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0 0drASACR66902C.1N70-19845AN EXPERIMENTAL STUDY OF A TYPE OF VORTEXSINK RATE S:ENS:ORS - A THESISRao V. ArimililiAugus-t 1969 -MC3=-ruLnnnL:i- r!FL (,1i40i4jj, N ,0 0 00 . 0i ::..::..S,.#00S0*00 00 0 0SDistr ibuted . . ' to foster, serve

and promote the nation'seconomic development

and technologicaladvancement.'

CLEARINGHOUSEFOR FEDERAL SCIENTIFIC AND TECHNICAL INFORMATION

000..: :.U.S. DEPARTMENT OF COMMERCE/NaUoflaI-Burea L6f Sfrds

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T E C H L I B R A R Y K A F 8 , N MI.)I M 1 1 1 1 1 1 1 1 1 H H h I 1 1 1 1 I I I H I I0 1 3 6 2 5 8 8-C )AN EXPERIMENTAL TunY OF - A - . T Y P X O F

VORTEX: SINK. RATET SENSQRSIy .

Raa v:.. Ariai-rrt

A. The.-.-is:

Submttedt the city .of

GUIDomri orr. CoI1egei n pa r t i a l fulfillment of thea re irements: fbr: t he:

Deg ree - a fT N te r a f Eg. inee r ing:i n .

T h e r m a l . E g i ne r i ng

August I69.

Approved by:.

Gennaro L. Goglia ,an of Dlapar ment:N70 -19845Ma j o r A d v i s o r a n d C h a i r m a n. T RUJL eproduced by theCLEARINGHOUSE(PACor Federal Scientific & Tnical1InomaonSpngedVa1(NA$ACR OR TMX OR AD NUMEjER,CATEG Y)

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I 1

ABSTRACT

In order to study the flow fieldd in. the sink: ragorr_ oa vortex Sink Rate Sensor, an experimental s:tudy wasi n i t i a t e d . Us i n g t w o p r o b e s , d n e f o r t h e t a L prssireme a s u r em e n t s a n d t h e o t h e r f o r t h e s t a t ic pr e s s u m e a s u r em e r i t s . d a t a w a s col l ecte d f o r t w o f l o w r a t e s, va r icus r t e s o frotation and at.various points in the sink: region. af the-L- f2 - o w .For the ;nsor (coupler inside d.:meter 51 inches: arid.h e i g h t 0. 50 i nch e s) w i t h s l e n d e r n e s s p a r am e t e r o f u n i t y t h n rimportant conclusions were drawn from the dat-a... At a given-_ location in the flow field the magnitude: of t he tanentaiLcomponent of velocity increased for decreased. fIow rates.Vi sco u s co r e d i d ex i s t i n t h e s i n k f l o w a n d o u t s - d o f i tthe tange ntial component of velocity was n:egIi:ibly: smalLWi t h i n t h e v i sco u s co r e t h e t a n g e n t i a l component : o f velocity.increased- in -a general manner with in creased: rates:- ofr o t a t i o n . T h e m a x i m u m of the tang.enaL com pone nt ofvelocity , occiired within- th e entranc:a region ta the sink-: t u b e : . .

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ACKNOWLEDGEMENTS

The author wishes to express his sincere appreciationto his advisor, Professor Gennao L. Goglia for his suggestionsand quidance during the various phases of preparation ofthis dissertation and for his timely help and understandingthroughout the author's graduate study.

The author also expresses his appreciation to Drs.G. L. Goglia and K. R. K. Sarma for their suggestions duringthe design stage of the experiment and to Dr. R. L. Ash forreadily sparing time for discussions on many occasions andfor his encouragement throughout the author's graduate study.

The author also expresses his appreciation to hiscolleagues for their help in collecting the data.

Last, but not least, the author wishes to thank NASALangley Research Ce erfQonspring this study throughResearch Gra t NGR47-003--007n particular, Mr.R. F. Heilbaum for his kind cooperation and helpful suggestions.

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CONTENTS

P a g eABSTRACT................ACKNOWLEDGEMENTS....... .C O N T E N T S ................... .LIST OF FIGURES...... .v LIST OF SYMBOLS.... -- GENERAL REMARKS ....... 1INTRODUCTION .................... .PHOTO GRAPH OF THE APPARATUS.......... .aDESCRIPTION OF APPARATUS. ...2T E S T P R O C E D U R E..........8ACCURACY OF RESULTS..........5DISC USSION O F RES ULTS............ 2 8CONCLUSIONS.......... 3 7REFERENCES ...................... .8

