbowinlet

Depth of duct at elbowinlet

Contains name of elbowshape ITYPE

System characteristics

Weight of component LC

,

pound

M

LabelVariable

Name Subs

LS

cript Description/Usage

1 Structure

2 Water (or fuel)

LC

1 Nacelle

2 Strut elbow

3 Strut diffuser

k Hull elbow

5 Athwartships length

6 Pump elbow

7 Transition piece

8 Pump

9 Nozzle

10 Reduction gear

11 Fuel

12 Prime mover

13 Lift from nozzledepression

14 Total weight

15 Spare location

CGS(LG.LC) Centers of gravity <

LG

component LC, excludingfuel, gearbox, or primemover, foot

1 Structure vertical centerof gravity (from keel)

^5

LabelVariable

Name Subscript

2

3

DELH(I.ICOMP)

ICOMP

8

9

10-15

CGSX

CGSZ

H20

TEMP

PV

RHOW

Description/Usage

Structure longitudinalcenter of gravity(from transom)

Water vertical center ofgravity, (from keel)

Water longitudinal centerof gravity, (from transom)

Total head loss up to andincluding component ICOMPat condition I, foot

Same as defined except

Nozzle head loss only

Total system head loss(including elevation),DELH(I,9)=DELH(I,8)+DELH(I,7)

Spare locations

Total longitudinal centerof gravity systemexcluding gearbox, primemover and fuel, fromtransom, foot

Total vertical center ofgravity of system exclud-ing gearbox, prime moverand fuel, from keel, foot

Sea water (3*5% salinity)properties

Temperature, degreeFahrenheit

Vapor head, foot

Density, pound forcesecond squared per footto the fourth

46

Label

TOLER

PSUB

VariableName

GNU

HA

DELTA

GERAT(NSTG)

SHP(I.NSTG)

RPM(I,NSTG)

PERF(L,IENGN)


Viscosity, footsquared per second

Atmospheric head, foot

Check for optimum system

Pump system

Gear ratio required forpump NSTG

Shaft horsepower perprime mover requiredat condition I for pumpNSTG, horsepower

Axial speed of pump NSTGat condition I, revo-lution per minute

Prime mover IENGNCharacteristics (L)

L

1

5

ETAP(I.NSTG)

Maximum normal horsepowerat design speed, horse-power

Maximum intermittenthorsepower at designspeed, horsepower

Specific fuel consump-tion (SFC) at design speedand maximum normal horse-power, pound fuel perhorsepower hour

Design speed, RPM

Prime mover weight, with-out auxiliaries, pound

Efficiency of pump NSTGat condition I

^7

Label

SHIP

NACLL

VariableName Subscript

I

7

6,8

DISP

RANGE

BEAM

HS

HE

HCL

XLS

XLPE

XLP

DRAT

DM

A TA J.

AIAUX

ELEXT

ELENT

Description/Usage

Same as defined except

Reduction gear

Spare locations

Craft characteristics

Craft displacement, pound

Endurance, nautical mile

Beam, foot

Depth of submergence offoil, foot

Height of pump centerlineabove mean water, foot

Height of pump centerlineabove keel, foot

Distance of centerlineof strut root from transom,foot

Distance of pump exitfrom transom, foot

Length of pump, foot

Nacelle characteristics

Diameter ratio, Dl/DM

Maximum external diameter,foot

Inlet area per nacelle,square foot

Auxiliary inlet area pernacelle, square foot

Length of forebody, foot

Length of lip, foot

kQ

Label

CONST

STRTC

INDEX

VariableName

ELAUX

ELDIF

ELN

AAX(I)

