SURFACE ROUGHNESS EFFECTS

ON THE MEAN FLOW

PAST CIRCULAR CYLINDERS

by

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

Sponsored by

National Science Foundation

Grant No. GK-35795

uHR Report No. 175

Iowa Institute of Hydraulic ResearchThe University of Iowa

Iowa City, Iowa

May 1975

i

ABSTRACT

The effeöts of surface roughness on the mean pressure distribu-

tian and the boundary-layer development on a circular cylinder in a uniform

stream have been investigated experimentally. Five different sizes %of

uniformly-distributed sand-paper roughness and several confïgurations of

rectangular meridional ribs have been tested over a Reynolds-number range4 5 -.

7x10 < Re < 5.5x10 . Measurements were also made on a smooth cylïnder

for comparison.

The experimental results .show a large influence of roughness

size and geometry on the mean pressure distribution as well as on the

boundary-layer development. In general, the effects of rib roughness

are lar to those of distributed roughness. In the case of large

ribs, howevér, rather strong local effects have been..óbserved. Some of

the important results have been examined in the light of boundary-layer

theory and previous data, nd supported by simple theoretical analysis..

In the analysis of .the data, special attentiOn has been gIven

to the variations in the drag coefficient and important pressure-distri-

bution parameters with surface roughness at large Reynolds numbers. When

the Reynolds number exceeds a. certain value, which is determined by the

roughness, the pressure distribution becomes independent of Reyñolds numbèr

and is dictated Only by the roughness geometry.

The present.study indicatés that su.bstantia]. reductions in the

magnitude of the ininimwn pressure coefficient on large cylindrical structures,

such as hyperbolic cooling towers, can be obtained by roughening the external

surface with meridionàl ribs provided the ribs are sufficiently large and.

spaced in an optimum manner. The results also indicate that pressure

distributions On prototypes can be reproduced on scaled models by employing

a proper combination of Reynolds number and surface roughness. 'A modelling

proàedure based on the experimentäl. resülts has been suggested.

A series of experiments was also performed with a rough-walled

cylinder and movable side-walls in the wind tunnel in order to study the

influence of wind-tunnel blockage on the pressure distribution. The results,

described in an Appendix, verify a blockage-correction procedure proposed

previously.

ACKNOWLEDGMENTS

ThIs study was sponsored by the National Science Foundation,

under Grant NO. GK-35795. Support for computer time was provided by the

Graduate College of the' University of Iowa. Proféssor John R. Glover

provided advice and .assistánce in the development of the compúterized mean

pressure data-acquisition system and the associated áomputer programs. Mr.

Federico E. Maisch assisted with some of the ekperiments. Dr. Elmar Achenbach

kindly, provided some of his unpublished experimental data. The experimental

equipment was constructed at the Institute shop ünder Mr. Dale Harris's

supervision. All these are gratefully acknowledged.

li

TABLE OF CONTENTS

Page

LIST op TABLES V

LIST OF FIGURES 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

5.1.3 Boundary-layer characteristics 119

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 - 160comparison 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 166roughness

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)

iv

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 45different rib configurations testéd

4.2 Summary of nìean pressure distribution data; 48nooth cylinder

4.3 Sununary öf mean pressure distribution data; 49cylinders with distributed roughness

4.4 Suriry of mean pressure ditibution data; 54cylinders with ribs

4.5 Cylinder with distributedroughness.No:24 boundary-layer data. 69Re = 154000. (Traverse at 1/8 in. above midsection)

4.6 Cylinder with distributed rougbnes.s No:24 boundary-layer 71data. Re = 154000.

4.7 Cylinder with distributed roughness No:24 boundary-layer 73data. 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

V

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 109roughness (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 atwaist = 44.6 m, height 105.1 m, shell thickness = t = 10 cm).

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

vi

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).

103.1 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 14taps at midsection .

3.5 Distributi9n of normalized dynamic pressure. of the approach. 16flow (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 17Z/r = -1.74. (End of contraction is at x/r = -8.80)

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

3.9 Arrangement for calibration f mean-pressure measurement 21system

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

vii

LIST OF FIGURES CONT.

viii

Figure

4.1 Smooth cylinder pressure distributions in the subcriticalReynolds number rañge.

4.2 Smooth cylinder pressure distributions in the critical rangeof 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; 37k/d l59xlQ3.

4.5 Pressure distributions on cylinder with distributed roughness; 38k/d = 6.2lxlO3.

4.6 Pressure distributions on cylinders with distributed roughness. 39

4.7 Pressure distributjon..on cylinder3.38x103, e lO°,first rib at

4.8 Pressure distributjön on òylinder3.38x103, O 5°, first rib at

4.9 Pressure distribution on cylinder3.38xl03, O 1O, first rib at

4.10 Pressure distribution on cylinder3.38x103, 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 41e = 0) Re =476,000.

with ribs RA-05 (k/d = 42O ±2.5), Re =-216,000.

with. ribs. RA-10 (k/d = 43O = ±2.5) Re = 179,000.

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

Distributed roughness, 68in. above midsection. Re=154,000.

Distributed roughness, 70

Distributed roughness, 72

Page

34

35

76

78

80

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 withdistributed roughness.

5.4 Variation of C - C with Re, and k/d as parameter. Cylinderswith 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- 121layer velocity profile at or near the location of minimum pressurecoefficient.

5.7 Boundary-layer separatiOn òriterion for à rough-walled circularcylinder.

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

5.12 Variation of.0bspacing of 5°f

5.17 EffeOt of angular= l.97x103.

LIST 0F F-IGtiRES' CONT.

Figure'Page

pm'

5.13 Variation of C and C with Re and kid för angular rib 134'pb pm.pacing of 10°.

5.14 Variation of. - C with Re and k/d for angular rib 135pb pmspacing of 100.

.5.15 Variation of C and C with Re and k/d for angular rib 136- pb pmspacing of 20°.:

5.16 Variation of C C with' Re and. kid for angular rib, 137spacing 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 139d pb pm

on C and C = C ....for k/d 140d pb pm

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

5.20' Effect'of rib spacing on Cb

- in the range of Reynolds 143number independence. p . pm

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

5.22 Local influence of ribs. RB-b (k/d = 1.97x103, s/k.= 14844.2)

5.23 Local influence of ribs. Comparison of résults for R2 and 149RA-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 = 15051.6) Re = 304,000 (Results obtained manually duringböundary 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 '155shown in (c), and only one rib for each configuration isshown in Cd)). .' .

X

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 , Cb

and C with k/d at .arge Re. (The 159value of s/k ishon next o each. point for cylinderswith ribs.)

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

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 cylindersand 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 andc -c -

- d pm pbpb pm

182.

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 coefficientpm -.

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 stäticpressure 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

xii

Ap differential pressure

LIST OF SYMBOLS CONT.

Reynolds number ( = V d/v)o

Reynolds number at which mean presure distiibütjon becomesindependeñt 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 ofp cylinder

V longituj component of potential-flow velocity upstream ofp 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 axispositive 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 pressurep coefficient

Re

Re1

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

xiv

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

2

roughness elements, in the form of either uniformly-distributed random-shapedelements 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. Thereis 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-tunnel4 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,

were tested.

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

the drag coefficient as shown in Fig. 2.1, adapted from Achenbach (1971). In

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), andAchenbach (1971) (thick lines) results.After Achenbach (1971).

I I t I

106 4x106

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

supercritical range of Reynolds numbers. For example, Fage and Warsap1s

lOOxT 2w/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 onrough-walled circular cylinders, Re 3x106.(Af.ter Achenbach (1971)).

7

C values for both k/dxlO3 = 4 and 7 are much lower than Achenbaôh's3 ''t' .5values 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,

the drag coefficient is only a function of the roughness Reynolds number for

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

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

each cylinder. Additional préssure taps were provided on one of the cylinders at

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)

IIu1

.tu1

-

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

C4Lflir,

'o'-1

JOint Ceiling

14.5"4. '9

+8" Level

+4" Level-. p.

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

was rotated until the pressure taps at e= ±30° gave the same reading.

13

Figure 3.3: Cylinder in the test section - view from upstream.

Flow

14

Pressure taps át 50 intervals

Pressure tars at 10° intervals

Figure 3.4: Definition Sketch, and Angular Distributionof Pressure Taps at Midsection

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

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 0.9954.004+0998 + 1.014 +1.0071.010 0.999

+ 1.001 0.991

+0.999 +0.991. 0.9830.987

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 /

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 liney/r = -3.84, z/r = -1.74. (End of contractionis àt x/r = -8.80.)

-10 -9 -7 -6x/r -

Figure 3.6: Lôngitudinal velocity distribution 'along tunnel axis(End of contraction is at x/r = -8.80)

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

than about 30 fps' (Re = 167,000). -

--

Pressure

tubesfrommodel

i Scanivalve andposition

¿ transmitterScónco48D3-1/STM

19

TQ pressure transducer

ScancoDS3-48-24vdcSolenoiddrive

ScancoctLR2/s3solenoidcontroller

IBM 1801Data Acquisition and

Contröl System

Figure 3.8: Scheme of Data Acqu-is-ition System for the MeanPressure Distributions.

StathamPM5TCdifferentialpressuretransducer

iAmplifier andbridge-balancingcircuit

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

mechanism described in the next section is also visible in this photograph.)

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

measurement system.

=

A

22

Figure 3.10: Photographs of mean-pressure data-acquisition

equipment.

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 Informationfrom the manufacturers was not available at that time

24

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

top view

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 roughness3

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

Type F Sheets Open Coat, Grit l2-4½

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)

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 respectb

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/kNo. (in) (in)

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

I1.97

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

23.38

±2.5

lO

36

0.929

25.8

RA-20

23.38.

±12.5

20

18

1.859

51.6

RB-OS

i1.97

±2..5

572

0.465

22.1

'w-10

i1.97

±2.5

10

36

0.929

44.2

RB-20

i1.97.

±12.5

20

18

1859

88.5

RC-05

36.47

±2.5

572

0.465

6.7

RC-lO

36.47

±2.5

10

36

.0.929

13.5

RC-20

36.47

'±12.5

20

18

1.859

26.9

RC-4o

36.47

±12.5

.40

.10

3.718

53.9

ftiPressureTap

R2

°U°'U°Ü°flo.fl

RA-05

oflo o

(C) RA-10

o o o 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

oe= _750

o o-85°

D

.30

RB-10

r77!?!77RA-10

RC-lo

- 0.0 0.5 inòh 1.0I

scale

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

RA-10, and RC-lO.

31

Figure 3.15: Close-up view of cylinder with ribs RB-05.

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 defined2

pin 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 -obtained from the Iowa Institute of Hydraulic Researòh upon request.

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

results of other investigations are presented in Chapter V.

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

I /

-1

.'

II

III»

ORe

2.07

ORe = lO5

Re = 1.11

x 10

(Achenbach,

x l0

(present

1968)

(Batham,

expt.)

1973)

ORe=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.

ff

jI

80

40

1

-3C

£ +8 in. level

+4 in. level

OMidsection

V-4 in. level

40

80

I120

!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.

II

Figure 4.4:

Pressure distributions ori cylinder with distributedroughness

k/d = l.59xiO3

1I

II

k/d

6.21

DRe = 0.86 x 10

ORe = 5.16 x

lO5

1ÒO

160

120

80

40

Figure 4.5.:

Pressure. distributions on

cylinder with distributed roughness

k/d =

6.21x103.

Ok/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

roughness.

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

f

0.00

A D

-e

3.00

6.00

9.00

AN

GLE

. (D

EG

RE

ES

/lW

CY

L.I

P«H

W R

IBSz

2(T

. PU

lPIT

Sb(

ST P

OIN

TS

12.0

015

.00

1x10

j18

.00

Figure 4.7:

Pressure distribution on cylinder with ribs R2 (k/d=

3.38x103,

0=l0°,

first rib at 0=00).

Re. = i.76x105.

. o . C,,

0.0

I

£

I

L.

30.0

60.0

90.0

AN

GLE

(D

EG

RE

ES

/lO)

7410

1S01

ER

ST P

OIN

TS

LP(

ST P

OIN

TS

£

120.

015

0.0

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 =

2.16x105.

N103102-

LE

T P

OIN

TS

IST

PO

INT

S

£

£

0.0

30.0

60.0

90.0

AN

GLE

(D

EG

RE

ES

/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.

015

0.0

I8O

..0

£N

1107

01

ER

ST

PO

INT

S.

£l(S

T P

OIN

TS

0.0

30.0

60.0

90.0

120.

015

0.0

180.

0A

NG

LE (

DE

GR

EE

S/tO

)

Figure 4.10:

Pressure distribution on cylinder with ribs RA-20

(k/d =3.38x103,

AO=20°, first rib at O=±25°).

Re =i.80x105.

Configuration Code. Method

45

the préssuré taps are all located midway between the ribs (see Fig. 3.13),

and as seen in Fig. 4.8 the data points show a smooth variation of pressure.

In the cases of RA-10 and RA-20, howevér, the pressure taps are at different

locations relative to the ribs (see Fig 3 13), and as a result, the tap

inediate1y following a rib registers. a lower value of pressure coefficient,

while the one inmtediately before a rib registers a higher value, in compar-

ison with the value expected midway between adjacent ribs. Whilé the

local influence remarked upon earlier fOr the Cases of Rl, P.11 and P.2 may

be attributed to the presence of the at the midsection of the cylinder,

the local influence of ribs displayed in Figures 4.9 and 4.10, where the

ribs span thé whole length of the cylinder, is of a fundamental nature, and

deserves special attention. The available data on this topic are not suf f i-

ciently detailed to enable a quantitative evaluation of the local flow fiéld

to be made at the present time. Consequently, the present study is restricted

to the examination of the effects of rib roughneSs on the overall character-

istics of the mean pressure distributions. The data points which are under

the local influènce of the ribs have therefore been disregarded and further

analysis is based On an overall "avérage" mean pressure distributipn as

determined either by the data points which. are free from the direct local

influénce of ribs r by the expected or measured values of the pressure

coefficient midway between adjacent ribs. The method by which the "average"

mean pressure distributions were determined for each of the rib configurations

is smuuarized in Table 4.1 below. Further discussion of the ratïonale

behind discarding some of the data points :fl Such analysis is givein

section 5.2.3 where the importance of the local influence of ribs is

considered in qreater detail.

Table 4.1 Determination of overall pressure distribution for

different rib configurations tested.

R1,R1,R2 Disregard data point at rib location

RA-05, P3-05, RC-05 Use all data points

PA-lO, P3-10, RC-lO Take the average of the two data points between ribs

to obtain the pressure coefficient midway betwèenribs

46

Table .4.1 Cont.

Configuration Code Method

RB-20 Disregard each data point. immediately after a rib

RA-20 .Disregard data points immediately after and befOre arib

RC-20 Same as for RA-20, except, the average of the Cvalue at 0=8d' and 0=85isused. p

RC-40 ' Disregard 'two data points immediately ai,ter a riband each data point immediately before a rib

ALL Configurations ' Use all data points in the wake region

4..14 Analysis and Summary of Mean. Pressure Distribution Data.

The results of the mean pressure distribution tests are summarized

in Tables 4.2, 4.3, and. 4.4. Included iñ these tables are the values of

Reynolds number, Re; drag coefficient, Cd; pressure coefficient at 0=180°,,

average base-pressure coefficient, Cb; minimum pressure coefficient,

C ; and the différenCe C - C '; 'both uncorrected and corrected for blockage,pm . pb pmcorresponding to each experiment. As indicated 'earlier, the complete results

havé been compiled in Appendix 2 Also included in the tables is the value

of 0'' the approximate location of the beginning of' the wake region. This

is defined as the angIe determined by the point of intersection 'of the tangent

with the contact of the highest order in the region of the pressure rise after

the minimum iñ the overall pressure distribution curve and the parallel to the

O-axis determined by Cpb (Niemann (1971), Farell and Maisch (1974)). The

procedure is illüstr,ated in Figure 5.3 in section 5.1.2.. The tables also

show the values of 0, the angular location of the minimum pressure coefficient.

The drag coefficient is defined in the usual manner and is obtained

from the.mean pressure distribition (the overall mean p±ésüré distribution

in the case of rib roughness) using the formula -

Cd = ½ JC cos O dM

The drag coefficient was calculated by numerical integration usIng the

trapezoidàl rule with a step length of 5 degrees. Actual data values were

47

uséd as far as possiblé. In regions where thé data are more sparsely

spaced, interpolated values were used: the interpolation was linear

in the wake region, and second-order-Lgranqian in the forward region

of the cylinder.

Thé base-pressure coe icient cb is the average of the pressure

coéfficient in the wake region. The value of C180 is included to emphasize

the variation of C iñ the wake region, and also because it is sometimes

quoted in the literature (ég. Bearman (1969),Roshko (1970)) as the basè

pressure.