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i v

LIST OF FIGURES

Figure Title P a g e1. Sketch of test section3 02. Sketch of probes and holders 3 13.Schematic diagram and coordinate system4. Plots for two flow rates showingdimensionless tangential-velocitydistribution as a function of thedimensionless radius for different

rates of rotation of the sensorwith D = 1 inch and r 0 = h = 0.250 inches 3 3

5. Plots for two flow rates showingdimensionless tangential velocitydistribution as a function of thedimensionless radius for differentrates of rotation of the sensorwith D = 1.5 inches and r 0 =h0.250 inches. 3 46. Plots for two flow rates showingdimensionless tangential velocitydistribution as a function of the

dimensionless radius for differentrates of rotation of the sensorwith D=2. 0 inches and r 0 =h=0.2 5 0 inches 3 5 .7. Plots for two flow rates showingdimensionless tangential velocitydistribution as a function of thedimensionless radius for differentrates of-rotation of the sensorwith D=2 . 5 inches and r 0 =h0.250 inches6fl

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IA

L IST OF SYMBOLSR - inner radius of coupler2h --spacing between plates or height of coupler2r 0 - inside diameter of sink tubeD - distance measured along positive z-axisfrom the lower surface of the sensor tothe probe location where data wascollected for various radii

- W -rate of rotation of the sensor-- volume rate of flow in cubic feet perminuter - variable radiusP - density of fluidS = f .2 . -slenderness parameter

hV - magnitude of velocity vectorVr -radial component of velocity vectorV - axial component of velocity vectorV 0 - tangential or circumferential componentof velocity vector

QU= r r - average axial velocity of the flow inthe sinkRe = 2r 0 U =2 - Reynolds number characteristic of sinki r v r 0 f l o w0 - 'local helical or stagnation angle' ofthe sink flow0 0 -reference angle'= (00 ) -true helical angle of sink flowr* - radius of viscous core

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GENERAL REMARKS

Avehicle traveling in space or in earth's atmospherelike a space craft or an Inter Continental BallisticMissile is subjected to forces which may cause thevehlcleto rotate about some axis. Wheneer this occurs, it isdesirable to know, for guidance and other purposes, theangular velocity of rotation and, if possible, the rateat which it is changing. . A vortex sink rate sensor,sometimes called a fluid gyroscope, is a fluidic devicethat is used to sense the rate of rotation of the vehicleon which it is mounted. In this sense, it seems moreappropriate to call it a vortex rate sensor.

The vortex rate sensor used in the present investigationhas a continuous flow of "air" through the manifold, thecoupler (sometimes called filter), the chamber and axiallythrough the sink (drain) into the atmosphere. The coupler,the chamber and the sink tube together are free to rotatewithin the manifold without any loss of flow. When the

sensor is rotated about its axis of symmetry, the couplersuperimposes a tangential velocity onto the other wiseradial flow. The fluid, after leaving the coupler, spiralstowards the sink and flows through the sink tube in ahelical manner. Due to conservation of angular momentum,the tangential velocity of the fluid increases as it movestowards the sink. Thus, a change in the angular velocity

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ofthe device causes a measurable change at the sink. ThePresent investigation is concerned with the velocities inthsink region.

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INTRODUCTION

n experimental study was made of steady flow in thesink region of a vortex sink rate sensor. The velocity.profiles weredetermined along the length of the sink tubefor various diameters of sink tube with the rates of rotation(w) , slenderness ratios () and the volume flows (Q) asparameters.

The object was to obtain a better understanding ofthe flow and to find the optimum location for the probe,should one exist, with respect to the sink tube (r and D)and the geometrical parameters.

Attempts were made to explain the flow field analytic-ally. To date, these were met with little success. Thecomplexity of the Navier-StokeS equations used in thisanalysis is further compounded by the nature of the finiteand nonuniform geometry of the problem. To date, nosolution was reported in the literature that is uniformlyvalid even for the pancake region.

Particular solutions like perturbation solutions arereported by 'W. S. Lewellen" {l}* and "Ostrach and Loper"{2}for confined vortex flows within geometries of uniformcross sections.

Ostrach and Loper {2} analyzed the problem of thevortex flow bounded by two stationary, parallel and finite

plates and driven by the tangential injection of incompressible*Numbers in brackets designate references listed at the end ofthe paper.

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. . .. ._ . . .-4-

viscous fluid. The solution they obtained by the momentum .Integral method was confined to the case .where theseparation distance between the two plates (s) is much lessthan the radius of the plates. They further imposed theclassical restriction that the inertia terms dominate theviscous terms (Reynolds number >> s 2>>1) except in theboundary layer regions near the two flat plates.

The authors showed, without regard to the manner ofexit of the fluid from the central core, that theboundary layer thickness is strongly dependent on the.imposed radial mass flow. The boundary layer, in fact,was found to grow thicker as the mass flow is decreasedand thereby having considerable influence on the outerflow..Forvery small radial flows, this influence pre-dominates, and as a consequence of the assumptions involved,the analysis no longer portr ays the physical flow.