PI

G

RHOD

TC

T

C

Tl

CI

CFM

IEVAL


Length due to auxiliaryinlet, foot

Length of diffuser, foot

Length of nacelle, foot

Portion of auxiliaryinlet area in use atcondition I, square foot

Constants

3.14159265

Acceleration of gravity,32.174, foot per secondsquared

Density of steel, 480,pound per cubic foot

Strut characteristics

Thickness to chord ratio

Thickness at root, foot

Chord at root, foot

Thickness at tip, foot

Chord at tip, foot

Chord at flying water-line, foot

Indices for programcontrol

<0

=0

Design/evaluation index

Evaluate at IEVAL points,no design

Design at cruise and take-off conditions only

49

LabelVariable

Name

IEQPT

ISTRT

NUMB

IENGN

Subscript

>0

1

3

1

3

2+|lEVAL

1

2

3

5

6

7

8

9

10

Description/Usage

Design at cruise and takeoff conditions and eval-uate at IEVAL points

No equipments or config-uration entered; totalsystem design/evaluation

Number of gas turbines isspecified

Number of gas turbines andnumber of pumps are speci-fied

Initial program condition

Design and/or evaluate

Evaluate only

Final program condition

Design only

Design and/or evaluate

Prime mover type

TF 35

TF 40

Proteus, 1500 rpm

Proteus, 1000 rpm

Tyne 1A

Tyne 1C

FT12A

LM 1500

LM 2500

FT4A-2C

50

LabelVariable

Name Subscript

11

Description/Usage

FT4A-12

12 FT^C-2

ITYPE Elbow shape

1 EllipseV

2 Circle

3 Rectangle

k Square

ICOMP Component index

1 Nacelle outlet

2 Strut elbow

3 Strut diffuser exit

4 Hull elbow

5 Athwartships length

6 Pump elbow

7 Transition piece

8 Pump inlet

9 Nozzle throat

NPUMP Number of pumps

NGT Number of gas turbines

IGEAR Type of reduction gear

1 Single reduction with idler

2 Planetary

3 Double reduction, doublebranch

ITABL Interpolation parameters

51

Label

CDRAG

WEGT

PUMM

VariableNames

CSTRT(I)

CPOD(I)

CSPRY(I)

XWD(NSTG)

XWW(NSTG)

XWG(NSTG)

XWF(NSTG)

QQ(I)

DlS(NSTG)

D2S(NSTG>

XNS(NSTG)

SM(I.NSTG)

PLP(NSTG)

NSTG


Computed drags

Computed strut drag atcondition I, pound force

Computed nacelle drag atcondition I, pound force

Computed spray drag atcondition I, pound force

Pump, gear and fuel weights

Pump NSTG dry weight,pound

Pump NSTG wet weight,pound

Gearbox weight associatedwith pump NSTG, pound

Fuel weight associatedwith pump NSTG, pound

Pump characteristics

Flow rate per pump atcondition I, cubic footper second

Inlet tip diameter ofpump NSTG, foot

Exit tip diameter of pumpNSTG, foot

Specific speed of pumpNSTG, cfs units

Suction specific speed ofpump NSTG at condition I,cfs units

Length of pump NSTG, foot

Indicator of pump type

1 Axial pump with singleinducer impeller

52

LabelVariable

Name

HEAD

SHI (I, NSTG)

XIM

HPP(I)

HSV(I)

THOM(I)

PHI (I, NSTG)

WF

WG

FRATE(I)

PINLP


2 Axial pump with inducerand one impeller stage

3 Axial pump with inducerand two impeller stages

k Centrifugal pump withmaximum of ten paralleldouble suction impellers

5 Spare location

Head coefficient of pumpNSTG at condition I

Number of parallel doublesuction impellers forcentrifugal pump

Number of impellers, notincluding inducer, forcentrifugal pump

Pump flow characteristics

Pump head at condition I,foot

Net positive suction headat condition I, foot

Thoma's cavitation indexat condition I

Flow coefficient of pumpNSTG at condition I

Working variable for fuelweight, pound

Working variable for gearweight, pound

Fuel consumption rate atcondition I, pounds perhour

Pump inlet piping para-meters

53

Label

WARN

NOZL

VariableName

ALPHA

IFUEL

IPUMP

TYGER


Junction angle

Warning generated duringevaluation

CAV(I,,J) J Cavitation indicator atcondition I at location J

1 Nacelle exterior

2 Strut exterior

3 Nacelle inlet lip

4 Strut elbow

5 Pump inlet

6 Pump impeller

Nozzle characteristics

JANGL Nozzle depression angle

***** Unlabeled common variables

.TRUE.

