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ARL 69-0176OCTOBER 1969

Aerospace Research Laborator ie l

ON THE STABILITY OF FLOW INROTATING PIPESH. M. NAGIBL. WOLF, JR .Z. LAVANA. A. FEJERILLINOIS INSTITUTE OF TECHNOLOGYCHICAGO, ILLINOIS DDCContract No. AF33(615).67.C.1406 FEB i 0Project No. 7116

This document has been approved for public release and sale;its distribution is unlimited.

OFFICE OF AEROSPACE RESEARCHUni ted States Air Force

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NOTICES

When Government drawings, specifications, or othei data are uNed for any purpose other than ilconnection with a definitely related Government procuireraent operation, the United States Governmentthereby incurs no responsibility nor any obligation whatsoever; and the fact that the Government myivhave formulated, furnished, or in any way supplied the said drawings, specifications, or other data. isnot to be regarded by implication or otherwise as in any manner licensing the holder or any otherperson or corporation, or conveying any rights or permission to manufacture, use, or sell imy patentedinvention that may in any way he related thereto.

Agencies of the Department of Defense, qualified contractors and othergovernment agencies may obtain copies from theDefense Documentation CenterCameron StationAlexandria, Virginia ZZ314

This document has been released to theCLEARINGHOUSEU.S. Department of CommerceSpringfield, Virginia 22151

for sale to the public.

IiI ltCopies of ARL Tech cal Documentary Reports should not he returned to Aerospace Research

Laboratories unless return i required by security considerations. contractual obligations or notices ona specified document. 11300 - December 1969 - CO4SS - 104-2274

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ARL 69-0176

ON THE STABILITY OF FLOW INROTATING PIPES

H. M. NAGIBL. WOLF, JR.Z. LAVAN

A. A. FEJERILLINOIS INSTITUTE OF TECHNOLOGY

CHICAGO, ILLINOIS

OCTOBER 1969

Contract No. AF33(615)-67-C-1406Project No. 7116

This document has been approved for public release and sale;its distribution is ,,nlimited.

AEROSPACE RESEARCH LABORATORIESOFFICE OF AEROSPACE RESEARCH

UNITED STATES AIR FORCEWRIGHT-PATTERSON AIR FORCE BASE, OHIO

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FOREWORD

This is the final report on the experimental portion of thework performed under Contract No. F33615-67-C-1406, lIT P:oject No.55019, "on the Stability of Flow in Rotating Pipes," covering theperiod of April 1, 1968 to April 1, 1969. The work was carried ou tfor the Aerospace Research Laboratories, Off-Ice of Aerospace Research,United States Air Force, with Capt. J. A. Decaire as project monitor.

Contributors to this report are Mr. Hassan M. Nagib,Mr. Ludwig Wolf, Jr., Dr. Zalman Lavan and Dr. Andrew A. Fejer.Dr. Mark V. Morkovin provided valuable assistance throughout thecourse of this investigation.

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ABSTRACT

The stability of flow in rotating pipes is investigatedexperimentally. The results of this investigation also have abearing on the stability of flow in the core of swirling flows instationary ducts and free vortices. Solid body rotat ion is foundto have a destabilizing effect when superposed on a pipe entranceregion axial velocity profile. The range of swirl ratios up tofour is investigated using two different approaches: dye streaksvisualization and hot-thermistor anemometry. As the swirl ratio isincreased from zero to four, the axial Reynolds number at whichlaminar flow breaks down decreases from 2500 to 900. These resultsagree in trend with the limit axial Reynolds number value of 82.9that was recently obtained by analytical investigations of thestability of a viscous fully developed axial velocity profilesubject to a rapid, almost rigid rotation in pipes. The presentresults also suggest that the destabilizing trenu due to solidbody rotation may also hold for other axial velocity profiles andindicates a possible new mechanism of confined flow instability thattakes place at lower Reynolds numbers than previously believed possible.

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TABLE OF CONTENTS

P.aFOREWORD iABSTRACT iiLIST OF ILLUSTRATIONS vLIST OF SYMBOLS vJi

CHAPTERI. INTRODUCTIOV 1A. Literature Survey 1B. Definition of the Problem 8

II. EXPERIMENTAL APPARATUS 9A. Rotating Pipe 9B. Drive Mechanism 15C. Modes of Operation 22D. Dye Injection 25E. Instrumentation 30

III. EXPERIMENTAL RESULTS 37A. Flow Field Determination 37

1. Flow Visualization Using Dye Streaks 382. Measurements Using Thermistor Probes 42

B. Study of Stability 451. Flow Visualization Using Dye Streaks 452. Measurements Using Thermistor Probes 53

C. Discussion of Results 63IV. LONCLUSION AND RECOMMENDATION 66

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Table of Contents (Cont'd)

APPENDI Pag7070A. Porous Media 70B. Hot-Thermistor Anemometry 78C. Hydrogen Bubbles 88

REFERENCES 94BIBLIOGRAPH% 98

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LIST OF ILLUSTRATIONS

Figure PageI Rotating Pipe Apparatus 102 Electr ical Supply and Speed Control.

Unit for D.C. Motor 183 DrLvt Mechanism Components 19 & 204 Electric Circuit for Measuring th e

Pipe Rotational Speed 22

5 Flovmeters and Dye Injection Probes 276 Dye Injection Components 297 Dye Streak Instability it Laminar and Turbulent

Axial Reynolds Numbers with No Rotation 328 Thermistor Probes 349 Electrical Instrumentation Components 36

10 Oscilloscope Traces for Discriminationof Solid Body Rotation 45

i1 Laminar and Turbulent Mean Axial Velocity Profi le 4712 Dye Streaks for Increasing Axial Reynolds

Numbers with No Rotation NRO = 0) 4913 Dye Streaks for Increasing Tangential ReynoldsNumber at a Fixed Axial Reynolds Number (N - 3300) 5014 Dye Streaks for Increasing Axial Reynolds

Number at High Rotation (NRO - 6700) 5215 Laminar-Turbulent Flow Regimes in RotatingPipe, Data Based on Dye Streaks Observation 5316 Oscilloscope Traczs at Different Reynolds

Numbers with No Rotation 56

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List of Illustrations (Cont'd)

17 RMS of Thermistor Output at Inrreaaing AxialReynolds Number * r Two Fixed "angentisaReynolds Numbers 5718 Oscilloscope Traces at Increasing Axial ReynoldsNumber for Two Fixed Tangential Reynolds Numbers 5 8, 59, 60 & 6119 Laminar-Transition-Turbulent Flow Regimes in

Rotating Pipe, Data Based on ThermistorMeasurements 62

20 Model, of Porous Media to Which Darcy'sLaw Is Applied /121 Pressure Drop Across One-inch of Porous

Material Versus Flow Velocity 7622 Constant Current Hot-Thermistor Anemometer Unit 8423 Typical Calibration Curve for a Thermistor Probe 8624 Mean Axial Velocity Profiles for Increasing

Axial Reynolds Numbers with No Rotation(NRG - 0), Obtained by Using Hydrogen Bubbles 92

25 Hydrogen Bubble Streaks for Increasing AxialReynolds Numbers with No Rotation (NRO - 0) 94

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LIST OF 9YMBOLS

SymLol DescriptionA Cross Section areaB Constant defined on page 74C Constant defined on page 74C' Constant defined on page 74D Pipe inside diameterE Potential differenceE Potential difference at zero flow velocityoG Flow rate per unit areag Gravitational constantK PermeabilityL Length of pipeI Length of porous plugNRZ AxiaT Reynolds number defined on page 14NR9 Taengential Reynolds number defined on page 14

Re ynolds number based on friction lengthdefined on page 73

A? Pressure differenceAP Radial pressure gradient due to rotationAPZ Axial pressure drop

Q Volumetric flow rate

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List of Symbols (Cont'd)R Electrical resistanceR Electrical resistance of cold thermistor0R Constant defined on page 80r Radial coordinateT TemperatureT Constant defined on page 800U, V, W Velocity components in the r,O and r. directionVXV yVz Velocity components in the x,y and z directionx, y, z Cartesian coordinatesz Axial coordinate0 Coefficient of shear resistance

Coefficient of inertial and compressible effectsSwirl ratio defined on page 14

y Angle, see Fig. 200 Angular coordinateAPFriction length defined on page 7314 Absolute viscosityv Kinematic viscosityp Density

Constant defined on page 73M Augular velocity

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CHAPTER IINTRODUCTION

A. Literature SurveySwirling flows in ducts are important flow phenomena from a

practical as well as a fundamental point of view. These flows areof great relevance to rotating machinery, heat exchangers, energyand mass separation devices, nuclear rocket engines and other po -tential applications. It is of course essential in all suchapplications to predict under what conditions the flow will alwaysbe laminar and when it may or will undergo transition. The latterquestion is the problem of hydrodynamic stability, which in turncan be phrased as the stability to infinitcs'mal or finite dis-turbances. In some problems these two approaches yield resultsin close agreement while in others they differ widely. Sinceswirling flowa are composed of axial and rotating motions, wefirst review the stability of these independent components andthen consider the combined flow.

Axial or Pipe FlowReynois 1in his classical investigation, in 1883, concluded

that the floi through circular pipes would be stable if a charac-teristic numjer associated with the flow is less than 2000.1I

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(This characteristic number is referred to as Reynolds number.)Such a limiting minimum value for the flow to remain laminarunder all conditions is commonly known as the critical Reynoldsnumber. Several investigators attempted to obtain analyticalsolutions to this problem considering infinitesimal disturbances.No instability was found when axisyiwmtric as well as non-axisymmetric disturbances were considered with fully developed

. 1)6flow. Sexl Pekeris. Sexl et. al5., Corcos et. al.,Lessen et. al. and Gill8 are a few of the investigators whostudied this problem.