"Lewellen" {l} discussed the axial variations offlow in a swirl superimposed upon a stagnation point sinkflow (with radial inflow) for large Rossby numbers (ratioof radial volume flow to characteristic circulation)which correspond to weak swirls. The results showed thatwhen the magnitude of circulation is decaying for increasingaxial distance, the ax ial velocity in an annulus about theaxis actually increases faster than on the axis itself.This causes the reduced axial pressure gradient on the axisand for strongly rotating flows this is further accentuated

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and the axial pressure gradient can- - be reversed to give a

reversed flow.For a slightly different problem, interesting results

were obtained bydd and Farris" i.3}. For the problem of.,the flow produced by the interaction of a potential vortexwith a stationary'surface, they similarity transformedthe "full" Navier-Stokes equations and integrated the result-- ing ordinary differential equations numerically. When

the vortex flow is far from the surface, Kidd and Farrisshowed that very close to the surface, the radial velocityis directed towards the axis and thereby the flow was ableto redistribute itself. This recirculation of flow isphysically necessary because there could be no net flow inthe radial direction for a potential vortex.

Classically, these problems were of interest in thestudy of tornadoes and hurricanes. Recently they havebecome of interest expecially in the design of nuclear.reactors.

Experimental studies of confined vortex flow s can bebroadly classified into two subcatagories. The first ofthese are concerned mainly with high swirl flow s. Due tothe fact that these flows are of practical importance asin the case of hydraulic cyclones, magnetohydrodynamicvortex power generators (nuclear reaction chambers),dust cleaners, etc., high swirl flow s received a gooddeal of attention. Savino and Keshock {4}have presented

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a:comprehensive study of high swirl.-and related vortex

flows for works up to 1965 in their report on "Experimentalrofiles of Velocity Components and Radial-Pressure

Distribution In a Vortex contained in a Short Cylindrical.Chamber." Lee {5} in his report on "An ExperimentalStudy of the Flow in a Low-Pressure -Swirl Chamber"listed the works of various other authors since 1965.Some conclusions of Savino and Keshock {4} are interestingand worthy of mention here. They concluded that the amountof :swirl (ratio of tangential to radial velocities)imparted to the fluid as it is injected into the chamberalone determines what fraction of the total mass flow willbe forced to flow inwardly within the end wall boundarylayers. When the swirl is low (the ratio less than0.5), the radial inflow will have enough inward momentumto penetrate the centrifugal field and inflow will existat all axial and radial positions away from the walls.When the swirl is high (the ratio greater than 10), theradial inflow is diverted axially; and if two stationaryend walls are present, all the flui d leaves the chamber byway of the boundary regions adjacent to these end walls.This letter conclusion is consistent with the results ofLwellen. {l}

The second subcategory of experimental studies ofconfined vortex flows deals mainly with low swirl flows.

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..-7-One such flow is the flow in a vortex sink rate sensor.Various studies in this connection were reported in refer-ences {6 through 101.

In the experimental studies. of Sarpkaya {6} using airas the fluid, attention was focussed mainly on the per-formance of pickoffs on the Sensor . 42 therein. Of partic-ular qualitative interest to the present study is the

conclusion reached by Sarpkaya that the output of thepickoff is linear for small values of '' and that it increaseswith increasing flow rates. The sink of the Sensor #2used by Sarpkaya was not of uniform cross section butinstead was initially tapered. The sink tube of thesensor used in the present study, although much longer,is of uniform cross section and similar to Sensor #1used by Sarpkaya. Sarpkaya in his investigation observed.that rotations in counter clockwise as well as clockwisedirections about the axis of symmetry gave identicaldifferential pressure signals. In view of this; thepresent investigation was restricted to the counterclockwise (viewing from top) rotations of the sensorwith the implied assumption that for clockwise rotationsthe flow will be similar except for the change in the direc-tion of the circumferential velocity.

Rakowsky and Schmidlin {7}, with water as the workingfluid, studied the .f low in the pancake region by photo-graphing the dye traces of the streamlines and then reducing

FA

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the resulting data. Angular momentum efficiency (ratioof angular momentum at any r to that at r = R 0 ) of themidplane of the pancake region was plotted as a functionof radius. These results were compared with the resultspredicted by a momentum integral method with an assumedparabolic momentum profile and the unknown matchingparameter was found.

Heilbaum {8} using the smoke trace techniques studiedthe effects of the geometrical parameters on the flowin the pancake region of the sensor. Of interest isthe conclusion that theratjo of circumferential to radialcomponent of velocity was observed to increase fordecreasing flow rates.

Qualitatively this can be explained in the followingmanner. For a given geometry of the sensor, theangular momentum imparted to the fluid per unit timeremains the same (assuming the rotation is uniform) andfor increased flow rates, this means, the amount ofangular momentum imparted per unit volume of the fluidper unit time decreases. Consequently, the ratio ofcircumferential to radial velocity decreases. This ratiowould further decrease due to the fact that for increasedflow rates, radial component of velocity increases. Theresults by Heilbaum seemed to indicate that an optimumcharacteristic radius to height ratios of coupler mayexist for various flow rates.

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Inaddition to the effect the coupler diameter hadon:the pickoffs, Burke and Roffrrn {9} studied theperformance of two different pickoffs (one axially slottedand--'one circumferentially slotted).. They observed thatfdr::couplers of smaller diameters the pressure outputdecreased.

