1

EXPERIMENTS ON THE FLOW PAST A ROTATINGCYLINDER.

By A. Thorn, D.Se., Ph.D., Carnegie Teaching Fellow, Universityof Glasgow.

Communicated by Professor J.D. Cormack.

Reports and Memoranda, No. 1410.(Ac. 531.)

Marcia,1931.

PART 1.

THE FLOW OUTSIDE THE BOUNDARY LAYER.In 1925 the writer made a series of measurements of the direction

and velocity of the air throughout the field about a rotating cylinder.The resulting velocity contours and streamlines were publishedat the time·, but later the data were worked upto give the distributionof vorticity throughout the field. This was found by graphicallydifferentiating the components of the velocity. Fig. 1 shows theobserved air directions and Fig. 2 the vorticity values.

The results of calculating the circulation round various contoursin this field is shown in Fig. 3. It is seen that there is no very markedchange in the circulation outside a contour of about twice thearea of the cylinder section. It will also be seen that there is nocirculation in the wake as a whole. The upper part contains positivevorticity and the lower an equal amount of (more concentrated)negative. This is in accordance with Prandtl's idea that a state ofbalance has been attained in the production of positive and negativeeddying above and below. The circulation corresponding to theactual lift on this cylinder is about 16 ft./sec. The discrepancy isonly apparent as the larger figure obtained in Fig. 3 refers to thecentre section, where the lift is 15-20 per cent. greater than themean as measured on the balance (see R. & M. 1082).

As these experiments gave no information regarding theconditions close to the surface of the cylinder, a series of measure­ments in the boundary layer was made in 1927. These experimentsare described in Parts 2 and 3.

PART 2.

EXPERBlENTS ON THE BOUNDARY LAYER OF ACYLINDER ROTATING IN STILL AIR.

The apparatus used in this experiment was that prepared toinvestigate the boundary layer on a rotating cylinder in an aircurrent (Part 3) and hence the cylinder used (4i in. diameter) was

• "The Aerodynamics 01 the Rotating Cylinder." Institution of Engineersand Shipbuilders in Scotland. 1925.

(7819) 1\

2

mounted in the 2 ft. \\ind channel. Measurements close to thesurface could not be made at the higher rotational speeds due tovibration troubles. A preliminary experiment gave the valuesshown in Table 1. These were obtained by a pitot and static tubemounted 8 mIn. apart so as to be the same distance (11) from thesurface and to be approximately parallel to the tangent. The pitattube was of glass 0·63 rom. outside diameter and the static tubewas aluminium tube flattened till the minor axis of the section(placed normal to the surface) was about 0·5 rom.

The results arc shown plotted in Fig. 4. It will be noticedthat the velocities at corresponding distances are relatively lowerat the higher rotational speeds. In other words, the boundarylayer is thicker at low speeds.

The weakness in the above method of measurement lies ill

obtaining the static pressure. In measurements of velocity inthe boundary layer on a stationary surface it is justifiable toassume the static pressure constant along the normal. As thesurface is approached, the velocity falls so that even if the curvatureis appreciable the centrifugal pressure remains small. When dealingwith the surface layer on a rotating cylinder the static pressuregradient along the normal due to centrifugal force may requireconsideration, since the velocities near the surface are high. Thusthe exact position of the static tube may be important and probablyit should be curved so as to be parallel to the surface.

To get over these difficulties and to get an idea of the magnitudeof the changes in pressure due to centrifugal force, it was decidedto measure the total head only and to calculate the static pressure.This pressure was assumed to be below atmospheric pressure bythe centrifugal pressure of the circulating air outside the pointconsidered and so (reckoning atmospheric pressure zero) at radius'l itis given by

"fv.

P=-e -r dr (1)

"111is expression contains v the quantity sought, thus introducinga difficulty which can be circumvented either by (a) a step-by-stepintegration, or (b) taking an assumed velocity distribution to caJculatethe static pressure and revising the caJculation when the velocityhas been obtained. Method (b) was used outside 5 mm. from thesurface. From 5 mm. inwards the following step-by-step methodwas used;-

At radius '1 let the total head be HI Ibs./sq. ft. and the pressurebe PI' At radius " = 'I - 61' let these quantities be H, andp, = PI - lJp. Then by Bernoulli's equation we have

2v.' ~ -(H. - P.l (2)e

3

and from the centrifugal effect

(VII VI)6'6P: " -+- ­'1 't 2

Hence

2{ "(v" V'J Jv l =- H -p +- -+- 6,: e I: I 2 "1 '.