Corcos et. al. investigated the stability of infinitesimalaxisymmetric disturbances in fully developed flow in a pipe bytreating the classic eigenvalue problem and concluded that alleigenvalues yield stable solutions and that for a given waven-.mber and Reynolds number only a finite number of eigenvaluesare present. These results appear to be substantiated by theexperimental investigation of Leite? who concludes that theflow is stable to small axisymmetric disturbances up to aReynolds number of 13,000.

Lessen et. a2 nvestigated the stability of Poiseuilleflow to non-axisymmetric disturbances (azimuthally periodic).

10Fox et. a].. investigated the same problem experimentally andfound a minimum critical Reynolds number of approximately 2150.

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Rotta investigated the laminar and turbulent regimesas well as their structure in flow through pipes. He alsostudied the changes in the axi~l velocity profile associatedwith these flow regimes along the pipe.

Orr,2 by means of applying the energy method to steadyviscous motions of liquids in pipes, was able to find a limitReynolds number value of 88 for sure stability of fullydeveloped flow. Joseph et. al.13 in their recent investigationfound a yet lower value of 82.88 for such a limit using a moregeneral approach.

Rotating Flow| 14Lord Rayleigh presented his criteria for inertial

instability of ro tat ing fluids in 1916, where he considerspurely rotating inviscid flow under axisymmetric disturbances.According to his criteria, an inviscid rotating flow isunstable if the sense of the local vorticity is opposite tothe sense of the angular velocity. A different way of statinghis criteria is: the stability of fluid motion in cylindricalstrata requires only that the square of the circulationincreases outwardly.

Taylor15 extended this work to Couette f'ow and tookinto account the effect of viscosity. In his analysis, th esmall gap approximation was made and a criterion for

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instability was obtained. Based on this analysis an instabilityin the form of torroidal vortices is to occur if a criticalnumber known as the Taylor number is reached. It should bepointed out that this kind of instability cannot occur whenthe outer cylinder is rotating at a higher angular velocitythan that of the inner cylinder. From this criterion itfollows that the flow is to be stable if the inner cylinder isstationary or absent, and hence pure rigid body rotation is

16always stable to infinitesimal disturbances. Sparrow et. al.extended this analysis to include wide gaps and rotation inopposite senses. For this phenomenon (Taylor instability)linear theory, finite disturbance theory and experiment are

17in excellent agreement. Coles presented a thorough inves-tigation of the same problem in relation to the different kindsof possible transition. He concludes that there exist twodifferent kinds: Taylor's instability, and what appears tobe regular turbulence. The latter occurs when the innercylinder is stationary or rotating, and the outer one rotatesat a very high angular velocity relative to the inner one.His work, in addition to its theoretical value, is an excellentreference to experimental investigations of rotating fluids.It should be pointed out that Taylor also observed the secondkind of instability. It is believed that this instability isnot due to eccentricities as it is stated in some of the

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18earlier works (Shultz-Grunow ), but is due to a differentmechanism of instability than that of the Taylor instability.The eccentricities in such a mechanism represent time-dependent finite disturbances.

Swirling FlowsChandrasekhar19 developed a stability theory for swirling

inviscid flows and attempted unsuccessfully to show thatRayleigh's criteria is also applicable to non-axis]umetricdisturbances. Di Prima30 extended this theory to viscousfluids between rotating cylinders with an axial flow andfound that the crit ical Taylor number increases with in-creasing Reynolds number. Chandrasekharl Krueger et. al.2and Datta23 studied the stability of swirling flows under smallaxisymmetric disturbances using the small gap approximation.

By extending Rayleigh's criterion Howard and Gupta 2 4

were the first to develop a stability criterion for non-dissipative swirling flows that has been extended to a largegap and non-axisymmetric disturbances. From this criterion itfollows that solid body rotation as well as the fully developedPoiseuille flow in a pipe (considered separately) are stableunder axisynmetric disturbances. Hughes and Reid25 extendedtheir analysis of axisymnnetric disturbances in a narrow gapto include a wide range of Reynolds numbers.

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Ludwieg 2 6 ' 2 7 attempted to treat the stability of swirlinginviscid flow confined to a narrow cylindrical annulus, consid-ering non-axisymmetric disturbances. He shows that a smallaxial shear is sufficient to destabilize such a flow only ifthat flow is in solid body rotation. In his work Ludwieg2 8applied the criterion developed in the early studies to thecase of flow over a delta wing.

Kiessling29 extended Ludwieg's work to viscous fluidsand found that the critical Reynolds number increases as theswirling flow deviates from solid body rotation.

Ludwieg, using a complicated experimental apparatus,verified hie stability theory and was able to observe a wavepattern of a helical shape. In his experiment the flow isconfined between two concentric cylinders with a relativelysmall gap. The cylinders rotate in either direction and acontinuous axial displacement is applied to the inner cylinder.

Pedley31 extended the results of Howard et. al.? andshowed that a cylindrically symmetric shear flow of an in-compressible fluid stbject to rapid, almost rigid rotationabout its axis is unstable to infinitesimal inviscid non-axisymnmetric disturbances. He succeeded in obtaining thisresult using non-axisyuunetric linear disturbances (the axi-symmetric analysis failed to show thit). It should be recalledthat Ludwieg25,26 obtained the same result using the narrow gap

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approximation. In Pedley's31 analysis the flow is boundedexternally by a rigid cylinder and internally it may be boundedby another rigid cylinder or the axis of the outer cylinder.In his later work Pedley32 investigated the same flow ,onsider-ing a viscous fluid and showed that the flow in unstable forReynolds numbers greater than approximately 82.9. Strohl 3 3

investigated the same problem as in Pedley's32 work using amore general numeric&l approach and obtained the same results.

There is a real surprise in Pedley's 3 2 and Strohl's33work in that they contradict the widespread belief that rotationalways has a stabilizing effect. A conclusion of their work isthat a slow Poiseuille flow in a pipe has a destabilizingeffect on a rapid, rigid body rotation and that a rapid, rigidbody rotation has a destabilizing effect on a slow Poiseuilleflow. It should be noted from the results of earlier worksthat each of these flows is stable by i tself.

The stability of axial flow in rotating pipes was34 35investigated experimentally by White and Cannon et. al.

The two investigations conclude that rotation is stabilizing.It is believed that their results disagree with the analysis ofPedley32 and Strohl33 because solid body rotation was not ob -tained in their experiments, and regions of recirculation werepresent. It was therefore proposed to construct an experimentthat will be .ree of these objections and will more closelyapproximate the study of stability of an axial flow with asuperposed solid body rotation.

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B. Definition of the Problem

An attempt is made toward the experimental investigationof the hydrodynamic stability of flow in rota t ing pipes. Theflow is to be a solid body rotation superposed on an axialvelocity profile that is free of recirculation. A fullydeveloped profile would have been desirable; however thisrequires a cumbersome length or an intricate entrance config-uration. It was therefore decided to use an axial velocityprofi le characteristic of pipe entrance regions. The workingfluid is water and a range of axial Reynolds numbers up to 7000is to be investigated. The classification of the flow conditioninto laminar and turbulent regimes is carried out by dye streakvisualization and hot-thermistcr probes. When the regularlaminar flow pattern breaks down slightly the flow is said tobe in the transition regime, and when a continuous state ofirregular motions is reached the flow is referred to as turbu-lent. It should be pointed out that these definitions are notprecise. A more precise and detailed study of the structure ofthe disturbed flow is one uf the problems contemplated forfuture investigation.

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CHAPTER IIEXPERIMENTAL APPARATUS

The rotating pipe apparatus shown in Fig. I was designedwith the following objectives in mind.

1) To control conditions at the inlet and outletof the rotat ing pipe in order to obtain a flowof solid body rotation and an axial flow whichis free of reverse axial components.

2) To provide a pipe of sufficiently large diameterin which quantitative measurements of the flowfield could be obtained and hich facilitatesvisual diagnostic approaches,

3) To allow a wide range of operating conditions.4) To permit the possibility of using different

fluids as working media.

The apparatus and the associated equipment are describedbelow.

A. RotatLng PipeThe rotating pipe apparatus consists of a 73-3/4 inch long

lucite pipe. The pipe has a 3-1/4 inch inside diameter and3-3/4 inch ou. ide diameter (L/D A 23). The tolerance, asstated by the manufacturers, is + 0.020 inches. However, the

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*1i, / w-4I-I-

(r,U-

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main tolerance is ini he wall thick . wh.ile the insidediameter is accurate to within + 0.005.

For any experimetital inve igation connected with thestudy of the stability of rotat ing flows, it is found(see Coles 18) that the tolerance in the concentricity betweenthe axis of the rotating body and the axis of rotat ion shouldbe minimal. The pipe is therefore constructed so that it willrotate about an axis that best coincides with the center ofthe inside diameter along the length of the pipe. This isachieved by cementing stainless steel sleeves to the outsidediameter of the pipe. The sleeves are machined to an outsidediameter of 4 + 0 inches and a maximum tolerance on their- 0.0015concentricity with the center of the inside diameter of + 0.005inches. This procedure is found to be time-consuming andrelatively expensive.