Later Burke {lO} studied the effect of the coupler

Might and the pickoff on the sensitivity (defined assignal output per unit rate of rotation) of the angularratesensor. Further, it was observed that for a givenrate---of rotation, the sensitivity (which now is a measure ofdifferential pressure) dropped rapidly as the anglebetween the axis of spin and the axis of symmetry increased.It-.-.was also observed that the maximum sensitivity wasfOund to occur when the two axis coincided. The sensitivitywasa1so found to increase with increased heights of thecouplers. Burke also discussed the time dependentphenomena like the noise frequency in the output of thepickoff, the transport time, and the threshold (ratio ofAR:-of signal to AP of noise). The threshold is consideredameasure of the amplitude of the noise. These phenomenaare:of importance in the practical use of sensors wherethe-response time is of importance. Though it is notexplicitly mentioned, the above study wa g confined to verysmall. (less than 1 revolution per minute) rotations.

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It should,.however, be noticed that sink tubes ofa--particular-diameter were used in ,-the studies by each ofthe above Investigators with their pickoff s located at afixed position except in the case of Rakowsky andScbxnIdlin.

In the present study, the ilbw was assumed to belaminar and incompressible due to the fairly small flow

rates involved. In addition, the flow was assumed to besymmetric about the axis of symmetry.

In this connection, though the asymmetry in the flowwas negligible and, in fact, unmeasurable in the presentstudy, its existence as observed in the pancake regionby Savino and Keshock {4} in their high swirl experimentsshould be remembered. Observations like this and othersseem to further substantiate the general remarks madebyLadyzhenskaya {ll} in connection with the results ofaparadoxca1 solution of the Navier-Stokes equationsobtained by Goldshtik. The result arrived at by Goldshtikhere quoted is:

"In the problem of the interaction between aninfinite vortex filament-and a plane, there isa unique solution with the symmetry as thatof the problem itself, provided that R (Reynoldsnumber) does not exceed a certain number R 1 , b u tif R exceeds a certain number R 2 >R 1 , there areno such solutions."

COmmenting on this result (and, others) Ladyzhenskaya.noted:

I.

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--.-... -.- .-4."This resultesult only shows that there ceases to exista.so1ution with the symmetry prescribed by theauthor,. starting from the corresponding symmetryof the data of the problem. It -is not knownwhether the problem has an asymmetric solution,but 1 suspect that it does."TherefOre., it would be difficult to conclude analytically - -whether the flow is asymmetric or not. It remains t o b eproven. The symmetry assumed in the problem only m eansthat:the asymmetries, if any, in the flow are assumednegligible. This is particularly true in the sink region,fnotin the pancake region.

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4

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4 7- . 7 1 I., . p l o w- (I)000(jQ )tylI F

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-2 -DESCRIPTION OF APPARATUS

The apparatus was designed foa large number of possiblecombinations of physical dimensions for the sensor. However,the.-investigation to date was confined to the case whereslenderness parameter '1T' is unity; The investigation willbecontinued for other values of this parameter.

The apparatus is shown in the photograph on page ha. Thetest-section of the sensor or simply the chamber is shownschematically in figure 1. The chamber is made of two plexi-glass disks separated by a porous coupling. The lower diskhas--an opening for the sink tube, whereas the upper disk hasattached to it a support to maintain bearing. Both thesedisks have grooves on the inside to allow proper seating ofthe porous coupler concentric to the axis of symmetry of thedisks. Spacers, symmetrically spaced around the entirecircumference, are used to ensure rigidity and uniform separa-tion between the disks. A sink tube, also made of plexiglass,was : rigidly assembled to the lower disk,-in so doing, addedrigidity to the chamber assembly.

The-chamber, supported at the top by a bearing, is freeat--the bottom to rotate within a brass bushing pressfittedto-the manifold assembly. Thus, the chamber is free torotate about its axis of symmetry inside the oil seals,which are also pressfitted to the manifold. The manifold,in.-turn, is regidly fastened to a platform on which also a

A

variable speed drive motor with its speed reducer is mounted.

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4 -3 -The speed-range of the motor after reduction allows a range -of 0 to 35 RPM. A gear pulley moutd on the bottom ofthe sink tube is coupled to the reducer shaft gear pulleyby a gear belt, thus, providing positive drive to the testsection.

Five interchangeable sink tubes with..1/4,3/8, 1/2,3/4 and 1 inch inside diameters a1lowfor variations in thesink tube size. The porous coupler used is similar to theone used by Burke {10}. The many advantages in the use ofthis type of coupler were discussed by Burke.he coupler was made from .0.025 inch thick aluminumrings with an inside diameter of 5 inches. Triangular groovesof 0.0157 inches in width (approximately) and 0.013 inchesin depth were cut radially towards the center of each of therings. Actually, the cut for each groove was made from theinside to the outside in order to leave the resulting micro-burrs on the outside of the ring rather than on the inside.The grooves were cut, side by side, such that on the insidecircumference of the ring, they are continuous, that is,without any flat tops between grooves. On the outsidecircumference, small flat tops formed between the grooves.In all, approximately 1000 such grooves were cut around theperiphery of each ring.