As indicated in Table 4.3, some of the pressure distributions on

thé cylinder with distributed roughhess exhibited a certain alfloUflt of

asymmetry. In particular, this was observed in three experiments with

k/d 1.59x103 and in one expêrimênt with k/d = l.98x:1&3. It is inter-

esting to nOte here that the asyrnmetzic pressuré distributioñs arise at

the critical Reynolds numbers. Bearman (1969) also ôbserved this feature

on a smooth cylinder at the critical Reynolds number, and has attributed

it tò the asymmetric formation of the so called "laminar-separation and

turbulént-réattachment bubble". Hé alsO cmmented on the difficulty Of

maintaining a stéády tunnel speed under these conditions. Similar problems

were encounteréd in thé present Study during the four experiments referred

to above, ùt since the pressure measurements on the opposite sides of the

cylinder were not made simultaneously, it is nt possible to draw a definitive

conôlusion concerning the orïg-in of the ôbserved asymmetry. Nevérthéléss,

it was found that the pressures in the wake region remained remarkably

constant even under these conditions and thereföré the values of the base-

pressure òoefficient are quoted in Table 4.. 3 Dúe to the asymmetry, howevar,

the table does not show the minimum pressure coefficient.

48

SMOOTH CIRCULAR CYLINDER

K/D= 0.00000

RESULTS CORRECTED FOR BLOCKAGE - SECOND LIÑE

I

EXP. WO. RE. NO. CD CP18O CPB CPM CPB-CPM THW TI-IM

7 3 2 30 1 '.2C'7F 06 1.231 -1.327 -1.303 -1.520 0.217 80. 63.:'.224E 06 1000 -0,592 -0.972 -1,157 00 186

73102306 0.410E 063.427E 06

0352 -0.447 -0.468 -3.130 2,66?'0.314 -0,334 -0,353 -2.806 2.453

130. 83,

73102307 0.463E 060.482e 06

O32i -0.429 -0.467 -3,110 2, 6430.287 -0,321 -0,356 -2.798 2.442

128, 830

73102308 .508E ('6 ').325 -0.467 -0.458 -3.130 2.632 128. 830.52SE 06 C90 -0o355 -0.384 -2.815 .43l

731026 U Jo 155E 060.168E 06

1.311 -1.395 -1.381 -1.580 0, 1991.056 -1.040 -1,025 -1,194 O 169

820 67,

73.026'2 Va2O8E 06 1.222 -1.326 -1,313 -1.550. 0,237 82. 67..225E 06 0.994 -0.993 -0.582 -1.185 0,203

73102604 0.357E 06 0.430 -0.543 -0.566 -3.080 2.514 130. 83..373E 06 0.380 -0.413 -0,434 -2,735 .2.302

73102303 0.307E. 06.,.327F 06

0.869 -1,034 -1.075 -2.250 1.1750.734 -0.794 -0.831 -1,867 1,037

118, .750

74040102 0.244E 06 1.147 -1.230 -1.252 -1.620 0, 368 80. 70.0. 263E °6 0.941 -0,92e -0.941 -1.259 0.317

74040103 0.294E 060.314F 06

0.966 -1Q75 -1.129 -1.770 0,6410.808 -0.816 -0,863 -1.424 00561

105, 70.

74040105 0, 440E 06 0.364 -0.456 -0.476 -.160 2,684 130. 90.00459E 06 0.324 -0,341 -0,355 -2830 2. 471

74040106 0. 563E 060.586E 06

0.336 -0,522 -Oo56L -30300 2,7390.300 -0.405 -0.441 -2.968 2. 528

122. 85,

Table 4.2: Sunary of mean pressure distribution data; smooth cylinder.

49,

RC.U;..R Y1 !NDE0 WITH D.TcI8UTED ROUGHNE:;S N: 12

?c/D= 0.00621

ES'JL CC;R?CED P0 BLOCKAGE - SECOND NE

EXP. NOo RE. ND. CD CPIBO CPB 'P" CPB-CPM THW THM

31 10301. .157 ù 111 -1.452 -1.374 -I80 0.606 97. 730).169F U(. q05 -10 108 -'1.041 -t.56 0.521

31 l0.3J2 0.212: f6 102J8 -1.471 -1.400 -1.97 fl,57Q 96.. 72.0.2Z9L. (t0 (J.B4 -1.12.0 -1,0.59 -104R 0,489

731 10303 0. 31 5F (Ú ,O26 -1.508 -1.421 -1.260 0.539 95. 72.0.341' & o004 1o146 -1.072 -1.523 0.461.

73.1 10304 0.363E 06 10 553 -1.439 0 0.541. 95. 72.1.:U6-1.182-1.084 -1.547 0. 462

73,110305 0.421E 06 1.257 -1.540 -1.451 -2.Hr 0.559 95. 72.0.455E 06 I .08 -1.170 -1.094 '?.571 0.4 78

71 10306 0.421E 06 l..50 -1.533 -lo4.3 -1.970 0.537 95. 72.0.455E 06 .1014 -1.165 -1.080 -1.539 0.459

731 10611 0.433E 06 1.241 -1.493 -1.423 -1.970 0.547 95. 72.').5'22E 06 .1.007 -1 133 -1,073 -1.541 0,468

7 ?0692 )0516E 06 l248 -1.476 -..430 -o96 0.530 95. 72.0.558E 06 loO 12 -10117 -1.071 -1.531 0.453

731 10603 00482E 06 .1.261 -1.542 -1.443 -1.980 0o537 95. 72.%

O 1.021 -1.171 -1.06 -1.545 045972110 801 00 860E 0 1.072 -1.301 -1.256 -1.990 0.734 99. . . .73.

0.923F 05 088ó -0,996 -0957 -1.594 0.63773110303 0.110E 06 1.161 -1.418 -1o347 1o980 0.633 . 97. ' 73.

0.119E 06 0.951 -1.082 -1.021 -1.566 0.54573i0804. )o158E 0&' 1.209 -1.4b0 -1.395 -2.000 0.605 95.. 72.

00171E 06 0.985 -1.110 -1.054 -1.573 0.519

Täble 4.3: Suxnmary of mean pressure distribution data, cylinders with

distributed roughness.

* Asymtietric pressure distribution

Table 4.3: continued

50

CJRC'.iLP CvI.INDER rrH 1)STRIsuTc ROUGHNESÇ NO: 4V

K/0 0.00159

RESULTS CORRECTED FOR BLOCKAGE - SECOND LINE

EXP. NO. RE0 NO, CD CPI8O CPB CPM CP-CPM THW THM

73111401 '.830E 05 1.307 -1455 -1.382 -1.500 0.118 78. 68..9O0F 05 1.953 -1.089 -1.027 -1127 00100

31 11402* )0108E 06 0,954 -0.972 -0.976!.11E 06 0.799 -0.72.7 -0731

73111403* ).1.08.E 06 0.849 -0.994 -1.0050.115E 06 0.719 -0.762 -0.772

731 1.14)4 1.127E 06 0.629 -0.905 -0.881 -2.320 1.439 106. 75.).134E 06 0.545 -0.715 -0.693 -1,989 1.295

73111405 ).156EC.166E

0606

0.881.743

-1.123-0.871

-1.118-0.867

-2.250-1,864

1.1320.998

10.2. 72,

7311 140* 0.114E 06 0.833 -1.025 -0.9989.121E 0 706 -0.792 -0.768

73111501 J.210E 06 .1.045 -1.291 -1.257 -2,100 0.843 100. 72..).225E 06 0.866 -0992 -0962 -'.695 0.733

73111502 ).311E 06 1.138 -1.372 -1.324 -2.030 0,706 97. 72.0.335E 06 0.934 -1.046 -1.005 -1.614 0o609

731x1 53 9o359E 06 1.153 -1421 -1.339 -2.330 0.691 950 72.t)o387E 06 0.945 -1.086 -1.015-16l1 0.595

73111 504 0.4.4E 06 1.177 -1.421 -3.361 -2.020 0.659 950 72..446E 06 0962 -1.082 -1.030 -1.597 0.567

73111505 0.309E 06 1.133 -1.424 -1,327 -2,040 0.713 950 72.9.333E 6 0930 -1.092 -1.008.-1.624 0.615

73111 50 0.309E 06 1.127 -1.422. -1.322 -2.030 0.708 970 2.&.333E 06 0.926 -1,091 -1.005 -1.616 0.611

r.: C! Cv. NJk 4 i. 'R1BUTED RIJGHNE15. NO: 24

J(/D 0.00266

RESULTS CORRECTC F FJJCKPGE CNL' LNE

r:xp. r ,i,Ç.Co 'I O

Table 4.3: continued

51

'D CP18O CP3 CP1 CPB-CPM THW IHM

731 2iU ì0163E 06 ì173 = 1.41)1 -1. 349 -1.931) 0.581 98. 70.00176E Co c'059 -1065 -1.021 -1.520 0.500

7i 20502 ()2'1 4E 06 1203 -1.48e -1.36 -1.900 0.531 910 70.i.221E 1)6 UoS8ú -lo 128 1e033 1.489 0.456

7 31205v 00316E (16 1288 bo5h2 1.461 '1.920 fl0459 950 72.a342E ¿J6. 11)40 10 183 lotS7 -1.488 o391

7312(1504 1)0 304E 'Jó i231 -1.556 -1453 -1.910 0.457 95. 13.1o32 06 '035 -1.1.79 t?9.1 - ,48. 0.390

721 2(1 0o.970,1045

1)5

061.0,7OS60

-1292-u.994

-1.256-0.963

-2.080-1680

0.8240.717

100. 72.

731 20 &2. 0iiiE 16 i1)89 -1.241 -1.236-1971) 0.734 990 7.3.j0I1:3E )6 O899 -u941 -00937 -1.573 0.636

73: 20603 1)13: 06 -22o - 21 -1.920 0.689 98. 73)0141E 1)6 t)877 -c:2 -0.9..7 -1.535 0598

73120604 )143 06 11.04 -1.258 -1.279 -1.930 0.651 98a 72.l54 c6 1)9Q9 -00q54 -0.972 -1.535 0.563

731206(15:.ó5F

1)606

1i93e91).

-1.226-C.928

-1.267-1.880-0.963 .494

0.6130.531

98, 12.

771 20ó6 0154E 0t 1.149 -1263 -1.341 -1.920 0.579 c8. 700)o16ôE 06 0.942 -11)37 -1.018 -1.517 0.499

Table 4.3: continued

52

CIRCULAR CYLIÑOER WITH r !buDR0uGHNS NC: 20K/D= 0.00355

RESULTS CORRECTED FOR B.flC.GE - CDND LIP

EX°. NO. RE. NO. CD CP18O CPB CPM (:P8-CP THw THM

731 23i01 0.980E).105E

C5'

061o)240.851

1.301-1.004

1.213-0.927

2.010-1.621.

0.797ii. 694

97, 72

73123 102 0.119E 06 1.072 2o240 1.256 -..980 0,724 99o. 72.).128E 06 0.886 -0.943 -0.957 -1.585 0.68

73123 10 3 0.133F 06 1.o39 -1.302 -Io266 -1.930 0.664 99. 72.0.143E 06 0.899 -0.994 -0.9(3 -1.538 0.575

73123104 0.146E 06 1.105. - i.79 -1.290 -1.910 0.620 98. 72.0.157E 06 0.910 -1.058' -0.981 -1.5 7 0.536

73123105 ).163E 06 1.146 -1.418 -1.315 -1.920 0.605 98 72.0.176E 06 0.940 -1a085 -096 -1.518 0.522

73 23106 1.163E 06 1.138 -1.385 -1.3.4 -1.960 0.646 . 97. 72.c.175E 06 0.934 -1.058 -0.96 -1,554 0.557

73123107 0.215E 06 1194 -1.422 -1.359 -1.920 0.561 97. 72.').232E 06 0.974 -1.080 -1.026 -1.508 0482

73123108 fl.317E 1)6 1.244 -1.476 -1.405 -1.920 0.515 95. 72.0.343E 06 1.009 -1.118 -1.057 -1.497 0.440

731 23109 0.367E 06 1.252 -1.461 -1o412 -1o910 0.498 95. 72.0.397E 06 1015 -1.103 -1.061 -1.487 0,426

731 23110 0.367E 06 1.266 -1. 542 -1.425 -1.910 0.485 95. 72.0.397E 06 1.025 -1.170 -1.070 -1.484 0.414

73 1.23 0. 317E 0Ó 1.241 -i.496 -1,404 -1920 0.516 .95. 72.!.343E 06 1.007 -1.135 -1.056 -1.498 0.441

731 23112 0. 190E 06 1.1.71 1.389 1.345 1.960 0.615 7. 72o).205E 06 0.958 -1.055 -1.018 -1.547 0.529

74010201 0.415E0.449E

0606

1.257ì..018

-1.496-1.132

-1.413-1.061

-1.890-1.469

0.477004.08

95, 72.

* Asyetric pressure distribution

Table 4.3: continued

.53

C!RCUL CY. tL'ER WiTH OYSTiBUED 1UGHNE NC: 36

K/D 0.00198

SEJL' C1)PREC1ED FC1F - SEflND LINE

¿:xP. t\a. RE. NU. CD CP1.80 CPB CPM . CPB-CPM THW TH

I

74010701 0.194E. 06 1.062 -1.302 -1,255 -2,010 0.755 98. 72.0.203E 06 0,879 -0,999 -00958 -1.613 0.655

74c.07Q' ).27E0.233E

0606

10930.901

-1.21-1.010

l,286-0.980

..99O-1,589

0.7040. 610

98, 72o

74010704 0.252E3.271E

0606

1.1280o927

-1G390-1.064

-1.33-0,997

-.970-1.564

0,6570.567.

98, 7?.

74010705 0.321E),346E

0606

1,1770.962

-1.420-1.081

=1.357-1.07

-1,950-.o57

0. 5930.510

98, 72.

74010706 ).322E1.347E

0606

1.1730,959

-1,453-.1.110

-1.35-1,029

-1c80-1,564

0, 6210. 534

98 72,

7401 07C8 J.36.5E 06 1.184 -1,418 -1.367 -1.940 0. 573 97. 72.0.394E 06 0.967 -1,078 1o0'4 -1.527 0,492

74010709 0.427E 06. 1.221. -1.477 -1.403 -1.950 0. 547 950 72.0.461E 06 00993 = 1.122 -1.059 -1.528 0.469

7401.0710 't ,_,z 1.216 - 1,463 -1,394 -1,960 056ó 95. 72.¿3.459E 06 0,990 - 1.111 -1,052 -1,537 0,485

7401071 i 0.176E 06 1,023 - 1o.c34 -1.98 0,757 99. 72.0.189E 06 0,850 -0,946 -0.936 -1.556 0.65.9

74010712 0.158E0.169E

0606

0.9940,829

-1,150-0.877

-1.197-0.918

-1,990-1,611

0.7930.692

100. 72,

74010713 3.l42'00 152E

0606

0.9660.808

-1,235-0.956

-10176-0,904

-2,030-1,65.2

0,8540.747

100, 72e.

74011714 0.129E 06 0,936 -1,163 1o164 -2,080 (3.916 100 72o0.138E 06 0,785 -0.898 -0899 -1.702 0.804

74r,i715 1.116Et), 123E

0606

0,8680.733

-1,098-0.851

-1.. 110

-0.862-2.190-1,815

1.1800.953

102, 72.

7401071 6 0.108E Oô 0,69.5 -0,924 -0,939 -2,200 1. 261 107. 75.OoIi4E 06 0,598 -Oo?22 -0,736 -1,865 1.129

74010717 Oo 970E0.102E

05Ó6

0,6250.542

-0.922-0.7.31

-0,885-0.657

-2,350-2,017

1.4651.319

11.2. 77,

74010118 0.850E0, 9. 8E

0505

1,2fl0,986

-1.296-0,969

-1.288-0.962

-1.430-1,084

0 1420.122

72, 67.

74010801 c.860E 05 1.133 -1.125 -1.181 -1.290 0, 109 72 65o0, 926E 05 0.930 -0.834 -0.882 -0.976 0.094

74') 10 80 2 0.900E 05 1,157 -1.196 -1.2.30 -1.380 0.150 72. 62.0.970E 05 0,948 -0.892 -0,921 -1.050 0. 125

74010803* 0.980E 05 0,847 -0.922 -0.9370.104E 06 0,717 -0.699 -0.712

74010804 0.161E3.172E

0606

1.01.50,844

-1.306-1.010

-1.216-0,9.31

-2.030-1,641

0,8140.709

98, 72,

54

CJ.i1 fr CYLNDE. WFH RIBS lU

t</D=.. 0.00197

E'SUL..î. C:iRSC EC R bLOCKAGE. SECOND LÑE

Table 4.4: Sunutiary of mean pressure distribution data; cylinders with

ribs.

cxp. N0 L'E, NO. C.D CP180 CPB CPM rp-(p THW THM

74050601 0. 1 80E. 06 0.776 -O.99.50o987 2,200 1.213 105. 77.0.191E 06 0.662 -0774 -0.767 -1.84.5 1.079

74050602 0.168E 06 0.738 -0,940 -0.953 -2.160 1.207. 105. 7500. 178E 06 0,632 -0.730-0.742 -1.819 1.077

740 50603 0.152E 06 0,695 -0.910 -0.913 -2.200 1.287 107. 78.0. !61F 06 0.598 -OolIO -0.713 -1,865 1.152

740506 i) 4 0. 152 06 0.696 -0.9.07 -0,914 -2.300 1.386 107. 7700. 16..E 06 0.599 -0.707 -0.713. -1.954 1,241

740 50605 0.137E 06 3.667 -0.886 -0.887 -2,300 i413 107. 78.0 145E 06 0,575 0.692 0.693 1o9.6l 1. 263

.74050606 00 1.1 9E

0. 125E0606

0.6300,546

-0.870-0.868-0,633 -0.6.8.1

-2.360-2.024

1.492 .

