Induced field point pressures of a ducted propeller system

1 Ala 1975

NAVAL SHIP RESEARCH AND DEVELOPMENT CENTER Bethesda, Md. 20084

INDUCED FIELD-POINT PRESSURES OF A DUCTED PROPELLER SYSTEM

by

John J. Nelka

APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED

SHIP PERFORMANCE DEPARTMENT RESEARCH AND DEVELOPMENT REPORT

Lab.

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Technische escnool

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The Naval Ship Research and Development Center is a U. S. Navy center for laboratory

effort directed at achieving improved sea and air vehicles. It was formed in March 1967 by II

merging the David Taylor Model Basin at Carderock, Maryland with the Marine Engineering Laboratory at Annapolis, Maryland.

Naval Ship Research and Development Center Bethesda, Md. 20084

*REPORT ORIGINATOR

OFFICER-IN-CHARGE CARDEROCK

05

MAJOR NSRDC ORGANIZAPONAL COMPONENTS NSRDC COMMANDER SYSTEMS DEVELOPMENT DEPARTMENT SHIP PERFORMANCE DEPARTMENT 15 STRUCTURES. DEPARTMENT 17 SHIP ACOUSTICS DEPARTMENT 19 MATERIALS DEPARTMENT 00 TECHNICAL DIRECTOR 01 11 OFFICER-IN-CHARGE ANNAPOLIS 04 AVIATION AND SURFACE EFFECTS DEPARTMENT 16 I COMPUTATION AND MATHEMATICS DEPARTMENT 18 PROPULSION AND AUXILIARY SYSTEMS I DEPARTMENT 27 I CENTRAL INSTRUMENTATION DEPARTMENT 29 _ NDW-NSRDC 3960/43b (Rev. 3-72 GPO 928-1,0 11 28

UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (When Data Entered)

DD1 FJANORM73 1473 EDITION OF 1 NOV 65 IS OBSOLETE

S/N 0102-014- 6601 UNCLASSIFIED

SECURITY CLASSIFICATION OF THIS PAGE (When Data Brtterad)

REPORT DOCUMENTATION PAGE BEFORE COMPLETING FORMREAD INSTRUCTIONS 1. REPORT NUMBER

4270

2. GOVT ACCESSION NO. 3. RECIPIENT'S CATALOG NUMBER

4 TITLE (and Subtitle)

INDUCED FIELD-POINT PRESSURES OF A DUCTED PROPELLER SYSTEM

5. TYPE OF REPORT 8 PERIOD COVERED Final

6. PERFORMING ORG. REPORT NUMBER

7. AUTHOR(s) John J. Nelka

E. CONTRACT OR GRANT NUMBER(s)

9 PERFORMING ORGANIZATION NAME AND ADDRESS Naval Ship Research and Development Center

Bethesda, Maryland 20084

10. PROGRAM ELEMENT, PROJECT, TASK

AREA &WORK UNIT NUMBERS

Task Area SF 43 432 103 Work Unit Numbers:

1-1528-025 in FY 73 1-1544-257 in FY 74

ill. CONTROLLING OFFICE NAME AND ADDRESS Naval Ship Systems Command Washington, D. C. 20360

12. REPORT DATE October 1974 13. NUMBER OF PAGES

47

14. MONITORING AGENCY NAME 8 ADDRESS(i( different from Controlling Office) 15. SECURITY CLASS. (of this report)

UNCLASSI F I ED

15a, DECLASSIFICATION/DOWNGRADING SCHEDULE

16. DISTRIBUTION STATEMENT (of this Report)

APPROVED FOR PUBLIC RELEASE: DISTRIBUTION UNLIMITED

17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, if different from Report)

18_ SUPPLEMENTARY NOTES

19. KEY WORDS (Continue on reverse side if necessary and Identify byblocknumber)

Blade-Frequency Duct Forces Blade-Frequency Pressures Cavitation

Ducted Propeller Field-Point Pressures

20. ABSTRACT (Continue on reverse side If necessary and identifybyblock number)

Total fluctuating pressures were measured on the internal surface of a 0-degree angle-of-attack duct of a ducted propeller system (Kort nozzle type). The effects of blade loading in uniform flow and propeller blade cavitation in nonuniform flow on the harmonics of the frequency propeller-induced pressure were determined. Also determined were the blade-frequency pressure-induced duct forces. Experimental results indicate that the blade-blade-frequency

(Continued on reverse side)

-UNCLASSIFIED

CLASSIFICATION OF THIS RAGE(When Dote Entered) (Block 20 continued)

pressures increase for an increase in blade loading with the second. and third blade=

frequency pressures being significant with respect to the blade-frequency _pressure.

Fluctuating blade-frequency vertical forces determined by integrating the pressure

results from nonuniform inflow noncavitating conditions were approximately 1-percent

of the mean thrust. In the experiments conducted at a given loading, cavitation on

the propeller blades tended to increase the blade-frequency pressure downstream of the propeller by as much as a factor of three.

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TABLE OF CONTENTS

LIST OF FIGURES,

1 Ducted Propeller Apparatus .0 . , _F 3

2 Drawing of Propeller 3714

3 Wake Screen

4 Wake Distribution .. . 9

Open-Water Experimental Apparatus I! 12

6 Instrumentation A V

7 Measured Blade-Frequency Pressure Amplitudes at Thrust

Coefficient Values KT = 0.052, 0.159., and 0.268 for

1-Percent Radius Tip Clearance , 17

8 Measured Blade-Frequency Phase at Thrust Coefficient

Values KT = 0.052, 0.159, and 0.268 for 1-Percent

Radius, Tip Clearance .. . 18

ABSTRACT . 9,6 0.

Page

ADMINISTRATIVE INFORMATION

INTRODUCTION

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EXPERIMENTAL EQUIPMENT' .., ... _,,, =, 0 .,

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EXPERIMENTAL :PROCEDURE re ii.: i A v: vs ,

DATA ANALYSIS. ... .... , ... . ...

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DISCUSSION OF RESULTS , _:.. .., 16

UNIFORM FLOWRANGE OF ADVANCE COEFFICIENTS NONUNIFORM FLOWADVANCE COEFFICIENT NEAR

MAXIMUM OPEN-WATER SYSTEM EFFICIENCY ._, 0 :

Noncavitating ".: . .., i. , ,. tai ii

Cavitating, . ,.

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PROPELLER-INDUCED DUCT FORCES . ..,

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SUMMARY AND CONCLUSIONS .. .: . -0 .. OF .

ACKNOWLEDGMENT . . .. .. .... - ,-,-

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APPENDIX DETERMINATION OF PROPELLER-INDUCED FORCES

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9 Measured Blade-Frequency Pressure Amplitudes as a Function

of Wake Screen Position at Mean Thrust Coefficient

KT = 0.159 and 1-Percent Radius Tip Clearance 27

10 Measured Blade-Frequency Phase as a Function of Wake

Screen Position at Mean Thrust Coefficient KT = 0.159

and 1-Percent Radius Tip Clearance 28

11 Cavitation Patterns of Propeller 3714 in 0-Degree Duct at

Various Cavitation Numbers 29

12 Real Time Analyzer Results of the Amplitudes of the

Various Multiples of the Blade-Frequency Pressure at Mean Thrust Coefficient KT = 0.159 and 1-Percent

Radius Tip Clearance, Nonuniform Flow 32

1 3 Calculated Blade-Frequency Propeller-Induced Forces as

a Function of Propeller Blade Position at Mean Thrust Coefficient KT = 0.159 and 1-Percent Radius Tip

Clearance 34

LIST OF TABLES

1 Duct Camber and Thickness Distribution 5

2 Axial Location of Pressure Transducers with Respect to

Propeller Reference Plane and Leading Edge of Duct 5

3 Ducted Propeller Open-Water Ahead Characteristics 11

4 Thrust Coefficients Selected for Water Tunnel Experiments 11

5 First, Second, Third, and Fourth Blade-Frequency Pressure

Amplitudes and Phases as a Function of Axial Position, Wake Screen Position, and Cavitation Number at Mean Thrust Coefficient KT = 0.159 and 1-Percent Ducted

Propeller Radius Tip Clearance 20

6 Ratios of the Second, Third, and Fourth Blade-Frequency

Pressure Amplitudes to the First Blade-Frequency Amplitude

for Cavitating and Noncavitating Flows 23

7 Comparison of First, Second, Third, and Fourth

Blade-Frequency Pressure Amplitude Results Using the

Interdata Minicomputer and the Real Time Analyzer 31

.