(3)

(4)

0'

( 6;) 2 v,'V.I 1-~ =-(Ht-PJ + -(), ..

r e '1Thus. if the velocity and pressure are known at any section and

the distribution of tOlal head has been measured. the velocity at asection just inside is found from (4) and the pressure from (2).These give the information necessary for the next" step".

Table 2 shows the results of total head measurements madewith a small glass tube (diameter 0·36 mm.) the rotational speedof the cylinder being 820 T.p.m. A graphical integration of (1) usingthe velocity measurements in Table 1 gave the pressure at n =5mm.as being -0·0089100. per sq. ft.

The results of the step-by-step calculation from n = 5 mm. tothe surface are given in Table 3. It is evident that the pressuregradient, though small, is appreciable.

The velocities are dotted on to Fig. 4 along with those foundusing the somewhat crude pitot and static tubes.

A knowledge of the torque necessary to rotate the cylinderwould enable the eddy viscosity to be found from the velocitygradient. The cylinder used in the present experiment being tooheavy for the balance used previously for torque experiments thiscould not be obtained directly. In R. & M. 1018 the writer gavethe results of some torque experiments on cylinders and spheres.Using the formula and values given there the torque required torotate the cylinder of the present experiment at 820 r.p.ro. is about5·4 X to- 40 ft. too. per ft. length of cylinder.Evidently·

Q = torque = 'btplrl d ~:r)

wherejJ, = coefficient of eddy viscosityl = length of cylinder.

Taking d (qJr)Jdr from a plot of the values found in Table 3,the following values of jA, were obtained :~

•.,-.:..(m_m.:...I-.,-----.,--~~~_._l.~ 0.21 0·4 0·,1,·0· 20 I~~ x 100s)ugs/ft.5ec. __ 0.40] 0·4 0·74 I-g: 2.9,6.2 22

• Lamb, Hydrodynanucs. 5 OOn., p. 556.

(7lI7') WLH!8003'%IU sn 1131 II",. G,71

4

These values are plotted in Fig. 6. The accepted value of thecoefficient of viscosity for air at the temperature of the experimentsis about It = 0·38 X lO-s slugs per ft. second. Thus, close to thecylind~r p, is approximately equal to ,u showing that turbulence isprobably absent.

From n = 0·4 mm. outwards it appears that the turbulenceincreases steadily throughout the region explored.

PART 3.

EXPERIMENTS ON THE BOUNDARY LAYER OF ACYLINDER ROTATING IN AN AIR CURRENT.

As yet, there is no satisfactory theory giving the lift experiencedby a rotating cylinder in an air stream. There seems, however,to be general agreement that the circulation is affected largely bythe eddies generated on the surface. It was accordingly decided toexplore the surface layer. The cylinder used was of brass, 4! ins.diameter. The channel speed throughout was kept at about8 ft. per sec. and the rotational speed at 820 r.p.m., giving a ratio

(Surface Speed)j(Wind Speed) = 2The low rotational speed was adopted to avoid vibration troubles.

To obtain uniformity with previous experiments, the above ratiowas chosen, and this fixed the channel speed.

The method adopted was to measure the total head and thestatic pressure separately, i.e. at different times. The pitot tubewas of glass 0·45 X O·36mm. external measurements at the end.The total head was compared with the pressure in a hole in thechannel wall some distance upwind. The pressure in this hole wasafterwards compared with the pressure on the front generator ofthe cylinder (when stationary) and the total heads recorded in Table 4and plotted in Figs. 7, 8 and 9 are referred to this front generatorpressure R o. The same remarks apply to the static pressure, so thatthe recorded pressure would be zero at a point of zero velocity ifthere were no loss of head.

The apparatus used was identical with that employed for theinvestigation of the boundary layer on a stationary cylinder describedin Part 2. A correction (d H) to the observed total head has beenapplied to allow for the fact that at low speeds a small pitot readshigh. The amount of this correction (see Table 4) may not be reliable,but errors from this source can hardly affect the general results.

Measurements of total head and static pressure were madealong lines normal to the surface at 0 = 0°, 20°, 40°, 60°, 80°, 90°,100°, 120°, 160°, 200°, 240°, 280° and 320° where 0 is measuredfrom the up-wind direction. On the sections at 0 = 240°, 280°and 320° at a short distance from the surface, the velocity changes

5

sign being no longer in the same direction as the velocity of thecylinder surface. This necessitated exploring these sections \"ith thepitot tube in both directions. The results for the tube facing thereverse velocity are given in Table 6 and will be found plotted withthe others in Figs. 7. 8 and 9. At the point on the sections wherethe two directions give the same pressure, the static pressure shouldalso have an identical value, unless the reversal of the tube causes achange in the flow. The agreement is as good as can be expected at0=280°, and 8 = 320°, while at 8 = 240° exploration with thetube in its Donnal position has not been carried far enough.