The sleeves are used to support the pipe inside fiveself-al igning ball bearings. Two of the five bearings arelocated close to each other on one long sleeve, which is alsoused to mount the drive mechanism pulley (located between th etwo bearings). These two oearings re located as close to eachother as the utilcknei.s of the pulley permits, z,-d t0- remairingbear ngs are eq,.al 'y spacid. The fivL, bearings are fotur Inchdiameter aelf 'aligning bAll bearings. Four -f them aremedium-dtuty pillow blocks and the fifth is a medium-duty

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flange unit. The flange unit bearing is mounted on a1-1/2 x 13 x 17 inch aluminum plate. Rotating oil seals aremounted at each end of the pipe.

A pressure-r ight settling chamber is provided ac th einlet of the pipe, while an open tank is used at the outlet.The pressure-tight chamber is made of an I inch long 7-1/4 inchinside diameter and 8-1/4 inch outside diameter lucite tube.The chamber is bounded on the downstream sie by the aluminumplate on which the flange unit bearing is mounted and aI x 10 x 10 inch aluminum plate from the upstream side.

The flow supply line is connected to the upstream faceof the pressure-tight chamber and a flow control valve islocated a small distance upstream of the aluminum plate inthe supply line. The downstream open tank is made of 1-1/2 inchplexiglass. The dimensions of the open tank are 15 x 20 x 36inches. The entire assembly is mounted on a 20 inch wide,12 feet long, aluminum channel resting on three lab tables.The drain, supply and connecting flow l ines consist of one-inch diameter tygon tubing. The downstream open tank is equippedwith a drain system that can maintain a constant head in the tankfor all axial Reynolds numbers used. The system is a two-leveldrain with a valve controll ing the lower drain, which is at alevel higher Ehan that required to keep the roLating pipe filledat all times.

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The apparatus is equipped w h a high head settling tankthst can be used for temperature control, as well as treatingthe water to eliminate the color from the dye injected whenoperating in a recirculating mode. The settling tank canalso be used to eliminate some of the air bubbles in the water.

When assembling the rotating pipe apparatus, the bearingswere aligned and the pipe was leveled horizontally within atolerance of + 0.005 inches, by means of shimming the bearings.In aligning the bearings, piano wire, under tension, was used.It is felt that this procedure, although introducing somestresses in tie lucite pipe, is necessary to insure chat the"pipe rotates concentrically about its axis.

The rotating pipe is equipped with porous plugs at bothinlet and outlet in an effort to create a flow field of solidbody rotation. It can be argued that if the pressure dropacross the porous plug, due to the axial flow, is large incomparison to the radial preasure gradient associated with thepipe rotation, the flow downstream of the plug should be freeof reverse axial components. In addition, if the plug is ofuniform thickness, the flow field downstream of it, (up tosome swirl ratio) should approximate plug flow superposed onsolid body rotation. This limiting swirl ratio is governedprimarily by the porosity of the plug as well as the otherproperties.

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The porous plugs used are made of General Electriclow-density nickel foametal. This material was chosen afterdifferent types of porous materials were investigated analyti-call- and experimentally. The upstream plug is taken from aone-inLh thick slab and the downstream, plug from a two-inchthick slab. The plugs are 3-1/4 inch in diameter and are madeto rotate with the pipe by placing them inside the ends of thepipe and ccment'Lg them with RTV. The pore size of the porousmaterial is in the range between 0.020 inch and 0.100 inch.There are from 11 to 25 pores per lineal inch. The porousmaterial is manufactured by means of foaming the nickel andis shaped by molding. The material has a bulk density of 27.of the solid nickel density. The foametal is also availablein other metals, such as copper, and in a wide ran-e of density,ranging from 27. to 657.. Although all the technical p.opertiesare supplied by the manufacturers, they are not available forthe low density range (below 207. density). The material can beeasily cut with a band-saw or other wood-working tools. Themanufacturer recommends impregnating the material in paraffinbefore machining and removing the paraffin after machining isfinished by soaking the material in degreasing solution. Thisprocedure was not used and direct machinirg on the lathe wa scarried out successfully.

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The pressure drop across the porous plugs was measured asa function of the flow velocity. The measuremenetshow that itis proportional to the square of the flow velocity and isindependent of the speed of rotation in the range of the presentexperiments. A simplified analytical approach is used toextend these results to the following more general and usefulrelation (see Appendix A).

Apr- a 0.004 r2 11.1AP

where r is the swirl ratio and is defined by the ratio of thetangential Reynolds number to the axial Reynolds nudber.

The tangential Reynolds number NRO is defined by

VD 2N - M PZ11.2Re v 2v

where V is the maximum tangential velocity and the axialReynolJs number N is defined by

WDN - 11.3Rz V

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where V is the mass flow average of axial velocity, Apr isthe radial pressure difference due to the pipe rotation, andAP is the pressure drop due to axial flow across one-inchof the porous material used. The ratio of the pressure gradientassociated with the pipe rotation, to the pressure drop acrossthe porous plug, due to the axial flow, remains much smallerthan unity (e.g., 1/100) , if the swirl ratio does not exceeda value of approximately four (based on a one-inch thick porousplug). Since the upstream plug is one-inch thick, one wouldexpect the plugs to be effective in imparting the solid bodyrotation only up to swirl ratios of approximately four.

B. Drive Mechanism

In order to allow rot-nion of the pipe over the range oftangential Reynolds numbere under investigation in a stableand accurate manner, a complicated drive mechanism has beendevised.

The reason for this can be explaine,1 as follows. Far apipe with an inside dimeter of 3-1/4 inch'sa. using water asthe working fluid, a rotational speed of about 0.27 RPM'scorrespond&; ro a tangential Reynoldr number (N ) of 100.'R9A covatercially available 1-l/2 horsepow-r variabie-cpeed D.C.ahurt motor, was found to operaLeat satiafactory atable, speeds,over an RPM renge of approximately 30 to 1400 RPN's. This

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requires a speed redvctc'u ratio of approximately 300 -- 1,in ordt.r to provide operation at thc. 'ceuire4 range oftangential Rt.tyuolds numbers.

Trw- drive mechanism used provides a range of sperdreduction ratios as high an 400 to I and ab law as 13 to 1.This offers stable cperation at etanbertial Reynolds numbersranging approxtmately from 75 up to 40,000. The fluctuationin the rotational speeds using this drive r-echanism is fout~dto be approximately 2%.

The n.C. shunt tnotir electrical supply and speed coutroluni. consi'-ts of the components shown scheinatically In Fig. 2.The speed control oi the totor ir cez3ted out by using theArmature-tcrminal-voltage control system. (This is the samecontrol syst, used in the Uird Leonard system.) This ,ortrolmt~hord, offering both constart torque and constant horsepowerspeed control, uti.lixes field control and armature-voltagecontrol. The control panel for the D.C,. shunt motor isshown in Fig. 3a.

The motor drives, through two pulVle,-s and a V-belt, avrriable reduction speed hydraulic transmission (Vickers3/4 H.P. Model No. TR8-HR18-FI8-20 Hydraulic transmissionunit). This variable reduction speed hydraulic transmissionoffirs reduction ratios irom I to I and up to '0 to I (see Fig. 3c).

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S> LL.

LU-JU CL

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z-J

0000

a131A lInH

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A. D.C. MOTOR AN D CONJTROL PANEL.

B- DRIVE MECHANISM GEAR BEJ AND PULLE-YIMDUTiED ON ROTATING PIPE

FIG. 3. DRIVE mcimCiAIm cavom0NU-s

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I)

O-w

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The variable reduction speed hydraulic transmissiondrives the rotating pipe through a transmission consisting offour gear belt pulleys and two gear belts (timing belts).The four gear belt pulleys have pitch diameters of 2.865 inches,24.828 inches, 5.013 inches, and 8.913 inches, respectively.The gear belts and pulleys provide a speed reduction ratio ofapproximately 13 to 1. The two intermediate pulleys locatedbetween the pulley on the output shaft of the hydraulic trans-mission and the pulley mounted on the rotating pipe, are mountedon a cormmon one-inch diameter steel shaft. The shaft rotatesinside two one-inch block bearings attached to aluminum channelson which the whole apparatus is mounted. All the components ofthe drive mechanism are shown in Fig. 3.

The rotational speed measurements are monitored by meansof a microswitch indicating the rotational speed which isactuated by the largest gear pulley (see Fig. 3d). A D.C.voltage source ( a 22-1/2 volt battery) and an electroniccolinter (Hewlett-Packard 5233L digital counter) are used inconnection with the microawitch. The schematic diagram inFig. 4 shows the electric circuit ,ised in the rotationalspeed measuring instrumentation. The counter output is inkilocycles, that can be converted to either RPM's or tangentialReynolds numbers. For high rotational speeds the microswItcharrangement is replaced with a magnetic pickup, placed against

2 . . . i I I . . . . . . . . . . .

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ccU;U

Lu

0 0LUI-dz

Nr dI-.LL

aid)

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the same gear pulley. Within the operatinG range, both thesmicroswitch and che magnetic pl:kup ciruit-ey offer an a&cnracyin the rotational speed measurements of approximately 0.1%.

The drive m,:chanism describj.d Abov offers numerouscontrol posrlbill._t.s. B, proper adjustments one can achievethe required tangential Reynolds nimber at operating conditionsthat are almost free of vibrations, Observation of the freerurface iL the downstream open tank, eveu the presence of slightvibrations in i.he assembly, can be re~dily detected with th enaked eye. Adjustments must then be made to eliminate thesevibrations since the absence of noticeable vibration is essen-tial in an invsetigation concerned with stability.

C. Modes of OoerationThe apperatum can be operated in a single pass mode where

water from the building supply line passes through the apparatusto a drain. It can also be operated in a recirculating modewith the water being recirculated through the apparatus by acentrifugal pump. The pump is capable of delivering a head of30 feet of water at a rate of about nine GPM'r.. This at. angementperr-its the adaptation of the apparatus to i range of differevtn3peratlng conditions and to different working fluids.

