Surface roughness effects on the main flow past circular cylinders

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SURFACE ROUGHNESS EFFECTS

ON THE MEAN FLOW

PAST CIRCULAR CYLINDERS

by

Oktay Guven, V. C. Patel, and Cesar Farell

_Vii

LIST OF SYMBOLs _xli

INTRODUCTION _i

BRIEF LITERATURE REVIEW ₃

EXPERIMENTAL EQUIPMENT AND PROCEDURES 8

3.1 Wind tunnel 8

3.2 Circular cylinder models

3.3 Approach flow and Referenöè velocity 15

3.4 Mean pressure dataacqüisition H 18

3.5 Boundary-layer traversing mechanism 23

3.6 Surface rougInesses 23

3.6.1 Distributed roughness 23

3.6.2 Rib roughness ₂₇

REDUCTION AND PBESENTATIOÑ OF DATA 32

4.1 Mean pressure distributions ₃₂

4.1.1 Smooth cylinder pressure distributions 33

4.1.2 Pressure d-istributions with distributed roughness 33

4.1.3 Pressure distributioñs with rib roughness 40

4.1.4 Analysis and suuunary of mean pressure distributión data 46

4.2 Boundary-layer data 67

4.2.1 Cylinder with distributed roughness 67

4.2.2 Cylinders with rib roughiìess 74

4.2.3 Sununary ¿f boundary layer data 108

V. DISCUSSIOÑ OF RESULTS 112

5.1 Effècts of distributed roughness 112

5.1.1 Dräg coefficient 112

5.1.2 Pressure distribution 114

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TABLE OF CONTENTS CONT.

Page

5.2 Effects of rib roughness 126

5.2.1 Drag coefficient 127

5.2.2 Pressure distribution 131

5.2.3 Local effects of ribs 145

5.2.4 Boundary-layer characteristics 152

5.3 Effects of roughness at high Reynölds number 158

5.3.1 Mean pressure distributions 158

5.3.2 Surface roughness and pressure rise to separation - 160

comparison with cooling tower results

5.4 Simulation of high Reynolds-number flows in wind tunnels 162

5.4.1 Reyrioids.number independence 163

5.4.2 Simulation by employing models with larger relative 166

roughness

5.5 Use of externàl ribs, on cooling toser shells 171

VI. SUMMARY 2ND CONCLUSIONS 173

REFERENCES 173

APPENDIX 1. Effects of wind-tunnel blockage 180

APPENDIX 2. Mean-pressure-distr-ibution plots and tables 184

(under separate .cover)

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LIST OF TABLES

able

i?age

3.1. Coimnercial naines of sand paper and roughness characterIstics

25

3.2 Geometrical chracteristics of rib roughnesses

27

Rib roughness confïgurations

28

4.1 Dêterùtinatïon of overall pressure distribution for

45

different rib configurations testéd

4.2 Summary of nìean pressure distribution data;

48

nooth cylinder

4.3 Sununary öf mean pressure distribution data;

49

cylinders with distributed roughness

4.4 _{Suriry of mean pressure ditibution data;}

54

cylinders with ribs

4.5 _{Cylinder with distributedroughness.No:24 boundary-layer data.}

69

Re = 154000.

(Traverse at 1/8 in. above midsection)

4.6 Cylinder with distributed rougbnes.s No:24 boundary-layer

71

data.

Re = 154000.

4.7 Cylinder with distributed roughness No:24 boundary-layer

73

data.

Re = 304000.

4.8 Cylinder with ribs Rl bou dary-layer data.

Re = 152,000.

77

4.9 Cylinder with ribs Rl boundary-layer data.

Re

287,000

79

4 10

Cylinder with ribs R2 boundary-layer data

Re = 118,000

81

4.11 Cylinder with ribs R2 boundary-layer data.

Re = 295,000.

83

4.12 Ciìinders with ribs RB-05 boundary-layer data.

Re = 295,000.

. 85

4.13 Cylinder with ribs RB-b boundary-layer däta.

Re = 295,000.

87

4.14 Cylinder with ribs RA-05 boundary-layer data.

Re

118,000.

89

4.15 Cylinder with ribs RA-05 boundary-layer data.

Re

200,000.

91

4.16 Cylindér with ribs RA-05 boundary-layer data.

Re = 295,000.

.93

4.17 Cylinder with ribs RA-10 boundary-layer data.

Re = 152,000.

96

4.18 Cylinder with ribs RA-10 boundary-layer data.

Re = 295,000.

97

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LIST OF TABLES CONT.

Table _Page

4.19 _{ylinder with ribs RA-20 boundary-layer data.} _{Re =152,000.}

99

4.20 _{Cylinder with ribs RA-20 boundary-layer data.} _{Re = 295,000.} ₁₀₁ 4.21 Cylinder with ribs RC-05 boundary-layer datá. _{Re = 295,000.} ₁₀₃

4.22 _{Cylinder with ribs RC-lO boundary-layer data.} _{Re =295,000.} ₁₀₅

4.23 :Cylinder with ribs RC-20 boundary-layer data. _{Re = 295,000.} ₁₀₇

4.24 Summary of boundary-layer data. Distributed 109

roughness (k/d = 2.66x103).

4.25 Sunmary of boundary-layer data. Cylinders with ribs. 110

5.1 _{Use of external ribs on a cooling tower shell.} _{s/k = 20.} ₁₇₂

(Weisweiler tower: mean diameter d = 52o5 m, diáxnter at

waist = 44.6 m, height _{105.1 m, shell thickness = t = 10 cm).}

A.l Effectsof wind-tunnel blockage. _{Summary of results.} ₁₈₁

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LIST OF FIGURES

Figure . Page

.2.1 _{Drag coefficient (corrected for blockage) of cylinders} 4

with distributed roughness Fage and Warsap (1929)

(thin lines), and Achenbach (1971) (thick lines) results.

After Achenbaóh (1974).

2.2 _{Mean-pressure and skin-friction6distr-jbut.jorj on rough-walled} ₆

circular cylinders, Re= 3,0x10. _{(AfterAchenbach (1971).}

10

3.1 Wind tunnel and cylinder

(Side view - Vertical Centerplane section).

3.2 Test Section and circular cylinder . 11

3.3 Cylinder in the test sectIon - viéw from upstream 13

3 4 Definition sketch and angular distribution of pressure 14 taps at midsection .

3.5 Distributi9n of normalized dynamic pressure. of the approach. 16

flow (y/y) , (V = 51 fps, x/r = -7.91)

3.6 Longitudinal velocity distribution along tuine1 axis 17

(End of contraction is at x/r = -8.80)

37 . _{Longitudinal velocity distribution along a line r/r} _-'3.84 ₁₇

Z/r = -1.74. (End of contraction is at x/r = -8.80)

3.8 Säheme of datà acquisition system for the mean pressure 19 distributions

3.9 Arrangement for calibration f mean-pressure measurement 21

system

3.10 Photographs of mean pressuré data-acquisItion equipment 22

3.11 Boundary-layer traversing mechanism, and cylinder, top view

24

3.12 Photographs of sand pa.pers (Flow is from left th right) 26

3.13 Location of ribs relative to pressure taps fQr the rib 29

conf-igurations R2, RA-05, RA-10 and RA-20

3.14 Sectional view of rIbs for configurations RB-lU, RA-10 and .30

RC-lO

3.15 Close-up view of cylinder with ribs RB-05 31

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LIST OF FIGURES CONT.

viii

Figure

4.1 _{Smooth cylinder}

pressure distributions in the _subcritical

Reynolds number rañge.

4.2 _{Smooth cylinder pressure}

distributions in the critical _range

of Reynolds numbers..