With the above exception, no attempt has been made to makethe tube face the air direction beyond placing it parallel with thetangent to the surface and this should be kept in mind whenexamining the curves of velocity obtained.

A preliminary estimate of the velocity having been made ateach point on every section, the corrections to the total head wereobtained and applied (see Table 4). The corrected values are shownin Figs. 7. 8 and 9, along with the static pressure. The finallyadopted velocities are given in Table 7, and are shown plotted inFig. 10. It is seen that in most cases the velocity tends to approachthe circumferential velocity of the cylinder as the surface isapproached. Fig. 11 shows contours of constant velocity throughoutthe region explored, the figure being distorted by enlarging theboundary layer in order to show the latter more clearly. In a previouspaper- the writer showed contours of velocity round a rotatingcylinder at the same ratio of circumferential speed to wind speed,namely, 2, but in that case the apparatus used could not be broughtnearer the surface than about O· 7 radius. Fig. 12 has been con­structed by combining the results of the two experiments. Thereis still an annular region not covered by either experiment. Thecontours have been dotted through this region. A few isolatedreadings indicated that these dotted contours are a?proximatelycorrect, but further experiment is required to complete this region.

The velocity curves in Fig. 10 were integrated and the integralcurves used to plot the streamlines shown in Fig. 13.

From the fundamental equations of steady flow we have

a(I 1) a,2 eft C= - OJ! P +2 evt +2eftt + 21' ox

aH a,~ - ay +2~a. (5)

In the present experiment, taking x along the surface and takingthe nonnal value of J.l. for air, 2 ,/J 0 Clox was found to be negligiblecompared to aHI'iJy so that if the flow close to the surface can berepresented by (5) the vorticity is given by

1 aH-2eu By'

• loe. cit.

6

The numerical results obtained by this expression are given inTable 8, and shown as contours in Fig. 14, the sign adopted beingshown on the latter diagrnm. In Part 2, it appears that for acylinder rotating in stiU air, the effective coefficient of viscosityincreases rapidly \\;!h the distance from the surface, so that it ispossible that in the present case the last term in (5) may becomeappreciable. For this reason, the results obtained for the vorticityare Dot above suspicion.

It is interesting to compare the static pressure close to thesurface as obtained by the small static tube with that obtainedby a different method in R. & M. 1082.· This comparison is shownin Fig. 15. Unfortunately, different cylinder diameters were usedin the two experiments. The influence of the channel walls will,of course, depend on the cylinder diameter. and possibly explainsthe differences between the two curves.

TIle writer has elsewhere shown that the circulation round acontour enclosing a rotating cylinder some distance from the surfacecorresponds with the observed lift. Fig. 16 shows how in thepresent experiment the circulation decreases rapidly in the firstmillimeter from the surface and thereafter more slowly as itapproaches Ule value corresponding to the lift .

• R . .t M. t082.-Tbe pressures round a cylinder rotating in an air current.

7

TABLE I.

Velocities near a Cylinder rotating in still ai, as ddermilud by Pilot "'IdStatic Tz~bes.

Diameter of Cylinder = 114 mm. R = 57 mm.

Distance Speed at Pitotfrom q!v= Surface Speed.

surface 100 nfR

" 410 r.p .m.!S20 r.p .m.II,230 r.p.mlz.o60 r.p.mmm. ••..,

0-44 0·76 O·BO 0·72 0·670-70 1·22 0·58 0·51 0·510·97 1·7 0·48 0·41 0-40',20 2·' 0·44 0·40 0·381·82 3·2 0·38 0·33 0·312·46 '·3 0·31 0·283·70 6·5 0·26 0·25,.8(1 8·5 0·26 0·21 0'207·40 12·9 0·28 O' 19 0·17 O' 169·9(} 17 ·3 0·20 O· 14

20·00 35·0 0·18 0·1028·00 SO'O O· 15 0-08

-

TABLE 2.

Total Head near a Cylinder Totating in Still Ai, at S20 T.p.m.

n = Distance of Tube from Surface (mm.).H = Total Head (Ibs. per sq. ft.).