NOTATION

AE Expanded blade area, A, = Z cdr

A, Disk area, A, = 7rD2/4

AE/A, Expanded area ratio

An _{Incremental surface area}

am Fourier cosine coefficient of the m th harmonic of the _{pressure signal}

a, Constant term of the pressure signal

az _{Fourier cosine coefficient of the blade-frequency harmonic of the}

pressure signal

bm _{Fourier sine coefficient of the m th harmonic of the pressure signal}

bz _{Fourier sine coefficient of the blade-frequency harmonic of the pressure}

signal

Cm Amplitude of the m th harmonic of the _{pressure signal}

Cz _{Amplitude of the blade-frequency harmonic of the pressure signal}

Blade section chord length Propeller diameter

FA,H,V Half-amplitude of unsteady axial, horizontal, and vertical

blade-frequency forces

fm _{Blade section camber}

Advance coefficient, J = VA/ND

Nondimensional pressure coefficient, Kp = p/pN2D2

Kpz Nondimensional blade-frequency pressure coefficient, _{Kpz =}Cz /pN2 D2

KQ Torque coefficient in uniform flow, KQ = Q/pN2D5

KQS Torque coefficient of ducted propeller system, KQs = Q5/pN2D5

KT Thrust coefficient in uniform flow, KT = T/pN2D4

KTD Thrust coefficient of duct, KT, = TD/pN2 D4

KTP Propeller thrust coefficient, KTp = Tp/pN2 D4

KTS Thrust coefficient of ducted propeller system, KTs _{= KTD KTP}

Propeller revolutions per unit time Incremental area index

Propeller blade section pitch Pressure Mean pressure Unsteady pressure Propeller torque QS System torque Propeller radius

Rn _{Reynolds number at 0.7R, Rn = co., -IVA2 + (0.77I-ND)2 /v}

Radial distance from propeller axis

VA

Xcos' Ycos' Zcos

x/R x, y, z Yc Hub radius Duct thrust Propeller thrust System thrust, ; = TB + Mean thrust

Propeller blade section maximum thickness Speed of advance of propeller

Direction cosines normal to a surface

Nondimensional axial distance from propeller plane; positive upstream Cartesian coordinates with origin at intersection of propeller axis and blade reference line

Camberline ordinate, fraction of chord

Blade number; subscript denoting blade frequency

Advance angle, 0 = arctan /27rrN)

rh

TB

Tp

vii

.0 Hydrodynamic flow angle

Phase angle

Blade-frequency phase angle with respect to propeller blade reference 1

line

Propeller efficiency, 7? = Tp VA /27rQN

System efficiency, rps = +.TD)VA /27rQsN

Phase angle of peak blade-frequency pressure amplitude relative to blade reference line

0co _{Wake screen angular position; positive counterclockwise looking}

downstream (06) = 0 for vertical upward) Kinematic viscOsity Of" fluid.

*Mas& density of fluid)

Propeller angular coordinate about shaft axis; positive counterclockwise looking downstream (4) = 0 for vertical upward)

ABSTRACT

Total fluctuating pressures were measured on the internal surface of a

0-degree angle-of-attack duct of a ducted propeller system (Kort nozzle type).

The effects of blade loading in uniform flow and propeller blade cavitation in

nonuniform flow on the harmonics of the blade-frequency propeller-induced pressure were determined. Also determined were the blade-frequency

pressure-induced duct forces. Experimental results indicate that the blade-frequency

pressures increase for an increase in blade loading with the second and third blade-frequency pressures being significant with respect to the blade-frequency

pressure. Fluctuating blade-frequency vertical forces determined by

integrat-ing the pressure results from nonuniform inflow noncavitatintegrat-ing conditions were

approximately 1-percent of the mean thrust. In the experiments conducted at a given loading, cavitation on the propeller blades tended to increase the

blade-frequency pressure downstream of the propeller by as much as a

factor of three.

ADMINISTRATIVE INFORMATION

The work reported herein was funded by the Naval Ship Systems Command under Task Area SF 43 432 103. This work was performed under Naval Ship Research and Development

Center (NSRDC) Work Units 1-1528-025 in FY 73 and 1-1544-257 in FY 74. INTRODUCTION

As part of the Navy's research effort on propulsors, various types of propellers are being evaluated to determine the effect of type on efficiency, cavitation, radiated noise, and

propeller-induced vibration.

This report deals with an initial effort to determine the effects of employing a ducted

propeller system on propulsor-induced vibration. In a complete evaluation of ducted

pro-peller effects on vibration, a comparison should be made between the vibratory levels

gener-ated by a ducted propeller and those genergener-ated by a conventional propeller with comparable propulsive characteristics. Those quantities which must be evaluated in such a comparison should be the unsteady forces transmitted through the shafting for both systems and those forces generated on the hull and appendages resulting from the unsteady pressure field generated by the propeller and transmitted through the fluid medium. The completion of

such a total evaluation was beyond the scope and funding of the current project. Therefore,

the report presents only a part of the evaluation, namely: unsteady forces resulting from the unsteady pressure distribution on the duct of a ducted propeller system.

In determining the propeller-induced forces from model experiments, there are two

Measurement of the dynamic response of the vibratory member and determining the excitation forces involved through extensive calibration.

Measurement of the pressure distribution and integration over the surfaces, assuming a rigid body.

Method 1 has the advantage of measuring the total force acting on the body but the

disadvantage of complicated dynamometry and analysis. Method 2 has the disadvantage of measuring only limited portions of the total force but the advantage of simple force analysis.

In nonuniform flow, the integration of the propeller-induced pressures over the duct

interior area will produce a resultant fluctuating force. This force, which is transmitted to

the hull through the duct mounting, could be a significant source of hull vibration.

In this report, pressure signals monitored on the interior of a duct of a ducted propeller system (Kort nozzle) operating in the 24-inch water tunnel are presented. The amplitude and phase of the blade-frequency portions of the measured induced pressures are determined for operation in uniform and nonuniform flow. Nonuniform flow results also include the effect of propeller-blade cavitation on the blade frequency pressures. Also presented are the

fluctu-ating forces derived from integrfluctu-ating the induced pressures acting on the duct. EXPERIMENTAL EQUIPMENT

Experiments were run in the closed jet test section (27-inch diameter) of the 24-inch variable pressure water tunnel with a ducted propeller configuration fitted on the downstream

shaft (see Figure 1 a). The ducted propeller configuration consists of a 0-degree

angle-of-attack duct (10.1-inch interior diameter, 5-inch chord) and a four-bladed propeller (Model 3714, 10-inch diameter). Thus, the clearance between the duct and the propeller tip is one percent of the propeller radius.

This ducted propeller system was selected because its performance had been evaluated

in model experiments.* Due to its acceptable backing characteristics it appeared to be a

sys-tem which could be expected to have possibilities for full-scale application.

The duct was attached to the downstream shaft by a ring-strut arrangement. Photographs of the duct and propeller appear as Figure lb with the geometry of duct ection and propeller

given in Table 1 and Figure 2 respectively.