.FALSE.

.TRUE.

.FALSE.

.TRUE.

Logical variable for fuelcalculation

Make fuel calculation

Do not make fuel calcula-tion

Logical variable for pumpcalculation

Pump design parametershave been calculated/speci-fied

Pump design parametershave not been calculated/specified

Logical variable for gearcalculation

Gear type is specified

5^

VariableLabel Name Subscript Description/Usage

•FALSE. Gear type is to beselected by program

55

Variable

PARM(3)

ENGN(3,IEGN)

EHP(I)

DEL(3)

DELMIN(3)

VK(I)

IPRNT

DISPL

IN

MAX

XJ

IK

IL

KM

Kl

WEIGT

IM

DISPL

I

IJ

J

VARIABLES USED IN H20JTNOT IN COMMON

Description

Working system parameters

Contains name of engine IENGN for output

Effective horsepower at condition I, horsepower

Initial step sizes of system parameters

Minimum step sizes of system parameters

Craft speed at condition I, knot

Print data set reference number

Craft displacement, long ton

Estimate of minimum number of gas turbinesrequired to power craft

Estimate of maximum number of gas turbinesneeded to power craft

Working variable for number of gas turbines

Working variable for craft condition I

Working variable for IN

Minimum number of pumps to be used for XJgas turbines

Maximum numberof pumps to be used for XJ gasturbines

Propulsion system weight, long ton

Working variable for prime mover character-istic L

Craft displacement, long ton

Index for do loops

Working variable for check on power adequacy

Index for do loop

56

Variable

ISAVE

N

XMIN

MK

JNUM

Description

Working variable for MAX

Working variable for output of prime movertype

Factor for minimum acceptable prime moverSHP operation

Working variable for prime mover character'istic L

Working variable for NUMB

57

Variable

APOD(I)

ASTRT(I)

ASPRY(I)

C(I)

TSUM

DSIG

TOTAL

SIGMA

SUMZ

SUMX

SUM

ZSUM

XSUM

SPD

J

JDRAG

1

2

LIST OF VARIABLES USED IN FCTNOT IN COMMON

Description

Difference between present and previousnacelle drag calculations at conditions I,pound force

Difference between present and previous strutdrag calculations at condition I, pound force

Difference between present and previous spraydrag calculations at condition I, pound force

Margin factor for thrust at condition I

Working variable for propulsion system weight,pound

Working variable for SIGMA

Total head less vapor head, foot

Head above vapor head, foot

Working variable for moment in vertical plane,due to weights, foot pound force

Working variable for moment on longitudinalplane due to weights, foot pound force

Working variable for system weights, pound

Total moment in vertical plane due to weights,foot pound force

Total moment on longitudinal plane due toweights, foot pound force

Working variable for jet velocity calcula-tion, foot per second


Indicator of acceptable drag accuracy

New drag calculation is within $% of previouscalculation

New drag calculation is greater than 5% ofprevious calculation, redesign strut andnacelle

58

Variable

ANGLE

COEF

1

KOUNT

I

PARM(K)

K

1

2

DDRAG ( I

)

DSPRY(I)

DSTRT ( I

)

DPOD(I)