" I H " IH

0·18 O' 191 I . 12 0·0400·28 0·160 ),50 0·0290·32 O· 118 2·30 0-0190·38 0-106 3·47 0·0120·48 0-073 6·15 0·0100·54 0-034 7'8(1 0-{)(}70·66 0·0580·93 0·043

TABLE 3.

Details oj Calculation of Static PrlSS1tre and Velocity mar Cylinder jro"J the ObservatiO'lS of Total Head.

n (mm.) 5-4. 4-3. 3-2. 2-1-5. 1·5-1. 1-0·7. 0'7-0-4. o+-.(). 2. 0·2-0·1. 0- 1-6.

--

r t ft. .. 0·20410 0·20085 0·19760 0·19485 0·19272 0·19109 0·19010 0'18911 0-18844 0·18810

6r ft. .. 0'00325 0·00325 0-00325 0-00163 0-00163 0·00099 0·00099 o.()(){)6<l 0·00033 0·00033

ql it./sec... 3-99 4 ·16 4-43 5· 12 5·77 6·65 7-58 9·3S 13·0 14·93

p.lbs./sq.ft. -0·0089 -0·0095 -o'OJ02 -0·0111 -0·0117 -0·0125 -0·0132 -0·0139 -0·015 -0'015

H,lbs·lsq.ft. 0·011 0-013 0-020 0·028 0·040 0·055 0'090 0·185 O·250?

q. ft./sec... 4·16 4·43 5· 12 5·77 6·65 7·58 9·35 12·96 14 ·93 16·3

p,lbs./sq.ft. -0·0095 -0·0102 -0·0111 -0·0117 -0·0125 -0·0132 -0·0139 -0·015 -0·015 -0·016

00

8 0° 8 ~o

TABLE 4.

9

Measurements of Tolal Htad.

n = Distance from Surface to centre of tube.R = Total Head at small pitat.Ho = Total Head in free stream.

a H = Correction for small pitat.

~ -• Oboe""" H-H. Observed

H-H. 6H lb. per • H-H• 6H H-H.

mm. lb./sq. ft. sq. ft.

Q·18 +0-166 0·006 0-160 0·18 0·127 0·002 Q·1250·32 0·100 0·009 0-091 0·32 0·089 0·003 0·0860·46 0·065 0·009 0·056 0·46 0·066 0-005 0·0610·60 0-046 0·009 0-037 0·60 0·047 0·005 0·0420·75 0·033 0·009 0-046 0·75 0-031 0·006 0·0251. 17 0-014 0-009 0-005 0·89 0'019 0-007 0-0121·6 0·008 0·008 0·000 )·17 0-015 0-008 +0·0072·3 0·002 0'001 0-001 1·6 0·004 0·009 -0·0053·0 0-001 0·000 0·001 2·3 0·006 0·009 -0·003H 0-001 0·000 0-001 3·0 0'001 0·009 -0·0085·8 0-001 0·000 0-001 4·4 0·003 0·009 -0·008

0_60°

o 90o 800

• IOboemd I 6H H-Ho • Observed I 6H IH-H.H-Ho H-Ho

0·18 0-052 0'001 0·051 0-18 -0·053 0 -0·0530·28 0·049 0-001 0-048 0·28 -0·028 0 -0·0280·38 0·044 0-001 0·043 0·38 +0-003 0 +0-0030·59 0-029 0-001 0·028 0·59 0-022 0 0-0220·79 0-016 0-001 0-015 0-79 0·022 0 0·0220·99 0·017 0·001 0-016 0·99 0·023 0 0·0231-40 0·007 0·001 0·006 1·40 0'019 0 0·019I·S 0-007 0·001 0·006 2·2 0·015 0 0·0152·2 0·011 0·001 +0-010 3·2 0·008 0 0·008,. I 0·000 0·001 -0·001 4·3 0·006 0 0·0066·3 0·005 0·002 +0·003 6·3 0·006 0 0·006

- - 0

0·18 -0' 141 0 -0·141 0- IS -0'100 0·001 -0·1010·28 -0·087 0 -0'087 0·28 -0·083 0 -0-0830·38 -0·052 0 -0-052 0·38 -0·055 0 -0·0550-59 -0·012 0 -0·012 0·59 -0·025 0 -0·0250-79 +0·002 0 +0·002 0·79 -0·005 0 -0·0051-20 0·009 0 0·009 '·00 -0-002 0 -0·0022·2 0·005 0 0·005 '·4 +0·001 0 +0·0014·3 0·004 0 0·004 I·S +0·003 0 +0·0036·3 0'005 0 0·005 2·2 -0-001 0 -0·001

4·3 -0·003 0 -0·003

10

TABLE 4--continued.