The duct contained five differential pressure transducers (CONSOLI)5ATED

ELECTRON-ICS CORPORATION (CEC 4-312, ±5 psid)) located internal to the duct at two

circumferen-tial locations (see Figure lb and Table 2). Resolution of pressure using these gages was

better than 0.001 psi. Plastic tubing was connected to the back side of the pressure

*Reported informally by N. A. McDonald in Ship Performance Department, Evaluation Report 507-H-01 (Feb 1973).

Figure 1 Ducted Propeller Apparatus, PAMBIENT rnrqueimmom

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WATER SURFACE PLASTIC TUBING FLOW IDIRECTIONI DUCT

PRESSURE GAGES#11., 3, ANID 5

'FILOW DIRECTION ISTBD SIDE 2 PACKING, GLANDS P LAST I C. TUBING Figure la .DUCT TOP PRESSURE GAGES #2 & #4

I - , st- a Figure lb 2,411a OD -1 1' j 7 4

TABLE II -- DUCT CAMBER AND THICKNESS DISTRIBUTION

TABLE 2 - AXIAL LOCATION OF PRESSURE TRANSDUCERS WITH RESPECT TO PROPELLER REFERENCE PLANE

AND LEADING EDGE OF DUCT

xi2 Ye Yc/fm II 11/21t/c

tit,.

0 0 I 0 h 0 0 / 0.0019 1 -0.00068 0,02000 1 0:01264 I 0.15066 0.0075 -0.00204 1 0.06000 I 0.02120. 0.25268 0.0170 1 -0.00370 0.10882 ) 0.02860 0.34088 I 1 I I 0.0301 =0.00602 0.17706 0.03596 0.4286 0:0468 1 -0.00857 0.25206 0.04286 I 0.51085 0.0669 -0.011132 0.33294 0.04936) 0.58832 0.0904 L -0.01408 0.41412 0.05484 0.65364' 0.1170 -0.01693 0.49794 0.06050 0.72110 0.1464 -0.01962 .0.57706 1 0.06576 0.78379 0.1786 -0.02237 0.65794 I 0.07126 0.84934 112132 -0.02468 0.72588 0.07500 0.89392 0.2500 =0.02686 0.79000 0.07770 I 0.92610. 0.2887 =0.02880 0.84706 0.07970 .0.94994 0.3290 -0.03050 0..89706 I 0.08120 0.96782 0.3706 -0.03193 0).93912 0.08214 007902 I 0.4132 -0.03298 0.97000 0.08290 098808 0.4564 -0.03369 )0.99088 0.08348. 0.99499 0.5000 -0.03400 1 1.0000 0.08370 0.99762 0.5436 -003393 ' 0.99794 0.08390 1.0000 0.5868 -0.03339 098206 0.08390 1.0000 1 0.6294 -0.03261 0.95912 0.08378 0.99857 0.6710 1 -0.03152 1 0.92492 I 0.08300 0:98927 0.7113 1 ,-0.02985 0.87794 I 0.08110 0.96663 0.7500 ' r0.02764 0.81294 0.07800 0.92968 0.7865 -0.02506 ) 0.73706 I 0.07388 0.88057 . 0.8214 -0.02196 0.64588 0.069081 0.82336 i 0.8536 -0.01800 1 0.52941 0.06342 0.75590 I 0.8830 -0.01442 0.42412 0.05684 0.67747 0.9096 -0.01108 0.32588, 1 0.05116 0.60977 0.9330 I -0.00816 0.24000" 0.04332 10.51633 0.9532 I -0.00554 0.16294 0.03608 .0.43004 0.9698 -0)00350 0.10294, 0.02900 0.34565 1 0.9830 I -0.00197 ,0.0579-4 0.02094 I 0).24958 I 0.9924 -0.00092 0.02706 0.01416 0.16877 0.9981 -000001 1 0.00029 0.00898 0.10703 1.0000 0 0 0 0 Transducer x/ R,

Distance from Leading Edge of Duct I in. +0.3312 0.843 3 40.1686 o 1.656 , 2.500 4 -0.1686 3.342 5 -0.3312 , 4.155 -1 2

RADII % & INCHES 100 5.000 95 4.750 90 4.500 80 4.000 70 3.500 60 3.000 50 2.500 40 2.000 30 1.500 20 1.000

PROPELLER 3714

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PITCH CURVE & INCHES

.003 R 032 12.500 .003R I 12.510 .003 R 12.525 .003 R-4---12.555 .003 R-4----12.620 PROJECTED R 12.790 EXPANDED .007 R 13.055 .011 R 13.425 .017R 13.850 .732 R 14.600 0 0 0 csi .031 R P-3714-L.H. 4-BLADES .002

TYPICAL CHISEL (EXPANDED) FROM 40% TO 95% R

Figure 2 - Drawing of Propeller 3714

DESIGNED BY DTMB DRAWING P-3714 187-0-NUMBER OF BLADES 4

EXP. AREA RATIO

0.450 MWR 0.221 BTF 0.029 P/D (AT 0.7R) 1.262 DIAMETER 10.000 INS. PITCH (AT 0.7R) 12.620 INS. ROTATION L. H. 0 -.059 .081 R -4-1.187

transducer with the other end of the tube exposed to the ambient tunnel pressure of the air above the water (see Figure I a). The face side of the pressure transducer was exposed to the ambient tunnel pressure; the static pressure due to water depth; and the dynamic pressure

produced by the flow and the propeller.

For nonuniform flow experiments, the ducted system was run behind the wake screenl

shown in Figure 3. It was necessary to rotate the wake screen through 360 degrees to

deter-mine the effect of the local flow on the induced pressures. Figure 4 presents the radial wake distribution generated by the wake screen.

EXPERIMENTAL PROCEDURE

Available open-water propeller results were used to establish various

ducted-propeller loading conditions in the NSRDC 24-inch water tunnel. The open water results, shown in Table 3, present duct, propeller and system thrust coefficients, system torque

coefficient, and system efficiency as a function of advance condition.

However, it was not the objective of this investigation to determine the duct thrust but

only to measure the propeller-induced pressures acting on the interior duct surface. Therefore

no provisions for measurement of duct thrust were made with the present apparatus.

Even if duct thrust were to be measured, it would be highly unlikely that the duct-thrust characteristics of the water-tunnel configuration would be similar to those of the open-water

ducted-propeller configuration (see Figures lb and 5). Different duct-thrust characteristics

would result because of the metal ring enclosing the duct and the protruding pressure gages.

Duct thrust is not needed to establish propeller-loading conditions, only propeller thrust. Propeller-loading conditions in the water tunnel are usually based on a thrust identity; that is, establish a particular thrust coefficient in the water tunnel even though the advance

coeffi-cient is slightly different from that of the open-water advance coefficoeffi-cient. This is due to

blockage and wall effects in the tunnel. Usual procedure is to set the rpm desired and then vary the water speed until the desired thrust is obtained.

Table 4 gives the thrust coefficients selected for the ducted-propeller investigation. These

thrust coefficients are for the propeller, only, operating in the duct and were chosen to show

the effect of loading on the propeller-induced pressures.

Propeller thrust coefficients established for uniform flow experiments were KT = 0.052,

0.159, and 0.268. At design KT, thrust was measured to within ±0.6 percent of the design

thrust.

Comstock, G. C., "Cavitation Study of a Propeller Operating in Nonuniform Flow Created by a Wire Grid Screen," David Taylor Model Basin Report 2185 (Mar 1966).