4.3

Smooth cylinder pressure distribution, Re= 4.1x105. - 36 (Spanwise variations in pressure coefficient)

4.4 _{Pressure distributions ón}

cylinder with distributed _roughness; ₃₇

k/d

l59xlQ3.

4.5 _{Pressure distributions on cylinder with distributed}

roughness; 38

k/d = 6.2lxlO3.

4.6 _{Pressure distributions on cylinders with distributed}

roughness. 39

4.7

Pressure distributjon..on cylinder

3.38x103, e _{lO°,first rib at} 4.8 _{Pressure distributjön on òylinder} 3.38x103, O 5°, _{first rib at} 4.9 _{Pressure distribution on cylinder}

3.38xl03, O _{1O, first rib at}

4.10 _{Pressure distribution on cylinder}

3.38x103, M

200, first rib at 4.11 _{Boundary-layer velocity profiles.} k/a 2.66xl03. _{Traverse at 1/8}

4.12 _{Boundary-layer velocity profiles.}

k/d = 2.66x103. _{Re = 154,000.}

4.13 _{Boundary-layer velocity profiles.}

k/d 2.66x103. Re =304,000.

82

4.18 _{Boundary-layer velocity profiles. Ribs}

RB-05.. Re = 295,00Ö. 84

4.19 _{Boundary-layer velocity pofiles. Ribs RB-lb.}

Re = 295,000. 86

4.14 _{Boundary-layer velocity pröfiles. Ribs}

Rl. _{= 152,000.}

4.15 _{Boundary-layer velocity profiles. Ribs}

Rl. = 187,000.

4.16 _{Boundary-layer velOcity profiles..} _R.ths

R2. Re. = 118,000.

4.17 _{Boundary-layer velocity profiles. Ribs.}

R2. Re = 295,000.

with ribs R2 (k/d ₄₁ e = 0) Re =476,000.

with ribs RA-05 (k/d = ₄₂

O ±2.5), Re =-216,000.

with. ribs. RA-10 (k/d = 43

O = ±2.5) Re = 179,000.

with ribs RA-20 (k/d = 44 O = ±12.5) Re = 180,000.

Distributed roughness, 68

in. above midsection. Re=154,000.

Distributed roughness, 70 Distributed roughness, 72 Page 34 35 76 78 80

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LIST 0F FIGURES coÑT.

5.1 _{Drag coeficient of cylinders with distributed roughness.}

(Vàlues corrected for blockage)

5.2 Variation of C ànd C with Re,. and kid as pàrameter.

pb pm

5.3 Variation of O with Ré, and k/d as parameter. Cylinders with

distributed roughness.

5.4 Variation of C - C with Re, and k/d as parameter. Cylinders

with distribut ''

roughness. (Symbols same as in Fig. 5.2) 5.5 Boundary layer on a cylinder with distributed rouqhness (k/d =

2.66x103) at two Reynolds numbers in the supercr-itica:l znqe.

5.6 _{Effect of surfaöe roughness and Reynolds fluer on the boundary-} 121

layer velocity profile at or near the location of minimum pressure

coefficient.

5.7 _{Boundary-layer separatiOn òriterion for à rough-walled circular}

cylinder.

5.8 Variation of C with Re and kid for angular rib spacing of 5°.

5.9 _{Variation of Cd with Re and k/d for angular rib spacing of 10°,} ₁₂₉

5f 10 _{Variation of Cd with Re and k/d for angula} _{rib spacing of 20°.} ₁₃₀

5.11 Variation of c and C with Re and k/d for angular rib spacing 132

.of59. p lLLL

Boundary-layer velocity profiles Ribs RA-05 Re = 118,000

Boundary-layer velocity profiles. Ribs RA-05. Re = 200,000.

Bourdary-layer velocity profïles. Ribs RA05. = 295,000.

Boundary-layer veloöity profiles Ribs RA-10. Re 152,000.

Boundary-layer velocity profiles Ribs RA-10. Re 295,000.

Boundary-layer velocity profiles. Ribs RA-20. Re 152,000.

Boundary-layer velocity profiles. Ribs RA-20. 295, 000

Boundary-layer velocity profiles. Ribs RC-05. = 95,OOÓ.

Boundary-layer velocity profiles. Ribs RC-lÖ. = 295,000.

Boundary-layer velocity profiles. Ribs -20. Ra = 295,000. Figure 4 20 4.21 4.22 4.23 4.24 4.25 4.26 4.27 4.28 I: 4.29 Page 88 90 92 94 96 98 100 102 104 106 113 115 117 118 120 125 128

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5.12 Variation of.0 b

spacing of

5°f

5.17 _{EffeOt of angular}

= l.97x103.

LIST 0F F-IGtiRES' CONT.

Figure

'Page pm'

5.13 Variation of C_pb and C

pm.

with Re and kid för angular rib 134'

pacing of 10°.

5.14 Variation of. - C _{with Re and k/d for angular rib} ₁₃₅

pb pm

spacing of 100.

.5.15 _{Variation of C} _{and C} _{with Re and k/d for angular rib}

136

- pb pm

spacing of 20°.:

5.16 _{Variation of C} _C _{with' Re and. kid for angular rib,}

137

spacing of 200pb . pm

5.18 Effect of angular rib spácing

= 3.38x.I03.

5.19 _{Effect of angular rib spacing on}

= 6.47x103.

with Re änd k/d för ang:u.lar rib ₁₃₃

.rib spacing on C ' ànd C '-. C for k/d 139

d pb pm

on C_d and C = C ....for k/d 140

pb pm

C ' and C_d - C 'for' k/d 141 pb pm

5.20' _{Effect'of rib spacing on C}

b - in the range of Reynolds 143

number independence. p . pm

5.21 _{Local influence of rIbs (adapted from Fig. 4.2 of Liu,} ₁₄₆ Kline, and Johnston (l966))

5.22 _{Local influence of ribs.} _RB-b _{(k/d = 1.97x103, s/k.=} ₁₄₈

44.2)

5.23 _{Local influence of ribs.} _{Comparison of résults for R2 and}

149

RA-10 (k/d 3.38x103, s/k = 25.8), Re = 4.33xl05.

5.24 _{Local influence of ribs.} _{RA-20 (k/d = '3.38x10, .s/k =}

150

51.6) _{Re = 304,000 (Results obtained manually during} böundary layer measurements, Re _{= 295,Ó00, are also shown)}

5.25 _{Local influence of rïbs.} _{RC-lO, RC-20 and RC-40.}

(k/d = 6.47x103)' .

151

5.26 _{Boundary layer on cylinders with'ribs.} _{(Only one rib' is}

'155

shown in (c), and only one rib for each configuration is

shown in Cd)). .' .

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LIST OF FIGURES COT.

Figure Page.

5.27 Boundary-layer velocity profiles near the location 156

of minimum pressure coefficient.

5.27 (ôontinued) 157

5.28 Variation of .0 , C

b and C with k/d at .arge Re. (The 159

value of s/k ishon next

o each. point for cylinders with ribs.)

5.29 Pressure rise to separation, C - C , as a function of . 161 pm

relative roughness, k/d, at. large Reynolds number.

Circular cylinders and hyperbolic cooling towers (The value of s/k is shown next to each point for cylinders

and towers with ribs.)

5.30 Reynolds number independence. . 164

5.31 Drag coefficient and minimum pressuré coefficient as a 1.68 function of roughness Reyncids number V k/v.

A.l Effect of wind-tunnel blockage on C-., C C and

c

_-c

-- d pm pb pb pm

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LIST OF SYQtS

A constant in Equation 5.1

B _{constant in Eqjzation 5.1}

b rib width

drag coefficient _{C = force! (area x 1/2pv2))}

Cf loàal friction coefficient _{C =}

CdR _{drag coefficient of a rib in a turbulent boundary layer} CfR "friction" coeffiôient due to a rib.

