UNCLASSIFIED

AD NUMBER

AD822486

NEW LIMITATION CHANGE

TOApproved for public release, distributionunlimited

FROMDistribution authorized to U.S. Gov't.agencies and their contractors; CriticalTechnology; 13 SEP 1967. Other requestsshall be referred to Naval Air DevelopmentCenter, Johnsville, PA.

AUTHORITY

USNADC ltr, 5 Oct 1971

THIS PAGE IS UNCLASSIFIED

DEPARTMENT OF THE ,!AVYU. S. NAVAL AIR DEVELOPMFINT CENTR

JOHNSViLLEWARMINSTW , PA. 1074

Aero-Electronic Technology Department

REPORT NO. 6ADC-AE-6731 13 Seote ,,nr 1967

WATER IAG E?'FECTS OF FLOWU 1INDUCED CABLE V! BRATIONS

PH.A.-SE P LonT

AIRTASK NO. A37S35000/2021/FI0!-13-07Work Unit No. 170

00 A study was performed on smooth, circular, flexible cables todetermin. the water drag characteristics that are dependen.up .the cable strumming phenomenon. The tast cable diamters

ranged frc 0.057 to 0.140 in. and the Rtjnolds nu b" werewithin 300 to 1300. The study was a prerequizite to developingcables with low drag and low straing characteristics.

Reported by:R.D~le

vVar Sensors Division

Approved by: . '

H. -Suter, SuperintandentSonar Sensors Division

D. W. i i ' . . . . ...

Technical Director

T do feAmt is subJat to aeciaZl a.v ver*ntr)t andcadz trwr-itta1 to forsgn govwrninto or foydilnatlat*Z mgy be na. aae nk with piyior qp,-~ Of Czn-Tf=0d-4 Off vters, XavaL Air Devto- Center.

'4%

DEPARTMENT OF THE i,'AVYU. S. NAVAL AIR DEVELOPMENT CENTER

JOHNSVILLKWARMINST0, PA. 18374

Aero-Electronic Technology Department

REPORT NO. WADC-AE-6731 13 Se1)te,r 1967

WATER DVAG EiFECTS OF FLOWINDUCED CABL, 'CIBRATIONS

PHASE REWORTAIRTASK NO, A37S33000/2021/FI0l..13-07

Work Unit No, 170

A study was performed on smooth, circular, flexible cables todetermino the water drag characteristics that are dependenIupon the cable strumming phenomenon, The test cable diamtersranged from 0.0S7 to 0.140 in. and the Reynolds rabazz werewithin 300 to 1300. The study was a prerequisite to developingcables with low drag and lw strumming characterlstics.

Reported by: 4g B2Dale -M. McCandless

one Sensors '-)ivision

Approved by: .,H. Su:-e,,-Superi'endent .....Sonar Sensors Division

D9- W.'P YNacki

Technical Director

A-14 d ownent i$subdeot to "*iaA. apoit &. vo andem* txamwftft to forin gom nto o- fkmiomutimaZ. ,w be =&e oln4- ei prior qprotvZ of cm-"id-g Offioez'* Ncv Air D*Mupzwng: Cgsntr.

......

NADC-AIE-6771

SUMMARY

INTR0DUCTION4

Single-clement or aultiple-eltment hydrophones 'sed ",ith moored ordrifting sonar systems are suspended by complex airrangements of long orshort cables of circular cross section. These cables are usually exposedto relative water flows in the 1/4- tn 3-kn ran~rci caused by In si.tu cur-rents or induced by the capricious effects of wind and waves.

'AAhw wae i-n-Pnttecbl nue eidc transverse vibra-tions, commonly called "lcaile stmundng." This strAnming 13 iniAallyexcited by localized low-pressure zones along the side of the ca??le. Thezones alternate periodically from side to ide, thereby -roducing alter-nating side thrusts. The zones are related t.o the fiow separation andvortex formations near the bass'of tha cable (cylinder). Vortices areshed into ; he flow wake and form on alternate sides of the flow center-line (yon Karman vortex wake). The strumming of tfie cable interfereswith sonar functions by causing pseudoacoustic signalsl from the hydro-phoncvs and adverse cable drag2 .

RESULTS

Vlexible cable drag coefficients can be determined to within 10 per-cen~t by measusring the cable drag angle of a towed streaming cable with atiiuinal weight standard.