1.343107. 78,

74050607 0.119E 06 0.614 -0.831 -O,85O -2,360 1.510 107. 80.0.125E 06 0.533 -0.0 -0,667 -2029 1.361

74050608 0.107E 06 0.5.86 -0,829 -0.846 -2.530 1.68'i 108. 80.0 113E 06 0510 -0,652 -0.668 -2.189 1 521

74050605 0.100E 06 0,584 -0o829 -0,8i6 -2.550 1.714 110. 80.0.105E 06 0.508 -0.653 -0.659 -2.208 1549

74050610 0.921E )5 0.575 -0.783 -0.81.3 -2.690 1,877 112. 85.0.968E 05 0.501 -0.612 -0640 -2,337 1.697

7405061 1. 0.704E 05 0,865 -0,995 -0.990 -1.600 0,610 lOO. 7009.749E 05 0.731 -0.761-0.756 -1295 0.538

74050612 0. 704E 05 1.015 -1.059 -1.l0 -1.620 0.490 104. 75.0, 75 4E 05 0.844 -0,795 -0.856 -1,284 0.427

74050401 .0. 178E 06 0.736 -0.907 -0.927 -2,070 1. 143 105. 750O. 189E 06 0,630 -0.701 -0719 -1.739 1.020

74050402 0.178E J6 0.737 -0.97.1 -0.947 -2.180 1.233 105. 75.0.188E 06 0,631 -0.758 -0.7.37 -1.837 1,1.00

74050404 0.276E 06 0,933 -1.154-1.i.38 -2.150 1.012 100. 7500. 29 5E 06 0,783 -0,890 -0.876 -1.764 0. 888

74050405 0. 331E 06 0.969 -1.229 -1,170 -2.10.0 0.930 10e. 75e0.354E 06 0,810 -0.950 -0.89 -1.712 00814

740 5040 0.385E 06 0.991 -1.222 -1.190 -2.100 0.910. 100. 7500.412E 06 0.826 -0.940 -0.913 -1.707 0. 795

74050407 0.439E 06 1.004 -1.255-1.206 -2.090 0.884 100. 75e,' I flf:'./0 T 06 0.836 -0.967 -0.924 -1.696 0.771

74050408 00493 E 06 1.008 -1.252 -1.208 -2.080 0.872 98. 75.f\J0 .#L. L 06 0.839 -0.964 -0.926 -1.686 0.760

55

Table 4.4: continued

CCULfl ryK/D

NDES 'p-' RTBS RU

5j'. Cfl E1 Fp. 3 1I( f.F - Z rrjfl LINE

FXP. NJ. o CU (P180 ro (;pM r Pe-CPM THW TH

740515i11. u017t 06. 0 793 -o. 988 -0.995 -2.150 1 .155 105. 770'. 190g 06 .675 -0.765 -0.771 -1.797 1.)25

740515C2 0.168E 0 0076 7 -0.970 -0.970 -2l30 1.160 105. 77.'.)..7BE C6 0.655 00 753 -0.753 -1785 1.032

74j15(3 ).155F 06 71 9 -0.920 -0.940 -2.160 1.220 l05 75o0.164E 06 0.617 -0. 7! .5 -0.733 -1.823 . .090

74151504 ).136E ii6 1.693 -0. 914 -0.909 -2.250 1.341 1060 7700.144E 06 0596 -0.705 -0.709 -1,910 1.201

74051.50 )O10F 06 -0 83. -089 -2.430 1.581 110. 80.06 00524 -0.652 -0.668 -2.095 1. 426

740515u7 0o200c 0.829 -1.027 -2.020 -2.090 I .070 105. 77.0.213E 06 0.703 -t). 794 -0.788 -1.735 0,947

74051508 250 Có 0.922 -10 139 -1.110 -2.070 0o960 1000 75.0.267 fl '. 774 -0. 879 -0.853 -1.697 0.843

74051 509 0.299E 06 0.948 = 1.144 -1,133 -2.050 0 917 lOCo 75.0.319E 06 00794 0. 879 -0.869 -1.673 0.804

74i1,10 0.349E (jó 0.981 lo 188 -1.156 -2.110 0. 854 lt1). 75.00373.E 06 0.819 - t) .912 -0.884 -1.631 Qo 746

CIRCULAR CYLINDER WITH RI3SR2

K/D= 0.00338.

56

Table 4.4: continued

r FSJL C

FXD0

EcEr Fì

E. NO0

B!. 2rKkG.E - SECOND LINE

CD CP18I CPB CPM CPB-CPM THW. THP

74051701 1.76E 06 lo119 -1331 -10243 -1.910 0,667 98. 75.10 18 9E 06 092U - 1.014 -0.938 -1.514 0,576

74051702 0 197E0.212E

0606

11320.930

-1.3060o990

-1.275-0,964

-1,920-10 52 G

0.6450. 557

100, . 75,

7405 170 0, 219E 06 1172.-1.396 -1,255 -1,920 0.625 95. 75.o c i 06 0,959 -,061 -0.974 -1,512 0, 538

74051704 0.247E 06 1188 -1442 -1.336 -1930 0.594 95 7500. 266E 06 0.970 -1.098 -1.007 -10517 0,510

74051705 271F Ob 1.200 -143O. -1.325 -1.930 0.605 95. 75.0 0253 F 06 i).978 -1086 0.9c6 -1.515 fl519

74051706 0 295E 06 1208 -1.468 -10357 -1.940 0.583 95. 75.'J0 319E 06 0.984 -1.117 -1.022 -1,522 0.500

74051707 00325E00 35 lE

06.06

1.2070.983

-1.427-1.082

-1.339-10006

-1,920-1.505

0.5810,498

95, 75.

74051708 0 34 3E0.370E

0606

1,2160.990

-1.442-1.093

-10359-1.022

-1.910- 1.0494

0,5510.472

.95, .750

74051709 0.380E.00410E

0606

12l90.992

-1.485-1.130.

-..343-1.008

-1.930-1.511

0,5870,503

.9 . 75,

740 ,1 71 C 0, 3 8 SE .06 1.223 -1.434 -1.370 -1.920 0,550 95. 75.0.420E 06 0.995 -1.085 -10!Q -1,502 0.4 71

74051711 00 43 3E0. 46 8E

0606

1.2260997

-1.458-1.105

-1 .356-1.018

-1,920-15O1

0,5640.483

95, 75.

74051 712 0, 48 6EO 525E

0606

1.2331.002

-1.49-1t05

-1.387-100 43

-1.940-1.5 11

0,5530.473

95, 750

74051801 00178E0 192E

0606

11280927

-1.346-1.026

-1.267-00957

-1096 U-1.556

0,6930,598

98. 75,

74051802 0,165E0 177E

0606

h0920901

- 1.296-0.988

1. 251-00 49

-1.930-10537

0,6790,588

98, 75.

74051303 06 1062 -1.220 -1204 -1.940 0.736 97. 7500160E Ob 0o879 -0.927 -0 .9 1 2 -1.552 0.639

74051804 0,136E 06 i064 -1.198 -1.205 -1.930 0,725 98. 75.0. 146E 06 0.880 -0908 -0,914 -1543 0.629

74051805 0. 126E (.L ui ?C.i.o'c.-' I 'io. 168 -1,950 0,782 98. 75,

00 13 5E 06 0852 -0.938 -0,888 -1,569 0,68174051806 00116E 06 1O2 -1,196 -10 173 -1.960 0,787 100. 75.

12 6E 0 0.849 -0,91.3 -00 893 -1.578 0,68674051807 i AL.0!' O .L L. 06 0.983 -1,217 -10 134 -1,960 0.826 100. 75.

0. 113E 06 0.820 -0,937 -( 86.5 -1q58 7 0.72274051 80 8 0.982E 05 .0.953 -1,092 -1.1.03 -1.930 0.827 102. 75.

105E 06 0.798 -0.833 -&842 -1,567 0. 72574051 909 0 903E 05 0.929 -1,095 -1.095 -2000 0,905 102. 75.

0.964E 05 0.780 -0,839 -0.83$ ..j33 07947405 1810 0.815E 05 0o865 1o0c.8. -1.057 -1.980 0.923 103. 75.

0 868E 05 0.734 -0.789 -0.81.5 -1 62 9 00 81474051811 ).695E

Go 73 7E050

0.7600649

-0,953-0,739

-00 941-0,728

-2,100-1.760

1.1591.032

103, 75.

74051812 ,,.p o -

00736 E0505

0.741U634

-0.904-0.698

-('091,5-0.708

-'-o-1693

.1.105 105. 75,

57 -r

(:v .NflR 1t B RA-05

K/() 0.00338

F I( S ECED F UCK!.GE - SFC[ND LINE

Table 4.4 continued

t

EXP0 NC.0 R0 ND. CD r180 CPB CPM CPB-CPM TH

7411150 i ' 2LóE 6 io 97 1.436 -1.373 -1..752 0o419 95e 76.), 234E 06 1046 -10074 -1.021 -1.377 0.357

741 015 2 24 5E 10 .332 - 1. 4611 -1.41)1 -1.805 0.404 95e 770Jo 266E (J6 10070 -1.089 -1.039 -1382 0343

74 0 150 3 o 294E 06 1. o 328 -.482 -1 40i -1.810 0.409 95. 76)031gE 06 1 06.8 08 -1.039 -1.387 0.347

741.1)1 5i14 .o 344g 1)6 1.344 -1.478 -1.41.1 -1.807 0.396 . 95 76.0374 F 06 J. 0 78 -1. 1fl2 -1O45 -l3.81 0.336

74' 505 e 392E 06 410437 -1.411 '1o807 0.396 95. 76.1) o 42 1)6 i080 ].o 109 -1.045 138 1 03.36

74101 5(1 .)o 538E 06 1333 -1.497 -1.401 1.826 0.425 95. . 76.o 584E 1) 71 120 -1038 -1.399 036l

74102801 1)0 1 c i.

2. 30606

12951.045

1.5071.135

-1406-1.049

-1.875-1,44.8

0.4690399

95. 76,

7411)28 'J 2 1)0 1 77E 06 1o29ó - 1.487 - 1... 424 -1.8S5 0.47.1 95. .7-5.0. 192E 06 i. 04.5 -1.118 -1.064 -1.465 0.401

74102803 .162E 06 1.283 - 1.412 -1.418 -1.922 0.504 97.01 75E 06 11)36 -1.11)7 - 1006 1 -1.491 0.430

74102 804 1 2 6E 06 3 .207 -1.335 -1.365 -10900 (i 2ro-a-.') -c.,o 77r i.

1) 136E 06 0.983 -11)46 -1.029 -1488 0,45974102 805 0. 105E 06 1.193 -1.440 1 .375 -1938 0.563 58. 76.

0 .11 'E 06 00973 -lo 056 -1.040 _1. i;-¿0 -' 0o48474102806 O 724F 1)5 1039 -lo 295 -lo 273 -02 5 0.752 105. 79

0. 176E 05 0.862 -0.996 -0.977 -1.631 0.654741)2807 .1)0176E

0.191E0606

1.2801.034

-1.427-10069

-10 3 97-1,044

-1.852-lo432

0.45500388

97., 76.

7410280e 01 76F co 1.305 -1464 -1.428 -1.898 1)471) 95. 76..1).191t 06 1.052 -1.097 -1.066 -1.466 0.401)

58

CY[ NOEP W! :1 RIBS RA-10

K/D= 0.00338

RSULT. C2CYED F ec K.GE - EC0ND 1!rE

Table .4 4:: continued

EXP. N. RE, NO, CD CPI8O CPB CPM CPR-CPM THW IHM

74103 102 00 179E 06 1.183. -1.429 -1.392 -1.986 00594 98 75.J0i93E 06 0,966 -1,088 -1.056 -1.567 0,511

741 . 3 106 1.1.14E 06 1.018 -1,267 -1.25e -2.033 0.780 102. 78.0,122F 06 0.846 -0.975 -0.963 -1.643 0.6 80

741131 ;4 7 ').lo6É00113E

o06

0,9490.795

-1.216-0.942

-1,203-0.931

-2.143-1o754

CI. 9400. 824

103, 77.

74'M3'; ç . 91 5E 05 0.85'. -1,042 -1.079 -2,121 1.042 104. 740)0973E 05 0.720 -0.804 -0,837 -1.758 00921

74103110 0.701E 05 0687 -0,974 -0.972 -2.27'. 1.299 1Ô9. 75.1.741E 05 0,591 -0.768 -0.767 -1.930 1.164

741 i) ill 0.701E 05 0,769 -1.069 -1,0.65 -2.575 1. 510 110. 75.0.743E 05 0.o5o -0,841 -0,837 -2.181 1.343

74110102 0.174E0.187E

0606

i13,2k.930

-1.375-1,050

-1.305-0.990

-1.92.5-1.525

00 6200535

98, 76,

74110103 10 199E 06. 10171 -1,458 -1.328 -1.93.8 0.610 97. 76.0.215E 06 0o958 -1o115 -1.003 -l528 00525

74' '.0104 ').21E 06 ....l69 -1,368 -1,316 -1,877 0.561 970 76..),235E 06 '),9.56 -1,038 -0a993 -1.476 0,483

74110105 0.246E).265E

0606

11951.975

-1.411-1.070

-1,338-1.008

-1,926-le12

005880.505

97, 76,

74110106 0.293E 06 1.223 -1,434 -1.355 -1.908 00553 97. 76.'.31 7F 06 0.995 -1.085 -1.018-1.491 0.474

74110107 0.343E 06 .' '171.0...L I i /1 _1 L&oti.' _IJØ 0,532 76..00.370E 06 Ò099() -1.073 -1.002 -1.458 0456

74' 1.0108 0.395E0.427E

0606.

12581,019

-1.480-1,118

-1.384-1,036

-1.911-1.487

0.5270.450

76,

741101C u,433E)0468E

06'16

1.2381.005

-1.426-1.365-1.076 -1,024

-1.909-1,489

0.5440.465

96, 76,

74110111 00489E 06 1.248 -1.459 -1.369 -1,9.22 0. 553 95 76.çk,52Ç 06 012 -1.102 -1.025 -1,498 0.473

74110111 00535E00 578E

0606

1,239!0O6

-1.438-1,086

-1.359-1.018

-1,905-1.485

0.5460,467

95, 760

74110112 '1.535E 06 1256 -1,428 -1.375 -1.917 0. 542 95. 76.0. 579E 06 1,018 -1.074 -1.029 -1.492 0.463

C YL ND E P Wt -I R ÍBS RA -20

w/D= 0.00338

59

Table 4.4: continued

JI. S C.iRSC' F.D FOR

EX0 ND. RE. DO

PrCKAG. - S!COND L!NE

CD CP1BO CPB. CP1 CPB-CPM THW THM

74UC701 ,.,o1P0 06 0939 -1.133 -1o109 2,(363 0.954 1(33. 78..192E 06 (3.7.87 -0.871 -08,50 -1.687 0.837

7411(3703 0.205E 06 0976 '-1.186 -1,157 -2.101 0.94. 102. 78.).2. gE 06 0o815-0o9110o886.-1.712 i.825

741 10704 0.224E0. 240E

0606

1.0190.847

-1.223 -1.196-0,937 0.913

-2.099,70(3

,9030,787

1(32. 78,

74110705 ).254 Ob 1.048 -1.277 -1.235 -2139 0,9(34 102. 78.0.272r 06 0.869 -0.979 -0.943 -1.728 0.786

741 10 70 0.304e1.327F

0606

1.0870897

-l.50 -1.274-1.036 -0.970

-2.119-1.702

0.8450.732

99, 78,

741107(37 354E 06 1.103 -1.42 -1.293 -2100 0.807 99. 77.0.381F 06 00909 -1,026 -0.984 -1.682 0,698

74110708 e4(34E).435E

0606

1,1360,933

-1.438 -1.319-1.104 -1.001

-2.128-1.699

0,8090,6 S 9

98, 78.

7 4 C) 70 Ç 0.445E 06 1.i34 -1.435 4,26 -2.1.10 0.784 99. 78.0.479E Co 0.931:-1.101 -1.007 -1.684 00677

741 1071C 0.499E 06 1,1.40 -1457 -1,332 -2.143 0.811 98. .. 78.0.537E Oo ,.935 -1.119 -1.012 -1.711. 0.70(3

74110111 0.546E 06 1130.-1.418 -1.328 -2,125 0.797 98. 78.(3. 588E 06 0.928 -1.087 -1,OiO -1.698 0.688

741 10712 (3. 546E0.588E

0606

1.15.50946

-1.427 -1.353-1.091 -1.027

-2.142-1.707

0.7890.68Q

9, 78,

7 1 1 07 3 02O5E).219

0606

09790.817

-1.245 -1.204-0563 -0927

-2.154-1.757

0,9590.830

lOO, 78.