Cf _{nooth-wal1 friction coefficient} C _{pressure coefficient} _{( = p-p/pv2)}

Cb

average base-pressure .cpefficient

C _{minimum pressure coefficient}

pm -.

C _{pressure coéffïcient at separation} C _{pressure coefficjet:at O = 180°.}

p,l80

d _{diameter of cylinder, mean diameter of cooling tower}

E _{subscript denoting edge .of boundary layer}

f _{force per unit length} shape factor (*/)

Ht total pressure in the boundary layer relative _{to stätic} pressure of uniform stream

H _{dynamic. pressure of uniform stream}

k rib height, roughness height

i _{span length of cylinder}

p static pressure

p _{static pressure of uniform stream}

P.LOC _{location of boundary-layer traverse plane}

relative to.a rib

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Ap differential pressure

LIST OF SYMBOLS CONT.

Reynolds number ( = V d/v)

o

Reynolds number at which mean presure distiibütjon becomes

independeñt of Re

r cylinder radius

s _{circumferential center-to-center distance between ribs}

s1 _{distance Of first pressure tap downstream from a rib} T subscript denoting laminar-turbulent transition t thiOkness of cooling tower shell

u velocity in boundary layer

velocity at edge of boundary layer

velocity at a póint in a plane upstream öf cylinder average velocity in a plane upstream of cylindér

VA velocity along the tunnel axis upstréam of cylinder at x/r= -6.78

V _{longitudinal cononent of a poténtlal-f].ow velocity upstream} _of

p _cylinder

V longituj _{component of potential-flow velocity upstream of}

p

cylinder at x/r = -7 V00 velocity at infinity

V approach velocity Of uniform stream

w width of wind tunnel test section

x,y,z _{right-handed Cartesian cOordinate system, x along tunnel axis}

positive in downstream direction, z along dylinder axis normal distance from smooth surface of cylinder

nOrmal distánce from top of rouqhness elements

shear stress radient normal to the wáll at separation

AC _{variation of local pressure coefficient from overall} _pressure

p

coefficient

Re

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r

LIST OF SYMBOLS CONT.

I(u/uE) error in U/UE due to local pressure variation angular spacing of ribs

boundary-layer thickness

boundary-layer displacement thickness

e _{meridional angle rnesured fröm the stagnation point} boundary-layer momentum thiákness

angular location of pressüre minimum

O angular location of separation

approximate angle of beginning of wake region

K Karman constant

V kinematic" viscosity

p mass density wall sheár stress

wäll shear stress at locátion of pressure minimum parameter in Equation 5.1 '

W parameter in Equation 5.2

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INTRODUCTION

The work reported here is part of, a wider research program under-taken at the Iowa Institúté of. Hydraulic Research to study the influence

of external surface roughness elements on the charácteritics of méà.n flow past circular cylinders and hyperbolic cooling tower shells. Resülts of experimental investigations of surface roughness effects on the mean pressure distributions on hyperbolic cooling tower models as well as an extensive

literature survey have been reported by Farell and Maisch (1974). Since

there are many similarities between the characteristics of flow past cooling

tower models and circular. cylinders, a more detailed experimental . and

theore-tical study of surface roughness effécts on the flow around circular

cylinders, including mean pressure distrìbutions and boundary-layer

devél-opment., was undertaken as part of this resèarôh program. The experiments

with circular cylinders are described in this report. In addition, a comparison of the essential features of the mean flow past circular oylinders ad cooling towers is made with special atténtion given to the application of present findings for circular cylinders to elücidàte the effects f surface roughness

on cooling-tower pressure distributions. . . .

These stud-ies were prompted largely by a controversy in thé

cooling tower in4ustr' concerning the influence of artificial surface roughness on the mean and fluctuating wind loads on hyperbolic cooling

tower shells. European manufacturers, notably in Germany, claim that thé

wind loads are substantially reduced if the prototypes are roughened extern-ally with vertical ribs or strakes. Their codes of building practice

reflect this claim and result in considerable savings in steel and cOncrete. Some American designers (see, for example, Rogérs and Cohen 1970) favor the use of ribs while others have remained unconvinced about the favorable effects of surface roughness due mainly to a lack of undisputed experimental

or theoretical evidence. Much of the present knowledge on the aerodynamics

of cooling towers has been obtained by means of model tests in wind tunnels at Reynolds ntbers generally two to three orders of maqnitude smaller than prototype Reynolds nÚbers. These model tests have disclosed that external

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2

roughness elements, in the form of either _{uniformly-distributed random-shaped} elements or geometrically regular

configurations of ribs or strakes, signif

i-cantly reduce the magnitudes of the negative pressures on the sides of the models (Niemann 1971, Fare].]. _{and Maisch 1974).}

Such elements are therefore favorable if they can be shown to have a similar effect on prototype

structures. _{Furthermore, experiments with models}

fitted with external roughness elements have produced mean pressure distributions representative of the

much greater Reynolds number flows past smoother-walled prototypes. There

is therefore a possibility of simulating prototype loading conditions _in wind tunnel tests for the _{purposes of experimentally investigating the static} and dynamic response of cooling _{tower shells.}

In view of the foregoing considerations, _{the present research}

program was undertaken with three main objectives: (a) to ôlarify the influence of surface roughness, especially at large Reynolds numbers, and investigate

the feasibility of simulating prototype conditions in wind tunnel experiments;

(b) to determine by means of _{systematic experiments the influence of different}

types, sizes and configurations of _{external roughness elements on the mean} pressure distributions so as to ascertain their relative merits for use on prototype structures; and (c) to identify the physical mechanisms responsible

for the observed roughness effects and _{elucidate the various observations by}

theoretical analysis. _{The experiments on cooling tower models reported by}

Farell and Maisch (1970) have verified that there is indeed a strong

favorable effect of surface roughness on the mean pressure distributions, and that wind-tunnel tests can be used _{to simulate the static wind loading of}

prototype structures. _{Experiments with simple circular cylinders described}

in this report, supplemented by theoretical boundary-layer and potential-flow analyses, to be described in greater detail in a separate report, also confirm these f ìndings. _{These experiments consisted of measurements of mean pressure} distributions, as well as mean velocity profiles in the boundary layers on circular cylinders in a uniform stream in a large low-turbulence wind-tunnel

4 5 .

over a Reynolds number range: 7x10 _{to 5.5x10} . Several sizes of

distributed-type roughness, provided by commercial sand papers, and several sizes and

configurations of ribs, modelled by means of flat wires of rectangular section,

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3

The results of the present study, _{as well as those of sorne other}

recent investigations, also indicate, a close connection between the

character-istics of the bouhdary layer and the mean pressure distributions. Although

the overall effects of distributed and rib roughnesses on the mean pressure distributions are qualitatively similar, there are a number of important differences in the details of the flow due to the local disturbances caused

by the ribs. _{These differences warrant a careful interpretation}

of the

experimental data and reqùiré modification Of the.usuaÏ theoretical treatment of rough-wall boundary layers in order _{to cOnsider rib roughness.} _Atx _attempt is made here to elucidate the basic differences betweeñ the two types of

roughness.

It must be noted that the, mean _{pressure distributions on cylindrical}

structures and hyperbolic cooling towers (as _{well as the statistical}

proper-ties of the. pressure fluctuations) depend not Only on the Reynolds rnmiber and

surface roughness, but also on such factors as the mean velocity distribution and turbulence characteristics of the free _{stream, the presence of other} large structures in the vicinity, and wind-tunnel blockage in the case

model tests (see, _{.g. Farell 1971), and even the span-to-diameter ratio (see,}

e.g. Acheribach 1968). _{Since wind tunnel blockage is of particular}

importance,

a series of experiments wïth a rough-walled circular cylinder _{was also made} in the same wind tunnel to study the influence of the proximity of wind tunnel side walls on the.mêan pressure _{istributions.} _{Thése experiments are described} in Appendix 1 and verify the correction _{procedure proposed by Psh]ço (1961)}

on the basis of the method of 'Allen and Vincenti (1944).