Description

Optimum nozzle depression angle , radian

Factor for nacelle drag calculation

Strut must be resized due to cavitation

Use nacelle design


Craft condition

Working variable for system parameters

VJVO

VIVO

Previous acceptable total drag calculation atcondition I, pound force

Previous acceptable spray drag calculation atcondition I, pound force

Previous acceptable strut drag calculation atcondition I, pound force

Previous acceptable nacelle drag calculationat condition I, pound force

59

Variable

ZK

SPO

PVP

SIGTV

JNUMB

I

CPEX

K

J

XD

DIDMX

QI

DI

CPIN

QIN

QC

QAUX

KDEX

VR

KNUMB

LIST OF VARIABLES USED IN NACELNOT IN COMMON

Description

Percentage of auxiliary inlet area permittingflow

Static pressure at inlet, pound per squarefoot

Vapor pressure, pound per square foot

Incipient turning vane cavitation number,referenced to diffuser exit velocity


Craft condition, also index for do loops

Peak external pressure coefficient

Working index for do loop for ELEXT/DM values

Working index for do loop for VIVO values

Length of forebody to maximum diameter ratio,ELEXT/DM

Maximum permissible diameter ratio

Flow rate per strut, cubic foot per second

Nacelle inlet diameter, foot

Peak internal pressure coefficient

Take-off flow rate per nacelle through inlet,cubic foot per second

Take-off flow rate per nacelle, total, cubicfoot per second

Auxiliary flow rate required to avoid cavita-tion, cubic foot per second

Counter for iterations on diffuser length

Velocity ratio at take-off condition, basedon flow through inlet


60

Variable Description

VIJ

PRLJ

YI2

PRL2

PTI

SPI

VIAUX

PRAUX

PTAUX

DYP

PC

QDIF

PHI

PHS

X

D2

Dl

ELMAX

ELMIM

II

Inlet velocity at evaluation condition,based on flow through inlet

Pressure recovery coefficient of lip atevaluation condition

Inlet velocity at take-off condition, basedon flow through inlet

Pressure recovery coefficient of lip at take-off

Inlet stagnation pressure immediately aft oflip at take-off, pound per square foot

Inlet static pressure immediately aft of lipat take-off, pound per square foot

Inlet velocity in auxiliary inlet, foot persecond

Pressure recovery of auxiliary inlet

Stagnation pressure inside auxiliary inlet,pound per square foot

Net dynamic pressure immediately aft of lip,pound per square foot

Average inlet stagnation pressure of combinedflow, pound per square foot

Working variable for diffuser flow rate,cubic foot per second

Equivalent angle of forebody, radian

Sine of equivalent angle of forebody

Length of auxiliary inlet, foot

Diffuser exit diameter, foot

Inlet diameter, foot

Maximum permissible length of diffuser, foot

Minimum permissible length of diffuser, foot


61

Variable

EL

DEL

ELD

ELL

ELFAC

DDM

XKT

REL

RED

DL

CDRG

ANGL

CDIF

POW

POWI

EM

AEXN

REND

DDIF

PLOSS

VAOUT

SQUAR

Description

Working variable for diffuser length, foot

Working variable for change in diffuser length,foot

Working variable for nacelle length, foot

Working variable for nacelle length, foot

Working variable for excess in nacelle lengthdue to diffuser, foot

Average diffuser diameter, foot

Form loss coefficient of diffuser

Reynolds number, based on nacelle length

Reynolds number, based on inlet diameter

Ratio of maximum external diameter to nacellelength

Computed drag coefficient

Equivalent half angle of diffuser, degree

Diffuser expansion factor

Power loss due to drag and duct loss ofdiffuser, horsepower

Previous power loss calculation for diffuserlength, horsepower

Factor in wetted surface calculation

Wetted surface area, square foot

Reynolds number, based on inlet diameter

Total pressure loss in diffuser, pound persquare foot

Total pressure loss in nacelle, pound persquare foot

Average exit velocity, foot per second

Factor in critical velocity calculation

62


VCRIT

VMAX

RENL

NL(2)

ML(2)

KL(2)

JL(2)

IL(2)

VRT(6)

XDT(IO)

PRLT ( 6

)

SIGI(I)

PTO(I)

XDTT(J)

CDUMX(K)

CDUMY(L)

CD(I)

DIDMT(J)

VRTT(J)

DLIP(I)

QO(I)

VELR(I)

Critical velocity in strut elbow, foot persecond

Maximum velocity at nacelle exit, foot persecond

Reynolds number, based on nacelle length

Interpolation parameters





Data array of velocity ratios

Tabulated forebody length to inlet diameterratios

Tabulated lip pressure recovery coefficients

Free stream cavitation index at condition I

Stagnation pressure at craft condition I,pound per square foot

Tabulated ELEXT/DM ratios for trim angle J

Dummy array of peak pressure coefficients forVIVO K

Dummy array of velocity ratios for ELEXT/DM L

Drag coefficients at craft condition I

Tabulated Dl/DM values for ELEXT/DM J

Dummy array of velocity ratios for angle ofattack (J), internal

Lip loss coefficient at craft condition I

Free stream dynamic pressure at craft conditionI, pound per square foot

Inlet velocity ratio at craft condition I

63

Variable

TLIP(I)