The rings are stacked with the grooved side of one ringagainst the smooth side of the next ring. The stacked ringsare held under compression in the assembly of the sensor

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forming triangular nozzles of O.25 inches in length. Theaggragatejet area was about 26% of:the inside area of the.

coupler. This coupler is practically uniform throughoutits-circumference. These rings,, therefore, can 'be stackedto-:any desired height to a maximum-of 1 inch with the presentapparatus, thus, providing flexibility in the height ofthe coupler.

Another set of these rings .were made, having an insidediameter of 10 inches, to provide a larger coupler. Thenumber of nozzles in this case is approximately 2000 with theaggregate area of the flow remaining the same as before.

To locate probes, in each of the sink tubes, six radialhOles of .062 inches in diameter, at 1/2 inch intervalslengthwise, were drilled through the tube. For convenience,thT-holes were countersunk on the outer circumference of thesink-tube. Due to the probe holders, only 4 of the 6 stationswere accessible for testing. While collecting data at oneof- - these stations, all other stations could be plugged withTfln so that the plugs wereof.-.the sink tube. At each oflength of the tube (hereaftercould be made to traverse theHOwever, since the flow was aprobe traverses were confinedo n l y , ,

flush with the inside surfacethe 4 locations along thecalled stations), the probediameter of the sink tube.ssumed axially symmetric, theto the 'radius of the sink tube

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Two probes, as shown in figure 2, were used; one for -total-or stagnation pressure measurements along the radiusof-'the sink tube, the second for static pressure measure-ments at the same locations.

The stagnation probe is a cylindrical tube (0.062inches outside diameter Monel tubing) with a hole 0.015inches in diameter, drilled for pressure measurements,such that the axis of the drilled hole is normal to theaxis of the tube. This probe could be positioned at any oneof the stations on the sink tube. One end of it is closedand attached to a specially designed holder which has atwofold purpose. The open end of the probe is connectedto tone limb of a U-tube manometer mounted beneath the lowerdisk of the sensor. The manometer, in turn, is open to theatmosphere. The probe holder mentioned above permits one topreset the probe at any desired radius in the sink andsecondly, allows one to rotate the probe at that radiusabout its axis through any desired angle, with respect to avertical reference line marked on the sink tube.

As shown in figure 2, the static probe was also madeof similar tubing as that used for the stagnation probe.One end of it was first closed by welding and the weld wasthen ground uniformly to the shape shown. Static pressurehole of 0.025 inches in diameter was drilled and 1/2 inchdOwnstream of it two pins were welded to support the tubewhen placed in the sink tube. The probe was placed in the

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1 6

sink tube through its exhaust end and was held in .a verticalposition on-the pins by two supporting tubes. These supportubes were inserted on either side o f the static probe throughthe holes on the surface of the sink tube (one level be lowthe station under investigation) thus, forming a cross withthe probe. The end of the support tubes, which were to comein contact with the static probe, had V-grooves to eliminateany relative motion. The other end of the support tubes wereattached to special holders. These holders were so made thatthe desired radial position for the static hole could bepreset relative to the outside surface of the sink tube. Theopen end of the probe was connected to one limb,of the mano-meter exposed to atmosphere.

Filtered and metered air at room temperature (approxi-mately 70F) was supplied to the sensor, th rough the six ( a ttimes four) 'symmetrically spaced inlets of the manifold.The flow meter measures the pressure drop across its element(composed of slots formed froman array of concentric thincylinders in which the gas flows through the annular spaces)which is linearly dependant on the flow rate. The pressuredrop is measured by a sensitive differential pressure gauge.For the case when r 0 = 0.1875 inches and Q = 3.164 cub icfeet per minute, the supply was found to be oscill atory.This may have been due to other d emands on the supply system.The flow rate in this case was adjusted until the maximumand minimum were symmetric about the desired flow rate of'

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3.164 cubic feet per minute. The maximum oscillatorystagnation' pressure was used as reference in determiningthe stagnation angle. This procedure, of course, was verytime consuming. At the stagnation angle, the mean of themaximum and minimum.was taken to be the, stagnation pressure.

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TEST PROCEDUREt each location in the sink flow, the local stagnationressure and the "true helical angle" (to be defined inthe following paragraphs) were measured using the stagnationpressure probe. The corresponding local static pressurewas then measured within a short period of time using thestatic pressure probe. As shown in figure 3, the localmagnitude of the velocity vector was calculated from theseressures and then with the use of the true helical angle,

the local circumferential and axial components of thevelocity were calculated.

The local stagnation pressure was found by monitoringthe probe until the pressure head shown' by the manometerwas a maximum. This, of course, occurs when the axis of thehole (the axis normal to and passing through the center ofthe hole) is coincident with the direction of the localvelocity vector.