II. BRIEF LITERATURE REVIEW

The first study on thé effects of surface roughness on the flow past circular cylinders was made by Fage and Warsap _(1929). _{In this well}

known work, they measured the drag. coefficieñts' _{of cylinders covered with}

roughness of the distìibuted type over the critical and supercritical

(see Achenbach (1971)) range Of Reynolds numbers. They also studied thé

effects of a pair of generator wires on the pressure distributions and the

effects. of grid-generated turbulence _{on the drag coefficients.}

Partial

accounts of their wOrk caîi also be found in Goldstein _{(1938), and Schlichting}

(1968). _{Fage 'and Warsap found a systematic effect of surface}

roughness on

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1.2 1.0 0.8 Cd 0.6 0.4 0.2 2x104 I

II

0. Re

Figure 2.1: _{Drag coefficient (corrected for blockage)}

of cylinders with distributed roughness.

Fage and Warsap (1929) _{(thin lines), and}

Achenbach (1971) (thick lines) results.

After Achenbach (1971).

I I t I

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5

particular, they attributed the increase of drag coefficient with roughness in the supercritical Reynolds nttÍer range to retardation of the boundary-layer flow by roughness and, hence, earlier separation. They mentioned also

that "It appears,1. .when the surface is very rough the flow around the

relatively large excrescences, and so around the cylinder, is unaffected by _a change in a large valué of the Reynolds number."

It was not unt-il recently that another systematic study was

published on the effécts of roughness on circular cylinders. Aòhenbach (1971)

reported measurements of pressure and skin-friction over a Reynolds number range which extended up to Re = 3x106. His measurements shöwed, among

'i other things, that in the trancritical range the drag côeficient is

inde-pendent of the Reynolds numbér, as suggested earlier by Fage and Warsap, and only a function of the relative roughness kid. This can be seeñ frôm hi results which are reprOduced in F-ig. 21. Furthermore, although detailed

boundary-layer developments were not. measured, his Skin-friction results

showed the close connection between the pressure distributions and the boundary

layer behavioro Fig. 2.2 shows the skin friction and pressure distributions

for k/d = 1 1x103 and 4 5x103 at Re = 3x106 It will be seen that the larger roughness results in greàter'retardation of the boundary layer (hiqher skin friction), earlier separation and a larger magnitude of thé base-pressure

coefficient. It is also of intérest to note here that the pressure

distri-button is affected not only by the locatioñ of separation but also by the boundary-layer development ahead of separation. For example, separation was found to occur at O = 110° for kid = l.1xl03 at Re 4.3xl05 and for kid =

4.5xlO3at Re = 3.0x106 but the pressure distributions,and consequently the drag coefficient,were fOund to be cönsideràbly different. This can be seen from Fig. 10 of Achenbach's original paper and can be attributed to the differences in the boundary-layer development ahead of separation.

A careful examination of Fig. 2.1 shows that there is a remarkable

difference between the results of Acheithach and the eaxlier ones due tO

Fage and Warsap. It would be see that the valués of thé drag coefficient

measured by Fage and Warsap under nearly similar roughness and Reynolds nber conditions are considerably lowér than those of Acherthach in the

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lOOxT

2 w/pV0

1.0

0.0 -1..

0 -2. 6 Static pressure 30 60 90 120 150 180 e

Figure 2.. 2: _{Mean-pressure and skin-friction distribution} _on

rough-walled circular cylinders, Re 3x106. (Af.ter Achenbach (1971)).

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7

C values for both k/dxlO3 = 4 and 7 are much lower than Achenbaôh's

3 ''t'

.5

values for k/dxlO = 4.5, at. Re 2.8x10 . As will be shown later on in

this report, however, the Cd values are. expected to be quite similar for

these roughnesses at such high Reynolds numbers. _{One pOssible reason for}

this discrepancy can be fotind in the expeiirnental _{arrangement of Fage and}

Warsap. _{In their study they used a 40-in.-löng cylinder suspended from} _a

drag balance in à 48-in.-wide test section. Two extension pieces of saine

diameter filled the remaining port-ion of thespan but 1/8-in. _{gaps were left} between the test cylinder and these extension pieces. _{Furthermore the}

span-» to-diameter ratio was 2Q2 or 7.88, depending on the diameter of the two

cylinders they used, as compared to 3.33 in the expetiinents o Achenbach.

Fage and Warsap point out that their results may have been affected by the

gapso _{Indeed,, with such gaps, the wake of the cylinder is supplied with} high presüre flu-id from the front and as a result smaller values of _{Cd are} expected mce the base. pressure is increased over the value it would

other-wise obtain. In addition, it is generally observéd that. values of _{Cd are}

smaller for cylinders with larger span -to-diameter ratio. Both the presence

of the gaps and the larger value of l/d could therefore have resulted in the

lower drag coefficients. n the subcritical range of Re, however, these

effects appear to be negligible. Indeed, Morsbadh (1967) found that in the subcritical range there is no effect Of san-to-dïameter ratio. _{Due to} these uncertainties concerning the experiments of Fage and Warsap further comparisons .ith their results are avoided in this report.

More recently, Batham (1973) has 'reporte6 experiments on the

effects of surface roughness of thé distributed type (k/a. 2.l7xlO3') and

free-stream turbulence on the mean and fluctuating pressure distributions on

circular cylinders at t Reynolds numbers (Re l.11xlO5 and Re = 2. 35x105),

and Szechenzi (1974) has made a study in which he measured steady drag coefficients and unsteady lift coeffiçients of rough walled c'1inders over a range of Reynolds numbers up to Re = 6.5xl06. Both investigators were interested in simulating the pressure distributions at high Reynolds numbers. in particular, Szechenyi (1974) plotted thé drag coefficient against roughness

Reynolds number Vk/v, and suggested that, in the supercritical flow regime,

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values of kid = 1.6x104 to 2x103. (Incidentally, _{this roughness Reynolds} number was also suggested by Armïtt (1968)). _{As will be discussed more fully} later on, however, this observation is at variance with the previous as well

as present findings.

In the foregoing, we have mentioned briefly _{those studies dïrectly} related to the problem at hand; and emphasized the effects of surface rough-ness on the mean flow past circular cylinders. _{A more extensive review of} roughness and other effects on the flow past circular cylinders can be found,

for example, in Farell (1971),. and in the E.S.D.U. (1970) data item.

While the effects of roughness of the distributed type on circular cylinders and the effects of the rib-type _{roughness on cooling towers and} cylinders of finite length have been studied in some detail there is very

little information at'ailable. on the effects of rib-type _{roughness on long}

cylinders (i.e., cylinders without a free end). A comprehensive study of

rib roughness, therefore, forms an important part of the present invest-igation.

III. . EXPERIMENTAL EQUIPMENT PND PROCEDURES

3.1 Wind Tunnel

The experiments were conduôted in thé largest low-turbulence wind tunnel of the Iowa Institute ôf Hydraulic Research. The original 24 ft.-long, 5 ft.-octagönal test section of the tunnel was modified for the present.study, as described below, in order to achieve two-dimensional

flow. _{The turbulence intensity Of the approach flow after the tunnel} modification. was 0..2 percent.