VRTEX(I)

VRMAX(I)

FRICT

Description

Working variable for DLIP(I)

Same as VRTT(I) but external

Maximum permissible velocity ratio at craftcondition I

Function statement, calculates Moody frictionfactor for smooth pipe, based on Reynoldsnumber

6J+

Variable

SHAPE(3tITYPE)

THETA(J)

XLOSS(J)

ROA(IO)

RE

FRICT

CORR

REMAX

KOUNT

IELB

FACTR

RIN

ROUT

RATIO

XN

N

1

2

3

4

VARIABLES USED IN ELBOWNOT IN COMMON

Description

Contains name of shape ITYPE

Data array of elbow angles

Data array of elbow loss coefficients withthin, circular arc turning vanes

Outside radius of splitters, foot

Reynolds number of duct


Function statement, calculates head losscorrection factor for different Reynoldsnumbers

Maximum Reynolds number permitted for splitterloss equation


Index indicating which elbow is beingdesigned/evaluated

Strut

Hull

Pump

Divergence

Factor used in splitter loss calculation

Inside radius of bend, foot

Outside radius of bend, foot

Desired radius ratio, 4.3

Number of subdivided elbov/s required toachieve RATI0=4.3

Number of subdivided elbov/s used

65

Variable

Nl

SUM

RIA

V

HGT

AA

RAD

XCORR

XKT

DIAM

VOLV

VOL

AREA1

IJ

IK

I

RATEO

HEAD

Description

Number of splitters corresponding to N

Working variable of sum of head times sub-divided elbow area, foot cubed

Inside radius of subdivided elbow, foot

Average velocity, foot per second

Height of subdivided elbow, foot

Equivalent cross-sectional area of subdividedelbow based on HGT , square foot

Equivalent radius of subdivided elbow, foot

Ratio of head loss correction factors fordiffering Reynolds numbers

Head loss coefficient of subdivided elbow

Equivalent diameter, foot

Volume of splitters, cubic foot

Volume of splitters and elbow structure,cubic foot

Duct area per elbow, square foot

Working variable for shape determination

Working variable for shape determination

Working variable for number of subdividedelbows N

Ratio of inside radius to outside radius ofsubdivided elbows

Average head loss in elbow, foot

66

Variable

THET2

EXPAN

ARATO

VL

SIGMA

SIGMI

CM

DEIN

WIDE

DEOUT

DEAVE

STRT

XLONG

STAN

THETA

ECOEF

FORML

VELIN

VLOUT

RES

CDS

CDSP

RE

LIST OF VARIABLES USED IN STRUTNOT IN COMMON

Description

Array of data of equivalent angle of dif-fuser, degree

Array of data of expansion coefficient

Area ratio of strut diffuser

Local maximum velocity, external, foot persecond

Local cavitation number, external

Incipient cavitation number, external

Mean chord, foot

Strut inlet equivalent diameter, foot

Width of duct at strut exit, foot

Strut exit equivalent diameter, foot

Average equivalent diameter, foot

Vertical strut length, foot

Actual strut length, foot

Arctangent of equivalent diffuser angle

Equivalent angle of diffuser, 29, degree

Diffuser expansion factor

Diffuser expansion loss coefficient

Average inlet velocity, foot per second

Average exit velocity, foot per second

Strut Reynolds number, based on mean chord

Strut drag coefficient

Spray drag coefficient

Duct Reynolds number, based on inlet velocity

67

Variable

PIPEL

TOTAL

HEAD

KOUNT

HGT

CGWS

Description

Duct friction loss coefficient

Total loss coefficient

Head loss of diffuser, foot


Elevation of strut, foot

Vertical center of gravity of duct, foot

68

Variable

DIAM

FRCTL

KOUNT

AJCT

FRCTJ

XLAMD

FLONG

AJCTL

AMIXL

V

XPUMP

RE

BETA(J)

ALAMD(J)