The angle the axis of the hole makes with the verticalreference line was defined as the 'local stagnation angle'or the 'local helical angle' (0) of the flow.

In the absence of rotation, the local stagnation anglemeasured at a given radius, at a station available farthestfrom the pancake region (that is, at D.= 2.5 inches) wasdefined, as the 'reference angle' (0) at that radius.

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For a given radius, the angle between the corresponding'reference angle (0) and the local helical angle (0) measuedat any station (any D) was taken as the 'true helical angle'4)) at that radius and D.

There was reason for measuring 0 at every radiusinstead of at the axis of symmetry and D = 2.5 inches, whilechanging the radial location of stagnation hole, the probewas free to rotate relative to the holder though the holderitself was not free to rotate relative to the verticalreference line. Therefore, the angle the axis of the holemade with the vertical reference line could not be heldconstant,thus,, the significance of the previous 0 0 was lostfor the new radius. Consequently, O had to be measuredwhenever the radius of the stagnation hole was changed.

In the absence of rotation, it was, therefore, implicitlyunderstood that far removed from the pancake. region (whereV>>Vr) he pressure head would be a maximum when theaxis of the stagnation hole was aligned in the axial directionand facing the flow. The angle corresponding to this positionwas taken as the reference for the axis of the hole at thatradius.

In the process of calculating the local magnitude ofthe velocity vector from the measured stagnation and staticpressures, it was assumed that the radial component of thevelocity vector was negligible and, therefore, thecorresponding impact pressure could be neglected.

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-It was found that the total pressure head remainedconstant-for as much as 20 degrees rotation of the probeabout the-helical or stagnation angle. Therefore, theelical angle was determined as the mean of the two angles(on either side of the exactly unknown helical angle)here the maximum pressure was found to drop by the same

height (less than .05 centimeters) from the maximum. Theassumption that locally the flc': was uniform, that is, ceimensional in nature justified the above averaging process

for finding the helical angle.These assumptions also justify static pressure

measurements.As the manometer and the probes were mounted on the

chamber, the fluid levels in the manometer could be readwhile the chamber was rotating. A cathetometer was used todo this. Everytirne it was desired to read the level of the:fluid, the telescope on the cathetometer was adjusteduntil the hairline in the telescope was in the plane formedby the rotating fluid level in the manometer. The effectof the centrifugal forces on the manometer fluid wasneglected.

The technique used in obtaining the data is herediscussed for a typical test run.I .he.stagnation probe with its holder preset at adesired radius for the probe hole was placed in the stationat D = 2.5 inches. The open end of the probe was connected

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-1 -to:one:1imbof the manometer.. .The flow of air was startedandincreased until the desired rate was reached. About10:minutes were allowed for the system to reach steadystate. The probe was monitored to find the approximateangu'ir region where the pressure was a maximum, withtheprobe facing the upstream flow. The probe was then16ck6don to the probe holder at one angle in this regionandthe hairline of the telescope was adjusted to thefIid:llevel in the manometer. The probe then was locked,the angle was given an increment towards one side of theprevious angle. The level of the manometer fluid, as.observed through the telescope, was checked to see if therewas zany drop. This procedure was repeated until there wasadef.inite drop in the level of the fluid from the maximumlevel. The corresponding angle,as shown by the protractor onthe-p;obe holder, was recorded.

This procedure was repeated on the other side of thatstarting angle and the angle corresponding to the sameamount--of drop as before was noted. The mean of these twoangles noted was the "reference angle" (6) for thecorresponding radius of the stagnation hole.11. After finding 00, the angle was given an incrementfrom:-0 0 and locked at that position. The motor was thenstarted and its speed was increased until the' chamberattained the desired rate of rotation. About 3 minutes

were allowed for the flow to reach steady state and the

3

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telescopic level was checked to:rnake sure that it was in:.the--plane of the manometer fluid level. Without distrbinthespeed regulator, the motor was stopped and the anglewas--given a further increment and the above process wasrepeated until there was a definite drop in the fluidlevel. The corresponding angle was noted. This procedurewasrepeated for the angles.on the other side of 00 a n dthecorresponding angle was found. The mean of these twoangles was the "local stagnation angle" (0) for thatradius and D. The probe was set at this angle and the levelof--'the-telescope corresponding to the maximum fluid level(hmax) was noted. At this time the atmospheric pressurewas:recorded from a Barometer ( h B ) . The motor was stoppedand the probe tube connected to the manometer was disconnectedwithOut disturbing the manometer. The level of the tele-seope:corresponding to the equilibrium level of the fluidin:.thtwo limbs of the manometer, both now exposed totheatmosphere, was noted (h a ). Therefore, 2 ( hmaxa )wasth stagnation pressure head above the atmospheric pressure.