7.4110714 t),].84E.(3.196E

0606

0.9360,785

-.L46 -1.148-0.883 -0.884

-2.078-1,700

(3.9300. 816

102. 78,

74l1071. 0.165E 06 0.875 -1.045 -1.058 -2.020 0.962 103. 78.0.176E 06 0.739 -0.803 -0.815 -1.6b3 (3,348

7ft1 lOI]. 7 9. 132E 06 . 7L'1OfU ....,. COL ( Ö7JO7L7.J I.Y7fJ .-0 1,113 . 109. 78,0.140E 06 0.651 -0.768 O,758 ,749 0,991

1411071 8 .l17F 06 (3.726 -0.960 -0,970 '2.379 1.409 1090 79.0.124E 06 0.623 -0.750 -0.759 -2.017 1.258

7 f. lIC) lIS 0.107E0.113E

0606

O7050.606

-0.927 -0.937-0,724 -0.733

-2.698-2.308

1,76110 575

1(39, 79,

741 10721 0.904E1.955E

0505

Oo672Q.579

-0.944 -0.921-0.744 -0.723

2.750-2.364

1.8291,641

110. 19,

7411(372.2 0.708E 05 0.643 -0,870 -0.872 -2672 1.800 115. 79.0.747E 05 0.556 -0681 -0.683 -2.302 1,618

60

CYLTNDER WIÎH RIBS RB-0.5 .

K/D= 0.00197 . . . H

FESfJLT C10EC FCF' bLL1CKGE FCÒND LTNF

Table 4.4: continued

EXP. NO. RE. NO. CD- CPÌ8O CPB . CPM CPB-CPM THW THM

741115J4 '01&7E 06 1.134 -1.303 -13I3 -2.010 0.697 98. 77.0.180E. 06 0.o931. -0.988 -0.996 -1.598 0.602

7411505 0.134E 06 1.056 -1,275 -1.251 -2,060 0.809 99. . 78..144E 06 0.874 0.976 0o955 -1.658 0.703

74 111 50 0.118E 06 0.931 1.180 ..157 -2.079 0.922 104. 78..126E 06 0.781 -0.913 -0.893 -1.702. 0o809

74111508 00884E 05 0.840 -10085 -1.102 -2,396 1.294 109. 82.0.940E 05 0.7.2 -0.344 -0.359 -2.003 1.144

74 1 .1 1513 1.l8E 06 1.103 -i.1 -1.211 -1.841 0.630 96. 750.194E 06 0.909 -1.001 -0.913 -1.458 0,545

74111514 ),206E 06 1.142 -l..13 -1.269 -1.919 0,650 97. 77.0, 222E 0.6 0.937 -0.995 -0.957 -1.517 0,561

741 L 15 0.24E.274E

0606

11440.938

-1.310-0,992

-1.255-0.944

-1.845-1.453

0.5900.509

96, 74

74111517 0.265E 06 1.178 -1,357 -1.271 -1.823 0.552 96. 75t).?8E 06 0.963 -1.027 -0,953 -1.427 0.475

74111518 0.304E 06 1.208 -1.373-1.315 -1.883 0.568 95. 75.0.329E 06 0.984 -,Q35 -0,986 -1.473 0.487

741 11519 .381E 06. 1.238 -1G424 -1.344 -1.843 0,499 95. 76.0.412E 06 1005 -1,074 -1,006 -1.433 0.427

74! 1152 0.445Ei).486E

0606

1.2531.016

-]a4421.087

-1.358-1.015

-1.8561,441

0.4980.426

95, 75.

741 1152 1 0.512E 06 1.253 -1.416 -1.353 -1.851 O498 94. 7501.554E 06 1.016 10 065 1.011 1.436 0.426

74111522 0.556E 06 1,266 -1.446 -1.373 -1,898 0.525 94. 75..602E 06 1.025 -1,088 -1026 -1.474 0.448

74111523 ).555E().601E

0606

1.2721.029

-1.439-1o081

-1.381-1.032

-1.888-1.464

0.5070.433

94, 75.

61

CY.N)E WUH RIBS RS-lO

KíO= 0.00197 .

REJ1TS C SCTEO FflP. ,r;CKÂGÈ SFCcND L!ÑE

Table 4.4: continued

E!X?. NO. REo NO. CD C.P180 CPB CPM CPE-.CPMJ THW THM

74112603 O 207E 06 ú8 36 -1,037 -102 -1.995 0.963 102. "o0.220E 06 0. 709 -0.802 0.798 -1.650 0.852741. 12604 Oo 227E ! 6 0. 883 -1.116-1.072 -2.045 973 102. 77

.)0242E 06 00 745 0o8b5 -0.826 -1.683 0.85714112605 1 255E 06 0. 907 lo102 -l.04 -:,)O6 Oo,912 102. 76

I 272F .06 00763 -0849 -0.842 -1.644 0. 802l'i 12607 0. 307' 06 0981 -1.174 -1,154 -2.09 0.865 98. 770

1.328E 06 0.819 0.900 0.883 -1.639 0.75674112608 06 1.03 -1o235 -,1194 1.975 0.781 980 75.

06 0. 860 -0.944 -0.909 -1.588 0,679741 1260c 145 3.E 06 1.062 -1.256 -1.217 -1.998 0.781 97. 76.

t)0 4 86E 06 0.879 -0o959-Q.92,5 -1.603 0.67874!1261c 0 5 1 6E 06 lo 81 -1.298 -1.242 -1.980 0.738 971 75.

( 554E 06 0.89.3 -0.992 -0.943 -1.583 064074i2611 0. 56 LE 06 1,073 -37 -1.241 997 0o756 97. 75,ì £3 Q U U L 06 0887 1o010 0.944 lo600 0.65674112612 0.561F

00603E(i 6co

1.0870. 397

-1.307-0o999

-1,2530.952

-2.003-.1.602

0.750 97, 75.74112.615 0.186E 06 0764 -1.013 -1.027 2o193 1l66 105. 70.0 197E 06 0.653 0.792 -0.804 1o842 1.0387411 2617 1.132E.

O0 1.3 9E0606

0.61600583

-0.940-0.739

-0.944-0.743

-2.451-2.094

1.5071.351

112. 78,

74'.,2618 :) 118E .06 0,647 -0.959 -09O8 -2.598 1.690 115. 82.Oo 124E 06 00 5 59 -0.761 -0.715 -2.234 1. 51.97112620 0.104E 06 0.636 0o907 -0.895 2.741 1.846 118. 84.., I 1C0 £L'?.. 06 0.550 -0.716 -0705 -2.366 1.661

41 1262.1 ). 934E 05 0613 -0.900 0.899 -2.958 2.059 120. 84.0.984E 05 0.532 -0.7i.3 -0.712 -2.568 1.856

74112623 00701 È00 754E

0505

1106O911

-1.157-0.866

-1.1c7-0.900

-1.536-1.194.

0.3390,2 93

80. 67,

62

vL NfE W1H RIBS .RB-20

K/D= 0.00197 .' . .

Table 4.4: continued

RESJL' Cfl FIFD. flF

EX°. NO. ILE. N..

3±'CK.GE.. SECOND LNF

CO CP18Ü CPB CPM CPB-CP'1 THW TH

74121 801 ).209F0.221E

0606

0.675 -0.900 -0.9120.582 -0,704 -09715

-2.322-1.979

1.4101.264

109. 82,

741 21 803 0.189E 06 0.624 -0,854 O.859 2.641 1. 782 117. 84..10199E 06 0541 -0.6'T -0,674 -2.27c 1.605

74121 80 Lt 0. 170E. 179E

0606

0602 -0,838 -0.8330.523 -0.658 -0.654

-2.764-2.396

19311.742

118. . 85,

74121806 ì.119F 06 0.522 -0.771 -0.755 -2.858 2.103 120. 84.'.l25E 06 0.457 -0.609 -0.594 -2.505 1,910

74121807 .1Q8E).114E

0606

0.614 -0.842. -0.8460.533 -0.660 -O664

-2.475-2.1.32

1.6291.463

115, 80.

7Lt 2! 808 '104 06 0.606-0.832 -0.845 -2.460 1.615 114. 81.,1.10E 06 .0.526 -0.652 -0.664 -2121 1.457

74121 eos 0.924E 05 0.815 -0.989 -1.018 -2a22'8 1.210 115. 81.9.982E 05 0.692 -0.763 -0.788 -1.861 1072

74121811 0. 703E0.751E

0505

1.130 -1.188 -1.2110.928 -0.889 -0.909

-1.451-1.116

0.2400.207

85, 65.

74121814 0.226E 06 '.671 -0.878 -0.873 -2.257 1.384 107. 81.0, 23 9E ')6 0.579 -0,685 -0.680 -1.922 1.241

74121815 0.252E0.266E

0606

.695 -0,892 -0,8920.598 -0.694 -0,694

-2.236-1.897

13441.203

107.. , 80,

741 21816 0.265E0.280E

0606

.0.718 -0,908 -0.9130.b16 -0.705 -0.709

-2.191-1851

1.2781.142

104.

74121817 0.285E,).302E

0606

0,748 -0.932 -0.9290.640 -0.722 -0.719

-2.118-1.779

1.1891.060

103. 79.

7412 1818 0.303E 06 '00759 -0.936 -0.942 -2.138 1,196 102. 79.O.321C 06 0.648 -0.724 -0.729 -1.794. 1.065

74I2181 0.375E 06 00831 -1,024 -1.019 -2.135 1.116 102. 80.0.399E 06 0,705 -0,791 -0.787 -1,775 0,988

74121820 0.448E 06 0863 -1.051 -1.052 -2.107 1.055 102. 7900.477E 06 0.729 -0.810 -0,811 -1,742 0.931

74121822 0.508E 06 0.876 -3 .066 -L066 -2,100 1.034 102. 79.0.541E 06 0.739 -0.822 -0,822 -1,732 0,912

74121823 0.554E 06 0.883 -1,096 -1.081 -2,117 1.0.36 100. 790i'),590E 06 0.745 -0,847 -0.834 -1.747 0.913

74121924 j,554C 06 0.879 -1.081 -1.077 -2.114 1.037 100. 7900.590E 06 0,742 -0.834 -0.831 -1.745 0.914

74121925 0.471E0.501E

0606

0.871 -1.064 -1.0640.736 -0.821 -0.821

-t.111-1,744

1,047'0.924

102, 79,

74 21826 0.408E 06 0.838 -1.032 -1,027 -2.095 1,068 102. 7900.434E 06 0.710 -0,797 -0.793. -1.734 0.945

74 21827 0.334E 06 0,785 -0,979 -0.975 -2.143 '1.168 102. ' 80.1.354E 06 0.669 -0.758 -0.755 -1,792 1.038

rYL!MER WIH RIBS RC-05

V 0.00641

PES')L. C!CTEC Ft'ÌP BLICKAGE SEC0ND L!NE

63

Table 4.4.: continued

xP0 rc0

74122604

74.122605

74! 22606

7122607

74122608

74122609

141 2.261C

712211

7111 22612

74122613

74122614

74122615

74122616

7'122 617

7'1 22618

74122619

7 4122 62 C

12262 i

74122623

7122624

RE0 NO0

.255E 06!)o27( 0600267È !6)289 06)0287E 06.3iO 06Oo306E 060331E 06

)0338E 06)0365E 060 377F 0600408E. 0604i,1E 0600445E 060453E 060o49OE 0600471E 060 509E 0600508E 060 549E 06Oo 43E 0600587E 0600 540E 0600584E 0600 200E 0600216E Ou0 186E 060 201E 0600167E 0600181E 060e 130E 0600 140E 06)0U6E 06O.125r 060. 107E 06)0115E 060.900E. 0150.970E 0500699E 05.10 1 -

CO CP1.8.0

1265 1.4331.0)24 -1.077i256 -l4801.018 -10119124.5 1o445loOl.0 -1.0911.271 -1.4881.028. -1.1231.237 -1.4831.004 -1.1251.252 -1.4761.01.5 -lo 1161.251 -1.4531.014 -1.097l2-34 -1.4501002 -10c71.233 -1.4361.002 1.-0851.212 -1.4500,987 -1.1011230 -1.46200999 -1.1081.238 i,4711.005 -1.1141233 -1.4671.02.-l.1121.265 -1.492I r j --- i I a¿0.-t ¿0 O

1.249 -1.4701.013 -1.1121.190 -1.4290.971 -1.087i.196 1.4220.975 '-100801.184 -1.3830,967 -1.0481165 -13800.953 -1.0491.154 -1.4260946 -1.090

CPB

1.411-1.058-1.401-1.051-1.388

lo042-i.421

-1.066-1.389-1.044-1.408--1.058-1.406-1.056-1.391-1.047-1.390

1o046-1.371-1.033

1o,398-1.053

1o405-1.058-1.41.5-1.067-1448_i¿0' '7

-1.422-.070-1.375-1.040-1.376-1.040-1.362-1.030-1332-1.007-1o36.i-1.036

CP4

1.911-1.485-1.908-1.485-1.910-1.488-1.939-1.508-1.936-151.2-1.951-1.522-1.942-1.515-1.944-1.520-1.932-1.510-1.928--1.511.-1.948-1.524-1.947-1.522-1.957-1.531-1.969

o

-1.890-1,471-1.935-1.521-2.005-1.580-1.992-1.571-1.931-1.523-2.116-1.685

CPB-CPM

0.5000.4270.50700'4330.5220.4460.5180.44?0.547-0.4680.5430.4640.b360458Oo553: .

0o4730.5420,4640.5570.4780o550-004710.5420.464Oo5420.4640.5210.45,0.4680.4000o5600.4810.6290.5400.6300.5410.5990.5160.7530.649

THW

95.95.

95.

95o.

950

950

95.

95.

95o

- 94,

95.-

94,

95.

96.

95,-

96,

98',

98,

97,

58.

.'

THM

74..

750

76

78.-

78,

72.

73.

73,

770

76.

75o.

72.

78,

72,

7,

75.

75.

71.

73,.

75,

64

CYLINDE WTH RIBS RC-lo

K/D= 0.00647

FE'J!.T C1RECTEC FCR 8LrCK!GE - SE(tND L!Nc.

Table 4.4: continued

EXP0 NC. RE. NO. CO CP1.8O CPB PM CPB-CPM THW IHM

7501020? 0.202E 06 1,2.94 '.,429 -1,393 -1.860 0.467 95. 76.1.219E 06 1.044 -1.069 -1.038 -1.436 0,38

750102C3 ¿),188E 06 1.311 -1.483 -1.404 -1.875 0.471 95.),2O4E 06 1.056 -1,112 -1,045 -1.445 0.401

75 t) 1Ò204 0.168E 06 1.00 -1.432 -1.407 -1,869 0.462 96. 75.).182E Co ..048 -1.070 -1.049 -1.442 0.393

7591020 ),131E0.142E

o06

13531.085

-1.521-1.137

-1.455-1.081

-1,895-1.454

0.4400.373

96, 7.75010215 0.230E 06 1.329 -1.470 -1.409 -1.855 0.446 96. 76.

0.250E. 06 1.068 -1.098 -1.046 -1,425 0.379750 1021 : 00 255E 06 1.30? -1.427 -1,380 -1,858 0,478 95. 75.

'0276E Ob 1.050 -1.066 -1,026 -1.433 0,407'75010217 0.287E

0.311E0606

1.3311.070

-1.492-1,iló

-1.421-1.056

-1,867-1.434

0.4460.379

96. 76,

75010218 0.333E 06 1.280 -1,403 -1.364 -1,844 0.480 95. 76.0.361E 06 1,034 -1.049 -1,016 -1.425 0.409

7501021 S 9.370E0.401E

0606

1.3241.065

-1,479-1.106

-1.416-1.053

-1.893-1,458

0.4770.405

96, 75,

75010220 '.408E 06 1.308 -1.444 -1.393 -i.861 0.468 96. 76.0.442E 06 1.054 -1.079 -1.036 -1.434 0.398

.75010221 0045IE 06 1.309 -1.472 -1.403 -1.879 0,476 95. 7500.489E 06 1.054 -1.103 -1.044 -1.449 0.405

75010222 0.510E.).553E

0606

1.2911,042

-1.457-1.093

-1.398-1,043

-1.923-1,490

0.5250.447

96. 76,

75J 10223 0.531Ei).576E

0606

1,3031.050

-1.490-1.119

-1.409=1O5O

-1.927-1,491

0,5180.441

95, 76.