A tractable analytical drag model was formulated to express the nor-mal struming drag coefficient C~s in terms of tliv normaal drag coefficientCD,, cable diameter d, and mass per .init length mc of the cable. The modelrepresents the struming cable as a circular cable with a larger dia'ueter,termed the virtual diameter. The expression for the struming drag coef-ficient has the form,

d2 I1+ amc

Verification of this concept is shown for cables with diffe~ent diametersand different values of moss. The best-fit values for the const ants are a10 and a a 1. Kith a nominal value of O.19S ft4/lb-sec2 for d2/mc an approx-imato criteria for the struing normal drag coefficient is 38 percenthigher tharn that of a circular cylinder.

i*Dale, J. R. and Mnmel, H. R., Dec 1966; F7-ow Induced Oacn.Zlationof Iiydropho, Cab e!I; LOAVAIRDEVCRN; 23rd Naval Underwter SoundSbWnoe1A~n ProocedZnge; 0)11 Rpt ACR-115 Paper 3A6 P0 411.

2. Dale, J. 1?. Dec 1,966; Hydrodynanic Ana~yisi of the AR/'SSQ-41Sonobzoy Rydrophone Suppowiton 5,Stmj NAVAIrDEVCEN Raport 5'o.NADC-AE-0636.

NAUC-Ar-6731

CONCLUSIOMS

irmsitional numinal vari&-ions ir c.rag coefficient o.£ 3) perentare shown to correspond to tone effec.:s, zhuac.eristic :,f a strummingcable in a varying flow, These transitions occur at discreto water Vel-ocities for a given cat-I1 1 ,igth and can be defined by the classical stringrquatircn _nd Strouhal nute.

Envelope values for tha stiumming normal dzag coefficient of a smoothcircular flexible cable can bo predicted by:

CDs = CD 11 + M. c ]

where d is the cable diar"ter and m. ". thw virtual mass o2 the cable perunit length. This ¢:.uation has been verified for cables fr-i 0.057 to0.140 in. in" diameat-3 and for a aus'.; range of 1.16 x 10-4 to 9.30 x10-4 slug', withi., the Reynolds number r i ge 300 to 1300.

- iv- __ _.__ __

NADC-AE-6731

TAI LE OF CONTENTS

Page

S~eeAY . . . . . . . . ........... .

Introduction. . . . . . . . . . . . ......... iiiResults ................... .... oConclusions .... .... . . . . . . ...... . iv

LIST OF FIGURES . . . . . ...... . . . . . ... vi

LIST OF SYMBOLS ...... ...................... vii

DISCUSSIO .. . . ... .................

A k r 4 . . . . . . . . . . . .. . . . . .. IDrft and Strains Measurtunts . . ........... 2An.lytical Model . .... . .............. 4Exprt.*ntal Studyd. . ..................... 7Cable Performance - Special Designs ......... ... 10

AC CLTDGMNT .......................... . 13

TABLE

I C lble Parameters . . . . . . . . . ...

APPWNIX

A Uerivation of the Stniming Cable Drag

rCoefficient, CDs .. ............... ,.. A-1

I

NADC-AE-6731

LIST OF FIGURES

.gur e Ti t 1 e P ag e

1 Instrunentation for Measurement of Cable DragAngle and Struning Accelerations .......

2 Acceleration (Struming) and the Cable DragAngle Signatures for a 0. 107 In. DiameterCable in a Gradually Decaying Flow. OneSecond Time Pulses Indicated. .................

3 Struming Drag Coefficient and Struming Forcefor a Smooth Cylindrical Cable 0.107-In.Diameter, 3 Ft Long ....... ........... ... 6

4 Drag Coefficients of Smooth Circular StruminZCables. . .................. . .. 9

5 Drag Characteristics of Special Cable Designs 116 Strumming Force Characteristics of Special

Cable Designs ...... .. ................. 12

vi

INADC-AE-6731

LIST OF SYMBOLS

a, a,, a" - Expei..meutal constants

C/Cc - Dampinj ratio for the vibrating cable

CD a Dimensionless normal cable drag coefficient ased on d fornormal flow past a smooth circular cylinder

CD5 a Dimensionless normal cable drag coefficient based on d fornormal flow past a struming cable