FRICT

LIST OF VARIABLES USED IN JUNCTNOT IN COMMON

Description

Duct diameter, foot

Friction loss coefficient for athwartshipslength


Length of fore and aft ducting to pump inlet,foot

Friction loss coefficient for junction

Working variable for AMIXL calculation

Length of athwartships ducting, foot

Total loss coefficient of junction

Mixing loss coefficient of junction


Number of gas turbines + 1


Data array of junction angles, degree

Data array of mixing loss coefficientcorresponding to BETA(J)


69

Variable

KOUNT

V

DIAM

RE

APIPE

FRCTL

XPUMP

XKT

XLONG

FRICT

LIST OF VARIABLES USED IN PIPENOT IN COMMON

Description



Duct diameter, foot


Length of fore and aft pipe to pump inlet,foot


Number of gas turbines

Friction loss coefficient of fore and aftlength

Length of athwartships pipe, foot


70

Variable

FRICT

KOUNT

RE

DIVL

DWGT1

DWGT2

DWGT3

WWGT1

WWGT2

WWGT3

CGWX1

CGWX2

CGWX3

DIAM

FRCTL

DIVLC

XPUMP

ANGLE

HEADL

FLONG

LIST OF VARIABLES USED IN DIVRGNOT IN COMMON

Description




Divergence loss coefficient, not includingfriction

Duct weight of divergence angle, pound

Duct weight of divergence length, pound

Duct weight of pump inlet angle, pound

Water weight of divergence angle, pound

Water weight of divergence length, pound

Water weight of pump inlet angle, pound

Longitudinal center of gravity of divergenceangle, from transom, foot

Longitudinal center of gravity of divergencelength, from transom, foot

Longitudinal center of gravity of pump inletangle, from transom, foot

Duct diameter, foot


Total divergence loss coefficient

Number of gas turbines + 1

Divergence angle, also pump inlet angle, radian

Total divergence head loss, foot

Athwartships length, foot

71

Variable

XLONG

V

ADIV

THETA(J)

COEF(J)

Description

Fore and aft length, foot


Divergence length, ADIV = XLONG/COS (ANGLE)

,

foot

Data array of divergence angles, degree

Data array of divergence loss coefficientswithout friction, corresponding to THETA(J)

72

Variable

KOUNT

XLPS

XFAC

XPUMP

ANOZ

XLNOZ

DT

DJ

XCORR

RE

AREA1

AJET1

QQ

FRICT

LIST OF VARIABLES USED IN NOZZLNOT IN COMMON

Description

Working variable fro craft condition I

Dummy nozzle length, foot

Check on whether nozzle exits through bottomor stern

Number of pumps

Optimum nozzle depression angle, radian

Nozzle length, foot

Nozzle throat diameter, foot

Nozzle jet diameter, foot

Nozzle head loss factor

Reynolds number, based on average diameter andvelocity

Throat pipe area, square foot

Jet pipe area, square foot

Flow rate per nozzle, cubic foot per second


73

Variable

K

J

I

XPUMP

THOMI

DRAT

XXLP

CW

QX

CA

CB

HX

RX

PHRAT

XNGT

ETAPP

HP

THOMS

HHP

BETA2

JNUMB

ETAX

LIST OF VARIABLES USED IN PUMPNOT IN COMMON

Description

Cruise condition indicator

Take-off condition indicator

Index for do loops

Number of pumps

Lower limit of Thoma's criterion for singleinducer axial pump

Hub to tip diameter ratio

Factor for pump length

Weight coefficient

Ratio of cruise flow rate to take-off flow rate

Factor for RPM calculation

Factor for RPM calculation

Ratio of design pump head to off design head

Ratio of design to off design pump RPM

Ratio of off design to design flow coefficients


Product of pump and gearbox efficiencies

Inducer head for one and two stage axialpump designs, foot

Thoma's cavitation criterion for inlet toaxial stage

Axial stage pump head, foot

Exit blade angle, radian

Working variable for numb

Ratio of off design to design purot) efficiencv

7^

Variable

XNNS

BD

CC

AA

IMPL

M

N

PC(K,J)

PCA(K.J)

PCC(K.J)

XRPM(M)