750 10224 0,51E 06 1.290 -1.460 -1.396 -1.908 0.512 94. 75.0.575E 06 1,041 -1.096 -1,041 -1.478 0.436

CYLINDER WITH RIBS RC-20

K/D= 0.00647

65

Table. 4.4: continued

PU1YS CDRREC7ED FÍJ

EXP. NO. 1.E. W),

B JCKGE -

CD CP18O

EC0ND L!NE

CPB CPM CPB-.CPM HW THM

7501(703 0 231E 06 1.384 -1.556 -1.458 -1.832 0.374 90. 76.).25lE 06 1.106 -1.161 -1.078 -1.394 0.31675910704 0.254E

0.276E0606

1.3991.116

-1.5.84-1.182

-1.471-1.087

-1.850-! .407

0o3790.320

90, 75.7510705 00 28 5E 06 1 .3 7.6 -1.509 -1.440 -1.800 0.360 90. 760

0.310E 06 1.100 -1.2.3 -1,064 -1.369 0.30575 10 7o ).335E 06 10368 -1.549 -1.443 -1.802 0.359 99. 80.o364E 06 l 095 -1.158 -1.068 -.1,372 0. 304

750c'7O7 !. 36 7E 06 I40 -10533 -1.429 -1.767 0,338 95. 79,0.399E 06 100 93 -1.145 -1.057 -1.343 0,286

7 50 le 708 40 1 E 06 1.379 -1.567 -1.446 -1.797 0.351 90. 770:., 436E 06 .1. 102 -l171 -1.06S -1.366 0.297

?5p107s ) 0447E 06 1.373 -1.561-1,453 -1,807 0,354 90. 78.). 486E 06 ..098 - IL.7 .o -1.375 0.300

750 1 0710 ) 490E0.533E

06co

1.3741.099

-1.553-1,160

-1.456-1.078

-1.803-1.372

0.3470.294

88, . 78.

75 Alu :1 52 1F.1,567E

0606

1,3951.113

-1. 576-1176

-1.485-1.099

-1.85 7-1.413

0.3720.314

88, 80.75ø07, 2 Oo 521E 06 1.392 -1.554 -1.474 -1.83 3 0.3.59 90. .77

0 56 7E 08 1111 -1.158 -1.090 -1.394 0.3037501001 0.197E 06 1384 -1.550 -1,450 -1.777. 0.3?7 90.)o21 4E 06 1,106 -1. 156 -.1.071 -1.348 0.276

75 bi 0903 0.i

6 7E 06 1.430 -1.624 -1. 519 -1,885 0.366 940 76.0.1 82E CO 1.237 -1.210 -1,122 -1.430 0.308

7501i904 C0 144E 06 1.422 -1,626 -1.5o2 -1.862 0.360 92. 77.0.157E 06 1.131 1.213 -1,109 -1.412 0.303

CYLTNDR Wfl"H RIBS RC-40

KID: 0.00647

66

Table 4.4: continued

r$uLTS C09'CTEr F)S B!1CKAGE -

FXP. RE. NO. CD C180

ECOND LINE

CPB. 'PM cPB-CPM TKW TIM

75011001 0.143E 06 1.326 -1.574 -1.472 -2050 0.578 93. 76.',155E 06 1o066-1.1871.j0-1,591 0.491

75011002 0.128F 0 1.353 -1.539 -1.507 =2.012 0.565 93. 76.o139E 06 1.085 -1.194 -1.125 -1.604 0.479

7.5U 11004 )01.l6E 06 1.306 -1.596 -1.455 -2.091 0.636. 93. 750?.126E 06 1.05 '-1.209 1.089 -i.630 0.541

750 11)05 1.105E 06 1271 -1.435 -1.420 -2.075 0.655 95. 7400.114E 06 1.027 -1.078 -1.065 -1.624 0.559

7501OO 0.811E 05 1.309 -1.504 -1.468 -2.116 0.648 94. 76.0.944E 05 1.054 -1. 130 -1.099 -1.65.1 0.551

75011203 ').238E 06 -1.567 -1.475 -2.052 0.577 90. 75..258E Co 1.078 -1.177 -1.099 -1.589 0489

750 112 Ô 5 0. 290E 06 1403 -1.616 -1.522-2.017 0.495 90. 7500.316E 06 1.118 -1.208 -1.129 -1.547 0.418

75u11207 0.377E 06 1.423 -1.645 -1.543 -1.997 0.454 . 87. 7400.411E 06 10132 -i.229 -1143 -1.526 0.383

75011209 1.457E 06 1.398 -1.617 -1.517 -2.014 0.497 87. 7500. 497E 06 1.115 -1,210 -1.126 -1.545 0.420

7501121.0 0.457E0.4S8

0606

i.42a1.134

-1.647-1.230

-1.552-1.150

'-1.994-1.523

(1.442t',372

87, .74.

750112 1.1 0.505E 06 i383 -1.617 -1.509 -1.982 0.473 86. 75.1.549E 06 1.105 -1.213 -1.121 -1.521 0.400

75011212 0.511E 06 1.421 -1677 -1,550 -2.012 0.462 87o 75.).557E 06 1.l3. -1.256 -1.149 -1.539 0.389

Here, Ht

67

4.2 Boundary-Layer Data

The results of total pressure measurements in the boundary layer

of rough-walled cylinders are presented in this seôtion. These measure-

ments were made by means of flattened stagnation tubes supported by the

boundary-layer traversing méchanism described in section 3.5. Almost all

boundary-layer measurements were made along a line 1 in. above the midsection.

This particular section was chosen in order to avoid any local influences

due to the roughness discontinuity at the midsection which was provided för

the pressure taps in the case of sandpaper roughness and in some of the

rib configurations. To assess.the local influence of the discontinuity, a

single sét of measurements was also made at a distance 1/8 in. from'the

midsection and comparisons with the two sets of data, presented fri the next

section, indicated that the effect of the discontinuity on the boundary

layer is negligible.

4.2.1 Cylinder with distributed roughness

The results of the boundary-layer experiments with the circülar

..3cylinder wrapped with Norton Co. #24 sandpaper (k/d = 2.66x10 ) are presented

in Tables 4.5, 4.6 and 4.7 and computer plots of the velocity profiles are

given in Figures 4.11, 4.12 and 4.13. The stagnation tube used in these

experiments was made of a flattened hypodermic needle of 0.020 in. outside

diameter. The size of the tip after flattening was 0.012 in. The normal

distance y quoted iz the tables is frOm the top of roughness elements

to the center of the tip of the stagnation tube. Presented in the tables

are the angular location O at which boùndary-layer traverses were made, the

corresponding pressure coefficient C as measured (or as obtained by inter-

polation) at that angi lar location, and the values of notmalized total

pressure:, Ht/H.I and normalized velocity, u/uE, across the boundary layer.

is the total pressure relative to the reference static pressure of,

the uniform stream measured by the stàgnation tube, B is the dynamic pressure

of the approach flow, u is the velocity in the boundary layer at a normal

distance y, and uE is the velocity at the edge of the boundary layer. While

Ht. H and C are obtained by direct measurement, u in the present case is

a derived quantity, obtained by assuming that the pressure in the boundary

layer is the same as that observed on the cylinder. The normalized velocity

in the boundary layer UiuE is therefore given by

('JD

oD

0.0

U!__o

68

DISTA,.

TTR. 73TTA. 83.TP(TRI. 93.

¡54000

o£+

Figure 4.11: Boundary-layer velocity profiles. Distributed roughness

k/d =2.66x103. (traverse at 1/8 inch à.bove midsection)

0.2 0.q 1.00.6U/UE

0.8

THETA=

73.00

CP

-1.849

Y(FT)

HT/HO

UIUE

THETA= .83.00

CP= -1.693

(FT.)

Hi/H

OU

./UE

.

TH

ET

A=

93.0

0

CP

= -

1.46

.6

Vt(F

i)H

'/HO

U/U

F

0.00150

'-1.029

0.536

0.00150. -1.239

0.411

0.00150

-1o3

530.

214

0.00

250

-0.8

400.

59.5

0.00

350

-0.9

870.

513

0.00

350.

-1.

265

0.28

50.

0035

OE

-.0.

597

.0.6

6:3

0.00

550

'-0.6

300.

63.0

0.00550

-1185

0.337

0.00450

-0.378

.0.718

0.00750

-0.210

0.74

40.

0095

0-0.924

0.468

0.00550

-0 084

0.7 87

0000950.

00210

00843

0001 350

-0. 588

(J

59'ó

0.00650

0.084

0.824

0.01150

0.546

0.914

0.01

750

0.00

00.770

0.00850.

0.588

0.92

50.

0135

0.

0.81

9.0

.968

0.02

150

0.50

40.892

0.01

050

0.81

90.968

0.0:

1450

;0.9.45

0.992

0.02.550

0.840

O.65

0.01

150

0.91

20.

984

0.01

550

0.94

50.

992

0.02

950.

0,945

0.987

0.01250

.1.008

1.001

0.01

750

0.98

7. 1

.000

0.03

350

0.9.

870996.

0.01350

1.000.

10000

0.01

950.0.987

1.000

0.03750

1.00

81,

000

0.01

450

0,98

70.

998

0.02

1.50

0.9.75

0998

0.0.41.50

1.000

0.99,8

TA

BLE

4.5:

CY

LIN

DE

R W

tTH

DIS

TR

IBU

TE

D R

OU

GH

NE

SS

NO

. 24

B/I

DA

TA

RE

15400.0.

(Traverse at 1/8 inch above midsection.)

70

a

d

-o

Oo

oD

o

o

o

00 0.2 .0.6U/UE

DISTA.. IsoTIETA. 68. 0TITR. 73. £TTA. 83. +TTfl. 93 XTITP. 103. 0

0.8 1.0

Figure 4.12: Boundary-layer vélocity profiles. Distributed roughness,

k/d = 2.66x103. Re = 154,000.

TABLE 4.6':

CYLINDER WITH DISTRIBUTED ROUGHNESS NO. 24

B/L DATA.

' RE = 154,000.

(FT)

THETA = 68

C= -1.819

HT/HO

U/UE

THETA

73

C= -1.870

pMT/HO

U/UE

'

THETA = 83

C= -17l4

'

p HP/HO

U/UE

THETA = 93

C= -1.471'

p HT/HO

U/UE

'

THETA = 103

C= -1.294

p HT/HO

U/UE

0.0015'

0.0025

-0.882

-0.693

0.576

0.632

-1.218

-1.071

0.476

0.527

'-1.261

'

'0.40,9

'

-1.378

0.194,

'

-1.294

-1.282

0.000.

0.074

0.0035

-0.378

'0.715

-0.798

0.610

-1.029.

0.502'

-1.261

0.292.

.-1.239

'0.154

0.0045

-0.084

0.785

-0.504

.0.689

0.0055

0.0065

'

-0.231

-0.462

0.853

0.900

-:0.189

0.084

0764

0.824

-0.693

'

0.613

.

-1.214

0.322

-1.261

0.121

0.0075

-0693

0.044'

'0.273

0.863

-0.357

0.707

0.0085

-0.882

0.979

0.546

0.916 '

0.00.95

1.000

1.000

0.714

0.948

0.084

0.814

.-0.924

0.471

-1.239

0.154

0.0105

1.008

1.001

0.819

0.967'

'

0.0115

00I25

..

''

0.966

0.981

0.993

0.996

0.504

0.904

'

00i35

0.0155

'

1.008

.

1.000

'

0.756

.0,966

Ó.954

0.994

-0.546

'

0.612

-1.218

0.182

0.0175

0.0185

'

'

1.000

1.008

1.000

1.002

0.021

0.778

-1.134,

0.264

0.0195

,

"0,966

0.994

'

0.0215

'.0.525

0.900

-1.050

0.326

0.0255

0.819

'0.964

0.0275

''

'-0.840

0.445

0.0295

0.0335

.'

'

'

'

.0.966

0.987

.

0.994

0.998

-0.546

0.571

0.0375

'.

'.

0.996

1.000

0,. 0415

'0.987

0.998

72

V,

Q

a

X.-Q

(Id

.Q

oo

0.0

a

XX

X

X

X

+

0.2 0.14 0.6U/UE

0ISTR.. .3014000

TPETA 73.TPTA. $3lIETA'. 93.lIETA. 98.

0.8

O£+X

1.0

Figure 4.13: Boundary layer-velocity profiles. Distributed roughness,

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

73

TABLE. 4.7: ZYL!NDER WITH D!STPTBUTED UGHNESS NO. 24B/L bA'A. RE 304000.

THETA= 93.00

CP= -1540

Y (FI) HI/HO U/UE

THETA= 98.00

CP= -1,456

Y (FYi HI/HOt U/UE

05() -1.448 0.191 0.004.50 -1.391 0.1640.00450 -1.4.02 0,234 0.00850 -1.391 01640.00650 -,368 0.261 0.01050 -1.268 0.1900.00850 . -1.299 0.309 . 0.01250 33 0.2250.01250 -1.046 0442 0.01450 . -1.284 0.2.660.01650 -0.701 0a5?6 0o01850 -1.1.26 0.368002050 -0.195 0.729 0.02250 -0,885 0o4840.02450 0.276 0,847 0.02650 -0.598 0.5930.02850 0.701 0.941 0.03050 -0.184 0.7220o03250 0.897 0.982 0.03450 0.172 0.8170o03650 0.970 0,996 0.03850 0.506 0.8970.04050. 0.989 1.000 0.04250 0,770 0.9550.04450 0,989 1.000 0.04650 0.931 0.9890.04850 0.989 1.000 0.04850. 0,931 0.989

0.05050 0.972 0.9980.05450 0.984 1.000

ETA= 73.00

CP= -1.3.75

Y(FT) Hi/HO U/UE

THET8= 83.00

CP= -1.7.4

Y(FT) HÎ/HC U/UE

0.00150 -1.550 0.338 0.001.50 -1.559 0.2530.00250 -1.489 0.369 0.00350 -.L.299 0.3980.00350 -1.264 0.464 0.00550 -1.044 0.5020.00450 -1.G17 0.550 0.00750 -0.684 06190.0)550 -0.795 0.616 0.00850 -0.339 0.7140.00650 -0.534 0.68.7 0.01050 0.034 0,8030.0O70 -0.c3S 0.759 . 0,01250 0.418 0.8860.00850 0.05.7 0.825 0.01450 0.734 0.9490.00950 0.250 0.865

. 0.01650 0.904 0.981O.i150 0.750 0.961 . 0.01850 0.949 0.990.0.01350 0.966 1.000 0.02050 1.006 1.0000.01450 Oo 966 1.000 0.02250 100060.01650 0.966 1.000

f f//f / Id/ 2

74

N ¡H C

[H ¡H -Ct,E o p

P. L OC O

downstream bet,eetace riLs

DeivjfJo sktc,

/

(4.1)

HtE is the total pressure at the edge of the boundary layer and 'Ht E/H =

1.0, barring any experimental error. Effects of turbulence in thé total

pressure measurements were not taken. into account in calculating the velocities.

4.2.2 Cylinders, with ribs

The boundary layer data for cylinders with ribs are presented

in Tables 4.Bthrough43d plots of velocity profiles are given in Figs. 4.14

through 4.29. Here,, the total pressure measurements in the. boundary layer

were made by means of a flattened hypodermic needle of bO50 in. outside

diameter. (A larger-diameter needle was used to reduce the response time.)

The size of the tip after flattening was 0.037 in. The normal distance y

given in the tables is measured from the smooth surface of the cylinder to

the center of the tip of.the stagnation tube. The location f the traverse

plane relative to a rib at éach measuring station is denoted by 0, 1 or 2

and identified in the .bles as P.LOC. For a traverse made at a station

between two ribs, P.LOC is 0. For a traverse at a station where there is

a rib, P.LOC 1 if. 'the traverse is made in the.plane of the downstream

face of the rib, and P.LOC = 2 if the traverse is made in the plane of the

centerline of the rib. This notation is illustrated n the sketch below.

The different traverse planes were' tried with a view to observe the local

influence of the ribs on the bòundary...layer characteristic's.

75

As in the case of the.cylinder with distributed roughness the

velocity in the boundary layer was obtained üsing Eq. 4a1. The overall

value of C defined previously was used to obtain the velocity even in

those cases wheré the présence of arib definitely influenced, the local

pressure. The overall values df used in data reduction are given in the

tables. WhIle the error in the välues Of u/uE obtained with this procedure

an be quite la±ge very close to a rib, the values of U/UE for y >2k are

expected to be reasoflably accurate. If it is ässumed that the "overall"

C is realized at the edge of the. boundary iayer., the relative error in

u/uE is given approximately (and, conservatively if C < O) by

¿(u/uE),,

¿C (y)

u/uE - T (Ht/H0 C) (4.2)

where ¿C(y) is the variation of the local pressure from the overall value

normalized by the dynamic pressure of the free stream aM (u/uE) is the

difference between the correct u/uE and the calculated u/uEo Using the

results for the cylinder RA-20, k/d = i.38xl03, Re 295,OQO (Table 4.20).

änd taking ¿C = -0.15 (see Figure 5.24) at e = 72.5°, the relative error- for

the first. data point (y 0.030 ft k, U/ÚE Ó.478) is found to be +13%.