CL a Cable 2iI coefficient

d n Cable diameter

d - Equivalent diameter of the cable projected on a transverseplane

dv - Virtual :able diameter (defined in appendix A)

f z Frequency of the transverse cable vibrations

fc = Normal drag force per unit length of the cable

F a Alternating periodic struming force which accelerate- thefixed end mass

= a Gravitational constant

Kx a Spring constant of cable in transverse direction

L a Cable length

z = Distance. between node!, for any specified wave segment

Ac a Virtual cable mass per unit length (physical mass plusmass of an equivalent volms* of water)

n w. Number of vibrating cable segments in the cable length L,n = L/L

NRO a Dimensionless Reynolds ntmber - dun/v

r A mplitude of transverse cable vibrations

St - Dimensionless Strouhal nuber v fd/unT a Tension in the cable

UO Free stream water velocity

Un * Component of water velocity normal to the cable

Ut a Harmonic velocity of the vibrating cable * 2wfr

a Experimntal constant

A • Increment of the paramoter

P a Density of water

- VYE_ -

NADC-AE-6731

LIS T O F S Y MBOL S (c on t inited)

v a Kinematic viscosity of water

a a Factor e: ,pressing effectiveness of flow blockage, definedin appendix A

W= Angular forcing frequency

Wh- Angular natural fr~quency of any standing wave segment

-viii-

NAIDC-AE-6731

~DISCUSSION

BACKGROUND

The dependence of norm~l cable drag on cable strtming ws observed onfrec strewaing cables with terminal weights 1 . Small variations in cableangle were observed simultaneously with changes in vibration amplitude.The dejendence of drag n rigid cylinder oscillations was shown by Bishopaixd Hassan3 . When their rigid cylinder was forced to oscillate at a fre-quencj in counterpoint with the natural wake frequency, an increase in dragwas observed. Also, this dependence has been inferred by high amplitudetransverse, resonant vibrations. Windijorst 4 reports such a condition fora spring motaited rigid cylinder when the natural vortex shedding frequepcycoincided with the spring-mass natural frequency.

The authors 5 have reported on similar resonant amplitudes as well ascable tone effects on flexible cables. Transverse standing wave vibrationswere forced by the interaction of the ;,ater flow with the cable. When theflow velocity was gradually varied, transitions in amplitude and frequencywere reported at discrete velocities each tire the number of standing waveschanged by one. The frequency interval between successive transitions anda specific scanding wavelength characterized a numbered partial vibrationmode. (The term partial is used instead of harmonic because the frequenciesare not even multiples of the fundamental.) Correlation was obtained withthe string equation,

where the forcing frequency was approximately defined by the Strouhalntuber,

St fd (2)

1. See pe iii.JI . Bishop, 9. D. and Hlassan, A. Y'., My 1963; The Lift and Dra

IForm on a Nrcular Cyinder O0seitating in a Fiooing Fuid;Vnivervity Col.ege, London, Dept of Aff.

4. Mier-Wndhorst; Aug 1039; Flo Induced Vibration of Cytindere inVhifon Pw; owieh Tchnis oh NoeHhechuic, Hydraulieche Inet. Wttt,Hieft 9.

6. DaZe, J. R., et at, Sep 1966; Dynwer.c Characteristics of UnderwaterCab s - Flow Induoed Transverse Vibrations; NAVAIRDEVC Report No.

NADC-AE-6620.

-I -

. ol I I ! I ! lm . !" ~ m mm m - -_ _

NADC-AE-6731

The amplitude of each standing xu:e vibration is a minimum for the vel-ocity just prior to each transition - frequently zero. Within each partialmode, a maximum a.plitude is reackhd when the forced vibration frequencyeauals the natural cable frequency of the vibrating segments. The normaldrag coefficient was expected to be directly dependent on these amplitudevariations.

DRAG AND STRUIJdlNG MEASUREMENTS

Because of the dependence of cable drag upon cable strumming, diagnosticinstrumentation was developed to measure both effects simultaneously.