Tests made in the initial, phases of the study with ä smooth

ôylinder mounted vertically in the original octagonal section revealed a rather complex three-dimensional flow pattern on and àround the cylinder. These tests consisted of measurements of the mean pressure distribution on the cylinder, measurements of velocity profiles in the wake at three different elevations, and flow visualization by means of wool tufts. Strong

cross flow ina direction away from the midsection were observed in the

boundary layer of the cylinder. _{The velocity profiles in the wake also}

exhi-bited strong three-dimensionality. _{For example, at a free-stream velocity} öf 70 fps, the velOcity at the tunnel axis 5.07 cylinder diameters behind the cylinder was 51 fps, whereas the velocities at 0.66 diameter above and

(24)

below this point weré both 63fps. _{Some asynétry was also obsered in} the pressure distributions on the cylinder.

In an attempt to eliminate the boundary-layer _{cross flows,}

fences were placed around the cylinder at. levels about i. i cylinder diameters

above and bélow the mi.dsection. _{Meañ pressure distributions obtained with}

i these fences did not show any substantial improvement.

The use of base plates was then attempted. _{Although these reduced the three-dimensionality,} they seemed to affect the approach flow conditions in a complicated manner It appeared that the velocity of the plow between the plates was higher than the velocity above and below _{In order to achieve two-dimensionality and} to eliminate uncertainties about the reference velocity and approaòh flow

conditiozis, it was finally dec±ded to implement _{a major modification of}

the wind-tunnel test section.

The originalj 24 ft. long test section _{was modified as shown in}

Fig. 3.1. _{There is now a 6 ft. long contraction leading}

to a 95 ft. long rectangular test section, followed by _{a 8.5'ft. long diffuser.} _{The present} test section has a width of 5 ft. and _{a height of 32.855 in.} _{The floor and} ceiling o _{the test section intersect the inclined faces of the original} octagonal section as shown in Fig. 3.2.

As a result of the modification, the th±ee-dimensionaiity _induced by the original octagonal section was removed and at the same time the maximum velocity in the test section was increased to about 120 fps from

the original 90 fps. _{Tests carried out after the modification showed that}

the approach flow was uniform across the test _section. _{These tests are}

described in section 3.3.

3.2 _{Circular Cylinder ModelS.}

Two circular cylinders, each with diameter d = 10.65 in., have

been used in this study. _{Two süch cylinders were constructed} _{so as to}

mini-mize delays in data collection while the surface roughness on one of the cylinders ;was.being replaced. _{The cylinders were turned on: a lathe from an} aluminum pipe, 10.75 in. nominal diameter. _{The resulting surface texture was} smooth to the touch and further tests indicated that _{the surface was} hydrody-nainically smooth. _{Fifty-three pressure taps were drilled at the midsection}

of

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Contraction 72.00 in. 46.875 in. Cylinder Flow Direction Axis Test Section Diffuser 114.00 in. 102.00 in. 24 ft. Figure 3.1:

Wind Tunnel and Cylinder (Side View - Vertical Centerplane Section)

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-Cylinder Support Coupling 4.', Il 60.0" 24.855" 10.65" Midsection

-4"

Level -8" Lével

F:igure 3.2: Test Section and Circular Cylinder

Floor 1/8 in. I.D. TYGON Ttthing C4 Lfl ir, 'o '-1 JOint Ceiling 14.5" 4.'9 +8" Level +4" Level -. p.

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12

a total of four levels above and below the midsection at ± 4 in. and ± 8 in. in order to assess the two-dimensionàlity of the flow. The circumferential distribution of the holes at the midsection is given in Fig. 3.4. All

pressure taps had a diameter of 0.040 in., and 1/8 in. inside diameter plastic Tygon tubing was used to transmit the p±éssures to the mean-pressure

measure-ment system described in section 3.4 'below. ..

The cylinders were built in two sections to facilitate the

construc-tion of the pressure taps. The joïnt was 14.5 in. above the midsection and

was sealed with silicone grease. Care was taken to ensure that there was no offset or misalignment öf the two sectjons at the joint. A sketch of

the cylinder and test sectioñ including only the important 'features and

dimen-sions i,s shown in Fig. 3.2. A photograph of the cylinder in the test section

taken from upstream is given in Fig. 3.3.

The blockage ratio, d/w, where d is the cylinder diameter and w

is the wïdth of the. test.section was d/w = 0.178. In the cylinder experiments

of Achenbaöh (1968) and in some of the eperiments'of Fage and Falkner (1931),

the blockage, ratios were 0.166 and 0.185, respectively.

The cylinder axis was located. 46.875 in. from'the end' of the contraction

as shown in Fig. 3.1. The midsection of the cylinder was set at about 1/8 in.

below the horizontal centerplane of.the tunnel. The cylinder was supported at the bottom by a board underneath the working section of the wind tunnel and it could be rotated on this board around its axis. Additional supports were.

provided outside the tunnel floor and ceiling to securely fasten thecylinder after its orientation relative to the oncoming flow was adjusted. During the early phases of this investigation the cylinder was oriented relative to the oncoming flow b' first roughly aligning the O = 00 generator (9 is defined in Fig. 3.4) with the vérticàl centerplane of the tunnel and then rotating the cylinder until the pressure reading at 9 = 0° was maximum. As revealed later by the pressure distribution resüits, this procedure resulted in an

error of the order of ±3°. This is primarily due to the fact that the pressure

distribution close to the stagnation point is not very sensitive to angular

position. (The correct angular positions at the pressure holes relative to

the flow direction are considered and reported in this work.) ' A better

procedure was. followed to orient the cylinder in the later phases of this

study during which' the data with rib roúghnesses were Obtained. The cylinder

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13

(29)

Flow

14

Pressure taps át 50 intervals Pressure tars at 10° intervals

Figure 3.4: Definition Sketch, and Angular Distribution

(30)

15

3.3 Approach Flow and Reference Velocity

Velocity measurements were made with the cylinder in place to check the uniformity of the oncoming flow after the new test seôtion was

installed. Velocity traverses were taken at a section 42.125 in. (3.95d)

upstream from the cylinder axis and the normalized dynamic pressure distri'

bútion (V/)'2 is depicted in Fig. 3.5. Here, denotes the average velocity

at the section, which was 51 fps. Similar measurements with. V 105.64 fps were made by Maisch (1974) 'with a hyperbolic coolïng tower model 'at a section 42.250 in. upstream of the model, axis, and similar results were

obtained. The data show á sufficiently uniform approach velocity distribution.

Iñ addition to the méasurement of approach velocity distribution, two sets of velocity measurements were made in the longitudinal direction to

detérmine the position where the referenòe velocity and pressure. should be measured,: one along the axis of the tunnel (y=0, .z=0), the other along a

line where y/r = -3 84, z/r = -1 74, where (x,y,z) is a right-handed Cartesian

coordinate system, with x along the tunnel axis ïn the flow direction, 'z

along the cylinder axis upwards, and the origin at the horizontal centerplane of the tunnel; and r is the radius of the cylinder. These experiments were also made at an approaôh velocity'of VA = 51 fps wheré VA is the velocity along the t,,,el axis at distance 36.12,5 in. (x/r = -6.78) upstream of

the áylinder axis. The normalized dynamic pressure (V/VA)2 distributions are

shown in Figs. 3.6 and 3.7.. Also included in these figures are the

longi-tudinal velocity' variations (V/V and (V/V72 corresponding to potential

flow, where V is the free-stream velocity 'at infinity, V is the

longitud-inal component of p0tential_f low velocïty, and V7 is the value of V at

x/r = -7. The measurements were ta,ke starting at a point 4.75 in. upstream

from the end of the contraction (x/r. -9.69) and both distributions show

therefore an increase in velocity due to the contraction, f011owed by a plateau from about x/r = -8 0 to x/r = -6 0 A corresponding decrease

or 'increase in velocity is then seen due to the. presence of the model. On

the basis of these results and a comparison with the poténtial-flow velocity distrIbution, it was decided to measure the reference velocity and pressure at a point 7.75 in. downstream from the end of the contraction (x/r -7.34) and 6.825 in. above the test section floor in the tunnel centerplane. This reference velocity will henceforth be denoted by V0, and the, reference

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16

\\

0985

1.0J4.0.998 ,1.009 1.1.006

.