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90 -, 1 -4 _14' -,t f; r r 4 7,7 , r -, 4 00 -zr4V I a 180°' I Figure 3 Wake Screen 01 270 ° A

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TABLE 3 - DUCTED PROPELLER OPEN-WATER AHEAD CHARACTERISTICS

TABLE 4 - THRUST COEFFICIENTS SELECTED FOR WATER TUNNEL EXPERIMENTS

Ahead J K_{IS 10 KQS} ris KTD KTP 0 0.540 0.740 0 0.173 0.367 0.05 0.525 0.726 0.0575 0.172 0.353 0.1 0.511 0.711 0.114 0.169 0.342 KTS: System KT 0.15 0.497 0.697 0.170 0.163 0.334 0.2 0.482 0.682 0.225 0.154 0.328 KTP: Propel ler KT 0.25 0.466 0.668 0.2775 0.143 0.323 0.3 0.448 0.652 0.328 0.1325 0.3155 KTD. Duct KT 0.35 0.429 0.635 0.376 0.119 0.310 0.4 0.408 0.616 0.422 0.105 0.303 0.45 0.386 0.595 0.465 0.090 0.296 KTS - KTP + KTD 0.5 0.361 0.5725 0.502 0.78 0.283 0.55 0.335 0.543 0.540 0.067 0.268 KQS: System KQ 0.6 0.308 0.511 0.576 0.058 0.250 0.65 0.278 0.473 0.608 0.05 0.228 ris: System 77 0.7 0.248 0.430 0.643 0.044 0.204 0.75 0.216 0.386 0.668 0.036 0.180 0.8 0.183 0.3425 0.680 0.27 0.156 0.85 0.150 0.298 0.682 0.20 0.130 0.9 0.118 0.254 0.668 0.12 0.106 0.95 0.085 0.209 0.621 0.004 0.081 1.0 0.053 0.162 0.520 0 0.053 1.05 0.020 0.113 0.291 0.012 0.032 1.08 0 0.083 0 0.015 0.015

Propel ler Number _{Thrust Coefficient}

3714 0.268

0.159 0.052

Figure 5

For the noncavitating and cavitating nonuniform flow experiments, a mean thrust

coefficient KT = 0.1 59 which corresponds to a condition near the maximum efficiency of

the ducted propeller system was established. Nonuniform flow was generated by a wake

screen.

The experiments for the noncavitating conditions were run at 14 and 20 rps while the cavitation experiments were run only at 20 rps. The cavitation experiments were conducted in nonuniform flow by starting from a noncavitating condition and reducing the tunnel pres-sure (and thus a) until cavitation appeared and/or until the cavitation pattern changed signi-ficantly. The cavitation patterns at various pressures were sketched.

In nonuniform flow and without blade cavitation, data were collected at 6- or 12-degree increments of the wake screen from 0 to 360 degrees. In nonuniform flow with propeller blade cavitation present, data were collected at 6- or 12-degree increments from 0 to 198

degrees.

DATA ANALYSIS

Pressure signals measured at each transducer and single- and 120-toothed gear pulses

were recorded on magnetic tape. The toothed-gear pulses were used to trigger an

analog-to-digital converter so that the analog pressure signals could be digitized and analyzed by an

Interdata Model 4 minicomputer. A schematic of the data acquisition and analysis procedure appears as Figure 6 with the instrumentation components defined.

The digitization of the analog signals from the pressure transducers was carried out by

the computer with the aid of a magnetic pickup-toothed gear arrangement. A single-toothed and a 120-toothed gear were attached to the propeller shaft outside the tunnel. The single tooth was aligned with the reference line of a blade of the particular propeller. The single pulse per propeller revolution triggered the computer to begin storing data. The data stored were those read from the analog signal when one of the 120 pulses was recognized by the computer. This meant that for each propeller revolution, the computer digitized 120 points of data from each of the five pressure transducers. In a given experimental run for a partic-ular propeller revolution rate, 200 to 400 cycles of voltage data were normally collected. The

signal averaging for each transducer was accomplished by adding the 120 data values collected during a revolution to those corresponding values previously collected and then dividing by

the sum total of revolutions at the end of a run. The pointwise values of theaverage wave

were then multiplied by the respective calibration slope values to produce the average pressure wave. The harmonic analysis of the average pressure wave and the desired

nondimensionaliza-tion and phase analysis were carried out on the Interdata Model 4 Minicomputer. The

CEC 4-312 PRESSURE GAGES 5 PSID

ENDEVCO 4402 CONSTANT VOLTAGE SIGNAL CONDITIONER

H

SINGLE-TOOTH PULSE 120-TOOTH PULSE

--1

PULSE SHAPER

MONITOR OSCILLO- SCOPE

SWITCH PANEL

AMPEX FM TAPE RECORDER _{MODEL 1300}

DATA ACQUISITION DATA ANALYSIS Figure 6 Instrumentation

r - -I

I SPECTRAL ! I DYNAMICS 1 !

REAL TIME

1---; ANALYZER I L __J 15 IPS

DANA DC AMPLIFIER MODEL 2820

I

r----1---1

1 I XY-1 I __PLOTTER I

L---J

A/D CONVERTER 32 KHZ SAMPLE RATE MONITOR MONITOR OSCILLO-SWITCH PANEL DIGITAL SCOPES VOLTMETER INTERDATA CENTRAL PRINTEC PROCESSING UNIT PRINTER MODEL 4 AMPEX FM TAPE 24 K MEMORY RECORDER MODEL 1300 15 IPS MONITOR

- DIGITAL

VOLTMETER

The total pressure at each transducer consists of a periodic time dependent fluctuation

about a mean value and can be represented by a Fourier series as:

00

p =a0/2 + tam cos mØ+ bm sin mcb] (1)

m = 1

where

ia0/2 00

Lam cos m0 + bm sin m01 = Cm cos (m0 -ym )

m=1 m=1

and

-yrn = tan- 1 (bm lam)

Equation (1) then becomes

00

p = a0/2 +cos (m0

-ym) (2)

m=1

Thus, the unsteady pressure at each transducer is defined as the total pressure lessthe

:mean pressure

00

p = p =

2-7

Cm cos (m0 -ym) (3)

ni = 1

if Z is the number of blades of the propeller, then the amplitude of the blade frequency pressure fluctuation is given by Cz and the phase angle of that harmonic is given by yz,

thus

Pz = Cz cos ',(Z(/) )/z)1

=

00

The maximum blade-frequency signal occurs when ZØ = 0. Therefore, the phase angle

for which p is a maximum is defined as

oz = 7z/Z (4)

The amplitude of the blade frequency harmonic is nondimensionalized as follows:

K =

Cz/pN2 D2

Pz

Some of the cavitation results were also analyzed by a Spectral Dynamics Real Time Analyzer, Model SD 301, to see if any significant differences existed between the two methods of data analysis. Significant differences were found for the higher harmonics only.

DISCUSSION OF RESULTS UNIFORM FLOWRANGE OF ADVANCE

COEFFICIENTS

Blade-frequency pressure amplitudes and phases were measured on the duct interior for

thrust coefficients KT of 0.268, 0.159, and 0.052 in uniform flow. A plane through the hub midlength and perpendicular to the shaft axis was used as a reference plane for the presenta-tion of data. This plane intersected the duct at x/R = 0.0 which corresponds to the axial

location of Transducer 3. Figures 7 and 8 show the effect of propeller loading on the

blade-frequency induced pressures, amplitudes, and phases for the ducted propeller system. The pressure amplitudes are presented in the form of nondimensionalized blade-frequency coefficients as shown in Equation (5). The figures show amplitude and phase as a function

of axial distance from the propeller plane.

Figure 7 indicates that the blade-frequency pressure amplitudes increase with increasing

propeller loading (increasing KT) as would be expected. Figure 7 also shows that the maxi-mum amplitude of blade-frequency induced pressure occurs in the region near the plane of

the propeller. Figure 8 indicates that the loading condition affects the blade-frequency phase

angles downstream of the propeller reference plane, with little change upstream and at the reference plane. A similar phase trend was noted by Hale and Norris.2

In general, the blade-frequency harmonic was the most significant portion of the pressure signal for all experimental results (this agrees with the results of Reference 2 and with

16

(5)

2Hale, M. R. and D. H. Norris, "Hydrojet Ducted Propulsion System," University of Adelaide, Department of Mechanical Engineering Report 66/3 (Nov 1966).