Cable Dra Coefficient

An experimental technique was developed to determine CDs for normalflow by towing a test cable through water. (The symbol CDs is used todesignate the normal drag coefficient for a strumming cable, while CD isused for a nonstrumming cylinder.) The lower free end of the cable wasattached to a smooth surfaced, 2-in. diameter, 0.504-lb sphere, used as astandard of know, weight and known velocity dependeitt drag force. The cble

drag angle at the tow point was measured photoelectrically using a rotatingvane, and correction was made for the bow in the streaming cable. The nor-mal water force per unit cable length was determined by summi'g the forcemoments about the tow point. The normal CDs was computed by using,, thisforce and the actual cable diametero-

The accuracy of the CDs determination was enhanced by a prudentselection )f cable length and drag to weight ratio of the sphere standard.Cable lengths from 3 to 4 ft were uzed because longer cables generally areexcited with multiple frequency beating effects which obscure the classicalsignature of the strumming signal. 1he CDs determination was estimated tobe valid within 10 percent when tI,.e angle and velocity were measured to 2and 3 significant figures, respectively.

Strunmming Force

The periodic strumming forces, representing cable tensio'i oscillations,were determined by measueing the accelerations of a spring mounted mass.The mass and spring supported the cable at the tow point (fixed end). Thespring constant and mass were selected such that the spring restoring forcewas small compared to the force to accelerate the mass. Accordingly, theforce determination was .essentially the product of mass times acceleration.

The instrumentation, is shown in figure 1. The test cable was towedby a rotating arm with a 7-ft radius. During each test the angular vel-ocity of the arm was varied such that the free stream tow velocity gradu-ally decreased from 1.2 to 0 kn in approximately 2 min. This provideddata over the Reynolds number range of interest, and spanned severalpartial vibration modes.

-2-

p

NADC-AE-6 731

0

*ro

LUU

44

tn 0

CL4

CL)

-4

NADC-AE.6731

A segment of the raw data recording for a 0.107-in. diameter, 36-in.

long cable is illustrated on figure 2. Three partial vibration modesare indicated by the three triangular forms of the acceleration signal.Starting from the high velocity end these modes correspond to the fourth,

third, and second partials with half wavelengths of 9, 12, and 18 in.respectively. The trace of the cable drag angle humps during these partialvibrations, iudicative of an increase in cable drag. The cable drag angleis responsive to the unstable bursts preceding the amplitude transitions

of the acceleration trace.

The normal drag coefficient, CD, for the strumming cable, and thePeriodic strumming force are plottea against Reynolds number in figure 3.The normal drag coef 4.cient, CD, for a nonstrumsing circular cylinder is

also plotted as a reterence. Each sawtooth form represents a discretepartial vibration. The minimum points were between the partials or nearthe transitions tther- t ie cable vibrations decayed to a low level. Asindicatod, the minimum pointn approached the nonvibrating CD referenceplot, which was expected for the low level vibrations. Both CDs and Fshow the same phase relationship. This implies that the drag is relatedto the amplitude of vibration, because the cable tension variation F isin phase with the elongation of the cable or transverse amplitude. Thepeak values must represent the trim partial vibration, where the naturalfrequency for that particular standing wave is in counterpoint with thefrequency of the water exciting function. This resonance effect is pre-sented in more detail by Windhorst 4 and the authors 5 .

The maximum and inimum points of these sawtooth characteristicsoccur at different NRe when the cable length is changed. This can beseen from the string equation (1), where a change in L will result in adifferent f for the same numbered partial n. The water forces excite thecable at this new f at a different velocity or NRe. The peak values ofthe parameters, therefore, describe a envelope which is independent ofcable length. (Envelope values will be inferred with reference to CDsand F for the balance of this work.)

ANALYTICAL MODEL

Present scaling laws 6 , describing the drag of bluff bodies, relatethe drag to appropriate parameters of the near wake. These parametersare associated with the well known alternately shedding vortices (Karmanwake). The near wake characteristics of a strumming flexible cable are

4. See pg 1.5. See pg 2.6. Roahko, A., Feb 1955; On the Wake and Drag of BZuff Bodies;

J of Aevo Seiencee; Pg 114.

-4-

NAD-AE-6731

CABLE DRAG ANGLE

STRUMMING

44 1

44

FIGUMS 2 -Accsoleration (Strmining) and the Cable Drag Angle Signatuesfor a 0.107 In. Dimetox, Cable in a Gradu~lly Decaying Flow.One Secohd Ti*e Pulses Indicated.

-5

NA,C-AE-6731

1.4 -

1.4

!.3

1.2

l,1..