The relative error, however, decreases away from the cylinder since Ht/H

icreasés and. IC(y) is expected to decrease as y increases. For example,

at y = 0.0065 ft = 2.17k the error will be about +3%, even if ¿C -.Ó.l5

is assumed as befôre. It is expected that the error in the values of u/uE

close to the ribs will be smaller for the tests wIth the smaller ribs

(kid = l.97x103) and larger with the larger ribs (k/d = 6.4'7xl03) owing

to the influence of k/d on, ¿C

Since the valües öf u/uÈ may be in error (smaller) very close

to the cylinder for stations under thé lodai influence of ribs, such results

Should be interpreted with caution. There. are, nevertheless, a number of

velocity profiles (indicated in Table 4.25) which äre free of such error,

and all the velocity profiles for y > 2k are expected to be reasonably

áccurate.

t

76

Figure 4.14: Boun4ary-.layer velocity profiles. Ribs Rl. Re = 152,000.

0Ø°001 =Y.L3HJ. 00°06 =!3L4i.

00001 000°! cZ800°0 000°! 000°t LO0°0

0660 9E5°0 Z9O0°1) 9L6°fl Z9c°0 SZÇOO°0 606°0 '°0 Z400°O ZL°0 85°0- SZ00°f) LS°0 ZZt- ZZ00°0

¿L

31)/fl OH/IN (ii) A 31)/fl ON/iH lid) A

Z =DO1°d 81°Z =d3 Z DY°d 4LO°Z dD

00°0 V13H1 0°fiL =V!3H.L

000ç1 =; 11WG '/9 t S91 -1.UM '.,33N:A3 :8f7 o-j

966°0 0000! L6°0 6°0

S86°O Ç000t L88°0 tL°O

LOZO°0 L8T0°0 L9!0°0 SL4TO°0

,.B°0 0Z°0 L?t0°0 866°0 000°T ÇZt0°fl SLL°O c2T°0 LO1O°0 001°! OTO°! Ç??!3°O ZS9°0 98Z°0 SL800°Ó 966°0 86°0 0T0°0 Bcc'O Z'ic°O SL900°0 8c6°O BLL°D cZO0°0 65,°0 88L°0 LzO0°O E06°0 5°0 Z?00°C' tt5°0 Z98°0 SLZOO°0 t08°0 000°O SDO°0 L&°0 L8°0 Z?O0°0 899°0 L,c°fi SZZOO°O

'31)/fl OH/IH (.L) A 31)/fl 0H/3-4 lid) A

'Z =3OVd t,Z°t dD z 01°d EO°t =dD

00001 00001 szcoo°o 186°0 L88°0 szbo°o LSÔ°0 SEL°0 c?E'0C°0

09°0 czzob°o

.o

o

"J

o

r.eo

oeo00

X

X

X

+

+A

s- 4 oo-çJ

X

z

X

0.2 0.4

78

0.6U/UE

f183 RI. FE

TIETRa 70.TIE TR. 83.TTRB 90.TPETRoIOO.

0.8

287XI

Figure 4.15: Boundary-layer velocity profiles. Ribs Rl. Re =287,000.

79

4.9: CYLiNIJES. flH. RB3 Rl B/L OTARE= 287000.

1:H.8T= 90.00

CP= -1.s98 P.LOC= 2

Y (Ft) HI/HO U/UE

THETÂ= 100.00

CP= -1.157 P.LOC=

Y (Fi) Hi/HO

2

U/UE

0.00379 -1.122 0.462 0.0Ó399 -1.173 0.106O.0t'.79 0.884 0.59 0.00499 -1.128 0o178U.tJU79 -0.701 0.608 0,00699 -1.075 . 0.237V.0067' -0585 0.642 0.01099 -0.857 0.3940.00779 -0.356 0.705 0.01499 -0.490 0.5650.00879 -0.128 0.763 0.01899 0.034 0.7500.00579 0.054 0.806 0.02299 0.571 0.8990.01079 0.283 0.857 0.02699 0.850 0.9670.01179 00475 0.898 O.0099 0.973 0.9960.01279 0.642 0.931 0.03495 0o580 0.5580.01379 0.808 0.964 0.03899 0.990 1.0000.01479 0.891 0.980 0,04299 0.990 .1.0000.01679 0.993 0.9990.01779 1.000 1.0000.01879 0.99, 0.999

.IHETA= 70.00

CP; -2.01.9 P.LOC= 2

Y (FI) Hi/HO U/UE

HETL= 80.00

CP -2.048 P.LOC

Y (FT) Hi/HO

2

U/UE

0.0O329 -0.765 0.644 0.00379 -0.995 05880.00429 -0.595 0.686 0.00479 -0.65. 0.o760.00529 0.156 0.785 0.00579 -0.422 0.7300.00629 0.116 0.841 0.00679 -0.181 0.7830.00729 0.388 0.893 0.00779 0.065 0,3330.00829 0.578 0.928 0.00879 0.302 0.8780.00929 0.752 0.958 0.00979 U.33 0.52000C1029 0.9.18 0.986 0.01079 0.737 . 0.9560.01129 0.570 0.995 0.01179 0.899 0.9830.01229 0.986 0.998 0.01279. 0.966 0.9940.01429 0o956 0.999 0.01.79 0.993 0.9990.01.629 1.000 1.000 0,0.1479 1.000 1.u00

0.01579 1.000 1.000.

80

In -e

.0.

0.0

.

X

!BS R?. F.I18000

TITA. 70. ,P.L.2 oTiTA. 83. P.1CC.? £TiETA. 90. ..PSLCC.2 +TiCTA.100. P.L0Cu2 X

XX

XX

X- X.

XX

X

L

.0.2 0.4 0.6 0.6 1.0U/UE

Figure 4.16: Boundary-layer velocity profiles. Ribs R2. Re = 118,000.

X X

81

TAeLE. 4.10: CYLINDER WITH RIBS R2 B/I DATARE= 118000.

f

THEIÂ= 90.00

CP= -1.630. P.LOC=2

Y (FT.) HI/HO . IJ/UE

THETA= 100000.

CP= -1.179 P.LOC=

Y (FTI Hi/HO

2

U/UE

0.00454 -1.031 0.477 0000454 -1.179 0.0000.00554 -1.031 0.477 Oo00554 -1.163. 0.08.80.00654 -0.992 0.492 0.00654 -1.122 0.164.0.00754. -0.850 0.544 0.00854 -1.098 0.196.Oo0O854 -0.772 0.571 0.01054 -1.041 Oo2550.009.54 -0.638 0.614 0.01254 -0.951 0.3280.01054 -0.520 0.650 0.01454 -0.854 0.3910.01154 -0.318 0.690 0,01654 -0.732 0.459001254 -0.228 0.730 0.01854 -0.520 0.5570.01354 -0.079 0.768 0.02054 -0.358 0.6220.01454 0.228 0.841 0.02254 -0.211 0.675Q.0i554 0.40 0.879 0.02454 0.008 0.7480.01654 .0.4.96 0.899 0.02654 0.187 0.8020.01154 0.630 0.927 0.02854 0.431 0.8710,01854 0.72.4 0.946 0.03054 0.569 0.9080.01954 0.819 0.965 0,03254 0.732 0.9490.02054 0.898 0.980 . 0.03454 0.805 0.9670.02154 0.931 Oo988 0.03654 0.878 0.5850.02.254 0.984 0.997 003854 0,919 0.9940.02354 1.000 1.000 0.04054 0.943 1.0000.02454 1.000 1.0.00 0.04254 0.943 1.000

0.04454 0.943 1.000

THEIA= 70.00

CP= -1.860. Po1OC=

Y (FT) HI/HO

2

U/UE

THETA= 80.00

CP -1.829 P.LOC=

Y. (FTI ÑT/HÓ

2

U/UE

0.00454 -0.529 0.682 0.00454 -0.707 0.6300.00554 -0.074 0.790 0.00504 -0.545 0.6740.00654 01.5? 0.840 0.00604 0.390 0.7130.007.54 0,372 0.883 0.00704 -0.195 0.7600.00854 0.554 0.919 0.00804 0.057 OoBl.60.ao 954 0.694 0.945 . 0.00904 0.2.85 0. 8640.01054 0.818 0.968 0.01004 0.463 0.9000.01154 0.901 0.983 0.01104 0.626. 0.9320.01254 0.934 0.988 0.01204 0.772 0.9590.01354 0.983 .0.99? 0.01304 0.854 0.9740.01454 .Q00 1.000 0.01404 0.951 0.9910.01554 1.000 1.00 0.01504 0.984 0.997

0.01604 1.000 1.0000.01704 10000. 1.000

('Jo

o

oso0.0 0.2

82

0.6U/UE

TPTR. 70.TTRò 83.TTR 93.TITAoIOO,

0.8

X

XX

a

X

XX

"2?

XX

Xy

X

+ + + + +

LAU

A L%0

RIBSR2. .295a.PL2 )O,PLC.2 £.P.LOC2 J +

' XX

1.0

Figure 4.17.: Boundary-layer velocity profiles. Ribs R2. R = 295,000.

CV

I Ir'J

DE

R'W

IT.H

RIB

S R

2BjL

DA

tAR

E=

295

U00

,

TH

;ET

.=70

.00

CP

= -

1.85

5'P

.L)C

= 2

TH

ET

A=

80.0

0

CP

= -

1.87

1P

,LüC

= 2

TH

ET

A90

,00

TH

ET

A=

100

.00

cP=

-1.

59

P:,

LOC

= 2

CP

= -

1.28

9P

.LC

.C=

2Y

(F

I)

0454

O. C

O 5

54Li

., 00

654

o o

0O

o'O

O 6

54t)

.th)5

540.

1054

JtI

1154

U0

JL

i. t)

£35

40o

0145

40.

C 1

554

0,01

654

0.01

754

0.01

854

HI/H

O

-1.5

13 671

-0.4

36-U

.. 25

7-0

.066

0.14

50.

339

O52

20.

684

0,83

40.

522

0.96

20.

984

1.00

01.

000

U/U

E

0.34

60.

644

07 0

50.

748

0.79

2U

. &7

0.87

70.

913

'0.9

430.

971

0.9

80.

993

0.99

71.

00.0

1.00

0

Y (

F7)

0. 0

050.

40.

0060

4O

. 0)7

040'

. 00

'304

0. (

'904

.O

.Uiu

O4

0,01

1,04

1204

0.01

304

O. I

J.t 4

0 4

U. 0

15(4

0.01

604

0.01

704

0.1)

180

40.

0190

4.U

.02u

04

0.0.

2104

0002

204

HT

/H)

-1. 5

65,

_0.5

72-0

.754

0.. 5

.60

-0.3

65-.

165

0.02

90.

250

0.42

50.

634

0. 7

440.

848

0.94

60.

974

0.98

8.0

.555

1.00

01.

000

:0/0

E

0,32

60.

559

0.62

4O

..p76

0.72

40.

7 71

0.81

30'

.859

0,89

4.0

.934

0.95

40.

973

G.9

910

995.

0.99

80,

955

1.00

01.

000

.Y (

FT

)

0.00

454

0.00

554

Go

0065

4.0

.00

754.

0.0

l 8 5

'*'(J

oDO

954

0.0

1054

0.01

154

C..C

12 5

4.0.

0135

40,

0145

40,

0155

4(1

.016

5400

0175

40,

0:18

540.

C.1

9 54

0o02

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Figure 4.18: Boundary-layer velocity profiles. Ribs RB-OS. Re = 295,00.0.

0.2 0.4 0.5U/UE

anso

(jd

0.8 1.0

85

TAeLE. 4.12: CYLiNDER WITH Ribs RB-05 B/I OARE= 295000.

t

THETA= 81.50

CP= -1.660 P.LOC= i

Y (FI) Hi/HO U/UE

IHETÂ= 92.50

CP -1.500 P.LOC= i

Y (FI) HT/HO U/UE

0.00175 -1.329 0.353 0.00175 -1.370 0.229(1.00275 -1.260 0,388 0,00225 -1.432 0.1660.00375 -1.110 .0.455 0.00325 -1.315 0.2730.00475 -1.014 0.493 0.00425 -1.219 Q.3.360.00575 -0.849 0.552 0.00525 -1.151 0.3750.00675 -O.67 0,608 0,00725 -0.586 0,4550.00.875 -0.301 0.715 . 0.00925 -0.740 0.5530.01075 0.08e 0.809 0.01125 -0.459 J,o470.01275 0.452 0.891 0.01325 -0.164 (1.733O.Ci475 0,753 0.953 0.01525 0.164 0.818.0.01675 0.518 0.984 0,01725 0,466 0.8890.01815 0,986 0.997 0,01925 0.671 0.9340.01915 1,000 1.000 0.02125 0,877 0,9780,02075 1.000 1U00 0,02.i25 0.959 0,994

0.02425 0.975 0.998(1.02525 0.986 1.0000,02625 0,986 1.000

THETA 67.50

CP= -1.810 P.LGC= I

Y (FU HI/HO U/tiE

THET4 77.50

CP -1.879 P.LÜC= 1.

Y (FTI HI/HO U/tiE

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O 2. 0L 0.6U/UE

Tî\E

iE, 4

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CY

LIN

DE

R W

ITH

R!B

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X

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Figure 4.20: Boundary-layer velocity profiles. Ribs RA-05. Re = 118,000.

oA+

o.» 0.6 0.8U/UE

X

+

89

TABLE. 4.14: CYLLNDÈR ITH RIB RA-05 b/L. cA1ARE 118000. .. ,.

Tl-ETA= 87.50

CP= -1.630 PLDC= 2

Y (FI) HI/HO U/UE

THETA= 92.50

C,P= -1.552 P.LOC= 2

Y (.FT) 1-it/HO U/UE

0.00454 -1.280 0.386 0.00454 -1.360 0,2740.00504 -1.264 0.393 0.00504 -1.320 0.3020o00604 lollt 0.433 000704 -1.200 0.371Q.00704 -1,040 0,488 0.00904 -1.072 0.4340.00804 -0.960 0.518 0.01104 -0.912 0.5010.00904 -0.856 0.554 0.01304 -0.720 0.5710.0.1104 'ø.584 0.639 0.01504 -0.528 0.6330.01304 -0.280 0.722 0.01704 -0.248 0.7150.01504 0.040 0.800. 0.01904 -0.056 0.766O.G704 0.344 0.868 0.02104 0.160 0.8190.01904 0.600 0.9.1 0.02304 0.44U 0o8830.02104 0.832 0.967 0.02504 0.640 0.9270.02304 0.936 0,987 0.02704 0.800. 0.9600,02504 1.008 1.000 0.02904 0.904 0.9810.02704 0.992 0o997 0.03104 0.960 0.992

0.0.304 1.000 1.0000.03504 1.000 io000

THEÍA= 6.7.50

CP -1.696. P.10C

Y (FI) HT/hO

2

U/UE

THETA: 77.50

CP. i.8L,0 P.Lc?C

Y (FI) T/hO

2

U/UE

O.U454 -0.608 0.638 0.00454 'l.OQO 0.5440.CC54 -0.448 0o683 0.00554 -0o880 0.5810.cJJ654 -0.280 0.7.28 0.00654 -0.o80 0.639u.00754 U.00u 0.797 0.00754 -0.52.0 . 0.6820,00854 0.19. 0.841 0.00854 -0.280 0.7410.9,4 .0.408 0.387 0000954 -0o064 0.791Oo.01054 0.560 0o919 0.01054 0.088. 0.824OoO1154 0. 120 0.951 001154 0240 . 0.8.560.01254 0,8.32 0.973 0.01254. 0.448 0.8980.G134 0.888 0.983 . U.0.354 0.6.48 0.9360.01454 0.952 0.995 0.01454.' 0.792 0.9630.0155'+ 0.976 1.000 0.01.554 0.904 0,9830.01654 0.976 10000

. 0.01654 0.36 0.9890.01754. 0.984 0.9970.01854 0o992 0.9990.01954 1.000 1.0000.02054 1.000 1.000

D. ,o0.0

90

XX

0.2 0.4 0.6-U/UE

RAOS. RE2O0OOO

TTRc 67.5 .P1°2 OTPT. 77.5 .PL2 £TPTRa 87.5 .PLOC.2 +TPTAI 92.5 .PLX.2 X

0.8 1.0

Figure 4.21: Boundary-layer velocity profiles. Ribs RA-05. Re = 200,000.

f

91'

TELE. 4.15: CYLINDER WITH RIBS RA05 B/I DATAiE= 20000.

I

THETA= 87.50.