The singl, pass mode offers a higher range of axial Reynoldsnumbers, since the supply line pressure is higher than th, head

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delivered by Lhe centrifugal pump. With water as the workingfluid, the single pass mode can be operated at axiaL Reynoldsnumbers ranginp from 0 to 12,000 and the recirculatit% modecan be operated at axial Reynolds numbers rarging from 0 to7,000,

When dye injectioa visualization is used Ohe single passmode is preferable since recirculation in this case is prac-t ically impossible over a long period of time. In that casethe dye injected wonld, within -3 hort time, color the waterin the .)ystem aad the visibil i ty of dye stceaks would rapidlydiminish with time.

There are however, several problems associated with thesing7.e pass mode:

I) The difference between the supply line w,,.terpressure and the room pressure. Due tothis diffe rence in pressure, a large numnber ofair bubbles ate formed in the pipe, which leadsto problems with both the dye visualization andthe hot-thermistor anemometry. In the case of thedye, the bubbles tend to disturb the dye streaks;and, in the case of the thermistor, the bubblescause a large amount of noise in the output signal.

2) The fluctuation in the supply line pressire. Thisis especially apparent during the d&y, and it hindersthe accurate adjustment of the flow rate.

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The recirculating mode provides a very stable and quietoperation. Unless dye is injected or the thermistor output isobserved, a person standing next to the apparatus cannot detecttae flow, except by observing the flowmeters.

Using the iecirculating mode, the flow rate can becontrolled to within 0.537 in the operating range of the presentinvestigatiou. The air bubble problem is also eliminated here.

The only problem connected with the recirculating mode isthe energy supplied to the system by the pump, which tends toslowly raise the temperature of the water. Although thisproblem did not have great effect on the stabilit- readingstaken by the thermisto'r, it had some eftwat orn the me,-,sure-ment of axial. and tazgential velocity fb:. ' (This ni dis-cussed in mote detail In Appendix B.) To miinimize tais prob--tlem, the system is left runnirvg for a long time, (until the

water temperLture reaches its equilibrium level) before per-foL'ming any experiments.

For %:heabove mentioned reasons, and in ,,-fw of -t-G factthat the present investigation i0 r.ncerrned wii.h stability, therecirculating mode has been chGsen for the quantitative messure-meaitc using the thermistor probes.

The flow rate through the aoparatus 13 monitored by arotanite" 4t ow f'cow rates and by a turbine-Lype Zlownieter

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(Potter Aero. Corp. Model 5/8-5570) at high flow rates. Therange of measureme'nts of both meters overlap in the range ofaxial Reynolds numbers from 1,300 up to 4,200. The two flow-meters combined can measure axial Reynolds numbers ranging from80 to 14,500. Both meters are calibrated in the apparatus andoffer the accuracy in the axial Reynolds numbcrs measurementsstated above. The output of the turbine-type flowmeter ismonitored by means of a Hewlett-Packard 5233L digital counter.The output is linear and is in kilocycles, which can be con-verted to axial Reynolds numbers. The flowmeters a-d thedigital counter are shown in Fig. 5a.

D. Dye IniectionThe rotating pipe inlet is equipped with dye injection

probes. The probes are made of 0.026 inch inside diameter and0.042 inch outside diameter stainless steel tubing. The dyeprobes are located at four radial positions. The innermostone is on the axis of the rotating pipe, and the outermostis in the vicinity of the wall (approximately 1/16 inch fromthe wall). The two other probes are located at equal distancesbetween these two (see Fig. 5b).

The probes are joined at their upstream ends and connectedto the dye supply tube. The connecting and supply tubes aremade of 1/16 inch inside diameter and 1/8 inch outside diameter

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- - U,

(f)

IDI

fl LID

U-i

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stainless steel t. Des., All the joint are made by means ofjilvr Roldering. The probes pass through the porous pluginside four stainless steel tubes of 1/8 inch inside diameter,attached to the poroun plug by means of epoxy. These tubesserve as bsarings for the probes. Ir-mounting these tubes,extra care was 'aken to have all four tubes parallel to the axisof the plug and hence to each other. The probes were thenplaced inside the sleeves through the porous plug rnd testedoALLide the apparatt"q. By injecting w^ter through the probes

and observing the emerging jets, it was found that within thelength oA. Lhe rotating pipe (6 feet) the jets remained paralieland at Pqual distancrs from each other. A picture of the dyeinjection probes mounted inside the sleeves and through theupstream porous plig can be seen in fig. 6a.

A snort length of a larger diameter stainless steel tube1I/4 inch outside diameter) is silver soldered to the supplytube. (The 1/4 iuch outjide di&h.cetei tube p*.rmi-s the uie of thesmallest commercially available oil seai,2, T,'e nil ;e~l is usedto uerve both the func:tions of the bearing and seal. The seal ispreis-fitteC at the, end cf the dye pressure chamber.

The dye pressarre chamber is cylindrical and is made ofaluminum. It is m4ivnted on the upstream n]ate of the pressure-tight se':t].ing chrmb, r, locsted at the inlet oi th. rotating pipe,.TVe dye is supplied to the dye pressure ctaib(- by Ineans of

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A. DYE PROBES (MUINTE THROUGH I NLET POROUS PLUG

B. INLET GiNIS R WITH DYE INJECTION COM~PONEI SFIG. 6. DY'E INJECTION C IMPONENTS

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tygon tubing from a large glass container and the amount flovingis controlled by a precision needle valve. Pressure is appliedto the container using a rubber hand pump. The dye injectionapparatus is shown in Fig. 6b.

The dye is injected a small distance downstream of thedownstream face of the porous plug. Since the plug rotateswith the tube, it appears that the dye is injected with notangential velocity relative to the flow.

The dye used in these studies consists of malachite greencrystals disolved in water. The density of the dye should bethe same as that of water. Alcohol is added to the dye solutionto effect density corrections. This is, however, an infrequentoccurrence since the amount of crystals needed to give the dyeits color is very small. The dye has a bluish-green color anddoes not lose its color even if left for several days.

The two main problems encountered in using the dye can besumnarized as follows: first, a high relative axial velocitybetween the dye jet and the flev velocity may lead to dye je tinstability. This instability was found to be a function ofthe relative velocity only, which in turn is a function ofthe difference between the dye injection pressure and thepressure of the flow at the location of the injection. It isalso found that this instability may occur in laminar orturbulent conditions in the flow field. By careful observation

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(see Fig. 7), one can differentiate between the turbulence Inthe flow field and the dye instability, since the latter hassmaller scale eddies. This problem is eliminated by carefullycontrolling the pressure applied to the dye so that the axialvelocity of the dye is the same as the exial velocity of the flow.

The second problem, which is less serious, is thedifferential in size and resistance between the dye probes.ThZs can also be seen from Fig. 7, where the dye Jet instabilityis occurring in some of the dye streaks and not in the others.

E. InstrumentationIn a recent investigation of the stabi l i ty of Hagen-Poiseuille

flow to non-axisymmetric disturbances by Fox et. al.? hot-thermistor anemometry was used. The probes were .zed in a con-stant current made to achieve a high sensitivity in meanuringthe velocity' fluctuatfon. The working fluid used in this inves-tigation is water. In comparison tu this study, Leite9 inves-tigated the stabi l i ty of the same flow to axisyuaetric dis-turbances using air as the working fluid. In his investigation,Leite used hot-wire an&ometry. Both investigations yieldpositive and successful results.

These Investigations influenced strongly the choice of theinstrumentation used in the present investigation. Although

10Fox et. al. concluded that they are continuing their experiment

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TEST S' CTIJN

LAMINAR FLOW~ JET PTIJTAP' Il11Y

FIG, 7, DYE STREAK INSTABILITY AT ;AMMiAR AND TURBULENTr AX IALREYNOLDS NLMBERS WITH- NO ROTATION3z

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using wedge-shaped film probes with the hope of better results,adequate reRults were obtained using the hot-thermistor ane-mometry as reported in their investigation. In view of this,it was decided to use hot-thermisotr anemometry for the presentinvestigation. This decision was supported by the results ofa survey of l i terature on hot-thermistor anemometry. The mainconclusions of this survey and other information on hot-thermistoranemometry are discussed in Appendix B.

In short, thermistors were chosen for this investigationsince their high electrical resistance permits easy filteringof noise introduced by brushes and slip rings and makes possiblethe use of inexpensive and convenient electronics. They alsooffer, in water, the possibility of spatial resolution and noiselevels that are better by an order of magnitude than those obtain-able with platinum film probes. The probes are rugged, inexpen-sive and are commercially available. The major problem encounteredis their low frequency responses. This however, does not limittheir usefulness ir. etermining transition from laminar toturbulent flow regimes. The probes were used in a constantcurrent mode.

The different types of thermistor probes used are shown inFig. 8. All the probes were cormercially acquired, but additionalwork was performed on them to make them suitable for the mountingused in the rotating pipe apparatus.

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A. PROBE 4, 1 AJND 2 (FROt IOFP TO BOTTCOKA

B. PROBE 14MOrfID INSIDE TEFLON SEAL

FIG. 8. THEFRMISTOR PROBES34

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The slip rings and brushes are homemade, though theunderlying idea is related to mercury-wetted slip rings thatare commercially available. The slip rings are made of two1/2 inch thin sheets of brass. Each sheet is cemented tothe outside of the pipe (around its circumference) and isjoined by soldering. The brushes are two 1/2 inch ribbons madecf brass screening. The ribbons are wrapped around the sliprings and connected to the two electric terminals located ona fiYed rod mounted next to the rotating pipe (see Fig. 9a).