0.6 0.5 (.7) 0.4 u_ 0 cc 0.3 UJ cc 1.1.1 0.2 0.1 0.0 Figure 7

Measured Blade-Frequency Pressure Amplitudes at Thrust Coefficient Values KT = 0.052, 0.159, and 0.268 for 1-Percent Radius Tip Clearance

./49N N 0-DEGREE PROPELLER = 1.01 UNIFORM DUCT 3714 _FLOW

/

/

//

\

\

\

KT _0.052 0.159 0.268 r/R

/

_/

/

\

\

n

0

0

/ / _t

\

\ k I _{/ /} 1 I / _/ I I I _/ i I I I / / 1 I I I

I....-0-.."

,

... N

\

I -4 % /

_/

...""

/

\

\ \

\

\

0

-- --* ..--... ..." .00. ...0 ... .... .0.- d-d-...

\

'

CA

\

\

\

El .... '''' ...-..., 6' ''' N

\

\

\ID,

.

.1\ .... N, ,....

,

"'"

''

... .... ,.... +0 3 +0 2 +0 1 0 -0 1 -0 2 -0 3 UPSTREAM x/R DOWNSTREAM

-

--D

-240 U) LU LU cc 0 Lu 0 2-160 Lu- (I) >- D 80 LU cc 0 0.0 Figure 8

Measured Blade-Frequency Phase at Thrust Coefficient Values KT

= 0.052,

0,159, and 0.268 for 1-Percent Radius Tip Clearance

0-DEGREE DUCT PROPELLER 3714 r/R

= 1.01 UNIFORM FLOW I KT 0.052 A A 0 0.159 0 0.268

o 0

o

B

0

A

0

A

o

o

o

+03 +0.2 +0.1 0 -0 1 -0.2 -0 3 UPSTREAM x/R DOWNSTREAM

-full-scale ducted-propeller results of Reference 3). However, unlike the results of Reference 3,

the second and third blade-frequency harmonics were significant when compared with the first-blade frequency harmonic.

From Tables 5 and 6 for both uniform and nonuniform flow, it can be seen that, in

general, the significant second and third blade-frequency harmonics occur at the pressure gage

nearest to the propeller tip (x/R = 0.0) with the influence of these higher harmonics

decreas-ing with increasdecreas-ing distance from the propeller reference plane. Thus, the difference between

the present model results and full-scale results of Reference 3 may be due to different

abso-lute propeller tip clearances.

NONUNIFORM FLOWADVANCE COEFFICIENT NEAR MAXIMUM OPEN-WATER SYSTEM

EFFICIENCY

Noncavitating

Figures 9 and 10 present the results of induced pressure measurements for a ducted-propeller configuration run at a mean thrust coefficient KT of 0.159 for 30 positions of the

wake screen (6- and 12-degree increments). The maximum values of blade-frequency-induced pressures occurred at the 0-degree position of the wake screen with a smaller maximum

occurring at the 180-degree wake screen position. This corresponds to the regions of heaviest

propeller blade loading since the inflow velocity was least through those regions of the screen. The other wake screen positions were combinations of higher inflow regions.

Cavitating

Table 5 presents the amplitudes and phases of the first, second, third, and fourth

har-monics of blade-frequency pressure as a function of axial position, wake screen position, and

cavitation number at a mean thrust coefficient KT = 0.159 and 1-percent propeller-radius

tip-clearance. Figure 11 illustrates cavitation patterns of Propeller 3714 in the 0-degree duct at

various cavitation numbers.

From Table 5 (Runs 35-40), it can be seen that the blade-frequency pressure increases by as much as a factor of three (compare Runs 35 and 39 at x/R = 0.1686) over the

non-cavitating condition. At a cavitation number a = 4.2 for which only the tip vortex is present,

the blade-frequency pressure has increased by only 23 percent over the noncavitating

condi-tion (Runs 35 and 37 at x/R = 0.1686). At a cavitacondi-tion number a = 2.76 where cavity

volume changes and cavity motions are present, the blade-frequency pressure has increased by

a factor of three over the noncavitating conditions. However, at a lower cavitation number

3Sontvedt, T. et al., "Loads and Response of Large Ducted Propeller Systems," Symposium of Ducted Propellers, The Royal Institution of Naval Architects, Paper 15 (Jun 1973).

TABLE 5 - FIRST, SECOND, THIRD, AND FOURTH BLADE-FREQUENCY

PRESSURE AMPLITUDES AND PHASES

AS A FUNCTION OF AXIAL POSITION, WAKE SCREEN POSITION,

AND CAVITATION NUMBER

AT MEAN THRUST COEFFICIENT KT = 0.159 AND I-PERCENT DUCTED

PROPELLER

RADIUS TIP CLEARANCE

Run Number Wake _Screen Position ow x/ R a CZ C 2 Z C 3Z C 4Z °Z 4)2z 03Z 94Z 1 Uniform +0.3312

13.10.2144

0.0289 0.0028 0.0012 210.7 211.8 179.3 53.3 Flow +0.1686 0.2549 0.2011 0.0613 0.0261 183.2 204.8 183.4 164.2 0 0.9980 0.7279 0.5137 0.3538 226.6 244.7 257.5 267.8 -0.1686 0.2448 0.0753 0.0286 0.0121 7.57

-7.66 8.3 21.4 -0.3312 0.0530 0.0077 0.0019 0.0013 - 39.0 - 76.8 252.8 222.0 2 Uniform +0.3312

13.10.1175

0.0238 0.00486 0.0017 223.4 209.9 190.7 149.6 Flow +0.1686 0.2492 0.0978 0.0387 0.0196 219.4 212.5 197.4 162.0 0 0.4155 0.3113 0.2377 0.1679 217.0 220.9 232.6 232.6 -0.1686 0.1408 0.0571 0.0371 0.0178 - 11.1 147.6 - 37.8 120.8 -0.3312 0.0262 0.0265 0.0108 0.00515 145.9 139.8 114.5 59.7 3 Uniform +0.3312

13.10.0806

0.0201 0.0049 0.0021 246.0 230.8 201.8 158.1 Flow +0.1686 0.1505 0.0714 0.0270 0.0160 246.4 242.1 215.0 192.1 0 0.2392 0.1450 0.0850 0.0513 208.4 214.6 223.7 229.7 -0.1686 0.0563 0.0338 0.0111 0.0045 132.3 133.9 176.5 - 76.1 -0.3312 0.0386 0.0024 0.0063 0.0008 98.2 19.7 247.5 96.4 4 90 +0.3312

13.10.0894

0.0112 0.0008 0.0011 269.1 - 49.5 75.4 176.9 0 +0.1686 0.3398 0.1151 0.0385 0.0119 231.1 245.3 244.2 233.4 90 0 0.3253 0.2028 0.1199 0.0688 250.9 - 71.1 - 36.3

-3.5 0 -0.1686 0.2911 0.0963 0.0357 0.0124 27.1 30.0 99.1 122.8 90 -0.3312 0.00241 0.0313 0.0110 0.0038 - 24.4 142.7 116.5 42.7 I I