1.006 +1.007i.1.006

.. 1.007 +0.992

+ 1.019

/

+1.013+1.002

1.009 + 0.990

+ 1.007

4.l.0I01.006

1.023 + 0.994

+ 0.995

+ 0.993 +0.999

0.992 + 0.975

_0.995

4.004+0998

_{+ 1.014 +1.007}

1.010 0.999

+ 1.001

0.991 +0.999

+0.991. 0.983

0.987 41.003.1.006 + 1.002 +1.004

+ 1.000

+1.011

+ 0.994 +1.011

+0.993

.

+0.9941.1.016

_{+1.004 +1O15}

+ 1.001

+1.000

_{+1.001 +1.008.}

+1.007

/

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1.05 1.00 0.90 0.80 1.05 '1.00 0.90 0.80 li -10 _-6

x/r e.

Figure 3.7: _{Longitudinal velocity distribution along a line}

y/r = -3.84, z/r = -1.74. (End of contraction

is àt x/r = -8.80.)

-10 -9 -7 -6

x/r

-Figure 3.6: _{Lôngitudinal velocity distribution 'along tunnel axis}

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18

pressure by Po. The reference velocity and pressure were measured by means

of a Prandtl type Pitot-static tube of 0.125 in. oütside diameter in con-junction with a micro-manometer with a precision of 0.001 in. alcohol. The velocity of the approach, flow was constantly monitored for steadiness during

the course of.each experiment. The air temperature in the tunnel and the

temperature in the vïc-inity of the alcohol manometer were also monitored.

These ' together with the barometric pressure and. dry- and wet-bulb

tempera-tures in the laboratory, were. used to determine the approach velocity

and kinematic viscosity V and hence the Reynolds number Re. = V0d/v, in the manner described by Naudascher (1964).

3.4 Mean Pressure Data Acquisition

The. Institute's IBM 1801 Data Acquisition and Control System

was used to obtain the mean pressure dàta. A schematic representation of the overall arrangement is shown in Fig. 3.8. The pressure tubing from the cylinder and the wind-tunnel reference Pitot-static probe were connected

to the terminals of a 48-terminal scanning valve. : The scanning valve was

driven, by a solenoid drive controlled by a solenoid controller. The solnoid

controller can be operated manually or- automatically through the IBM 1801

System. In automatic operation it steps the scanivalve at prescribed time

intervals so that each terminal is scanned in succession and the pressure at

each terminal is fed -to à pressuré transdúcer. The signals from the pressure

transducer are passed through a Model 2850 v-2 DANA a.ntplifïer with a low-- pass filter set at 0.010 kHz bandwidth,and monitored, averaged, and recorded

by the IBM 1801 System. During the experiments, an averaging time of 5

seconds was employed at each terminal and, a. waiting timè of 0.6 seconds was

used to allow for the damping out of transients due to the switching before

thé averaging began. The waiting time was based on- the response of the

set-up to a step input of pressure at a scanivalve termiña.. The time- of rise was found to be about O.3'seôonds. The 5-seconds averaging time was found to be sufficient for the detçrmination of the mean pressures based on

preliminary experiments.

One -of two Stathain PM5TC differential pressure transducers, with ranges of ±0.15 psi and ±0.30 psi, was' used depending on the magnitude of

the approach velocity: the former.giving accurate resúlts for velocities less

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- --Pressure

tubes

from

model

i Scanivalve and

position

¿ transmitter

Scónco

48D3-1/STM

19

TQ pressure transducer

Scanco

DS3-48-24vdc

Solenoid

drive

Scanco

ctLR2/s3

solenoid

controller

IBM 1801

Data Acquisition and

Contröl System

Figure 3.8: Scheme of Data Acqu-is-ition System for the Mean

Pressure Distributions.

Statham

PM5TC

differential

pressure

transducer

i

Amplifier and

bridge-balancing

circuit

(35)

20

The reference lead of the pressure trandider was connected to the wind tunnel statïc pressure through a pressure chamber. Such a chamber was necessary since the dynamic pressure of the approach flow was monitored

constantly during eaòh experiment. A similar chamber was used for the total

pressure, which was connected to one of the scanïvalve terminals. W-ith

this arrangement all the pressures were measured relative to the wind tunnel

reference static pressure p0. The pressure data were finally obtained in

the form of punched cards for subsequent ana1yis on the IBM 360/65 computer. The pressure taps on the cylinder were scanned in sequence in a counter-clockwise manner (see Fig. 3.4), starting from the tap at 9 0, and the

last two terminals of the scanñing välve. were used fOr the .reference total

and static pressures. In most of the experiments, the maximum variation

of the reference dynamic pressure during each test, periOd (about 4.5 minutes)

was less thin ±2%. In the few cases where 'a drift in the wind tunnel speed

was observed"only 'the pressure measurements obtained for the west 'sideof

the,cylinder (negative angles) were considered in subsequent data 'analyses.

If the drift was more than 2%, the ecperiment was discarded altogether. The

cause of the drift was traced to a defective circuit in the servo-control mechanïsm of the wind tunnel drive and periodic maintenance work was necessary

to correct the situation.

Before each series of experiments a static calibration of the

system was obtained by applying known pressures to a scanivalve terminal.

and examining the (typed) output from the IBM 1801. The calibration curve was linear In order to provide the desired calibration pressures, a simple

apparatus was designed which essentially consisted of a flexible U-tube partially filled with water and a small-volume pressure chamber connected

to one end of the U-tube. By moving the' U-tube up or down the desired

pressures were generated in the chamber due to small volume changes of the

trapped air. The overall calibration arrangement is shown in Fig. 3.9. 'A

photograph showing, some. components of the measurement system and the:

calibra-tion apparatus is given in Fig. 3.10. (The boundary-layer traversiíig

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21

Flexible J-tube and Stand

r Alcohol Manòxnetèr

LAPr

Pressure Chamber.

I-r

.aIBM 1801

Scanivalve P. Transducer

Figure 3.9: _{Arrangement for Calibratioñ. of mean-pressure}

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=

A

22

Figure 3.10: Photographs of mean-pressure data-acquisition

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23

3.5 Boundary- Layer Traversing Mechanism

The boundary-layer tötal-pressure and mean-velocity profiles

reported in section 4.2 were obtained by mean s of stagnation tithes made from flattened hypcdermic needles and supported or the traversIng meòhaÁiiSm

described by Patel et al. (1973). _{The essential features of the traversiñg}

mechanism are shown in Pig. 3.11. The mechanism consists of,a rigid rod

mounted on a slide sïtuated outside the tunnel, arid provides the rod with

three different modes of motion in the horizontal àenterplane of the tunnel: -motion along the length of the rod, motion along the slide situated outside

the tunnel, and rotation about a pivot oñ. this slide. The rod enters the

tunnel through a narrow slit out Of the tunnel wáll. The qrtión of the slit

not occupied by the rod. is sealed by a rubber sheet to prevent air leakage.

With this arrangement it is possible tO thke traverses in the direction normal

to the cylinder surface at any desired station between.O 65° and O 120°..