The brushes are sprayed with water which remains in theform of droplets (due to surface tension between the tinysquare openings of the screen material). The amount of noiseproduced by the brushes is very low and can be suppressed veryeasily using an R-C filter, since it is of a much higher fre-quency than the output of the thermistor probe. A single appli-cation of water to the brushes is adequate for three hours ofcontinuous operation.

The output of the thermistor anemometers is connected tothe following instruments (shown in Fig. 9b):

1) Hewlett-Packard 3440A digital voltmeter equippedwith a 344A D.C. multi-function unit to measurethe D.C. component of the output.

2) TQA type 55D35 RMS unit to measure the root-mean-square of the A.C. component of the output.

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A. SLIP RINGS AND BRUSHES

B. AN'EMaTTRY IMPNITORING INSTRt)1ENTS

FIG. 9. ELECTRICAL INSTRUM1ENTATION~ XOPOWJNTS3oU

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3) Tektronix type 502A dual-beem oscilloscope tc. monitorthe output.

4) Tektronix type 564 storage oscilloscope equipped withtype 3A3 dual trace differentiai amplifier unit and atype 2B67 time base unit to store the output fortaking pictures such as are shown in Fig. 16 .

5) General Radio type 1564-A Souitd and Vibration analyzerto analyze the frequency of the output,

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CHAPTER III

EXPERIMENTAL RESULTS

In the present investigation the study of the st3bility offlow in rotating pipes is approached by means of two techniquestdiagnostic dye streak flow visualization and quantitative hot-thermistor anemo-etry. The diagnostic flow visuali-stion6 areperformed in the single pass mode of operation due to reasonsexplained in Cbapter II.D. The rest of the experiments areperformed in tne recirculating mode of operation.

Since the knowledge of the flow field is important for theinterpretation of the stabllity results, an attempt is also madetoward a comprehensive understand.Lng of t:he flow field using thediagnostic technique and the quantitatLve techrique mentioneeabove. A discussion of result& is presented in tfis chapter,The results obtained by the two methods are compared and thedifferences are discussed. In addition jome zesul.s obtainedusing the hydrogen bubble visualization tecnnique are pr, 'entedend dincussed in Appendix C.

A. Flow Field Dctermuit.ation

The flow field is invesctgateO in relation to the Sxi4 Iveiocity distribution, tLi tangentia. velocIty distribution

36and t0e e-trance and exit flow conditions. Fejcr et. 9l. n

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The experiments related to the first two of these questionswere conducted using the dye probes described in Chapter II.D.A different dye probe was used in the experiments related to thethird question. This latter probe is a 1/4 inch inside diametertygon tube connected to a pressurized dye container.

To study the axial velocity distribution, short dye streaks(about 1/2 inch long) are pulsed and observed as they propagatedownstream along the pipe. This test is carried out at laminarflow conditions for the stationary pipe as well as for differenttangential Reynolds numbers. It is found that the dye streakpulses propagate downstream at the same rate and thus remainat the same relative axial position to each other. The onlyexception is the dye streak in the vicinity of the wall (pre-sumably in the boundary layer formed downstream of the entranceporous plug). Hence, it is concluded that within the range ofthe three inner dye streaks (about 2/3 of the diameter of th epipe) the axial velocity is almost uniform.

The most important results from the dye visualizationare the ones relevant to the presence of solid body rotation.Since the probes are all located on the same angle of the pipesection, the streak lines should remain on a single radial line,in the case of solid body rotation, as they advance downstream.This yields a pattern that looks like a ribbon twisted alongthe axis of the pipe. If the flow is not in solid body rotation,

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the streak lines will tend to be oriented at different anglesas they propagate downstream, yielding a pattern of four streaklines which appear to be different sizes of concentric helicalspirals of different pitches.

Performing the above observations, it is found that for afixed axial Reynolds number, as the tangential Reynolds numberis increased, the time required to achieve solid body rotationis increased. Furthermore, when solid body rotation is achieved,its region extends over the whole length of the pipe between theporous plugs. The flow is indeed essentially in solid bodyrotation for swirl ratios less than or equal to four as waspredicted in Chapter II.A. When the swirl ratio is larger thanapproximately four, it is impossible to achieve solid body ro-tation, with the 2% dense plugs, even if the pipe has beenrotating for a very long time. The time required to reachsolid body rotation for swirl ratio of say three is found tobe approximately ten minutes.

Since the presence of flow reversal is possible at theentrance and exit regions of the rotating pipe, (see Lavanet. al.7 and Fejer et. al.8), these regions were investigated.

A number of experiments were performed by observing thedye streaks, injected through the four probes in the rutatingpipe, and noting the direction of the dye propagation. Inthese experiments the axial Reynolds number was fixed and the

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tangential Reynolds number was increased up to swirl ratiosof approximately 20. These experiments were performed fordifferent axial Reynolds numbers. No evidence of reversed flowsalong the rotating pipe between the two porous plugs was observed.

When the 1/4 inch tygon tube was placed against the centerof the upstream side of the inlet porous plug and along its axis,and dye was injected, the following was observed: for relativelyhigh swirl ratios, the dye enters the porous plug at the axis andreturns in the opposite direction (toward the upstream of themain flow) in the vicinity of the wall. When dye was suppliedat the exit plug from its downstream end the following wasobserved: for relatively high swirl ratios the dye enters theporous plug at the axis (toward the upstream end of the pipe)and returns in the main flow direction in the vicinity of thewall. When the dye probe is moved slightly downstream and awayfrom the rotating pipe, the dye injected follows the main flowas it comes out of the probe, and hence one may conclude thatthe observed recirculation is not due to the velocity of thedye relative to the flow.

These results agree with the conclusions of the study by37Lavan et. al. that predicts regions of recirculation for

large swirl ratios and indicate that, within the operatingrange of the present investigation, the recirculating regionsat the inlet and exit of the rotating pipe are maintainedinside the porous plugs.

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2. Measurements Using Thermistor Probes

The experime-kts performed using the thermistor probeswere mainly concerned with the axial velocity distribution.In addition, the condit ions at which the flow remains in solidbody rotation were alej investigated at the section where th estability measurements were conducted.

Since the probe is mounted radilly in the pipe androtates with it, it should not sense any tangential velocitiesif the flow is in solid body rotation. Hence, if the flow isat a fixed axial Reynolds number and is in solid body rotat ion,the D.C. component of the probe output should remain constanteven with changing tangential Reynolds numbers. The onlyrestriction is the requirement that the axial velocity dis-tr ibution should remain the same as the swirl ratio is increased.This restriction is satisfied for the range of swirl ratios lessthan four, where the tangential motion does not substantiallyaffect the axial velocity profile (see Talbot ,9 T.avan et. al.?7

and Fejer et. al. 8). This is true then for all radial positionswhere the sensing element in the probe can be locAed.

A series of experiments were performed for different fixedaxial Reynolds numbers and increasing tangential Reynoldsnumbers. The D.C. component of the thermistor output wasobserved on both the digital voltmeter and the oscilloscope.The oscil loscope sweep for these experiments was maintainedat a very low rate (I see/division). The sa-ne experiment

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was repeated for different fixed tangential Reynolds numbersand increasing axial Reynolds numbers. It was observed in bothsets of experiments that the output remains constant at swirlratios less than approximately four. For swirl ratios largerthan four, the digital voltmeter reading is periodically chang-ing, while the output on the oscil loscope for these casesappears in the shape of a sinusoidal wave (see Fig. 10). Theperiod of this output, measured on tht' oscilloscope, is foundto correspond to the pipe rotat ion.

The preceding procedure was repeated for three differentradial positions of the sensing element in the probe. Probe 2and Probe 3, which were used in this study, gave identicalresults.

A series of experiments were also performed in connectionwith the axial velocity distribution at different axial eynoldsnumbers with the pipe being stationary. The experiments coveredaxial Reynolds numbers up to 7,000 in steps of 500. The probewas placed at eight different, equally spaced radial locationsbetween the wall and the axis of the pipe, at an axial distanceof approximately i9 pipe diameters downstream o( the pipe entrance.

It was found, within the accuracy of the measurements,that the shape ol the axial velocity profile remains essentiallythe same for tile range of Reynolds numbers within the laminar

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A. LAMINAR FLOW IN SOLID BODY ROTATION ( 4

B. LAM1INAR FLOW NOT IN SOLID BODY ROTATION~(T 4

FIG i0 OSCILLOSCOPE TRACES FOR DISCRIMINATION OF SOLID BODY ROTATION(SWEEP =1SEC/CM; SCALE 1 N/CM)

I~l qlmla,5

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regime., As the flow changes from the laminar regime to theturbulent regimte, the axial velocity profile changes and remainsessentially the same fc the whole range of axial Reynoldsnumbers within the turbulent regime. Tile laminar and tkirbulerntaxial velocity profiles are shown in Fig. 11.

B. Study of StabilityThe study of the stclility of flow in rota t ing pipes was

performed in the present investigation by means of diagnosticand quantitative techniques. It is to be noted that the onlydifferernce in applying th2 two techniques is the position alongthe rotating pipe where the technique is used. The dye streakvisualization technique was centered on a section about threepipe diameters downstream of the porous inlet plug, while thethermistor probe measurements were performed at a section about19 pipe diametcrs downstream of the inlet. In both cases theemphasis was on the determination of the dependence of thetransition from the laminar to the turbulent regimc on theaxial ant tangential Reynolds number.