8 = 1000

0_200

0 ... 240

0'"" 160

8-320

Observed H-HI Observed• H-HI/:;H lb. per • H-HI

/:;H H-HI

mm. sq. ft. mm.

0·18 -0·088 0·001 -0·089 O· 18 -0·097 0·010 ~'I07

0·28 -0·083 0-(1(11 ~'084 0·20 -0·088 0·010 -0·0980·38 -0·082 0·001 -0-083 0·28 -0·085 0-010 -0·0950·59 -0·052 0 -0·032 0·48 -''''80 0·010 -0·0900·79 -0·012 0 -0·012 0·56 -0·060 0·009 -0·0691·20 0·000 0 0·000 0·93 -0·035 0·006 -0·0411·6 +0-003 0 +0-003 )·47 -0·017 0-005 -0-0222·0

+0'003

10 +0·003 H -0'017 0'001 -0·018

H +0·001 0 +0·001 4·2 --0·020 0 -0·0203·0 -0·001 0 -0·001 6·0 -{I·OU 0 -0·021

• •

ooom'di /:;H IH-H·I Observed /:;H H -HIn n H-HIH-HI

O· 18 +0'0761 0·008 4-0·068 0·18 +0-138 0·00-1 +0·1340·27 +0·025 0-010 ·0·015 0-25 +0-102 0·006 0·0960·36 -0·015 0·009 -0'024 0·32 +0-082 0·009 0-0730·54 -0·051 0·009 -0·060 0·46 0·027 ' 0·010 +0-0170·73 -0.0&1 0·009 -0·073 0·60 -0·009 0·010 --0·0191·09 -0·067 0·008 -0·075 0·82 -0·031 0·003 -0·0391·99 --0·052 0·009 -{H)6! 1·6 -0·067 0·002 --0·0693·8 -0·009 0-010 -0·019 3·0 --0·074 0·002 -0·0765·6 +0-003 0-010 -0·007 ... --0·07. 0·002 -0·0767·4 +O·()()4 , 0-010 I --0·006 , 5·8 --0·076 . 0-002 . -0·078

• •

0-18 +0-096 0-007 +0-089 0-18 +0·095 0·009 +0-0860-31 +0-058 0-010 +0-048 0-31 +0-049 0-010 +0-0390-43 +0-032 0-010 +0-022 0-43 +0-025 0·009 +0-0160-56 +0'011 0-010 +0-001 0-56 +0-019 0·009 +0-0100·68 -0·01 I 0·009 -0-020 0·81 -0-028 0-(08 -0-0200-94 -0-033 0·008 -0-041 I- 19 -0-042 0-005 -0·0471- 32 -0-041 0-007 -0-048 1-44 -0-053 0-004 -0-0571·94 -0'053 0·006 -0·059 1-82 -0-051 0-004 -0-055,.. -0-049 0-003 -0·052

3· I -0-054 0-002 -0-056•

0- 18 0-172 0-007 0- 1650-32 0-114 0-010 0-1040-43 0·059 0·009 0-0500-56 0-026 0·008 0·0180·68 +0-008 0-005 +0-0030·'" -0·009 0 -0·0091·32 -0·012 0 -0-0122-6 -0·015 0 -0-015

1l

TABLE 5_

Obseroations ofStatic P,essu,~ neara Rotating C)'linderin anai, stream.

v = 8 ft. per sec. Surface velocity = v = 16 [t. per sec.

Static Static

0 • ",,",ure0 • Pressure

mm_ p-H. mm. p-H,lb. sq. ft. Ib./sq. ft.

0" 0·47 -0·036 120" 0·47 -0·204-2,' -0·037 1·40 -0·2194·2 -0·036 2-4 -0·2636-0 -0'033 3·3 -0·341

4·:! -0·39520° 0·47 -0·145 5· I -0'420

3-3 -0·128 7·5 -0·3906-1 -0'115

160" 0·47 -0·10140" 0·47 -0·295 1'40 -o·1J9

1·40 -0-289 ',2 -0·1284·2 -0·267 7-. -0-1327·. -0-236

I 200' 0·47 -0·08060'