-= . , 1 1 ,

-TABLE 5 (Colltifiu0d) Run Number Wake _Screen Position 61 co X/ Fl Cz C-2Z 02Z 'C53Z 19 270 +0:3312 1-3:1 1 0.0765 6.0102 1 0.00039 0.0025 - 87.1 =, 34.7 268.2 121.7 180 +0.1686 0,2356 0)857 0.0259 0.0111 247.6 262.9 11 257:5 218.4 270 0 1 0.274 0.1t560, 1 0.0866 0.0503 252.5 --ri 64.3 1 = 23.9 17.5 180 .0.1686 11 0.2042 0.0690 ' 0.0464 0.0237 3.3 127.-1 2.1 132,1 .. 270 -0,3312 0.0832 O018 0.0138 0.0071,4 1224 I 5191 - 59.5 258.1 I 34 190 +0.3312 13.1 0,1373 0,0045 0.0072 0.0018 - 763 I -..--- 72.4 188.1 164.3 0 +0,11686 0.6469 0.2219 0.0582 0.0062 239.3 255.8 258.9 209.3 90 0 0:504 0.2775 0.1554 0:0901 262.0 = 56,2' - 13.5 30,2 'Q ,-20.1686 0.5802 0.1016 0.0780 1 0:0108, 26.6 16.8, 1165 161.7 37 90 '90 -0.3312 +0:3312 4,2 0.1035 0.1186 1:0243 0.0120 0.0265 0.0127 I 010105., 0.0180 135,0 11 - 59%5 1126,4 4,91 4:6 121.3 =, 9.6 220.0 .0 +0.1680 0,6265 0.1166 0.0219 0.0331 261.2k .- 322 189.9 209.5 90. 0 0,4658 0.2855 0.1595 0.0722' 265.8 - 5L7 = 0.3 42.3 ,0 90 -0.1686 -0.3312 0.7154 0.1348 0.6874 00250 0.4727 0.0284 0.2779, 0.0130 - 36.2 110:6 10.0 1440 109.5 33.3 238.2 233.2 38 90 +013312 i 2.70 0,2124 0.0644 0.0398 0.0233' -= 47.3 44.4 284.4 .--=-80.7 0 +0.1686 0.572 0.0762 0.0434

0.0190- '62,9'

= 72.9 267.8 51.7 '90 ,0 0 -0.1686 0.4565 1 1.467 0.2727 , 0,8007 0.1005 0.2657 0.0547 0.3295 262.2 = 426 - 37.5 82.6 ' 5,4 - 74.5 72.5 132.0 .90 -0,3312 i 0.2301 0,0422 '0.0218 0.0156 125,5 88.7 178.0 124.5 39 90 +0.3312 2.15 0.1554 0.0518 100152 0k0064! - 39,4 247.9 165,7 120,4 IQ +0,11686 1 0.5201 0.1257 0.0338 0.01621 = '50.5 - 75.0 '257.1 - 80.5; .90 0 0.4897 02382 0.1102 0.01421 263.4 - 50.9 27.1 ' 44.3 0 0t1686 i 1.757 0.2619 0.4636 0.2970 26.4 207.8 103.8 . 2.4 90 -0.3312 . ii ,0.1474 0,074 0.0241_ 0.01,591 164.3 227.2 - 28.2 - 47,9 u C

--

--

-TABLE 5 (Continued) Run Number Wake _Screen Position ow x/ R () C z C2Z C3Z C4Z °Z C52Z 03Z (/),IZ 40 90 +0.3312 1.66 0.0084 0.0021 0.0065 0.0008 95.5 - 15.5 3.2 205.9 0 1-0.1686 0.3967 0.1112 0.0317 0.0080 49.0 - 69.2 - 88.3 221.3 90 0 0.6036 0.0624 0.0784 0.0112 - 63.6 - 42.8 - 17.1

-4.9 0 -0.1686 1.390 0.5329 0.1270 0.0985 4.5

-3.1 - 70.7 205.3 90 -0.3312 0.2055 0.0554 0.0249 0.0479 226.5 52.0 - 30.3 180.4 75 186 -0.3312

13.10.0997

0.0354 0.0236 0.0094 124.1 151.3 - 48.2 - 34.5 96 +0.1686 0.2859 0.1034 0.0323 0.00672 - 84.4 - 59.6 - 23.7 66.5 186 0 0.5353 0.3063 0.1642 0.0932 - 87.5 - 24.3 35.8 91.4 96 -0.1686 0.0765 0.0298 0.0301 0.0191 - 50.6 199.5 - 78.0 56.4 76 186 -0.3312 4.2 0.1396 0.0801 0.0264 0.0047 96.7 158.1 - 48.8 93.7 96 +0.1686 0.2474 0.1021 0.0385 0.0213 - 70.0 - 62.6 - 30.4 77.0 186 0 0.4778 0.2580 0.1702 0.1213 - 80.0 - 26.9 31.6 93.1 96 -0.1686 0.1003 0.0314 0.0374 0.0362

-4.7 196.5 - 76.7 73.2 77 186 -0.3312 2.76 0.2167 0.1461 0.0416 0.0232 128.6 179.6 18.2 189.4 96 +0.1686 0.1706 0.0751 0.0567 0.0052 258.6 - 75.9

-8.1 150.0 186 0 0.4038 0.1962 0.1535 0.0561 265.6 - 43.5 33.3 117.6 96 -0.1686 0.0596 0.0664 0.0494 0.0176 132.1 182.2 - 25.7 26.2 78 186 -0.3312 1.66 0.0539 0.0533 0.0209 0.0259 - 32.4 265.0 79.4 241.9 96 +0.1686 0.5120 0.1827 0.0400 0.0121 - 47.6 255.3 153.1 102.4 186 0 0.4217 0.2234 0.0878 0.0178 - 62.0 - 36.3 32.1 8.8 96 -0.1686 0.5335 0.2048 0.1178 0.0988 - 62.3 118.2 - 26.5 182.3

-L

-1

-'1

-TABLE 6 - RATIOS OF THE SECOND, THIRD, AND FOURTH FREQUENCY PRESSURE AMPLITUDES TO THE FIRST

BLADE-FREQUENCY PRESSURE AMPLITUDE FOR CAVITATING AND NONCAVITATING FLOWS

Run Number Wake Screen Position Ow x/ R a C2Z C3Z C4Z Cz _{Cz Cz} 35 90 +0.3312

13.10.03

0.05 0.01 0 +0.1686 0.34 0.08 0.01 90 0 0.55 0.30 0.17 0 -0.1686 0.17 0.13 0.02 90 -0.3312 0.23 0.25 0.10 40 90 +0.3312 1.66 0.25 0.07 0.09 0 1-0.1686 0.28 0.07 0.02 90 0 0.10 0.12 0.02 0 -0.1686 0.38 0.09 0.7 90 -0.3312 0.26 0.12 0.23 42 102 +0.3312

13.10.27

0.01 0.02 12 +0.1686 0.32 0.07 0.06 102 0 0.68 0.38 0.22 12 -0.1686 0.26 0.16 0.7 102 -0.3312 0.075 0.13 0.06 45 102 +0.3312 1.66 0.23 0.02 0.09 12 +0.1686 0.21 0.06 0.03 102 0 0.61 0.35 0.26 12 -0.1686 0.17 0.09 0.04 102 -0.3312 0.22 0.14 0.04 46 114 +0.3312

13.10.20

0.01 0.015 24 +0.1686 0.34 0.09 0.01 114 0 0.64 0.37 0.22 24 -0.1686 0.49 0.19 0.12 114 -0.3312 0.30 0.21 0.09

TABLE 6 (Continued) 24 nry-. Run Number Wake Screen Position Ow ..x/,R t C2 Z , C3Z C4Z C_z C_z C_z , 1 47 114 +0.3312 1.66 019 0.27 0.12 24 +0.116861 0.27 0.04 0.05 1114, 24 0 ' -0.1686 I 0.27 0.22 0.09 H 0.06 0.05 0:05 -49' 114 126 -0.3312 +0.3312 111 0.43 0.16 0.15 0.015 0.10, 1 0:02 36 126 +0.16861 , 0 ; 0.35 0.60 0.07 0.37 0.01 0.22 36 Ii -0.1686 0.39 0.25 I 0.13 126

-0.33t2 J.