CP= -1.640 P.LCC=2

Y (FI) Hl/HO U/UE

THETA= 92.50

. CP= -1.489 P.LOC= .2

Y (FT) Hf/HO U/tiE

0.00504 -1.299 0.359 . 0.00504 -1.362 0.2260.00604 -1.223 0.397 '0.00704 -1.292 0.2810.00704 -1142 0.434 0.00904 -1.194 0.3450.00804 -1.034 0.479 0.01104 -1.067 0.4120.00904 0o564 0.506 0.01304 -0.899 0,4870.01104 -0,684 0.602 0.01504 -0.716 0.5580.01304 -0.416 0.681 0.01704 -0.520 0.6250.01504 -0.154 0,750 0.01904 -0,281 0.6970.01704 0.1.54 0.824 0.021,04 -0.014 0.7710.0.1904 0.441 . 0.889 0,02304 0,225 0.8310.02104 0.684 0.938 0.02504 0.463 0.8870.02304 0.852 0.972 0.02704 0.618 0.9210.02504 0.950 0.990 0.02904 0.772 0.9540.0?704 0.989 0.958 0.03104 0.88.5 0.9780.02904 0.994 0.999 0.03304 0.927 0.9860.03104 1.000 10000 0.03504 0.969 0.995

0.03704 0.583 0.9580,03904 0.994 1.0000.04104 0.994 1.000

THEIA= 6T050

CP: -1.661 P.LÙC= 2

Y (FI) HI/HO U/UE

THETA= 77.50

CP= -1.801 P.LOC= 2

Y (Fil HI/HO U/UE

0.00454 -0.889 0.539 0.00454 -1.056 O516O.0O54 -0.65á 0.615 0.00554 -0.952 0.5500.00654 -0.489 0o664 0.00654 -0,798 .0.5980.00754 -0.22? 0.736 0.00754 -0.588 0.6580.00854 0000 0.791 0.00854 -0.454 06940.00954 .175 0.832 0.01054 0.01,4 08050.01054 0.406 0.882 0.01254 Ø353 0.3770.0114 0.581 0.919 0.01454 0.658. 0.9370.01.254 0.725 0.948 0.01654 0.368 0.9.760.01354 0.858 0.914. 0.01854 0.966 0,9940.01454 0.93 0.988 0.02054 0,989 0.9980.01554 .0.96.7 0.95 0.02154 0.997 0.9990.01654 0.981 0.997 0.02254 1.000. 100000.01754 0.994 1.0.00 0.02354 1.000 1.0000.01854 0.994 1.000

92

oX.o

('J

¿

o

oo

0.0

- Xx +

X

++

0.2 0.4 0.6U/UE

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TITRD 675 .P.L:.2. OTTÑ. 77.5 .P..LOC'2 £TPTA. 87.5 .P.L..2 4.

TPTA. 92.5 .P.L.2 xX

A

4

;0

X

BBO

B O

X...

0.8 1.0

Figure 4.22: Boundarylayer velocity profiles. Ribs RA-05. Re = 295,000.

I

u...o

93

TI6LEO 4.16:. CYLNDER WITH RIBS RA-05 B/I DATARE= 295000.

THETA= 67.t) THETA= 77.50

I

T-E'(A= 87.50

CP= -1.ô40 P.LCC= 2

THETA= 92,50

CP -1.519 P.LOC= 2

Y (FTJ HI/HO U/UE Y (FT) tT/Ho 0/0E

0.00504 -1.399 0.302 0.00504 -1.420 C. 1cc0.Q0604 -1.295 0.361 0.00704 -1.360 0.2510.00704 -1.244 0.388 0.00904 -1.295 0.2980.00804 -1.159 0,427 0.01104 -1l79 0.3680.00904 -1.085 0.458 0.01304 -1.066 0.4240.01104 -0.868 0.541 0.01504 -0.881 0.5030.01304 -0.575 0.635 0.01804 -0.589 006080.01504 -0.291 0.715 0.02104 -0.220. 0.7180.01704 0.000 0.789 002404 0.155 0.8150.01904 0.298 0.857 0.02704 0.459 0.88o0.02104 0.570 0.915 0.03004 0.699 0.938.0.02304 0.764 0.955 0.03304 0.881 0.9760.02504 0.894 0.980 0.03604 0.946 0.9890.07U4 0.965 0.9.94 0.03904 0.984 0.9970.02904 0.997 1.000 0.04204 0.995 0.9990.0.3104 0.997 1.000 0.(4304 1.000 1.0000.03304 0.997 1.000 0.04504 1.000 10000

CP= -ioólO P0LOC= 2

Y (FT) HI/HO U/UE

CP= -loica P.Loc= 2

Y (Fi) HT/HO U/UE

0.004.54 -0.865 0.542 0.00454 -1.154 0.4770.00554 -0.767 0.582 0.00554 l.064 0.5100.00654 -0.587 0.637 0.00654 -0.942 0.5510.00754 -0.399 0.690 0.00754 -0.759 ).6080.00854 -0.194 0.744 0.00854 -0.603 0.6520.00954 0.046 0.802 0.01054 -0.179 0.7600.01054 0.260 0.8.50 0,01254 0.205 . 0.8460.01254 U,657 0.934 0.01454 00555. 0.9170.01454 0.886 0.979 0.01654 06806 0.9650o016.54 0.977 0,996 0.01854 0o545 0.9900.01854 1.000 10000 0.02054

. 0.994 0.9990.02054 1..00o 1.000 0.02254 1.000 1.000

0.02454 1.000 10000

X.

L__.ro

(JD

DD

0.0

In eO.

'4

0.2 0.6U/UE

m-10. .A&'152000

TFTA. 65. .P.LoQTIETA. 15. P.L(.OTTR. 8S.. .P.L'0TTa. 92.5 .P.L.L

0.8 leo

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Figure 4.23.: Boundary-layer velocity profiles. Ribs RA-10. Re = 152,000.

95

TABLE. 4.17: CYLÌNDER WITH JBS RA-IO 8/L DATARE= 152000.

f

THETA= 85.00 .

CP= -1.d21. P.LOC= O

Y (FI) HI/HO U/UE

THETA= 92.50

CP -1.532 P,LOC= i

Y (FI) HI/HO U/UE

0.00154 -1.741 0.168. 0.00300 -1.393 0.2350.00254 -1.468 0,354 0.00400 -1.104 0.4110.00354 -1.194 0.471 0.00500 -1.045 0.4390.00454 -0.945 0.557 0.00600 -'0.570 0.4710.00554 . -0.647 0.645 0.00700 -0.896 0.5010.00654 -0.488 0.688 000800 -0.796 0.5390.00754 -0.323 0.729 0.00900 -0.697 0.5750.00854 -0.155 0,768 0.01000 -0,547 06240.01054 0.19c 0.846 0.01200 -0.323 Oo691

0.01254 00557 0.918 0.01400 0.050 0.7900.01.454 0.796 0.963 0.01600 0.348 0.862O.a1654 0,545 0.990 0.01800 0.572 0.9120.017.54 0.985 0.997 0.02000 0.796 0.9590.01854 1.000 1.000. 0.02200 . 0.920 0,9840.01554 10000 1.000 0.02300 0.955 O991

0.02400 0.970 0.9940.02.500 10000 1.0000.02600 1.000 1.000

TP.ETA= 5.00

CP= -1.763 P.LOC= O

Y (FTI HT/HO U/U.E

THETA= 75.00

CP= -1.900 P.LOC= O

Y (FT) MT/HO U/UE

0.00154 -1.253 0.430 0.00154 -1.542 0.3510.00254 -0.915 0.553 0.00204 -1.517 0.3630.00354 -0o31 0.724 0.00304 -1.343. 0.4380.00454 0.217 0.847 0.00404 -0.945 0.5140o00554 Qa455 0.896 0.00504 -0.498 0.6950.00654 0.606 0.926 0.00604 -0.224 007600.00754 0.732 0.950 0.00704 0.075 0.8250.00854 0.808 0,965 0.00804 0.224 0.8560.00954 0.884 0.9.79 0.00904 0.373 0.8850.01054 0.94c 0.991 0.01004 0.572 0.92.30.01154 0.585 0.997 0.01104 0.711 0.9450.01.254 1.000 1.000. 0.01204 0.896 0.9820.01354 1.000 1.000. 0.01304 0.955 0.992

0.01404 0.990 0.9980.01504 1.000. 1.0000.01604 1.000 1.000

96.

a

RR-rO. REa29S000

TETR. 65. ,P.L.QTETÑ. 75. . P,L.QTETRo 85. P.u.oflTA. 92.5 .P.LOC.$

Figure 4.24: Boundary-layer velocity profiles.. Ribs RA-10. Re = 295,000.

t

oz.

0(V)

XX

>-

(J

XX...

Xo

-s

dX

+.+ 88.

XXX

+

L OoO

o0.0 0.2 0.4 0.6 0.8 p.0.

[J/UE

IO£+X

97

TABLE. 4.18: CYLINDER WITH RIBS R!i-10 B/L DTARE= 295000.

f

THETA 85.0O

CP 10 770 P.LOC

y (FT) HT1O

.

O

U/LIE

THETA= 52.50

CP -1.480 P.L0C iY (FI) HT/Hb U/LIE

0.00204 -1.609 0.241. 0.00400 -1.476 0.0400.00254 -1,605 0.241 0.00500 -1.297 0,2720.00354 -1.45 0o337 0.00600 -1.190 0.3420.00454 -1.3.16 0,405 0.00700 -1.117 0,3830.00554 -1.02' 0.519 0.00800 -1.064 0.4100.006.54 -0.878 0.5o8 0.00900 -0.989 0.4450.00754 -0.6o5 0.ø32 0.01000 -0.891 0.488Oo00854 -0,505 0.6.76 0.01200 -0.678 0.5690.01054 -0.19 0.755 0.01400 -0.439 0.6490.01254 0.180 0,839 0.01600 -0.199 0.7200.01454 0.515 0.9.09 0.01800. 0.030 0.7940.01654 0.745 0,953 O020(?0 0.346 0,8590.01854. 0.911 0.984 0.02200 0.572 0.9110.01954 0o951 0.991 0.02400 0.771 0.9540020,54 0.984 0.997 0.02600 0.878 0.9760.02154 0.996 0.999 0. 02900 . 0.971 0.9950.0254 1.000 1.000 OoO3IOO. 0.991 0o9990.02354 1.000 1.000 0.03300 0.993 lo000

0.03500 0.993 1.000

TFETA= 65,00

CP= -1.709 P.LuC= i)

Y (FU HT/Hfl Li/LIE

THEA= .15.00

CP= -1.859 P.LOC= O

Y (FI) HI/HO U/UE

0.00154 -1,121 0.466 0.00254 -1.379 0.4230.00254 -1.100 0.474 0.00354 -1.273 0.465O.354 -0.913 0.542 0.00454 -1.074 0.5330.00454 -0.567 0.649 0.00554 -0.723. 0o.,370.0v554 -U.Ifl 0.76 0.00654 -0.458 0.7050.00654 0.12u 0.822 0.00754 -0.186 0.7690.0074 0.287 0.858 0.00854 0.027 0.815'0.0( 854 0.44.7 0.892 U. 01054 0,378 . 0.8860.00954 0.620 0.927 v.01254 0716 0.950001054 0.740 0.951 0.01454 0.508 0.9840.01154 0.867 0,575 0.01.654 0.981 0,9970.01254 0.927 Oo986 O01854 0.995 0.9990,01354 0.960 O.93 0.02054 1,000 1.0000.014.54 0.991 0.998 0.02254 1.000 1.0.000.0154 1.000 1.0000.0.1654 1.0.00 1.000

-xD

.mD

('JD

sD

osD0.0

92

+

LAO

+

ee

RR-20. RE»!52000- TPTA. SS. P.LØo TPT. 80. .P.L.O

TFTAuIOO,

0.8 1.0

o£+

Figure 4.25: Boundary-layer velocity profiles. Ribs RA-20. -Re = 152,000.

t

0.2 0.' 0.6U/UE

TH

ET

A=

65.0

0.

.

CP

= -

1.8.

2.5

P0L

OC

= O

TH

ET

A=

8000

CP

= -

1.90

P.L

OC

= 0

.

TH

ET

A=

100

.00

CP

'-1.2

15P

.LO

C=

O

V (

Fil

I-IT

/HO

U/U

EY

(F

TJ

PiT

/Ha

U/U

EY

(F

I)H

I/HO

U/U

E

0QO

154

-0.2

70.0

.742

0.0.

0154

0.62

00.

673

0.00

154

-1.1

250.

202

0.00

204

-0.1

300.

775

0.00

204

-0.4

800.

707

'Oo0

0254

-1.1

000.

228

0.00

.304

0.57

50.

922

'0.0

0.30

4-0

.130

0,78

60.

0035

4.-1

.050

'0.

273

0.0.

0404

0.90

00.

982

0.00

404,

..0

.260

0.86

60.

0045

40.

950

0.34

600

0504

0.97

509

.96

0.00

504

0.49

00.

910

0.00

554

-0.8

500.

406

0.00

604

0.99

00.

998

0.00

604

0.76

00.

959

0.00

654

0:.7

500.

459

0.00

704

1.00

0Io

000

0.00

704

0.87

00.

978

0.00

754

-0.6

500.

506

0.00

804

.1.0

001.

000

0.00

804

0.96

00.

993

0.00

854

0.45

00.

588.

0.00

904

0.01

004

0.98

01.

000

0.99

71.

000

0.01

054,

0012

54-0

.165

' 0.1

50'

0.68

90.

786

0.01

,104

1.00

01.

000

0.0,

1454

0.40

00.

855

0.01

654

0.01

854

0.62

00.

775

0.91

1,0.

949

0.02

054

:0.9

000.

978

0.02

2:54

0.99

5'1

.000

'0.

0235

40.

995

1.00

00.

0245

4.0

.995

1.00

0.

TA

aLE

., 4.

19':

CY

LItD

ER

WIT

H R

IBS

RA

-20

8/L

DA

flR

E'

1520

00.

o-o

+

loo

0.60.2U/UE

-20 RE.29500Q

TITR. S .P.Laco oTITR. 72.5 ,P.Loe.L. ATPTRa 80. .P.L0C0 +.TETA. 85. ,P.Ltt'OE XTTÑa 92.5 .PLOE.ITpT3oo. ,P.L0C0 +

XX.xx_jI&+l

o

+

4

4

0.8 1..0

Figure 4.26: Boundary-layer velòcity profiles. Ribs RA-2O. Ré = 295,000.

101

TABLE 4.20: CYLINDER WITH RIBS RA-20 B/L DATARE = 295000.

I

=85.00CP = -1.973 P.LOC O

Y (FT) MT/HO U/UE

-TRETA = 92.50 -

ÇP = -1.620 P.LOC.= iY (FT) HT/HO U/tiE

1REA I00.Ó0.CP = -1.320 P.LOC OY (FT) HP/HO U/tiE

0.00154 -0.880 0.606 0.00300 -1.645 0.000 0.00154 =1.307 0.0760.00254 -0.860 0.612 0.00400 -1.028 0.475 0.00254 -1.300 0.0930.00354 -0.647 0.668 0.00500 -1.807 0.557 0.00454 -1.280 0.1310.00454 -0.480 0.709 0.00600 -1.664 0.604 0.00654 -1.227 0.2010.00554 -0.296 0751 0.00700 -1.520 0.648. 000854 -1.113 0.2990.00654 -0.140 0.785 0.00800 -1.387 0.686 0.01054 -1.000 0.3720.00754 0.047 0.824 0.00900. -1.213 0.733 0.01254 -0.787 .0.4800.00854 .240 0.863 0.01000 -1.073 0.768 0.01454 -0.627 0.5470.00954 0.447 0.902 0.01200 0.227 0.840 0.01754 -0.300 0.6630.01054 0.647 .0.939 0.01400 0.493 0.898 0.01954 -0.040 0.7430.01154 0.773 0.961 0.01600 .0.720 0.945 0.02154 0.200 0.8100.01254 . 0.880 0.980 0.01800 0.885 .0.978 0.02354 0.400 0.8620.01354 0.947 0.991 0.02000 0.967 0.994 0.02554 0.560 0.9010.01454 0.973 0.996 0.02200 0.993 0.999 0.02754 0.700 0.9340.01554 0.987 0.998 0.02400 1.000 1.000 0.02954 0.807 0.9580.01654 0.993 0.999 0.02500 1.000 1.000 0.03254 0.920 0.9830.01754 1.000 :1.000 . 0.03554 0.973 0.995.01854 1.000 .000 0.03854 0.997 1.000

0.04054 0.997 1.000

THETA=65.0.0CP -1.920 P.LOC = 0Y (FT) MT/HO U/UE

THETA= 72.5CP =-2.100 P.LOC = iY (FT) MT/HO U/UE

THETA= 80.00CP = -.2.067 P.t1Öc = oY (FT) MT/HO U/uE

0.00154 -0.080 0.794 0.00300 -1.533 0.428. 0,00154 -0.920 0.6110.00254 0.216 0.855 0.00350 -1.047 0.583 .0.00254 -0.740 0.6580.00354 0.393 0.890 0.00450 -0.233 0.776 0.00354 -0.540 0.7060.00454 0.544 0.919 0.00550 0.107 0.844 . 0.00454 -0.267 0.7660.00554 0.667 0.941 0.00650 0.340 0.887 0.00554 -0.027 0.8160.00654 0.799 0.965. 0.00750 0.533 0.922 0.00654 0.273 0.8740.00754 0.893 0.982 0.00850 0.680 0.947 0.00754 0.524 0.9190.00854 0.967 0.994 0.00950 0.793 0.966 0.00854 0.667 0.9440.00954 0.987 0.998 0.01050 0.873 0.979 0.00954 0.792 0.9650.01054 1.000 1.000 0.01150 0.940 0.990 0.01054 0.884 0.9810.01154 .1.000 1.000 0.01250 0.973 .0.996 001154 0.933 0989

0.01350 0.993 0.999 0.01254 0.973 0.9960.01450 1.000 1.000 0.01354 0.993 0.9990.01550 1.000 1.000 0.01454 1.000 1.000

0.01554 1.000 1.000

102

RC-O5. RE.295000

ncîn. 67.5 ..icx.sTTÑ 17.5 .P.Lt.LTPT. 87.5 ,P.LLX.tTCT. 92.5 P.Lt

Figure 4.27: Boundary-layer velocity profiles. Ribs RC-05. Re 295,ÔOO.