1. Flow Visualization Using Dye StreaksDye streaks are introduced by the dye probes into the flow

field ii order to determine the transition irom laminar toturbulent regimes. These tests can be subgrouped in thefollowing manner:

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7,UILLIL

00 >

0

hJ3

of o

0C5z

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1) Dye streak observations for non- 'otat ing pipe withincreasing axial Reynolds numbeis.

2) Dye streak observations for differeut fixed axialReynolds numbers with increasing tangentialReynolds numbers.

3) Dye streak observation for different fixedtangential Reynolds numbers with increasingaxial Reynolds numbers.

The dye streak observations were performed in the samemannei as those of the historical investigation of Reynolds,in which he determined the transition from the laminar to tLheturbulent regime in circular pipes.

Photographs of the dye streaks for various axial Reynoldsnumbers with the pipe stationary (NRo = 0) are shown in Fig. 12.At the low axial Reynolds numbers the dye streaks are undisturbed,indicating Lhat the flow Is laminar. As the axial Reynoldsnumber is increased, the dye streaks become more and moredisturbed and eventually break up, indicating a turbulent flow.

In Fig. 13 photographs of the dye streaks are presentedfor a fixed axial Reynolds number (one that is laminar withthe pipe stat ionary) and increasing tangential Reynolds numbers.It is observed that the flow becomes turbulent as the tangentialReynolds number is increased. Observations at different fixedtangential Reynolds number (not shown) indicate that transitionto turbulent flow occurs at a lower tangential Reynolds numberwhen the axial Reynolds number is higher.

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N Z 359+

5OM 5nFIG, 12, DYE STREAKS FOR INCREAS. NG AXIAL REYNOLDS NMImBEPSWITH NO ROTATION (N = 0)

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~NO

2450 0J

91-50 M90FIG. 13. DYE STREAKS FOR INCREASING TAN~'GENTIAL REr L]Y, NLWiERAT A FIX(ED AXIAL REYNOLDS NUCER N ~ 13300

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The increasing tangential Reynolds number was also foundnot to change the turbulent regime to a laminar one for anaxial Reynolds number yielding turbulent flow when the pipeis stationary. This result disagrees with the results obtained

34 35by White and Cannon et. al.

The dye streak photographs shown in Fig. 14 are for fixedtangential Reynolds number and increasing axial Reynolds number.Here it is observed that transition to turbulence occurs at lowervalues of the axial Reynolds number when the tangential Reynoldsnumber is increased.

While studying the dye streaks as they change from theundisturbed to the disturbed patterns, indicating transitionfrom the laminar to the turbulent regime, it was observed thatthe streaks revealed at first a regular wavy pattern (see Fig. 13and Fig. 14) before amplifying and breaking into irregularpatterns.

It was also found that the dye streak observations are muchclearer and easier to interpret in those experiments using th efixed tangential Reynolds numbers and increasing axial Reynoldsnumber than in those using fixed axial Reynolds numbers andincreasing the tangential Reynolds number. This is due to anumber of factors; the most important being the long timerequired to reach solid body rotation at high tangentialReynolds number. The observations of the dye streaks aresummarized in Fig. 15, where a curve of transition from laminar

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N 25WO ALO

32 10 3 410

37803CjFIG. 11.DYE SlREAKS FOR INCREASING AXIAL REYNOLDS, N fBEFR ATHIGH ROFATION NeR 6700

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z u-w0- 0 U-

cr 0

0

0 000 ix L

/ o0/ I

CL

0 0 0 wlzc1O a:\,i~3Nv

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to t urblulIe'it. reg ime s i I owiL as a Ini- t iol of axi al. Wadtalngent ial. Reynolds numbers.

2. Measurements Using Thermistor Probes

From the dye streak visualizatiou stability data it was-concluded Lhat it is more conveatent to use fixed tadugeritialReynolds number and increasing axial Reynolds numbers ratherthan using fixed axial Reynolds numbers and increasing th eLangential Reynolds number. It should be also noted that th etwo approaches yield the same results (points on the samecurve). Hence, the first method was the only one used in th ehot-thermistor anemometry measurements.

Transition from laminar to turbulent regimes can bemeasured using sensing elements with a limited fiequencyresponse. This is possible since the spectrum of turbulenltvelocity fluctuations covers a wide frequency range. Inaddition, the amount of energy in the low frequency range isusually larger than that in the high frequency range. Thisexplains that a typical turbulence spectrum has usually anoverall iegative slope (see, e.g., Hinze40 and Schlichting 41).

Thermistor Probes I and 4, which were used for th estability measurements, have maximum frequency responses ofapproximately five c.p.s. and ten c.p.s.,respectively. Thus,it should be uiderstood that the probes sense only the energycontained in the range of velocity fluctuations In the flowfield, which is bounlded by their maxiimm frequency response.

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By mtciitoring the output of rhe proben on thle oscu Iloscope

and at the same Lime recording the RMS value of th, A.C. componentusing a true PNS meter, adequate information about tranni nonfrom che laminar to the turbulent regime wan obtained. Typicaloscil loscope traces at different flow couditiotns ustig differ-ent sweep rates are shown in Fig. 16,

The RMS values of the thermistor output as a function ofaxial Reynolds number were obtained at different fixed tangentialReynolds numbers. Two of these curves are shown in Fig. 17.

While obtaining these readings, pictures of the oscillosc-opetrace were taken. Two sets of these pictures are shown inFig. 18, for the stationary pipe and for a tangential Reynoldsnumber of 1735.

Studying the curves, it is concluded that the first straightline portion of the curve corresponds to the laminar regime,the second to the transition regime, and the third to the turbu-lent regime. These data are replotted in Fig. 19 to show th ethree regimes as a function of axial and tangential Reynoldsnumbers.

Similar information can also be deduced by studying th epictures in Fig. 18. It should be apparent from these pictureswhere transition from laminar to ,rurbuleat regimes starts andwhere it ends, for both the ,otating and the ion-rotating flowconditions. Some of the conclusions which are obvious fromthe pictures are:

I w I:' 'I: ' . C=-C)

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SWTLJI SL.C/D.\

7rnr

tWJ

S-..i -. u .,. _ .--

,.}tI sT -chiv

FIG. 16, OSCILLOSCOPE TRACES AT DIFFERENT AXIAL REYNOLDS NLFBERS WITH NO ROTATION(SCALE =1 MV/DIV)

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2.2-

2.0

Av

0*Z 1.2-

0 . -02 0.60 - 0 NR/ 0

04 a N.~e=I720

0.2-o a L1l 1 I 1

0 1 2 3 4 5 6 7AXIAL REYNOLDS NUMBER, NRz X 10-3FIG. 17. RMS OF THERMISTOR OUTPUT AT INCREASING AXIAL REYNOLDS

NUMBER IFOR TWO FIXED TANGENTIAL REYNOLDS NUMBERS.

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FIG. 18. OSCILLOSCOPE TRACES AT INCREASING AXIAL REYNOLDSNUMBER FOR TWO FIXED TANGENTIAL REYNOLDS NUMIBERS

NO= 1735 FOR LEFT COLUMNN O 0 FOR RIGHT COLUMNJ

(SWEEP =0.2 SEC/DIV; SCALE =1MV/DIV

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FI 8. (CNTD

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FIG. 18 coUTrD)

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FIG. 18 (CoNT D)

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F7Y7VT T

0X

w ,U 0or2~ 12 Ai uiIA' xtw0w

zu

40

-K J.000

ID g N - 0C 01 x *'N 'k13efnm SOU1ONA3--1 -I1VIN39NVJ.

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1) The pictures on the first page (of Fig. 18) indicatethat both the rotating and non-rotating flows are inthe laminar regime (N < 1000).

2) 1 At, pictures on the second page indicate that therotating flow is in the transition regime while thenon-rotating flow is still laminar (1700 < NR < 3000).

3) The pictu-Le on the third page indicate that th,.rotating flow is in the turbulent regime while thenon-rotating flow is in the transition regime(3200 < NRz < 4200).

4) The pictures on the last page indicate that therotating and non-rotating flows are in the turbulentregime (NRZ > 5500).

All the hot-thermistor measurements leading to the curvespresented here were performed with the sensing element of theprobe located at the axis of the pipe. Similar information(not shown here) was also obtained for other radial locationsof the sensing element (excluding the boundary layer). Theresults indicate only a small shift of the curves of Fig, 19toward lower values of Reynolds numbers. It is thereforebelieved that the results obtained at the axis are adequateto describe the transition phenomenon.

From curves such as those shown in Fig. 17, it was observedthat a high RMS value was measured at an axial Reynolds numberof approximately 450, and it was found that this phenomenon isindependent of the tangential Reynolds number. Further

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investigation revealed a distinct frequency on the oscilloscope.The output signal under these conditions (NRz m 450) is shown inFig. 16 revealing a frequency of approximately 6.5 c.p.s. Thefrequency was also measured using the octsve band analyzer andthe same result was obtained. No explanations are available atpresent for this observed phenomenon.

C. Discussion of ResultsThe results pzesented in this chapter are concerned with

the flow field determination as well as investigation of thestability. Two different techniques were used to achievethe results; one is diagnostic and the other is quantitative.For the stability results the diagnostic approach is only usedto indicate the trend of the stability of flow in rotating pipesand to confirmn the results obtained by the quantitative approach.For mean flow measurement both approaches are of equal significance.