SM'C CIRCULAR CYLINDER

1.0 IESELSBERGER. GOTINGEN)

S 0.4z -

-0.3LaJ

/00f20.2z3E STRUMMING TRANSITIONS

0.1 - OUTER ENVELOPE

600 700 0 900 1000 1200REYNOLD'S NUMBER - NRe

FIGURE 3 - Strwmmng Drag Coefficient and Strwming Force for a Smoo'hCylindrical Cable 0.107-In. Diaumter, 3 Ft Long

-6-

tDC-A.-6731

known to deviate from thO classical Karmm wake concept" 7. 6eause oftke lack of guidelines to formulate a tractable drag oquatiQi for thestruming c€ble, a drag model with a virtual diameter was postulated.

The transverse vibrations of a smooth circular strumins cable areAsstmue to appear to the flow as a laxner diameter (virtual diameter, dr),

sooth, circular, Pontrmtry cable. The virtual diamter is then related

to the euivalent projected diameter ti"s a factor which expresses theeffecti.veness of this projected diameter in blocking the flow. Thiseffectiveness factor is the ratio of the assumed harmonic transverse cablevelocity to the free stream velocity.

The struming cable drag coefficient for normal flow has the form:

a d v a .Lr-Ds- CD 7-Pt CD (1 + ! ).

In terms of cable parmeters the equation reduces to:

d2 1 +(4CDs CD 1+ (- ) +O 4

where e. and a an ccstnts to be determined from experimntation. Cnis seen to be depent'e only on the drag coefficient CD for a circula!'noustrnng cable of diameter d, the cable diameter d, and the cablevirtual mass per unit length mc. Details of this derivation are presentedin appendix A.

EuRIurrAL STUDY

Equation (4) was verified by experimental determination of CO. overa diameter Tange from G.7 to 0.140 in. and a d2/Mc range from 0.123 to0.31S ft4/lb Sec2 . al cables were smooth ad flexible with circularsections. (A: cable is considered flexibla when the inter-al reactingbending moments are small relative to the external bedt4 Ooments.)

Correspomding cable parameters m Aisted in table I. Each testcable was towed throqh a gradally decreasing velocity rafge from about1.2 tu 0 ka. The drag aqle asd the periodic accleratizs of the fixedOn Tss were meaSured siaultameouly.

4. S"Pq 1.?. Sai5* Le 0., t ats Oat 19$6; An Imwetifatzon of Povaea on

an OtoiZating Cytid5r for 4p~ioation to Growd Wnd Load@ onLawo VKeZu, MNT Aerapyios Lab rR 1a.

1 __________ ___ -- _ _ _ _ _

ADC-A -6731

TABLE I

CABLE PARAMETBRS

d d2/M Measured *Equation (2)

(in.) L sec2 ft 2 ) (ft4/lb sec2) CDs/CD CDs/CD

0.057 1.16 X I0-4 0.195 1.25 1.38

0.107 4,.6 x 10-4 91195 1.36 1.38

0.128 3.Lj) x 10-4 0.315 2.00 1.99

0.128 9 . x 10-4 0.123 1.04 1.15

0.140 6.84 x 10-4 0.199 1.52 1.40

* For experiaental scaling const'mts a = 10, and a - 1.

By interpreting the numbered partial vibration modes from the acceler-ati or signature, the highest CDs value for each specific partial wasdetemined. The highest CDs value was generally found where the acceler-ation amplitude was the highest. This generally coin.ided with the humpIn the drag angle trace. In this way the envelope of the Crjs values wasdefined for each cable. Three cables were selected with avnn oxatelythe same d2/mc ratio of 0.195 ft 4 /lb sec 2 but with diameters of u.057,0.107, and 0.140 in. (Insulated electrical cables over a wide range ofdiameters will generally have ratios around this value since mc variesapproximately with d2 .)

Th. data points and corresponding envelopes &re shown on figure 4against NRe. By plotting the data against NRe, the relative magnitudw ofthe CDs val;m can be compared to the reference CD curve for a smooth, eir-cular (nonstrmming) cable. Each of the three curves runs approximatelyparallel to the CD reference curve, implying that CDs is independent ofwater velocity in accordance with equation (4). The data points for thesecables fall vithin a CDs rase of 1,3to 1.6 and appear to be approximatedby a constaut factor times CD as inferred by equation (4) - particularlytrue for the 0.057 and 0.107 in. diameter cables.