XD1(M)

RPK(M)

XPUP(M)

YLP(M)

XERAT(M)

APUP(NSTG)

WRAT(NSTG)

WD(M)

WW(M)

Description

Non-dimensional specific speed

Impeller exit width ratio

Factor in flow coefficiect calculation

Factor in flow coefficient calculation

Maximum number of impellers permitted forcentrifugal pump, =10

Working variable for number of centrifugalpump impellers

Working variable for NSTG

Inducer head curve coefficients

Inducer plus axial stage head curve coefficients

Centrifugal pump head curve coefficients

Working variable for off design RPM ofcentrifugal pump with M impellers , RPM

Working variable for inlet tip diameter, D1S,foot

Working variable for design RPM of centrifugalpump with M impellers, square foot

Working variable for centrifugal pump area withM impellers, foot squared

Working variable for centrifugal pump lengthwith M impellers, foot

Working variable for gear ratio required forcentrifugal pump with M impellers

Inlet area of pump NSTG, square foot

Weight ratio of pump NSTG, including pumpdry and wet weight, gearbox and fuel

Working variable for XWD(NSTG) for centri-fugal pump with M impellers

Working variable for XWW(NSTG) for centri-fugal pump with M impellers

75


WWG(M) Working variable for XWG(NSTG) for centri-fugal pump with M impellers

QQ(I) Flow rate per pump at condition I, cubicfeet per second

76

Variables

CFS

CA

CD

N

XN

TI

UK

XJ

I

H

SHPP

SHNG

M

WT(ITIME)

DIS(ITIME)

VJJ(ITIME)

ENN

LIST OF VARIABLES USED IN FUELNOT IN COMMON

Description

Constant for SFC calculation

Cruise condition drag to lift ratio

1 + total system head loss coefficient,based on jet velocity

Number of intervals endurance is divided into+ 1

Number of intervals endurance is divided into

Time to cover one range interval at constantV0(1), hour

Index for shifting SFC curves

Factor to convert SFC if SHP is less than 70#of design SHP

Working index for N

Head required, foot

Total thrust required, horsepower

Total thrust required per engine, horsepower

Working index for N

Weight of fuel used in time increment ITIME,pound

Displacement at time increment ITIME, pound

Jet velocity at time increment ITIME, footper second

Working variable for XJ

77

Variable

PSI(N)

THETA(N)

PHI(N)

DEL(N)

DELMIN(N)

DIR(N)

SAVE(N)

S

SPHI

SPSI

NUMB

RHO

ICALL

K

I

N

SIGN(N)

LIST OF VARIABLES USED IN PTTRNNOT IN COMMON

Description

Current basepoint coordinate of parameter N

Previous basepoint coordinate of parameter N

Present exploratory point coordinate ofparameter N

Current step size of parameter N

Minimum step size of parameter N

Last successful direction of parameter N

Working variable for PHI(N)

Working variable for function value

Working variable for function value at PHIcoordinates

Current best function value at PSI coor-dinates

Counter for minimum step size check

Step size change factor

Indicator of current point move

Index for do loop

Index for do loop

Number of parameters of search

Directed step size of parameter N

78

Variable

IPRNT

J

SUM

I

DRATO

IK

XNGT

K

L

LL

KLL

H

NIMP

TFM

WTRAT

WRATF

ENGN(IENGN)

YJRAT(I)

VIRAT(I)

HEADL(I.ICOMP)

CONDS(2,I)

ELBWS(2,IK)