With regard to the flow field determination, several areaswere investigated. One of these concerns the existence ofreversed flow in the flow field. This area wi investigatedonly by means of the diagnostic flow visualization technique andthe results obtained were found to agree with the analyticalinvestigation of Lavan et. al. It is concluded from theseresults that the flow field in the rotating pipe betweer, theporous plugs is free of reversed flow within the range of theresults of the present investigation.

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The results relevant to the tangentia l velocity profile,obtained by the two measurement techniques, are in agreement. Itshould be noted that the dye streak visualization technique coversthe whole length of the pipe, while the hot-thermistor measurementsare performed at only one section of the pipe (the location at whichthe stability measurements are performed). From these results it isconcluded that the flow is in solid body rota t ion up to swirl ratiosof approximately four.

The lesnostic technique does not contribute to the axial velocityprofile measurements except by providing some sunport to the datapiovided by the quantitative technique. These results agree favor-ably with results from similar cases (laminar and turbulent. velocityprofiles for the entrance region of circular pipes) quoted by Prandtl42 41 4et.al., Schlichting and Goldstein.3 They also agree favorably withthe results obtained using hydrogen butbles which are presented inAppendix C.

The results of the diagnostic dye streak observations arepresented here for two reasons. The first is to confirm the resultsobtained by the quantitative hot-thermistor anemometry techniquesince they both agree on the effect of rota t ion on the stabilityof flow in rotating pipes. The second is to present a comparable

34 35technique to the one used by White 3 4 and Cannon et.al. in a similarinvestigation. The resu - in their investigation and the destabi l iz-ing effect of rotation on iie stability of flow in rotating pipes asgiven in Fig. 15 are conrradictory.

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The results ubtained by the two different techniques used inth, present inves.igation (see Fig. 15 and Fig. 19) are not incomplete agreement. This is believed to be due to the followingreasons:

1) The por-us plugs are known to introduce small scale eddies,due to shLdding from the porous face of the plug. Theseeddies tend to affect the dye visualization data, sincethe dye streaks are being observed a small distance down-stream of the I.Jug. These eddies die out within a shortaxial distance du- to vie-ous effects and hence will notaffect the thermistor Probe measurements. (The probe islocated about 19 pipe diameters downstream of the upstreamporous plug.)

2) Dye visuatization experiments are performed in the singlepass mode, in which stable flow rates cannot be maintained(see Chapter II.C.). The fluctuation of the flow rate iGbelieved to affect the dye streak data. Hot-thermistormeasurements are performed in the recirculating mode, inwhich stable flow races are obtained.

Despite these discrepancies, the destabilizing effect ofrotation can still be determined from the dye streak data. Theopposite effect is concluded oy the similar inve~stigation of White 3 4

and Cannon et. al.5 The results obtained using hydrogen bubb~es andpresented in Appendix C confirm the stability results obtained 'isiagdye streaks and thermistor anemometry.

The results obtained by the hot-thermistor measurements arebelieved to L accurate. 1 should be pointed out that they agreein trend with the results of the recent analytical investigations

32 33by Pedley 3 2 and Strohl.

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CHAPTER IVCONCLUSION AND RECOtXhENDATION

Solid body rotation is found to have a destabilizing effect onflow through pipes. The flow field investigated consists of solidbody rotation superposed on an entrance type pipe flow profile. Thedestabilizing effect of rotation i nr'ascd continuously with increasingswirl ratios in the range investigated. The results obtained (seeFig. 19) agree therefore in trend with results obtained analyticallyby Pedley32 and Strohi33 who investigated a fully developed axialprofiln at high swirl ratios. They found that in the limit of veryhigh rotation the flow will be unstable for axial Reynolds numbersas low as 82.9. The present results suggest that the destabil izingeffect due to solid body rotation may also hold for other axialveloci ty profi les iud for the core of swirling flows in stationaryducts and free vortices. At the operating conditions of the presentinvestigation solid body rotat ion was maintained up to swirl ratiosof four: hence, this was the upper limit of the swirl ratios in-vestigated. Two different measurement approaches are used; one isdiagnostic and the other is quantitative. The diagnostic i'- the .lowvisualization technique using dye streaks and ',he quanti tative it bhot-thermistor anemometry recho iquL. Both ipprocthes yield imilarresults tor the breakdown of tiie laminar Hlow. A iimited nviwst ig.t-t ion of the flow tield and the stability of tlie tfowW as ;Ita,( q-ducted ,ising the hydrogen bubble visualizatrion tchnique (scLe Appendix

C . The results obtained agree favorably wiLYh the resu tI ohbaiiudusing thcl two other measurement approaches.

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White 3 4 and Cannon et. al.5 investigated experimentally theeffect of rotation on the stabi l i ty of flow in pipes and concludedthat rotation is stabilizing. The results cobtained in the presentinvestigation contradict their- conclusions. It is believed thatthe cesults obtained by White are strongly influenced by reversedflow components that would indeed exist at the high swirl ratiosused in his investigation (see Lavan et. al. 7). The results ofCannon et. al.?5 are subject to a similar criticism, since theyobserved a core region in their pipe that was stationary whilethe pipe was rotating.

The present investigation indicates a possible new mechanismof confined flow instability that takes place at lower Reynoldsnumbers than previously beLieved possible. This conclusion issupported by the recent analytical works of Howard et. al,4Ludwieg,27 Kiessling, 9 Pedley,32 Strohi33 and Joseph et. al.13In view of the fundamental aspect of this work, it is thereforesuggested tc continue and extend the investigation. The mainobjectives of the extension of the present study are:

1) To create predictable axial velocity profiles and tom'easure them precisely.

2) To generate higher swirl ratios while maintaining thedesired axial flow profiles unchanged

3) To carefully analyze the disturbances in order tocompare them to the analytical predictions and toclearly idenil'fy the structure of the disturbed flow.

,) To increase precision and accuracy in all phaseb.|0

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In an attempt to meet these objectives, two better andmore advanced flow visualization techniques for mean flowmeasurements are presently considered; hydrogen bubbles andthymal blue. Hydrogen bubbles have been successfully used by

44Lennemanx eL. al. in moderately rotating systems for quantita-tive diagnostics. Baker45 introduced a visual measurementtechnique for small fluid velocities using thymal blue(thymolsulphonephthalein). The thymal blue is simple touse and since it remains in an ion solution density differenceand centrifugal effects characteristic of hydrogen bubbletechniques are absent here.

In order to directly observe the wave patterns calculated32 33by Pedley and Strohl, a visualization technique utilizing

30aluminum flakes is suggested. Ludwieg successfuliy usedsuch a technique to visualize the wave patterns in a similarinvestigation. This technique may however, introduce someproblems with the porous plugs.

Presently the use of more dense porous plugs is beinginvestigated. Such a modification may permit the extensionof the present investigation to higher values of swirl ratio.rlugs made of 207%dense material are currently being inves-tigated.

In order to create experimentally a fully developed axialprofile that will permit comparison with the investigations ofPedley 3 2 and StrohlJ 23 two ideas are proposed. Pedley's 3 1 ' 3 2

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analysis 18 valid for the flow in an annulus with solid bodyrotation at high swirl ratios. Thus, by introducing an innercylinder in the apparatus that rotates with the outer pipe, onecan conveniently investigate such a flow. If the gap betweenthe pipe and cylituder is of sufficiently small size, the flowin the annulus will be fully developed within the length of theapparatus.

The second possible method is to use contoured porous plugs inorder to obtain fully developed Hagen-Poiseuille flow. Suchan approach requires an extensive amount of work in investigatingporous media and shaping the porous plugs.

The use of glycerin as a working fluid is also underconsideration. This would permit the use of more sensitivemeasuring elements, since the mean flow velocities would behigher for the same range of axial Rayrolds numbers. This wouldalso make possible investigations at lower axial and tangentialReynolds numbers.

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APPENDIX APOROUS MEDIA

The mathematical model that leads to Darcy's law for flowthrough porous media neglects inertia effects and considersa multiplicity of identical cylindrical passages through theporous medium.

A x

FIG. 2 MODEL OF POROUS M~EDIA TO IWili DARCY 'S AW IS PPLIED

Darcy's law applied to a porous volume element as shown inFig. 20 yields (see e.g., Str..ator4 6

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Q IL rdP+ pgsin] A.

where Q is the volumetric flow rate and dP/dI is the staticpressure gradient in the direction of flow. This can begeneralized to be represented in terms of velocity components,

V - 6 A.2a

V . - D A.2b

V .- +PA.2c.

where Vx V and V are velocity components along x,y and zand K is the permeabil i ty of the porous m aterial .

The law thus shows that the pressure drop across a porousmedium is proportional to the flow velocity. Darcy's law isapplicable to porous media that do not consist of identicalcylindrical passages, as long as the Reynolds number based onthe effective particle diameter does not exceed unity. (Theeffective particle diameter is the dimension of the basicelement in the porous material structure.) When this Reynoldsnumber exceeds unity, the inertia effects become non-negligibleand Darcy's law is no longer valid.

For the porous material used in the present investigation,the Reynolds number based on the effective particle diameter isfound to be much larger than unity.

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47 48 49Arthur, Bernicker and Hill present a more general

approach that is applicable to this situation. In general, onemay assume that a fluid (either compressible or incompressible)flowing through a porous medium encounters two kiuis of resis-tance. They are:

1. Pressure drop across the porous medium due to the actionof shear stress. This can be expressed in the form,

Sdl' dz CrPW A.3

where ot is the coefficient of shear resistance.2. A flow loss which is believed to be associated with

sudden expansions and contractions along the flowpassages and with the inertial effect at the turnsand bends of the channels. This source of lossesis not completely understood. It is usually expressedin the form,

dP 2dz = 0 A.4

where 0 is the coefficient of inertial and compressibleeffectu.