Two additional cables were selected with identical diamete2s of 0.128in., but with d2 /x ratios of 0.123 and 0.315 ft4/Ib sec2 . These extremevalues were obtained using cables with a mercury filled core and a hollowcore, respectively. The cable with the high ratio had a high CDs envelope,about 2.0 on figure 4, while the low ratio cable had CDs values falling

-8-

MADC-A,-6731

0

/ n0 0

UjU

00

4.(

0 1 0

ii r1iz 'FE - i

MU cc

or.

+ C; C

\V

cccc 0U,

-9 *

.........

7

NADC-AE-6731

close to the reference CD vrve at about 1.0. Again, the envelopes inferindependence of water velocity by paralleling the reference CD curve. Ingeneral, the magnitude of the strumming forces on the fixed end mass showeda direct relationship with the ratio dz/mc.

To obtain a check on the absolute values of CDs for the various cables,each cable was tabbed at discrete intervals to minimize the strumming ampli-tude. (The CDs values should then fall close to the reference CD curve.This would check the ability of the drag measuring technique to reproducethe reference CD curve and add credence to the absolute values of CD forthe strumming cables.) The test cables were tabbed with 1/2 in. maskingtape l-in. long, applied as localized flow splitters. They wrre placed atniear antinode positiins for the range of standing -'svelengths expected anda slight correction was made for the localized decrease in CD caused by thetabi. Most of the resulting CDs values fell within S percent of the CDcurve, with an occasional high or low velocity point falling within 10percent.

The constants from equation (4), a and a , were evaluated from thedata of figure 4. The best fit values were a = 10, a = 1. Using thesevalues in equation (4), predicted values of CDs/CD were compared with themeasured values of CDs/CD in table I. Reasonable correlation was obtainedbetween .hese ratios for the range of d and mc tested. If a nominal valuefor d2/mC ii 0.195 ft4/lb sec2 for insulated electrical cables, equation(4) reduces to CDs/CD = 1.38. For a rule of thumb, cable strumming resultsin approximately a 38 percent increase in the normal drag coefficient.

CABLE PERFOMANCE - SPECIAL DESIGNS

Drag coefficients and strumming force levels have been determined forfour cable designs with interesting characteristics. These dosigns were.

1. twisted pair,2. antinode splitters,3. weathervane fairing, and4. "haired" streamers.

The strumming normal drag coefficients are shown on figure 5 and -theperiodic struming forces on figure 6. A physical description is schemat-ically illustrated on figure 5, and values of the respective parametersare plotted with the 0.107-in. diameter smooth circular cable for reference.

TWisted Pair

These data were included becanse of the simplicity of fabrication.The diam-ter of each cabh6 was O.Oi7 in., *.rJ the integrated diameter usedfor the drag coefficient w .s 0.093 in. Both CDs and F were lower, comparedto the reference cable. Best results were obtained when the pitch wasabout .15 diameters, based on 0.057-in. diameter.

- 10 -

NADC-AE-6731

1.9

1.1 HAIREDSTREAMERS

1..5 \REFERENCE(SMOOTH ROUNDCABLE)

| L3

TWISTED PAIR,1.1 d

00.9

07Imx 4m.mjii~~0

ANTINODE N0. 7 SPLITTERSfl 1.0d0.5

O 7 d - WEATHERVANES*FAIRING

°..0.4 0.6 0.8 1.0 1.2 1.4

WATER VELOCITY - un (KNOTS)

FIGURE 5 - Drag Characteristics of Special Cable Designs

- 11-

9'

NADC-AE-6731

0.4 VBRATION MODES

(REF ANTINODE SPLITTERS)I fn2 )'9 IN.

0.3 REFERENCE(SMOOTH ROUND' *ATNDCABLE) SPLIlTERS

t I

U0.