The normal distance from the cylinder Surface can be adjusted and measured from outside the tunnel with a esolution of 0.001 ft. The boundary-layer probe supported by the traversing mechanii was so òonstriicted that méasure-ments were madé in a plane 1 in. above the centerplanê for reasons explained in

sectiOn 4.2. _{The pressure dist±ibútion on the cylinder was not affected by}

the preseñce of the probe. _{The total pressure from thé probe ws measured}

by means of an alcohOl micrO-manometer. -

-3.6 Surface roughriesses

3.6.1 Distribúted roughness:

The distributed surface.rouqhnesses used in this. study were

commercially available s _{paper purohased f:rom the Norton Ço. and the} 3M Co. _{The commercial names of the various kinds of sandpaper used and the} average particle sizes k, as quoted by the manufacturers, are summatized

in Table 3.1.1 Also included in Table 3.1 are the relative roughnesses kid

based On the ooth cylinder diameter d (= 10.65 in.). Closeup photographs of these sandpapers are given in Fig. 3.12.

It should be noted that the value of k are reported differently in (18)

where they were estimated on the basis of the grit numbers Information

(39)

24

Figure 3.11: Boundary-layer traversing mechanism, and cylinder;

(40)

25

The sand paper was carefully wrapped around the cylinder in two

pieces,. leaving a gap of 1/16 in. above and below the center of the pressure

holes at the main measuring section. Double-sticking tape was used to stick the paper with the seam located at the rear of the cylinder. Care was taken to ensure that the paper fit snugly around the cylinder. The.thickness of the various papers, together with the double-sticking tape, varied from about

0.03 in. to about 0.065 in. On account of these small thicknesses, Reynolds

numbers were calculated on the basis of smooth cylinder diameter.

Table 3.1: Commercial names of sand paper and roughness characteristics

Commercial Name Roughness size k (mm) Relative roughness 3 k/dxl0

NOR'ION-ReSiflall, Adalox Paper, 0.430 1.59

Closekote Aluminum Oxide, Grit 40-E

NORTON-Resinall, Adalox Paper, 0.535 1.98

Closekote Aluminum Oxide Grit 36-E

NORTON-Resinall, Durite Cloth, Type 0.720 2.66

3, Closekote Aluminum Oxide, Grit 24-S

3M-Resinite, Floor Surfacing Paper 0.960 3.55

Type F Sheets, Open Coat, Grit 20-3½

3M-Resinall, Floor Surfacing Paper 1.680 6.21

(41)

i i i :1 Norton Co.

_#36

3M Co. #20.

26 i 21 Norton

Co. #40

Norton

Co. #24

3M Co. #12

Figure

3.12:

Photographs of sand papers.

(Flow is from left to right. Scale is in inches)

(42)

3.6.2 Rib roughness

The geometrical characteristics of rectangular wires used to obtain the various rib roughnesses are summarized in Table 3.2. These wires were purchased from the New England Wire Co..

Table 3.2 Geometrical Characteristics of Rib Roughnesses 27

* Height, k, includes thickness of the layer of adhesive of approximately

0.003 in.

The wires were glued along the cylinder (by means of Eastman 910 Adhesive) symmetrically about the leading generator (0=0) at equal angular

spacing 0. Several different configurations thus obtained are summarized in

Table 3.3. Included in Table 3.3 is a rib-roughness configuration code,

together with the corresponding rib type number, relative roughness height, location of the first rib in relation to the leading generator, angular

spacing 0, total number of ribs, and, also circumferencial spacing s,

and spacing ratio s/k. In all cases the ribs spanned the whole length of

a generator, except for the cases with the configuration codes R]., Ril

and P2. In the cases of Rl and R2, a gap of 1/16 in. (total 1/8 in.)

was left above and below the main measuring section, and in the case of Ru the gaps at the angular locations O = ±60, ±70'& ±80°were closed by glueing

additional pieces of wire. The relative locations of the ribs with respect

b

to the pressure taps along the circumference (between 0=-70 and 0=-95), for the rib configurations P2, RA-05, RA-10 and RA-20 are shown in Figure 3.13. Sectional drawings are presented in Fig. 3.14 for further illustration for the rib configurations RA-10, PB-lO and RC-lO. A close-up photograph of the cylinder with the RB-05 rib configuration is given in Fig. 3.15

i 0.021 0.036 1.97 1.71

2 0.036. 0.066 3.38 1.83

3 0.069 0.132 6.47 1.91

Rib Type Height*,k Width, b k/dxl b/k

(43)

Config-. uration Code Rib-type Number

.

Table 33 Rib Roughness Configurations

Circum-.

ferent:ial Spacing s (in)

Spacing Ratio s/k

Relätive Roughness k/dxlO3 First Rib at Angular Spacing 1O Total Number . of Ribs Ri I 1.97 0.0' 10 36 0.929 44.2 Ru R2 RA-05 i 2 2 1.07 3.. 38 . 3.38 0.0, _.0.0 ±2.5' . , iO 10 5 36 36 72 0.929 0.929 0.465 44.2 25.8 12.9 RA-10 2 3.38 ±2.5 lO 36 0.929 25.8 RA-20 2 3.38. ±12.5 20 18 1.859 51.6 RB-OS i 1.97 ±2..5 5 72 0.465 22.1 'w-10 i 1.97 ±2.5 10 36 0.929 44.2 RB-20 i 1.97. ±12.5 20 18

1859

88.5 RC-05 3 6.47 ±2.5 5 72 0.465 6.7 RC-lO 3 6.47 ±2.5 10 36 . 0.929 13.5 RC-20 3 6.47 '±12.5 20 18 1.859 26.9 RC-4o 3 6.47 ±12.5 . 40 . 10 3.718 53.9

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fti

Pressure Tap R2

°U°'U°Ü°

flo.fl

RA-05

oflo

o

(C) RA-10

o

Cd).. RA-20

Figure 3.13: Location of ribs relative to pressuré taps for

rib configurations R2, RA-05, RA-10, and RA-20. 29 .929 in. O66 in. Scale 2:1

fl:

0 1/8

in. .0

o

e= _750

o

-85°

D

(45)

.30 RB-10

r77!?!77

RA-10

RC-lo

-

0.0

0.5 inòh 1.0 I scale

Figure 3.14: Sectional view of ribs for confIgurations RB-b,

(46)

31

(47)

32

IV. REDUCTION AND PRESENTATION OF DATA 4.1 Mean Pressure Distribution

Mean pressure distributions were obtained over a Reynolds number range of 7x104 'to 5.5x105 with the uooth cylinder, with each of the five

different sand papers listed in. Table 3.1, and with each of the rib conf

1g-urations listed in Table 3.3. The detai1edresults of the experiments have

been compiled in a. rather lengthy append-ix (Appendix 2)*to this report. This contains the computer plots and. tables of the variation of the pressure

coefficient C with the angular position O. Iñ theeplots, the data pöints

which belong to east and west sides of the cylinder (positive and negative

angles, respectively) are plotted with différent symbols in order to

illus-trate the symmetry of the mean flow. The pressure coéfficient C is defined

2 p

in the usual Ùanner:. C p - p/½pV, where p is. the pressure on the cylinder

at thé angular position O and p, Po and V are the mass density, static prssure and velocity óf the approach flow respectively. The data reported in Appendix 2 have not been corrected for blockage. The computer plots

were obtained by means of Simplotter, a high level plotting system ('Scranton

'and Màndhester, 1973). Ìi interpolation, mode, whïch made use of a

second-degree Lagrangian interpolation polynomial., wa selected as best suited to

draw curves through the data points for the cases of the smooth cylinder,

cylinders with distributéd roughness. and cylinders with the rib configurations

Rl, Ru and R2. - Due to the nature of the data (see Section 4.1.3), curves

were not drawn for the remainïng rib configurations, and only the data points

were plotted. Data points which were considered to be "bad" were disregarded

in the constructiön of the curves but are shown in the plots and given in

the tables. A "bad" point is one belonging to a pressure tap which consistently

g-ives a result removed from the other points, due. to, for example, a clog in

the measurement system, as revealed-by later ecamination. There was, at most,

one such point in some experiments. For the curves constructed for the

cases of' rib configurations Rl, Ru and R2,. the data points affected by the

local influence of the ribs, discusedtiength later on, were also

disregarded.