By combining these two pressure loss terma, the followinggeneral expression results:

"d P W + 0 PW 2 A.5dz

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This expression can be rewritten in the form,

dF cygiG A.6

where X is called the friction length and Is equal toG is the mass flow rate per unit frontal area and is equal topW. One should note that within the present context a anddefine completely the permeability of a porous material inde-pendently of the flowing fluid. Normally t and X (or ctand 0) as well as other properties are published by themanufacturers of the porous material.

Since the friction length X, is of length units, wedefine a Reynolds number

N A

The general equation for the pressure drop across a porousmedium can therefore be expressed in the form

.2 dz NRA (I + NRA) A.7

where2 2 2

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For an incompressible fluid passing through a given porousmaterial, #2 is constant.

By comparing equations (A.5) and (A.7) it can be shownthat:

a) For NRX > 1 the coefficient of inertial andcompressible effects (0) determines the pressuredrop, i.e., the pressure drop across the porous mediais proportional to the square of the flow velocity.

For the porous material used in the present investigationneither a nor X are available from the manufpcturers;thus, an experimental determination was made. The results areshown, in Fig. 21, where the pressure drop across one-inch of theporous material is plotted versus the flow velocity on a logarithmicscale. The range of flow velocities corresponds to the range ofaxial Reynolds numbers from 0 to 5,000. The equation fitted tothis curve is

AP - CW2 +B

W C'N 2+B A.8R7

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2.0111 11.0 000

i0.5u)

z~0.20 -

a:70w 00crU)wc 0.05

a-60

o6o

0.02

0.0o I liii I .0.1 0.2 0.5 1.0 2.0 5.0FLOW VELOCITY, W INCHES/SECFIG, 21. PRESSURE DROP ACROSS ONE-INCH OF POROUS

MATERIAL VERSUS FLOW VELOCITY.

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where

C' = 3.66 x 10-7Ib/ft2

and

B - 0.0293 lb/ft 2

This result shco's that the pressure drop across the porousmaterial is proportional to the square of the velocity. Thisleads to the conclusion that, within our operating range, NRXfor the material used, is always larger than unity. This resultcould have been easily reached if the properties of this materialwould have been known a priori.

Assuming solid body rotation in the flow field, the radialpressure difference can be expressed in the form

22 2aP - N-.r 2 2 R2 A,9

where D is the pipe inside diameter and V is the tangentialvelocity at this diameter. The axial, pressure drop is

AP (AP - B) - C'NR 2 A.10

Dividing the two expressions we obtain

Ap 2 2r - .I. r A.11AP z2pD 2 C,

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wherer NNRz

For water flowing across one-inch of the porous material atroom temperature, and with the outside diameter of the plug equalto 3-1/4 inches, the above expression reduces to

S-".004 r2 A.12"AP

By using this simple relation, the range in which the pcrousplug imparts solid body rota ion to the fluid can be estiated.(See Chapter II.A). The comparison with experimental results isdiscussed in Chapter III.A.

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AFPENDIX BHOT-THERM I STOR ANM(IETRY

Thermistors have been investigated In thp last ten yearsfor their potentia l applicat ion as sensing elements. Theseinvestigations are mainly concerned with their properties,calibration and the possible areas of use. Thermistors areoxide semi-conductors with high negative temperature coeff ic i-ents of electrical resistance (usually some combination ofdi-valent and tri-valent oxides such as CuO, NiO on one sideand Mn2 0 3 and C0 2 0 3 on the other side). Lumley-0 Laneet. al51 and several other investigators contributed sub-stantially to Lhese investigations, Pertinent information salso published by the major thermibtor manufacturers. However,few publicat ions deal withthe use of thermistors in fluidmechanics studies. This Appendix attempts to present a surveyof thermistors and their technoiogy; electrcaic circuity,calibration procedure, and frequency response measurements, inparticular, are discussed.

The two most coimmon working fluids used in the fluid-mechanical experimental investigations are water and air, Thedifferences between the two fluids which strongly affect th echoice of the sensing element used are:

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I. Typical vel:ctties encouatered in air tend to be muchhigl'her than those occurri ng iL wate:r.

2. Water tende to contain more impurities than ai rsinee many foreign particles have very nearlythe same density and are, therefore, more diffi-cute to remove.

3. The electrical conductivity of water is much higherthan that of air.

For the above reasons, hot-wire anemometry, although verysuccessfully used in air, is not commonly used in water. Insteadthe most frequently used sensing elements in water, and otherliquids, are hot-film probes. Some of the hot-film probematerials are platinum or platinum alloys.

The principle of operation of both hot-thermistor andhot-film sensing elements is similar. If the sensing elementis immersed in a still fluid and a heating current is supplied,it reaches thermal equilibrium with i ts environment when theinternal heat generation rate is equal to the heat transferrate by natural convection to the surrounding fluid. When thefluid is in motion, the sensing element temperature will drop,owing to the higher heat transfer rate by forced convection(the amount of drop being related to the fluid velocity).This drop in temperature will cause a change in the resistanceof the sensing elemeait.

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The above introduc" ory remarks lead to the conclusion thata choice between hot-film anemometry and hot-thermistor ane-mometry has to be made. Lumley50 in his investigation, presentsa thorough comparison between the two types of sensing elements.

50L.UU.Kyso coLucludes from his investigation that thermistors

offer in water the possibility of spatial resolution and noiselevels that are better by an order of magnitude than thoseobtainable with platinum film probes. This is due to their largeresistivity and temperature coefficient of electricalresistivity,which are an order of magnitude larger than platinum. Theresistivity as a function of temperature (T) hao been experi-mentally found to be

To/TR = R e B.1

where T is in the order of 20000 K to 50000 K and R varies0from one ohm to 75 megohms.

In addition to the above advantages, thermistors have lowerdensity and smaller thermal conductivity than platinum. Theseproperties have dif; rent implic3tions; one is the need toinsulate the probes. The most important consequence is thelimitation of frequency response. An attempt to overcome thislimitation using film deposition is presently in a developmentstage (see, e.g., Lumley 50). rhis property though does not limit

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their use in sensing transition from laminar to turbulentregimes. The probe usually consists of a thermistor beadmounted on a short support, and the bead ip encapsulated insome insulta ing material, such as glass. The probes are alsorugged, and their high electrical resistivity permits the useof simple electronics.

Lane et. al.1 introduced hot-thermistor anemometry for lo wvelocity flow measurements. A method of cal ibrat ing the probesis explained in their work and the wvter temperature effect isalso investigated. They concluded that hot-thermistor anemometrymay be used to measure steady-state and t ransient velocitit'sin the range from 0.1 to 6 inches per second, and that individualprobe calibration is required. Except for measuring the responseto step velocity changes, no attempt to measure frequency re -sponses is reported.

Rotating systems introduce an addit ional problem in the us eof sensing elements like hot-films or thermistors. In order tocommunicate the electric signals between the sensing elementand the other artemometry components, one may use brushes andslip rings. Since the brushes and slip riijgs introduce ooise,which is usually of a relat.vely high frequency, filtering isrequireed. The large resistance of the sertsing element makes th efiltering easier and requires tess expoe:sive bruilhes a.td sliprings.

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Based on the above discussion, hot-thermistor anemometryis chosen for the quantitative measurements in the presentinvestigation. The probes are to be operated in the constantcurrent mode, rather than the constant temperature mode, toachieve a higher sensitivity to velocity fluctuation and toreduce the cost of the electronic circuitry.

The different components forming the constant ct? renthot-thermistor anemometer unit used are shown in Fig. 22.The 24-volt D.C. supply consists of two 12-volt medium-sizedcar bi t teries connected in series. The capacitance shown formsan R-C filter for suppressing the noise from the slip ringsand brushes. The value of the resistance R used, is 4K ohmfor the stability measurements, and 48K ohm for the flow fieldmeasurement. The reason for this is explained later in thisAppendix.

Four different types of thermistor probes are used; thetechnical specifications of each are:

Probe 1. A GE thermistor (Cat. 81B 202) with the thermistorbead of 0.043 inch maximum diameter encapsulatedin homemade insulation made of epoxy. (R. = 2000 ohms)

Probe 2. A GE thermistor" (Cat. 81G 202) with the thermistorbead encapsulated in a glass rod of 0.100 ichmaximum diameter. (R = 2000 ohms)

Probe 3. A VECO thermistor probe (Cat. P32A129) with theLhermistor bead encapsulaLed in a glass rod of0.060 inch maximum diameter. (R = 2000 ohms)

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w

(L wOM0Qoi-.M -U.

Irv 0 LU.z

cc.

cr 0 0LU0:

+I

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Probe 4. A VECO thermistor probe (Cat. AZ3IA70) with thethermistor bead encapsulated in a glass rod of0.020 inch maximum diameter. (R - 1000 ohms)0

All four probes are mounted at the ends of stainless steeltubing of diameters ranging from 1/16 to 1/8 inch. The thermistorconnecting leads pass through the stainless steel tube. Theprobes are mounted inside teflon seals inserted in the wall ofthe pipe. The connecting leads of the thermistor are solderedto the slip rings. (See Fig. 8 and Fig. 9a.)

All probes were calibrated and a typical calibration curveis shown in Fig. 23. Probe 1 was the first probe to be used.It was subsequently found that the calibration is stronglydependent on the flow temperature. Furthermore, the A.C.component of the thermistor output affects the accuracy ofreading the D.C. component, particularly in turbulent flowregimes. Since temperature variations were observed when thesystem was operating in a recirculating mode, (see Chapter I.C),it was decided to use less seas