The stagnation probe was removed with its holder andthstatic pressure probe was inserted through the exhaustend:ofthe sink tube. The static pressure probe was heldon.--.the support pins, by the support tubes and their holders,which were inserted at one level below the level wherestagnation pressure was measured. These holders were alsopreset to the same radial position for static hole as before..

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t-. -3 -Th&EQpen end of the probe was connected to the manometer-by atuhe passing through aslant hole at the bottom of the,--,--,,sink..tube so that the manometer, the probe and the connectingtub:would be free to rotate with the chamber.

The motor was started again and about 3 minutes wereallowed for the system to reach steady state. Then thelevel. corresponding to the static pressure level of the fluidin:the manometer was noted froi the level of the tele-scope-:(h 5 ). The atmospheric pressure (hB) was once againnoted at this time. The motor was then stopped and theconnecting tu be was disconnected without disturbing themanometer. The level of the telescope corresponding. to theequilibriu m level of fluid i n the two limbs of manometerwas:no.ted (h). Therefore, 2 ( h S-ha) was the staticpressure head above the atmospheric pressure.

After reading the stagnation pressure head, it tooklssthn 10 minutes to read the corresponding staticpressure head. It was noted that the atmospheric pressurenever :..changed appreciably within the observed 10 minuteintervals. Thus, without using the atmospheric pressure inth,:calculations, the velocity head was found by subtractingftom:the stagnation pressure head above atmospheric level,th.static pressure head above atmospheric level.III.. Without changi ng the. radius of the probe holes, theprocedure in step II was repeated for all other D'savailable.

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- 2 4 -

IV. The T rate of rotatio n was then changed to another desiredvalue and the procedure in steps I, II and III were repeated,until al l the rates of rotation of interest were completed.Vhe radius of locat ion of stagnat ion and static holeswere changed to a different desired value and the procedure..in all the previous steps were repeated until the data forall radii o f interest were compiled.VI. The above steps in turn were repeated for the secondflow rate of interest.VII. The sensor dimensions were then changed and the abovesteps were repeated. Results, are presented for threegeometrical sizes of sensors, two flow r ates and five ratesof rotation.

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ACCURACY OF RESULTS

Inherently, static pressure is difficult to measureaccurately within 2% error. The acceleration of the flow -around the probe causes the pressure at the hole to fallbelow its value in the absence of the instrument. For theprobe size used, the diameter of thestatic hole was

..considered large compared to the diameter of the probeitself. This causes a further increase in the standard2% error.* Due to the presence of the static pressureterm under the square root sign in the Bernoulli's equation,this accuracy will have an improved effect on the calcula-tion of the magnitude of the local velocity vector. Further,as V 0 = V sin and V 0 = V cos , the error due to static

pressure has little effect on the calculated V 0 because wasfound to be generally small, whereas, on V it will havethe same effect as it had on V itself.

Turning attention to the stagnation probe, the measuredhelical angles were found to be very small for the smallrates of rotation under investigation. This, therefore,substantiates the assumption, not explicitly mentionedthus far, that the probe was not in its own wake.

For the stagnation probe, within the errors of measure-ments, the magnitude of the velocity vector may be erroneousdue to the neglect of Vr, but not the helical angle. How-

* Calibration details are provided in a report submitted to NASA.

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ever, nearithe wall, due to boundary layer effects, gradients of Vrcould.be:lrge. In fact, determination of helical anglesear.:thewalls was found to be difficult in general.

Iii-thabsence of other errors, the effect of theneglected :radial component of velocity on the measuredstatic-pressure, with the probe hole facing the nearestwall,. was:to increase it from the actual value. The effecton: stagnation pressure was to decrease it from the actualvalue. Applying Bernoulli's equation locally, for theactuaLquantities involved,

p==p+..1 PV2r= /2(PoP)gcg cDenotingthe measured quantities and the quantities cal-cuitedfrom them with subscript m,M.:CI..Lt-therrors due to neglecting Vrin various quantitiesberepresented by A.of the corresponding quantities. Fromprevious discussion, it may now be written that

A PS-nd= POM+ tP0(Po-P);(AP pAPO }

Lt:M : th error in V = V - V..Av..f2(POPS) - f2{(Pp_ps)(PpAPc)}

PAs tP 0 and L iP 5re positive quantities, when L iP 0 >LiP,

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MUwillbe positive and, therefre,V > V, whentVwill be negative and, therefore,V < V and when

error in V due to neglecting the contributionb 7 V r On stagnation pressure measurement is compensatedby the error in static pressure measurement.

In view of this, the assumpLion that Vr is negligiblecan:now be relaxed somewhat. Instead, it is now assumedfcir:the validity of the data that the contributions bythe--radial-component of velocity on the stagnation pressureand-'static pressure are the same. It is, however, difficultto---estimate the magnitudes of these contributions.

Stagnation pressure readings were reproducible towithin 5% and the stagnation angle to within 1 degree. Asaresult, the maximum deviation in V 1 as well as V, wouldblss than 5%; whereas, that in V 0 would be dependant onthemagnitude of 4 itself. The accuracy of the flowrneterusedis within 2.5% over its entire range. The leastcount of the cathetometer is 0.1 millimeters.