,0·47 -0·436 1·40 -0·0751-40 -0·424 '-2 -0-0734·2 -0-397 7'9 -0·0777-. -0·357

240" 0·41 -0·081SO' 0·47 -0·483 0·75 -0·080

1·40 -0·449 I . 17 -0·0792·4 -0·477 I-BS -0·0813·3 -0'49-1 3-3 -0-0785- I -0·474 '-7 -0-0807-0 ~:H55 7·5 -0·079

90" 0·47 -0'405 280" 0·47 -0·0531·40 -0·375 I . 17 -0·0572-' -0·404 ',7 -0·0573·3 -0·468 8·. -0·054',2 -0·5025- I -0·483 320<> 0·47 -0-0046-0 -0·474 3·3 -0·0067-. -0'456 7·5 -0·008

100" 0·47 -0-3831-40 -0-3392-' -0·3963·3 ....(1,430'·2 -0·4815-1 -0·4877-. -0·453

12

TABLE 6_

Total Head.

Tube Reversed.

(} _ 280"

n Observed H-He ObservedH-H.

6H lb. per nH-H, 6H H-H.mm_

sq. ft.I

0-39 -0-087 0 -0-087 0·46 -0-064 0 -0-0641·17 -0-084 0 -0-084 0·75 -0-065 0 -0-065I-B -0-085 0 -0-085 I -B -0-064 0 -0-0642-3 -0·078 0 -0·078 3-0 -0·061 0 -0·0613-0 -0·082 0 -0·082 4-4 -0'062 0 -0·0624-4 -0·076 0-000 -0'076 5·8 -0·041 0-000 --0·0415-8 -0-075 0·002 -0·077 7-4 -0·019 O' OC)J -0·0197-4 -0·076 0·002 -0·078 10·1 -0·005 0-003 -0·005

{J "'" 320"

~0·39 -0-009 I 0 -0-009

JV0-89 -0-007 0 -0·0071·17 -0·008 0 -0-008t-B +0-002 0·002 0-0002-3 +0·001 0·004 -0·0033-0 +0·008 0·004 +0·0044-4 +0·004 0-004 0-0005·8 +0-004 0·004 0-0007-4 0·000 0·003 -0-003 R<lVcrsro Tubz.

-

13

TABLE 7.

Velocity near Rotating Cylinder in an AiT Stream.

n = distance from surface (mm.).Velocities are given in ft. per sec.

~I 0·2 0·5 1·0 2·0 I 3·0 I 4·0 I 6·0

0° 12·3 B·6 6·3 5·B 5·B 5·B 5·520° 14·9 13·0 11·6 10·7 10·3 10·1 9·640° 17· I 16·7 16·1 15·7 15·5 15-1 14·760° 18· I 19·5 19·4 19· 1 18·8 18·3 17 ·960° 18·2 19·5 19·4 19·9 20·6 20·4 19·990° 16·9 17 ·6 17 ·6 18·1 19·4 20·4 19·9

100° 16·4 16·4 16·8 17·8 IB·8 19·8 -1200 9·6 to·8 11·9 13·8 15·9 17 ·6 18·1160° 11·3 6·9 5·7 7·3 B·S 9·B 10·2200° 13·1 8·6 4·7 2·0 I·B 1·3 + 1·62400 11-5 8·9 5·6 4-1 - - -280° 10·1 7·4 4·5 + 1·7 + 1· 7 0 - 4·03200 11·6 5·1 0 - 2·0 - 2·2 - 2·5 - 2·5

TABLE 8.

Vorticity near Rotating Cylinder in an AiT Stream.

As given by :-

6'04·02·01'00·50·2

0° -2500 -1300 -350 -56 020° -1300 - B56 -160 -20 040° - 60 - 260 -60 -20 - 5 060° +1000 + 250 -10 -20 - 4 060° +1900 - 600 +56 - 10 0 090° + 650 +5&1 + 35 - 4 - 13

100° + 320 + 970 +110 - 8 - 10120° + 350 + 620 +320 0 - 7 -7160° -2600 -1600 +60 +160 +150 0200° -1600 -1700 --800 -200 0 02400 -1400 -1200 -460 -200 - -280° -1500 -1250 --800 - 55320° -2500 -2500 -756 0 0 +70

~I

R.&M.1410.

FIG. J.

EXPERIMENTS 01'< fLow PA5T A RarAl"ING CYLINDER.