_{0.44 038 H 0.08} 52 1_26 .36 +0,3312 +0.1686 , 1.66; 033 0.20 0110 i 0(08 I 01.21 . 0.05 H 126 ₀ , 1 1 0.17 0.13 0.04 36 -0.1686 0.46 0.05 0.03 , h 54 126 . 138 -0.3312 +0.3312 131 0.45 H 013 0.24 0.02 019 10:01 48 +0.1686 0.34 009 0)02 138 Ii _{0.59 0.35 0.24} .. , , 57 48 1138 138 -0.1685 -0.331.2. +0.3312 - 1,66 0.55 0.68 0.07 0.23 0.20 0.03 L 0.18 0.11 0.03 48 +0.1686 0.14 0.07 0.04 138 0 0.17 0(11 0.08 48 -0.1686 0.61 101 a 0.05 . , I 138 -0.3312 1 0.54 0.42 0.28 1 '59 , 150 +0.3312 1 1 13..11 0.09 . 0.04 0.02 60 +0.1686 ! 0.33 0.11 0.03 150 0 ! 1 0.65 0.37 0.22 1 60 -0.1686 1 1.13 0.39 0.19 1 , 150 -0.3312 1 0.83 0.28 0.13 62' 150 ' +0.3312 1.66 1 0.29 0.07 1 0(04 1 1

601

H 150 +0.1686 0 1 , 0.10 0.23 0.05 1 0(07 0.06 0.08 ij 1 60 0.1 686 0.60 0(17 0.17 150 -0.3312 0.49 0.32 0.21_ a 0

TABLE 6 (Continued) Wake Screen , x, /ft C2Z C3Z C4Z Cz-. C_{-_z} C_-z

Number Post ition

1 Ow 63 162 ' +0.3312

H 13.10.17

0.04 0.02' 72 1 +0.1686 0.29' 0.06 1 0.02 162 0 0.71 01.45 ! 0.27 72 1 -0.1686 0.96 0.57 0.18 I, 6e 162 , 162 72 ' -0.3312 +0,3312 +0.1686 1 '1 :66, ' 0.59 0:08 r 046 01.07 0.07 0.21,11, Oi.011 0:01 162 0 0.31 0.18 0..10 72 -0.111686' 0:48 0.30 1 0.17 162 =03312 I --

-

7-167 1174 +0.3312 . 111 H 0.25 0.03 002 .84 +0.1686 0.26. 0.08 0.0411 174 84 0, -0.1686. 0.70 047 0.43 0.38 0.27 0.25 1174 -0.3312 --

-

-70 174 84 +0.3312 +0.1686 1.66, 0.19, 0.39 0.07 0.10 0.04 0.04 174 0 0.301 0.20 0.12 64 -0.1686; 0.32 0.A3 0.08 174 =0.3312 H -_---71 174 , +03312 13.1 i .:

-"84 +011686 01.27 008 0.01' 174 0 0.70 0.44 0.27 84 -0.7686+ 0.45 0.35 0.25 174 ' -0.33112 1 1.191 0.61 1 0.14 1 74 174 +0..33112 1.66 .=-' =

-64 +0,1686 0.03 0.01 C.)1.03 174 0 0.27 0.21 0.14 84 -J0.1686 0.32 0.13 0.07 174 -0.3312 0.47 0.25 0..10 o 0.08

-TABLE 6 (Continued) 26 Run Number Wake Screen Position 0 co 1 I x/R a . , C2 Z C3 Z 4Z Cz ,Cz _Cz 75 186 +0.3312 131

-

-

-96, 186 +0.1686 0 , 1 0.36 0.57 0.11 0.30 1 0.02 0.17 96, 186 -0.1686 -0.3312 -0.38 0.35 ' 0.39 0.23 0.24 0.09 78 186 +03312 1_66

--

1

-96 I +0.1686 0.35 0.07 I 0.02 186 L 0 1 0.52 0.20 0.04 496 _=0.1686 II 0.38 0.22 H 0.18. , 1186 =0.3312 0 98 0.38 0.48 791 198 =k0331I2 113.1

-108 --1-0.16816 0.37 008 00.1 198 0 0.50 0.29 0_19 108 -0.1686 0.24 0.45 0.30 I 1198 -0.3312 I 0.08 0.23 0.03 82 1198 +02312 I 1.66

-if 08, 198 +0.1686 11 0 , 0.11 , 0.46 70.05 i 0.04 0.02 0.20 108 =0.1686 0.40 0.17 0.05 198 L -0.3312 1:07 I 062 1 0.23 I

--

-0.0

0

0=DEGREE DUCT PROPELLER 3714 OR =

1.01 -x/R 0 +.3312 I 1

L

+.1686

0

.0

0-1686

0 -.3312 ______-,

0

, _ ,

0

0

_ .

0 0

_

0

_

0

a

0

0

000

00

0

o

0

,,

La

n

._ C3

a n A

@ A

0

0 0

A

o

@

a

0

El 01

0

Di 1

-0----I:

-0

_1=1

o

<> 0 <> <> <>

6 8 .:).

o 0. 0 00°0008(00 0

<> o 0,

I 3601 288 312 336 264 72 96 120 1144 168' 192 216 240 Ow , WAKE

SCREEN POSITION (DEGREES)

Figure 9

Measured Blade-Frequency Pressure Amplitudes as a Function of Wake Screen

Position at Mean Thrust Coefficient KT = 0.159 and 1-Percent Radius Tip Clearance

24 48 0.5

0

0

0

0

0

0

0

1 1 ,

320 240

0

0-DEGREE DUCT PROPELLER 3714 r/R

= 1.01 I I x/R 1686 _.0 1686

0

-.3312 I

n

-

8

4 +.3312 +

-0

Do

L

0

₀

8

0

Riononoi=.0

DI o,,p_i n,

_{0 0}

0

no8

o S6aL,L980Agno

ono

Lin

0

L

0

OPO .0

0-00z1,0°0noinFi

DADLOn <>

0 0 0.

0

/-\

v

. .

0

,\

v

0

0

0

0

0

)

00

o

c

0

0

000

o

0

Quo

3

0 ,.., L,

0

n

0

0

o

0

0

o

0 24 48 72 96 120 144 168 192 216 240 264 288 312 336 360 Ow

WAKE SCREEN POSITION (DEGREES)

Figure 10

Measured Blade-Frequency Phase as a Function of Wake Screen Position at

Mean Thrust Coefficient KT = 0.159 and 1-Percent Radius Tip Clearance

160

0

1 I I

-a = 4.20

a = 2.76

a = 1.66

Figure 11 Cavitation Patterns of Propeller 3714 in 0-Degree Duct at

Various Cavitation Numbers

a = 13.1 NO CAVITATION

(dr = 1.66) the blade-frequency pressure decreases. This phenomena is attributed to thrust

breakdown. It has been determined previously by Denny4 that both thickness and loading

contribute to the total induced blade-frequency pressure. However, for thrust breakdown, it cannot be determined whether the reduction of the blade-frequency pressure is caused by a change in the loading due to local flow conditions, a change in the "apparent" thickness due

to change of cavity shape, or a combination of both loading and thickness changes.

Except for the occurrence of thrust breakdown, these results agree with those presented by Huse5 who indicates that the tip vortex contributes very little to the induced pressures but that the volume change and motion of the cavity significantly increase the induced

pres-sure. Also from Table 5 it can be seen that the pressures downstream of propeller reference

plane are those most significantly affected by propeller cavitation. The phase angles also presented in Table 5 show that the phase angle of the blade rate harmonic is a function of both wake and cavitation number.

Table 6 shows that the second and third blade-frequency-pressure amplitudes contribute significantly to the total propeller-pressure amplitude. Previous experimental induced-pressure results6 indicated that the second and third blade-frequency-induced-pressure amplitudes did

not contribute significantly to the total propeller-induced pressures. However, these results were for a minimum propeller radius tip clearance of 10 percent. Thus, the ducted propeller results presented here seem to indicate that the higher harmonics (second and third)

contrib-ute to the total pressure signal more significantly as the propeller-radius tip-clearance decreases. Figure 12 and Table 7 present pressure results as determined by a Real Time Analyzer. Figure 12 shows that the second and third blade-frequency-pressure harmonics are more

signi-ficant for x/R = 0.0. Table 7 presents the comparison of the Interdata Minicomputer results

and the Real Time Analyzer results. It is seen that the blade-frequency pressure results for

the two methods of analysis differ by about seven percent. However, the Real Time Analyzer

analysis does not yield any phase information, whereas the Minicomputer analysis does. Since it is necessary to have phase information to determine propeller-induced forces, the Real Time

Analyzer results are insufficient for this purpose and were just used for confirmation of the

Interdata Minicomputer analysis technique.