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DISCUSSION OF RESULTS

The results for the sensor with the sink tubediameter of 0.250 inches are presented in figures 4through 7 for the mass flow rates of.3.164 and 6.328cubic feet per minute of air at standard atmosphericonditions.

, as well as V 0 (not shown in the figures), canbe seen to increase in magnitudes for decreasing flow.rates. It means that the increase ins not due tothe decrease in Q alone, but is also due to the increasein V 0 itself.V 0From these figures with w as parameter,an beseen to increase with decreasing D. This feature is betterseen in the plots for the higher flow rate. For the lowerflow rate, the increase in !Las D decreases, was relativelysmall., .It can also be seen from these figures in a generalmanner that Lincreases with increasing w. The resultsUshow that within the axial region available for testing,

V 0the maximum of - occurs at D = 1 inch. However, it maynot necessarily be the absolute maximum.

In addition, the results strongly substantiate theexistence of a viscous core which rotates almost like arigid body. Y .Q reaches a maximum at the outer' edge ofthe viscous core and it is negligibly small outside of theviscous core. The dimensionless viscous core radius (c.)r0

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29-.is less than 0.04, but it is more likely near 0.02. Thephysical magnitude of r, corresponding to - = 0.02, isr 00.005 inches and f or smaller radii than this it is notpossible to preset the probes accurately enough in orderto establish the viscous core radius exactly.

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r-I-

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V e

t v.z

ve= V sinVz= V cos

COORDINATE SYSTEM

SCHEMATIC DIAGRAM OF REGIONS

1 1 1

FIGURE 3.

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0

0H

---F-------LflH-ILOC)CCN 0H

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1 - 4oU..o x :1pq

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r : L l

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HU0NHz zz

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zH0U )U )N

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zNH

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- 3 7 -

CONCLUSIONS

The purpose of this study was to make accuratemeasurements of the velocities in the sink region of avortex.-sink rate sensor and to determine the factors thatinflencethe fluid motion.

Fora given sensor, one means of increasing V 0 i s' thuse of smaller flow rates. While in actual operation,.however., the flow rate should be large enough in orderthat--differential pressure is of large enough magnitudeto:.b:measured accurately. . The maximum of V 0 seems tooccur:within the entrance region to the sink tube. Thisandtheexistence of the viscous core suggest that the

V 0optimum - occurs within the entrance region and at theouter:edge of the viscous core.

While using differential pressure probes, it isadvisible to measure the diffential pressure across theviscous core diameter.

These conclusions are based on the results from thestudy of the one sensor with slenderness ratio of unityand-'sink tube diameter of 0.250 inches. U pon compilingthresults from the rest of the sensors, more definiteconclusions can be drawn.

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- 38 -

REFERENCES

1... Lewellen, W. S., "Linearized Vortex Flows," AIAAJOurnal., Vol. 3, No. 1, January 1965.

2. Ostrach,. S., and Loper, D. E., "An Anlysis of ConfinedVrtex:Flows," AIAA Paper 66- 68 presented at 3 rd AIAAAerospace Science Meeting, 1966..

..3. Kidd, Jr., G. J., and Farris, G. J., "Potential VortexFIbwAdjacent to a Stationary Surface," J. of AppliedMechanics, June 1968.

4.. Svino.;. J. M., and Keshock, E. G., "ExperimentalPofils of Velocity Components and Radial PressureDistributions in a Short Cylindrical Chamber," Paperpresented at 3rd Fluid Amplification Symposium, 1965.

5.. Lee, .J.D., "An Experimental Study of the Flow in aLOw-Pressure Swirl Chamber," Aerospace ResearchLaboratories, Report ARL 68-0072, April 1968.

6, Srpkya, T. A., "A Theoretical and ExperimentalIv.estigation of the Vortex-Sink Angular Rate Sensor,"Paper , presented at 3rd Fluid Amplification Symposium,1 9 6 5

7:. RakOwsky, E. L., and Schmidlin, A. E., "Fluid VortexPhnomenain F luidic Applications," Design Technology,1966 .or:l967.

8.. Hllbum, R. F., "Flow Studies in a Vortex Rate Sensor," Pesented at 3rd Fluid Amplification Symposium, 1965.

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- 3 9 -

9. Burk, J., and Roffman, G. L.,"A Pickoff Element forn:Angular Rate Sensor," HarryDiamond Laboratories,

Washington 25, D.C.0,. B1rke.J;F;, "Evaluation of a Flueric Angular-RateSnsor:with High Sensitivity" ASME Publication67WAjFE-36, Paper presented at the Winter AnnualMetingand Energy Systems Exposition, November 1967. 11.. Ladyzhenskaya, 0. A., "The Mathematical Theory of

Viscous Incompressib1e Flow," Gordon and Breach, Scond:Printing 1964, Pages 1-7.