0 .TWI TE

0.1 00/BSTEMR

WEATHER VANE

%.2 0.4 0.6 0.8 1.0 1.2WATER VELOCITY -un (KNOTS)

FIGURE 6 - Struin Force Characteristics of Special Cable Designs

j -12

Antinode Splitters NADC-AE-6731

When localized splitters were attached at the antinodes for a specificpartial, the strumming forces at frequencies equal to or less than thepartial were less than the noise threshold of *0.003 lb. Considering thetest cable length of 36 in. with a 9 in. tab pitch, this condition existedfor parTlals 1 and 2 with segment lengths of 36 and 18 in., respectively.As the frequency increased to higher partials, the forces became progres-sively higher, and the level of the nontabbed reference cable was reachedwhen the tabs were at the nodes. This condition was reached at the 4thpartial, with a 9 in. segment ena'1. The affect of the higher levelstrumming at the high velocities -.. s reflected in the CDs plot. The mosteffective tab geometry was 10 diameters with the stream and 20 diametersalong the cable.

Weathervane Fairing

This was an omnidirectional fairiing that was effective in reducingthe drag coefficient and kept the strumming force level below the noisethreshold of *0.003 lb.

Haired Streamers

This was a promising omnidirectional design, because of its simplicity.The hairs were oriented spirally on about a 9-in. pitch. Cotton thread,No. 50 grade, was used for the hairs. The strumming forces were belowthe *0.003 lb noise threshold. When the hairs were not spirally attached,best results were obtained with the hairs attached to tne downstream edgeof the cable. The drag coeffi.cient increased at the lower velocitiesbecause the hairs bent outward - their natural position.

ACKN0WLE DGEMENT

Acknowledgement is made to Mr. G. Goss for his assistance in obtainingand reducing the experimental data.

131- 13 -

X WC-AR-6731

APPENDIX A

DERIVATION OF THE STRUMING CABLE DRAG COEFFICIENT, CDs

The normal drag coefficient for'a strumming cable, considering a unitcable length, is defined as:

CDs = (A-1)2

The transverse itanding wave vibrations are illustrated schematicallyin figure A-I and t.%* assumed to appear to the flow as a circular non-strumming cylinder with a larger diameter, termed the virtual diameter,

ad v . The normal drag force per unit length of the cylinder is:

2un (A-2)fc " CDdVP 2g

Combining equations (A-1) and (A-2) gives:

CDs = CD T- •A-3)

The virtual diameter is assumed to be the sum of the cable diameterand the increase in diameter resulting from the cable vibrations:

" d + Adpa (A-4)

where Ad is the change in the effective projected diameter (on a planeparallel to the transverse vibrations) and a represents the effectivenessof the flow blockage. Equation (A-3) th3n reduces to,

CDs = CD ( + a) (A-S)

The change in projected diameter Adp is obtained by dividing the projectedarea of one wave segment by its length 1. Assuming the cable curvature tobe a sine f' ction as illustrated on figure A-I,

Adp - f r sin Y d - (A-6)0

- A=i =

NADC-AS-6731

The a factor is assumed to depend on the ratio of the transverse harmoniccable velocity to the water velocity normal to the cable. By dimensionalanalysis and application of the Strouhal number,

Ut ra- a (2 it,)(A)

Combining equations (A-S), (A-6), and (A-7),

a 4r r ;CDs - CD (1 + a w (2S d) ]

or equating the constant to a!,

CDs a CD [1 + a' (M ) (A-8)

To determine an approximation for the cable amplitude r in terms ofphysical parameters, each vibrating segment is assumed to be representedas a resonant spring-mass system, or:

r -(A-9)

Kx /l + (2 C

For resonance w -w I - (C/Cc)V , Kx is approximated as 4T/t and themagnitude of the lit force F is assumed to be represented byF - Cj,dpu/2g. Equation (A-9) then reduces to,

8g CLP,, r - . .. ... .(A-10)'g .V4CIC,,)2 - 3CC/Cc) 4

Upon substitution of the string equation (), and the Strouhal number (2),-I

: CLO, r = dl1ac) (A-11)

2 I/C)4St8g 4 (C/Cc) 2 - 3CC/Cc)

Assuming the coefficient of ,d2/mc to be constant for smooth circularflexible cables equation (A-I1) reduces to,

CsCD [ + a (d 2/mc)1 + a] A-12)

A-2 -

--- -

NADC-AE-6731

- Idli

L r

I . _ x

FIGURE A-1 - Analytical Model Showing TransverseStanding Wave Cable Vibrations

- -3-

4 _ .lm i ,., iS

"III

I I

UNCLASS-IFIEDSecurity Clesificadion

DOMlAENT CON4TROL DATA - UIt D(Stranit? Classification of titio. .1 .bamct dfl ad iInoi*ng swettA swat be anowt d of MA.,e o i ev.,f to classiiod)