5bort Full Uno:,; ,;kow the Ob5Q:rv~d

Air Din:d:ion a.t their Mid - poil"t.

l'Wiphera.1 5p0zd.;. M<zan Tu nrd 5p<ozd - 2

-------=---------=-------- ------------- -----~-- -~ -- ...:::...-=------ ------ ---- --- - --::-- - .~~ - - -~..:::-

~-=:::-;:-(~:)~:::;::-:::~........ ,..--... ,~-.... -- ":::-'---=:---~ // ~ ~ :.-- - - ---/'- + ~ ~~---:_=--- ':\\""X~ -- "-~- \",~ ---- - - .....-.........-------..:::-~-::: ----- -=-.:::-::--=-- - - ---::::-- - ~~- -----------------------~----=-=-----~

-=-=-==---=--=:_=_:::~

----------------------- - ----------=---~

RAM 1410.

FIG. 2.

exPERIMENTS ON FLOW PA5T A RrrATlNG CYLINDER.

y..IUlZS of the Vortidt\l. ~r~x _bu./o':!

d<zdUClZd From I:h<z Ob:'lZrvlZd Vdocil:ilZS.

~ lintZ is Lil"'\~ cF Minimum \kb:::ity.

+1 +1_4 0 _I

•

-,•

.,

.,

.,-5 _.

-I _5

... +7

•-._1 -ll -n!. -..., +... +1

·U +6 -5

" +' -5.'+1 +1 _1 -'I +1 +J +1 _I _I 0 0 .. 6 ...+

,

Circulation:. fur- V~r;ous ~c\::aQgI~~ a~ d~dua:d From thlZ(hyzr-ved VVocit~.

A...... il"Cl.>letionfl;~/:a«.

~l,l&ol"C ee' - ..-0

· .", - "iH'0 A!'I - 1,,·9

Sl:np I - 0-20 , ·.,· • 0

· 4- .'0 • ·.,

0 • - 0'"Rc:ctal"lQlc A 0 - ..,l.P" I'M. rJ strip I .. I·...... 0 0 0 I - \.,Uppo- • 0 · , .. 1·3...... · · , -1<1Uppv • · • • • ••..... 0 0 o • - 0'•

o

A..

T 8

c

I

U 3 4 5 ••

I 2'!

I -. .. -0' r-,

9'/>I

l'..24' -. .

floor of Che.J'V"CI.

"The: dol:tc:d Iinr: i~ 'in~ cR- rninilT"\Um vdocH:y.ihiz' l:eJJule.t:d values of ~ c;rcul",\:;iOf'"'\ an: ur"'\CVta'ln 1:0 ! 0·2

• 5TILL AIR. fiG. 4., R .. ~In of Cylil'\dtr .. 57 ........

8 , no .. Oi.~ fro", s.......f.,cc.

'0q .. Velocity "I: Fbi"'l:., \. v .. Vcooty of Sur-Fttet:.

• , .~ ~.;~;nl' . 0 8tO .. B~ Pi~ot:-SI;,.,t:.ic

• • 12!>O ~ Tubr.>., .0 "'.. .\.• • ----- VAlUd c:&.1a..1eJ:Rd f1-am 1i:hI. Hcaod,

•., (Sa. T..blc ~) '20 ,..."."..,or>i.....

,1+-- t-' -"-,

0,, , , ,

"100 ~Al,ObMr-vJ:ion~ d: Toc.,.) H.od I . I

FIG. 5."".....

eo Cylinch:r r-ol:ab~ in 5bl1 Air.

.,

\"--

0 , , , 8

o·

o

o·

o·

o·

o·

o·

RsM.l410.

C.XPERIMENT5 ON FLOW PA5TA ROTATING CYLINDER. F"'5.4-6

VELOCITY NEAR A CYLINDER ROTATING INqfvo·

o·

'''-.. I

•/'

,/ •

,/./

y .... o.J.p"':'"104n..Oi

0 0" "0 , ,

R.&M.1410.

2 3 4 b e 7Dial:.",nce from r,u,.face (mm.).

EXPERIMENTS ON FLOW ~T A

ROTATI NG CYLINDER. fiG. 7

TOTAL HEAD ANQ STATIC PRESSURE NEARA CYLINDER ROTATING IN AN AIR STREAM.

C> , 8_00

c>' ....... TotAl H""d.0 --'- stilie Pra&U;:tr----C>I0.,

6=200

C> • ...... T.H.0

-(>'~-f----

S.p.__c::

--<>...

1-... T.H-0

... : ·().I l-.e 82400

ff<> J. 5.FL ~- ---~-()3 =il 0,'

T.H.~

ot 0.-

-0-19=60'

-C>

-C>,

-04. 5.p. - -"-~ "-

0"IT.H.

0 /,

-0-' , a-6fl~O'2

--<> /1---..L _s.P. _ ---- --<>0 / --

------

___. iP.'-=_i:;:-=-=_:±_=_=±=---1-1(--

T. H.

-..-..,

-... S.P.