LIST OF VARIABLES USED IN OUTPUTNOT IN COMMON

Description

Print data set reference number

Working variable for condition I

Total duct head loss, excluding elevation,foot

Index for do loop

Strut diffuser area ratio

Index for number of elbows in system


Index for do loop

Index for implied do loop in output statement

Working variable to point to correct headloss for output

Working variable to point to correct formatstatement for head loss output

Index for implied do loop in output statement

Number of impellers in pump

Strut thickness at flying waterline, foot

Total propulsion system weight ratio

Propulsion system weight ratio, excluding fuel

Contains name of engine IENGN

Jet velocity ratio at craft condition I

Inlet velocity ratio at craft condition I

Head loss of component ICOMP at craft con-dition I

Label for craft condition I

Label for elbow IK

79


PC (I) Propulsive coefficient at craft condition I

LABEL(5,M) Labels for output

VK(I) Craft speed at condition I, knots

L0CAT(6,J) Labels for cavitation locations

80

APPENDIX B

PROGRAM LISTING

SAMPLE INPUT 82

SUBROUTINE H20JT 84

SUBROUTINE FCT 92

SUBROUTINE ELBOW 97

FUNCTION CFS 102

FUNCTION TABLE 103

SUBROUTINE STRUT 106

SUBROUTINE JUNCT 111

SUBROUTINE PIPE 114

SUBROUTINE DIVRG 116

SUBROUTINE NOZZL 120

SUBROUTINE PUMP 122

SUBROUTINE GEAR 133

SUBROUTINE FUEL 136

SUBROUTINE NACEL 138

SUBROUTINE PTTRN 149

SUBROUTINE OUTPUT 153

BLOCK DATA 160

Note t Statement numbers in right hand margin indicatestatements retained from design program listed inreference 1

•

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APPENDIX C

USERS* MANUAL

REQUIRED INPUTS FOR OPTIMIZATION I63

OPTIONAL INPUTS FOR OPTIMIZATION 164

SAMPLE INPUT FOR OPTIMIZATION I65

SAMPLE OPTIMIZATION OUTPUT 16?

REQUIRED INPUTS FOR EVALUATION 170

OPTIONAL INPUTS FOR EVALUATION 172

SAMPLE INPUT FOR EVALUATION 173

SAMPLE EVALUATION OUTPUT 176

162

REQUIRED INPUTS FOR OPTIMIZATION

Symbol Required Units

VO(l) feet per second

V0(2) feet per second

REST(l) pounds

REST ( 2

)

pounds

STRTD(l) pounds

STRTD(2) pounds

SPRAY(l) Pounds

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POD(l) pounds

POD(2) pounds

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TRIM(2) degrees

RANGE nautical miles

DISP pounds

BEAM feet

TYGER (none)

163

OPTIONAL INPUTS FOR OPTIMIZATION

Symbol

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XK(<0

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THATA(3)

THATA(^)

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ALPHA

Required Units

(none)

(none)

(none)

(none)

degrees

degrees

degrees

degrees

degrees Farenheit

feet

feet

feet

feet

feet

(none)

(none)

(none)

(none)

(none)

(none)

degrees

Default Value

1.5

1.5

1.5

2.0

90.

90.

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30.

59.

5.

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2.

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2.

8

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REQUIRED INPUTS FOR EVALUATION


STRTD(I) pounds

POD(I) pounds

SPRAY(I) pounds

REST ( I

)

pounds

VO(I) feet per second

TRIM(I) degrees

AIN feet squared

AJET feet squared

AREA(l) feet squared

AREA(3) feet squared

AREA(8) feet squared

RANGE nautical miles

DISP pounds

BEAM feet

TYGER (none)

DRAT (none)

DM feet

AIAUX feet squared

ELEXT feet

ELENT feet

AI feet squared

ELAUX feet

ELDIF feet

ELN feet

170


TC (none)

T feet

C feet

Tl feet

CI feet

IEVAL (none)

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NPUMP (none)

NGT (none)

NSTG (none)

RPM(2,NSTG) revolutions per minute

QQ(2) cubic feet per second

DIS(NSTG) feet

D2S(NSTG) feet

PLP(NSTG) feet

HPP(2) feet

JANGL radians

171

OPTIONAL INPUTS FOR EVALUATION

Symbol Required Units Default Value

XK(1) (none) 1.5

XK(2) (none) 1.5

XK(3) (none) 1.5

XK(4) (none) 2.0

THATA(l) degrees 90.

THATA(2) degrees 90.



TEMP degrees Farenheit 59.

HS feet 5.

HE feet 10.

HCL feet 2.

XLS feet 20.

XLPE feet 2.

IENGN (none) 8

IGEAR (none) calculated

ALPHA degrees 0.

WGTS(2,11) pounds 0.

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