1. ORIGINATING ASIIY~epm, vw REPORT SECURITY CLASSIFICATION

AERl0LECKC CL OGYDPA R IEW UNCLASSIFIED

JOIINSVILLE, WARMINSTER, PENNSYLVANIA 189743. REPORT TITLE

WATER DRAG EFFECTS OF FLOW INDUCED CABLE VIBRATIONS

4. DESCRIPTIVE NOTES (2)'p. of FepWl and MrClIUSV. d~t..)

PHAE REPORTS.AUTHOR($) (First RSMe, asi;dE. initial, f~eel...

J. R. DALE AND J. M. McCANDLESS

.NbOTDATE 78. TOTAL NO. OF PACES ib. NO OF "RS

13 SEPTEMBER 1967 24 17 C(FOOTNOTES).C ONTRACT OR GR1ANT NO. Ike. ORIGINATOR-S REPORT NUMSERIS)

b. PROJECT No. NADC-AE-6731AIRTASK A37533000/2021/FlO1-13-07______________________WORK UNIT NO. 170 h roe")EOTNS)(ll Uwnibt ie e eee

10. DISTRIUUTION STATEMENT

THIS DOCUM4ENT IS SUBJECT TO SPECIAL EXPORT CONTROLS AND EACH TRANSMITTAL TOFOREIGN GOVERNMIENTS OR FOREIGN NATIONALS MAY BE MADE ONLY WITH PRIOR APPROVALOF CCN44ARDING OFFICER, NAVAL AIR DEVELOPMENT CENTER.

II. SUPP EMENTAMY NOTES 12. SPONSORING MILITARY ACTIVITY

NAVAL AIR SYSTEMS COINDDEPARTMENT OF THE NAVY

1S. ABSTRACT

A study was performed on Smooth, circular, flexible cables to determine the waterdrag characteristics that are dependent upon the cable strumming phenomenon. Thetest cable diameters ranged from 0.057 to 0.140 in. and the Reynolds numbers werewithin 300 to 1300. The study was a prerequisite to developing cables with lowdrag and low struming characteristics.

DD 1 NO..1 473 (PG 1) U C L ASS I P IE DS/N 0101.807.6801 security Clemsltlcation

RyWRSLINIIH A LINK a LtIK C

HOLZ WT IIOLS WT HOLZ WI'

WATER -DRA-

DDI Ps600v 14 73 (BeAcK) U N C ASI FI ED

-C1-

M-

to 99a; a i - eo, ad p .-

C0 . :W 0 O

04 -0-

.j h. -i -l - 0-. 6 a C3-

X0 04 ao~ .L . T! 10 0

I. .L .a .- -s1a

4t a a . . 1

11.

0 -4 0 N t 0-

co.4 a0 Jto 04 IL0

w. 3. -O3 so~a 3a 1

*~~~~~ W4~M o N* ~ 0

a. am -C wm- 4 ~'m a a m. 4 4 4M. T0 c-- A

06M

a. 3! aC- B 3 ~~~31,N o oas

W) C3 4=~ 4.0 .J 3

1 '

cm ca!-a

a

C. 0 j! 0b- 00 0 .

*0 It *4

1- 6. 111 .0a "a 9L 0a

1, 311- 0 0.00 V" - AN 'L0

0 a w e A11 .4 a w 4* .Jn ~ -

0

-6 0ab-0

CC' a~ 0 I Oa b4 a 0 -0

IA.~~0 -. -Ita 0.8 0 C ... d6 do 0 w .~ C4

w~a N)-.No. a w le

agtdcm 4a a 31 4Cn~ 8k 0! 2 v0 aa$

0 j a NC g WNA

4L. "j Z *0- 0- a) a a~~~~~~~~- c . ~ P

_ ~ ~ ~ ~ 0 5 cc. A ~ - . .

11- ac m C,4@.4~0 0 403

C3.

*~ $-04WI- a so

5-

4~C C * .i 40 j - 0 -

.0p - 0

0 0 0 40,

U) 3U3 W0 i

I0 4

I---

3W *

S. S -1