T.H.

I 2 ~ 4 ~ &7n' o;st"""", from surfoce (mm.).

- -- ~--

e =1200

~+...."-,,.::::_:t--=-t=-+---!----I---I

410.

ENTS ON flow Fl'.5T A RoTATING

CYLINDER,EAD AND STATIC PRES5lJRE NEARrn ROTATING IN AN AIR STREAM.

"IOtA1 HeAd.

R.&M. I

EXPERIM

TOTAL HACYLIND

0,'

0F

-01

-1)-2

-0·3

-0 --0'

-<>6

.,.,0~

'0'

-0

-oaN..,"'-a~

01~~

~ 0~

-01

-0 ?"'

-0

-00

In

011\

0 "--<>1

'00

,

o. ,<>1

T.H B-2oo·~

0

5P........---i-- •

'<>1

R&M.l410.

EXPERIMENTS ON FLOW PAST A fiG. 9.

ROTATING CYUNDER,

TOTAL HEAD AND STATIC PRESSURE NEAR A

CYUNDER ROTATING IN AN AIR STREAM

1

e2280•~H.,

,,,,"~-t~~~~F:.':!2f:-.?Jb.' ~--.- --- .- , --

1

'I \;H. el240'

o "-R<v<rsed tub.T~'k

~.J;hA: '" ~-I-~

-<>

o·

7I 2 3 4 !t .6

n.. ·DiMance from 6U....fe.ce ""m~.

I'T.H e!520'1

\ R<v<ro<d b;b< T.')sp'J

,o

o·

-<>'0

R.&M.l410.ExPERIMENT5 ON FLow PAST

A ROTATING CYLINDER.FIG. 10.

~~

"- 24Q"

200"

",'I~ 40"

1\'- 20'

'- 0"

~ ~.

120·

Ii.""'- 160"

"r-~

~5 ","-- _'21!Y0

5 j

o20

1:5

o I 2 ~ 4 ~ 6n.. D~t"nce Fi-om Surf"ace (mmJ

Iklocj~ ......",.. '" C\jlinder l"Otzlti~ in an Ai~ Stream.

Tunnel Iklocit.y - 8 Fl:./:=. Cylinde~ Diam.- 4t in.5urf"ace \klocity -16 Fl./""c. -114 mm

2'20

15

"5o

25

20r;~ 15

~"~ 5'-'.J' 0..,'0 20j 15

.!: 10<l:

R.&M.1410.

FIG. I I.

EXPERIMENTS ON FLOW PAST A

ROTATING CYLINDER

VELOCITY CONTOURS CLOSE TO ROTATING

GYLINDER IN AN AIR 5TREAM.

zoft:;/nc~

.s

R.&MI41O.

EXPERIMENTS ON FLOW PAST

A ROTATING CYLINDER.

fiG. 12.

SKETCH SHOWING DISTRIBUTION OF VELOCITYIN THE NEIGHBOURHOOOOFA CYUNDER ROTATING

IN AN AIR STREAM.

Circul'rlfizrentitJ speed d cylinder. = 2Air stream Velocity.

R.&M.1410.

fia.13.

EXPERIMENTS ON FLOW ~ST

" ROTATING CYLINDER

APPROXIMATE SfREAMLINES CLOSE TO

CYLINDER ROTATING IN AN AIR STREAM.

~-----...,\I

!,,J

RsM,14IQ,

fiG. 14.

EXPERIMENTS ON FLOW PAST A

RoTATING CYLINDER.

'vORTICITY C'ONTOUR5 NEAR CYUND£RROTATING IN AN AIR SfREAM.

o

R.&M.1410.

EXPERIMENTS ON FLOW 8"§T A

ROTATING C'YUNC£R,

,---.-.-.-.--.-.,-.,---,---,----,----,---,---r-,--,-Fi='G~.=15='r.-,•

o 40 80 160 e 2DO 2AO 280 ~20 360

fiG. I€>.CIRCUL.-.TION ROUND CIRCLES AT

VARIOUS DISTANCES """'" SLJRFil>ICE.

2 3 .... 5 6 7

0;-= fh>rn !!Ur"""'" (mmJo

I.I.14

~

,. \. 'vI. Diam.-11·4crn.

{"10

•~• j f--4 .!! C;~ cOn-cspond~ to kL"'72 ~

the Ij ft c:oeffic;ent~ byFI-e~re I Integmtion (Fio.l~).

0 •

,