Owing to its length, Appendix 2 is produced under separate cover and can be

(48)

33

4.1.1 Smooth cylinder pressure distributions

Typical pressure distributions for the smooth cylinder are presented

in Figures 4.1, 4.2 and 4.3-. Some of the results Of Achenbàch (1968),

Batham (1973), añd Fage and Fàl-knèr (1931) are included in Figures 4.1 and

4.2 fOr òomparison. Except for the results of Batham, the data shown in

these Figures have not been corrected for blockage. There is of coúrse -a

large amount of data reported in the literature for smooth cylinders within the Reynolds-numbers range of this study. The available data are, however,

not cônsistènt, especially in the critiòal and supercritical Reyno1dsnu±nber ranges, due to the differences in the surface texture Of the different

cylinders and alo to the differences -in the free-stream turbulence chàrac-teristics and blockage ratios of differenttunnels. In the present study, it was therefore considered necessary to obtain the smooth cylinder data so. as to establish a useful reference for the effects of roughhèss. At the

saxnè -time, these experiments served to assess the degree of twö-dimensiona-lity

and to verify the experimental set-up and procedures. It òan be seen-from -Fig. 4..3 that the flow over the middle half (8 in, above -axd below -midsection)

of the cylinder is reasonably two-dimeñsional insofar as the pressure

-coefficient is sibstantial1y constant along the span. As ±nd-jcate earlier, -the two diÈensionality of -the mean flow was also verified -by making measurements

of velocity profiles in the wake at severäl spanwise statiOns. -.

4.1.2 Pressure Distributions with Distributed Roughness .Tyicai pressure distributions with distributed roughness,

uncorrected for blockage effects, ae presented in Figurés 4.4, 4.5 and

-4.6 for purposes of a general comparison. Included in Fig. 4.6, are some

results of Achenbac-h (1971) and Bàtham (1973) (the latter inclúde blockage

corrections). -A preliminary examination of these f-igures reveals the influence

of both the surface roughness and Reynolds number on the mean pressure

distri-butions. Detailed discussion of-thése effects and comparison with the

(49)

Figure 4.1:

Smooth Cylinder pressure distributions in the subcritical Reynolds-number range.

-1

-1 S .e 120 80 40 i'

yO

120 160 180 80

.1

I

/

-1 .' II III»

ORe

2.07 ORe = lO5 Re = 1.11 x 10 _(Achenbach, x l0 (present 1968) (Batham, expt.) 1973)

(50)

O Re=3. 57x105 Re=3; 35x105 Re=2,. 39x105 180 160 I

(present experiment) (Fage & FaÏkner,1931:) (Batham, 1973)

Figure 4.2:

Smooth cylinder pressure distributions in the critical range of Reynolds numbers.

f

j

(51)

80 40 1 -3 C £ +8 in. level +4 in. level O Midsection

V

-4 in. level 40 80 I 120 ! I o

-*

Figure 4.3:

Smooth Cylinder Pressure distribution, Re = 4.1 X lOs. (Spanwise Variations in Pressure Coefficient)

160 l8 1.80 )60 120. I I

(52)

Figure 4.4:

Pressure distributions ori cylinder with distributed

roughness

(53)

1 I I I k/d 6.21

D

Re = 0.86 x 10 O Re = 5.16 x lO5 1ÒO 160 120 80 40 Figure 4.5.: Pressure. distributions on

cylinder with distributed roughness

k/d =

(54)

O

k/d = 2.66 x 1O, Re = 2.14 x 10

(present expt)

-kid = 4.5 x 1O, Re = 1.7 x 10 (Achenbach,1971

A kid = 2.17 x iO, Re

= 2.35 x

(Batham, 1973)

Figurè 4.6:

Pressure distributions on circular cylinders with

diétributed

(55)

40

4.1.3 Pressure Distributions with Rib Roughness

The mean pressure distributions obtained with ribs are different in detail from the pressure distribùtions.with distributed _{roughness due to} the local effects of the ribs _{Typical computer plots of pressure}

distri-butions with ribs are. presented in Figures 4.7, 4.8, 4.9 and 4.10. (In

these figures, EAST POINTS and WEST POINTS, belong, respectively, to poitive

and negative values of O).

Figure 4.7 shows the pressure distribution with the rib

configura-tion R2. Recall that in this case the ribs were located at 10-degree

intervals starting from O = 0, and that the ribs had a discontinuity (or gap) of 1/8 in. at the midsection of the cylinder. .Therefore t1e .pressure

readings at the taps located at angular positions.corresponding to integral

multiples of 10 degrees were influenced by the presence of. the discontinuity.

This influence is rather large in the forward portion of the cylinder, but

littlé influence is observed in the wake. region. This particular rib conf

1g-uratiori was chosen with the objectives of determining the pressure doefficients midway between the ribs and observing the srnmletry of the presure distriu-tion at the same time, since most of the pressure taps on the east side of the cylinder (positive angles) were located at 10-degree intervals. No

definite influence of the gaps on the readings of the pressure taps midway

between ribs was detected, however, when the results were compared with the

results of the tests with the rib configuration RA-10, as discussed at length

later on in section 5.2.4. The results of the tests with the rib conf

Igura-tions Rl and Rl]. displayed asimilar influence of the gaps, as can be seen frOm the plots presented in Appendix 2. The influence was smaller in these cases than that observed with the rib configuration R2,due to the smaller

dimensions of the ribs in cases à]. and Ril. It may be noted that the

angular distribution of the ribs was the same in all three cases, but iii the

case of P.11 the gaps at the angular locations ±60°, ±70° and ±80° were closed.

Comparison of the resu.lts of the R]. tests with those of P.11, also showed no

systematic difference in the values of the pressure coefficients midway

between the ribs. .

Figurés 4.8, 4.9 and 4.10 show the pressure distributions for.configura-tions RA-05, RA-10, and RA-20 in which the ribs spanned the entire length of

the cylinder. (i.e. without gaps at the midsectiòn). In configuration RA-05

(56)

0.00 A

D

-e

3.00

6.00

9.00 ANGLE. (DEGREES/lW

CYL.IP«H W RIBSz2

(T. PUlPITS

b(ST POINTS

12.00

15.00

1x10 j

18.00

Figure 4.7:

Pressure distribution on cylinder with ribs R2 (k/d

=

3.38x103,

0=l0°,

first rib at 0=00).

(57)

.

o

. C,,

0.0 I

£

I

L.

30.0

60.0

90.0 ANGLE (DEGREES/lO)

74101S01 ERST POINTS LP(ST POINTS

£

120.0

150.0 L

¡80.0

Figure 4.8:

Pressure distribution on cylinder with ribs RA-05 (k/d =

3.38x103,

O=5°, first rib at O=±2.50).

Re =

(58)

N103102-L

ET POINTS

IST POINTS

£

0.0

30.0

60.0

90.0 ANGLE (DEGREES/lO)

A

Figure 4.9:

Pressure distribution on cylinder with ribs RA-10 (k/a

3.38xl03,

O=l00, first rib a-t O=±2.5°).

Re =

-l.79x105.

120.0

150.0

(59)

£

N110701 ERST POINTS.

£

l(ST POINTS

0.0

30.0

60.0

90.0

120.0 150.0 180.0

ANGLE (DEGREES/tO)

Figure 4.10:

Pressure distribution on cylinder with ribs RA-20

(k/d =

3.38x103,

AO=20°, first rib at O=±25°).

Re =