4Denny, S. B., "Comparison of Experimentally Determined and Theoretically Predicted Pressures in the Vicinity of a Marine Propeller," NSRDC Report 2349 (May 1967).

51{use, E., "Pressure Fluctuations on the Hull Induced by Cavitating Propellers," Norwegian Ship Model Experiment Tank Publication 111 (Mar 1972).

6Teel, S. S. and S. B. Denny, "Field-Point Pressures in the Vicinity of a Series of Skewed Marine Propellers," NSRDC Report 3278 (Aug 1970).

TABLE 7 - COMPARISON OF FIRST, SECOND, THIRD, AND FOURTH

BLADE-FREQUENCY

PRESSURE AMPLITUDE RESULTS USING THE INTERDATA MINICOMPUTER

AND THE REAL TIME ANALYZER

Run Number Wake _Screen Position xiR a Interdata Analysis

Real Time Analyzer Analysis

Ratio of Interdata Minicomputer Analysis Results to Real Time

Analyzer Results ow CZ I C2Z I C3Z1 C4Z1 CZI* C2 Z I C3Z1 C4Z1 CZR** C2ZR C3ZR C4ZR CZR C2ZR C3ZR C4ZR 38 90 +0.3312 2.76 0.2124 0.0644 0.0398 0.0233 0.20 0.055 0.0325 0.0125 1.06 1.17 1.22 1.86 0 +0.1686 0.572 0.0762 0.0434 0.0190 0.56 0.06 0.03 0.01 1.02 1.27 1.45 1.90 90 0 0.4565 0.2727 0.1005 0.0547 0.437 0.237 0.100 0.04 1.04 1.15 1.01 1.37 0 -0.1686 1.467 0.8007 0.2657 0.3295 1.475 0.70 0.225 0.277 0.994 1.14 1.18 1.19 90 -0.3312 0.2301 0.0422 0.0218 0.0156 0.215 0.025 0.015 0.01 1.07 1.69 1.45 1.56 *Subscript I

denotes Interdata Minicomputer analysis results

**Subscript R denotes Real Time Analyzer results

-I

-200 400 200 400 FREQUENCY (HERTZ) Figure 12

Real Time Analyzer Results of the Amplitudes of the Various Multiples of

the Blade-Frequency Pressure at Mean Thrust Coefficient KT

0.159 and

1-Percent Radius Tip Clearance, Nonuniform Flow

0.6 0.1 x/R = 0.0 Ow = 90 200 400 FREQUENCY (HERTZ) x/R =.1686 Ow = 0 04 200 400 FREQUENCY (HERTZ) FREQUENCY (HERTZ) 0.6 x/R = +.1686 Ow =0 cL 0.4 LU (i) Lu cr a_ 0.2 0-DEGREE DUCT x/R = +.3312 PROPELLER 3714 u-) 0 =90 r/ R = 1.01 a = 13.1 0 0 600 200 400 FREQUENCY (HERTZ) 0.4 (1) 0,2 x/R 0. w (7)

PROPELLER-INDUCED DUCT FORCES

In nonuniform flow, the integration of the propeller-induced pressures in the axial and circumferential directions will result in the total fluctuating pressure forces7 acting on the duct. Although it has been determined that the higher blade-frequency pressures are

signifi-cant, only the forces due to the first blade-frequency pressures will be calculated for the non-cavitating, nonuniform flow conditions. From the results of Figures 9 and 10, the maximum fluctuating vertical, horizontal, and axial duct forces were calculated to be 0.578, 0.231, and

0.042 lb, respectively. These results represent 0.98, 0.39, and 0.07 percent of the propeller

thrust. Figure 13 presents the fluctuating forces as a function of angular position of propeller

for the wake flow as generated by the wake screen for the position shown in Figure 4. Details

of the integration method are presented in the Appendix.

SUMMARY AND CONCLUSIONS

I. The induced pressures were found to increase with increasing propeller loading.

Higher order blade-frequency harmonics (second and third) were significant percent-ages of the first blade-frequency harmonic.

In nonuniform flow, the blade-frequency pressure is a function of the local flow

conditions. In the vicinity of the propeller reference plane, the ratio of the maximum

blade-frequency pressure to minimum blade-blade-frequency pressure is approximately 3.0.

The blade-frequency phase angles were essentially independent of axial distance

upstream of and at the propeller reference plane but varied significantly with downstream

distance.

The induced pressures were found to increase with increasing blade cavitation

(decreasing cavitation number) by as much as a factor of three. This applies to pressures

downstream of or in line with the propeller reference plane.

At a cavitation number of 1.66, the induced pressures sometimes decreased from the value obtained at a higher cavitation number but was still greater than the blade-frequency

pressure obtained for no blade cavitation. This phenomenon is attributed to thrust breakdown.

Propeller-induced blade-frequency-pressure forces acting on the duct were determined

to be approximately one percent of the mean thrust.

ACKNOWLEDGMENT

The author sincerely thanks Mr. Stephen B. Denny who provided invaluable guidance

during the experimental phase of this project.

7Biskup, B. A., "Periodic Forces Developing on a Propeller Duct," Symposium on Ducted Propellers, Royal Institution of Naval Architects, Paper 17 (Jun 1973).

0.7 0.6 1 0.1 0.0

051

-0.6 0 24 0-DEGREE DUCT PROPELLER 3714 1 1 1 I I

/

I

/

I / I I I I 1 1 1 I 1

I

Ii

/

I

lul

I I 1 I

Y1

1

!VI

I 48 72 96 120 144 168 192 216 240 264 288 312 336 360 q)

, PROPELLER BLADE POSITION

(DEGREES)

Figure 13

Calculated Blade-Frequency Propeller-Induced Forces as a Function of

Propeller Blade Position at Mean Thrust Coefficient KT = 0.159 and

1-Percent Radius Tip Clearance

/ _{I I} I _/ 1 1 1 /

'I

/ Fv 1OFA I I

APPENDIX

'DETERMINATION OF PROPELLER-INDUCED FORCES

The propeller induced forces were determined by integrating the propeller-induced

pres-sures over the interior of the duct in the following manner:

L. The interior duct surface was divided into 150 approximately equal incremental

areas.

2.

Direction cosines°

'cos, Y_{cos' Zcos} f the n,ormals to each of these incremental ,areas

were calculated.'

3.. The nonuniform flow phase angle results were then adjusted to be with respect to

the vertical upward. position and not with respect to the ,propeller blade reference line-.

4. The pressure amplitude and modified phase angle results were then integrated in the

following manner to yield vertical, horizontal, and axial blade-frequency propeller-induced

pressure forces as a function of propeller blade position in the duct 150

FVERTICAL - An (Zcos )n (C) Cos (Z0 'Yzn)

n=1

150

HORIZ'ONTAL An (Ycos (CZ )n cos (Z4)

- n=1

150

FA XIAL

1-7 An (--)(co)n (Cz)n

COS (Z(I) -YZn

n=1

where An .= incremental surface area

(Cz)n .= amplitude of the blade-frequency induced pressure acting on the n th

incremental area

FAHV = axial, horizontal, vertical blade-frequency pressure induced forces = incremental area index

7Zn = adjusted phase, of the blade-frequency induced pressure acting on the n th

incremental area = 400)

angular propeller blade position

=

=

; 7Zn

-= 0

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