103

TABLE. 4.21: CYLINDER WATH RIES RC-05 b/ DATARE= 295000,

I

THETA= 87.50

CP= -1..b40 P. LUG: i

Y (FT) lIT/HO U/UE

THETA 92.50

CP= -1.500 P.LOC= i

Y (FT) HI/HO UÌUE

0.00729 -1.393 0.306 0.00729 -1.406 0.1940.00779 =1.352 0.330 0.00829 -1.359 0.2380.00879 -1.292 0.363 0.00929 -1.345 0.2490.00979 -1224 00397 0.01029 -1.326 0.2640o01179 -1.087 0.458

. 0.01129 -1.304 0.2800.01379 -0.883 0,535 0.01.329 -1.209 0.3420.01579 -0.645 0.614 0.01529 -1.114 0.3940.01779 -0.390 0.688 0.01729 -0.992 0.4520.01919 -0.109 0.762 0.01929 -0.802 0.5290.02179 0.190 0.833 0.02129 -0.639 0.5.880.02379 0.435 0.887 0.02329 -0.448 0.6500.02579 0.652. 0.932 0.02529 -0.245 0.7100.02779 0.795 0.960 0.02729 0.0.00 0.7.760.02979 0.910 0,983 0.O299 0.224 0.83.20.0.3179 0.971 0.995 0.03l9 0.428 0.8800.0.3379 0.992 0.998 0.03329 0.602 0.91.80.03479 1.000 1.000

. 0.03529 0.747 Co9500.03579 1.000 1.000 0.03729 0.836 . 0.9680.03929 0.891 0.9810.04129 0.951 0992004329 0.978 0.9970.04529 0,992 1.0000.04729 0.952 1.000

THETA= 67.50

CP= -la 780 .P'.LCC= 1

Y (FT) Hi/HO U/UE

HETA= 77.50

CP= -1.860 P.Loc= i

'y (.FT) HT/HO U/UE

0.00625 -0.57 0.516 0.00625 -1.163 0o4940.0725 -0.788 0.598 0.00725 -1.073 Uo5240.00825 -0.604 0.651 0.00825 -0.931 0.5700.00925 -0.414 0.701 0.00925 0.754 0.6220.01025 -0.174 0.760 0.01025 =0.605 0.6630.01125 0o041 0.810 0.01125 -0.421 0,709.0.01225 0.245 0.854 0.01225 -0.217 0.7580.01325 0.426 0.891 0.01425 0.190 0.8470.01425 0.585 0.923 0.01625 0.495 0.9070.01.525 0.725 0.950 OO1825 0.747 Oo9550.01625 0.850 0.973 0.02025 0.924 0.9870.0172.5 0.925 0.987 0.02225 0.578 0.9960.01825 0.955 0.993 0.02325 0.992 0.9990.01925 0.986 0.998 0.02425 1.000 1.000.0o02025 0.997 1.000 0.02525 1.000 1.0000.02125 0.957 10.0O

104

Figure 4.28: Boundary-layer velocity profiles. Ribs RC-lO. Re = 295,OOQ.

TIE

T.A

=72

.50

C.P

= -

1.84

0P

.LO

C=

i

Y (

FI)

HT

/HO

U/U

E

TH

ET

A=

. 82.

50

CP

= -

1.76

0P

.LO

C=

i

Y (

Fil

Hi/H

OU

/U;E

TH

ET

A=

92.5

0

CP

= -

.1.5

59P

.LO

C=

i

Y IF

flH

i/HO

U/U

E

0.00

575

-1,9

750.

000

0O05

75-1

.781

0.00

00.

0057

5-1

.452

0.20

50.

0061

5-1

.468

0.36

20.

0067

5-1

.507

0.30

30.

0067

5.-1

.425

0.23

00.

0077

5-1

.021

0.53

50.

0077

.5-1

.247

0.43

10.

0077

5-1

.384

0.26

20.

008.

75-0

.753

0.61

80.

00a7

5-1

.103

0.48

.8(3

.008

75-1

.356

0.28

20.

0097

5-0

,586

0.66

40.

0107

5-0

.918

0.55

20.

0097

5-1

.315

0.31

00.

0107

5-0

.486

0.69

00.

0127

5-0

.6i8

0.62

60.

0117

5-1

.253

0.34

60.

0117

5-0

.329

0.72

90.

0147

5-0

.404

0.70

10.

0137

5-1

.185

0.38

30.

0127

5-0

.192

0.7.

620.

0167

5-0

.137

0.76

7.

0.01

575

'1.0

680.

439

0.01

375

0000

00.

805

0.01

875

0.21

50.

846

0.01

775

-0.5

450.

491

0.01

415

0.15

60.

838

0.02

.075

0.50

00.

905

0.01

975

-0.7

950.

548

0.01

575

0.33

60.

815

0.02

275

0.71

00.

946

0.02

175.

-0.6

710.

591

0.01

675

0,48

609

.05

0.02

475

0.87

00.

976

0.02

375

-0.4

520.

659

0.01

775

0.65

80.

938

0.02

675

0.95

20.

991

0.02

575

-0.2

670.

712

0.01

875

0.75

30.

956

0.02

875

0.99

710

000

0.02

775

-0.0

480.

770

0.01

975

0.83

604

971

0.02

975

1000

0.1.

000

0.0.

2975

0.15

80.

821

0.02

075

0.91

10.

984

0.03

075

1.00

01.

000

0.03

175

0,33

80.

863

0.02

115

0,Ç

590.

993

.0.

0337

50.

525

0.90

50.

02'2

?50.

986

0.99

8.

0.03

575

0.67

10.

936

0.02

375

1.00

01.

000

.0.

0377

50.

760

0.95

50,

0247

51.

000

1.00

0.

0.03

975

0.83

60.

970

0.04

175

0.91

10.

985

0.04

375

0.95

50.

995

0.04

475

0,98

61.

000

0.04

575

0.98

610

000

TA

BLE

. 4.2

2:C

YLI

IDE

R W

1TH

RIe

S R

C-lo

8/L

DA

TA

RE

= 2

9500

0G

oX -.-D

.m

LL

>-

.

X0

£LDo

0.0. 0.2 0.11

106

LA

+

I0.6

U/UE

RC-20. RE.295000

TFTfl. 72.5 .P.L.L OTITR. O. .PSL0X LTPTR. 92.5 .P.LII +TPTA.IOO. .P.L°0 X

X

X

AO

4.

+

X

+

X

0.8 1.0

Figure 4.29: Boundary-layer velocity profiles. Ribs RC-20. Re = 295,000

107

TABLE. 4.23: CYLiNCER WITH RIBS PC20 B/L DATA.RE= 295000.

THETA: 12.50 THETA=.. 80.00

IHETA= 9250,

cP= -1.600 P.LDC= i

Y (FT) HI/HO U/LIE

THETA= 100.00.

CP= -1.437 P.LOC= O

Y (Ft.) HT/H0 U/LIE

0.00575 -1.616 0.000 0.00154 -1.465 0.0000.00675 . -1.548 0.142 0.00254 -1.479 000000.00775 -1.345 0.311 0,00354 -1.487 0.0000.00875 -1.205 0.391 0.00454 -1.493 0.0000.01075 -1.000 0.482 0.00554 -1.479 0.0000.01275 -0.856 0.536 0.00654 -1.476 0.0000.01475 -0.671 0.599 0.00854 -1.431 0.0540.01615 -0.493 0.654 0.01054 -1.382 0.1520.0.1875 -0.315 0.705 0.01254 -1.319 0.22.10.02075 -0.068 0.770 0.01654 -1.153 0o3440.02275 0.096 0.810 0.020.54 -0.931 0.4590.02475 0.308 0.859 0.02454 -0.639 0.5760.02675 0.49.3 0,900 0.02854 -0.333 0.6770.02875 0.685 0.940 0.03254 -0.014 0,7690.03075 0.808 0.965 0.03654 0.278. 0.8440.03275 0.877 0.979 0.04054 0.556 0.9090.03475 0.945 0.992 0.04454 0.722 0.947

.0.03675 0.973 0.997 0.04854 0.875 0.9800.03875 0.586 1.000. 0.05254 0.944 0.9940.04075 0.986 1.000 0.05654 0.972 1.000

0,06054 0.572 1.000

CP -1.779 :P.LÜC

Y (FI) HT/HO

1.

uluE

CP -1.800 P.LOC

v (FI) HT/HO

O

U/LIE

0o00575 2aÓ82 0.000 OoOOl54. -1.493 0.3310.00675 -1.475 0,i29 0.00254 -1.411 0.730.00775 -0.663 0.635 0.00354 -1.288 0.4280.00875 -0.253 0742 0.00454 -1.144 0.4840.CQ97 -0.U86 0.731 0000554 -0.952 0.5500.01075 0.055 0.814 0.00654 -0.774 0.6050.01175 0.200 0.84 0oOO854 -0.356 0.7180.01275 0.356 .0.8.78 .0.01054 0.068. 0.8170.01375 0.493 0.905 0.01254 0.411 0.8890.0147.5 0.610 0.928 0.01454 0.644 009340.0.1515 0.712 0.948 0.01654 0.8.15 0.9660.01675 0.815 0.967 0.01854 0.526 0.9870.01775 0.877 0.979 0.02054 0.959 0.9930.01815 0.932 0.989 0.02254 0.993 0.9990.01975 0.973 0.996 0.02354 1.000 1.0000.02015 0.993 1.000 0.02454 1.000 1.0000.0t.175 0.993 1.000

108

In order to reduce the error in U/tiE in the vicinity of the

ribs one could assume that C (y) I décreased. linearly from a value of

C at.y =.k, where. tC is the variation of thé local pressure coefficient

downstream of a rib from the overall pressure coefficient, to zero at y 2k.

Such assumptions have, however, been avoided due to the absence of accurite

information on the pressure field normal to the cylinder in the vicinity

of the ribs.

4.2.3 Summary of boundary-layer data.

The veloòity profiles shown in Figures 4.12 and 4.13 for the

distributed roughness (kid = 2 .66x103) wére analyzed to determine the

nominal boundary-layer thickness , the displacement thickness 6, and

the momentum thiökness e. The boundary-layer thicknéss 6 is defined

These integrations were performed using smoothed values of u/uE and the

trapezoidal rule, with a step length of 0..056. The results are shown in

Table 4.24, where the normalized values 6/d, 6*/d, and /d are tabulated

as functions of thé angular position 8. Also tabulated are the values

of the local pressure coefficient C and the shape factor H E The

values of 5, and were not evaluated for the case with the travérse

at 1/8 in. above midsection of cylinder and only the values of 6 and C

are listed for this case. The complete pressure distributions corresponding

to these experiménts can be found in Appendix 2.

For the case of rib roughness, the integral boundary-layer para-

meters were not evaluated due to the basic uncertainty concerning the

applicability of the usual boundary-layer concepts in the neighborhood

of the ribs. The large local pressuré variatiOns réferred. to earlier not

only introduce errors in the values of U/ilE but also make the usual boundary-

layer assumptions doubtful in the vicinity of the ribs. Fürthermore,

as. the value of where U/UE = 0.995, and the displacement and momentum

thicknesses are defined in the usual manner by

5* j(l - -fl-) dy (4.3)

OEJ (l--23dy (4.4)Jo tiE t

Re = 154,000

C S/dx].O3 d*/dxlO3 &ìdxlo3 H

Re = 154,000 (traverse at 1/8 in. above midsection)

Re = 304,000

o 5/dxlO3 5*/10 /dx103

109

Table 4.24: Summary of bOundary-layer data. Distribúted

roughness (k/d 2.66x103).

cS/dxlO3

t

68 -1.819 0.1 2.38 1.55 1.5473 -1.870 1 14.1 3.38 1.95 1.7383 -1.714 17.5 5.08 2.85 1.7893 -1.471 33.2 11.94 5.19 2.30

73 -1.875 14.6 4.96 2.52 1.9783 -1.734 21.4 6.67 3.09 2.1693 -1.540 41.1 15.60 6 17 2.5398 -1.456 56.3 24.85 8.32 2.99

73 -1.849 13.583 -1.693 18.093 -1.466 36.0

o Cp

(a) Rl. (k/d=1.97x103) (b)R1. (k/d=l.97x103) (c) R2. (k/d=3.38x103)Re 152,000 Re =287,000 Re = 118,000

6/didO3 O 6/dxlO

110

38

(d) R2. (k/d=3.38x103) (e) RB-05 (k/d=1o97xlO) (f) RB-b (k/d=l.97x103)Re = 295,000 Re= 295,000 Re = 295,000

t

e 6/didO3 8 6/dxlO3 O 6/dxiO3

70 18.6. 67.5 12.1 65 : 9.080 20.3 77.5 15.2 75 11.390 31.0 87.5 21.1 85 l4l

lOO 56.9 97.5 26.2 92..5 18.0102.5 41.7

70 5.63 70 12.7. 70 15.2

80 7.89 80 14.4 80 16.990 11.49 90 18.0 90 25.4

100 20.28 100 34.9 100 43.5

the velocity profiles close to the cylinder in the région of local influnce

of the ribs display fundamental differences from each other depending on

the location of the traverses relative to the ribs. This can be seen, fbr.

example, by a comparison of the profiles at 8 = 72.5°and O 806 in Fig.

or in Fig. 4.29. In previous studies with rib-type roughness, the integtal

parameters have been usually evaluated using the rib height as the lower

limit of integration in the definitions of 6* and O (see# for example, Liu,

Kline and Johnston 1966). Hôwever., whilê this procedure may be acceptable.

in cases where the boundary-layer thickness is large compared with the rib

height and the ribs are closely spaòed, its applicability is questionable.

in rib configurations examined here, especially with the two larger ribs

(rib type numbers 2 and 3) On the other hand, the nominal boundary-layer

thickness 6 (measured from the smooth wall) retains a certain amount cf

physical significance and can be determined with acceptablè accuracy. The

values of 6/d for the boundary-layer experiments with rib roughness are

shown in Table 4.25. Further discussion of the significance of the boundary_

layer data and their usefulness in the interpretation of the pressure

distributions is given in Chapter V.

Täble 4.25: Summary of boundary-layer data. Cylinders with ribs.

Ré = 295,000

e 6/dxlO3

lii

Table 4.25: continued

Cm.) RA-20 (k/d=3.38x103) (n) RC-05 (k/d6.47x1O) (o) RC-lO (k/d=6.47x103)Re = 295,000 Re = 295,000 Re= 295,000

Velocity profiles free of error.due to local influence of ribs.

ç

(g) RA-05 (k/d=3.38x103)Re 118,000

(h) RA-05 (k/d=3.38x1&3)Re =20Q,000

(i)' RA-05 (k/d=3.38x103)Re = 295,000

e 6/dx103 O 5/dxiO3 O d/dxlO3

67.5 16.4 67.5 .5 67.5 18.677.5 19.787.5 27.6

.77.5 21.4.87.5 29..3

77. 5 22.087.5 30.5

92.5 36.6 92.5 39.4 92 ..5 43.9

(j) RA-10 (k/d=3.38xl0) (k) RA-10 (k/d=3.38x1«3) (1) RA-20 (k/d=3.38x103)eL= 152, 000

. Re 295,000 Re = 152,000

e 6/dxlO3 e 5/dxl03 . e

o,i,io3 e s/dxlo3 O cS/dicio3

65* 10.1. 67.5 20.8 72.5 24.. 872.5 13.5 77.5 25.1 82..5 30.480* 14.1 87.5 35.8 92.5 49.385 16.3 92.5 48.492.5 22.5

100* 40..0

(p) RC-20 (k/d=6.47x103)

65 12.4 65 15.8 65* 5.675 5.2 .75 18.0 . 80* 9.685 19.2 85 22.5 100*

. 24.892.5 27.0 92.5

. 32.7

72.5 22.28Ò 23.792.5. 39.4

100 59.3

11 2

V. DISCUSSION OF RESULTS

5..l Effects of Distributed ughness

.5.1.1 Drag coefficient

The variation of the drag coefficient (corrected for blockage

effects as described in Appendix 1) with Reynolds number and relative

roughness is shown in Fig. 5.1. This figure also Shows theresults obtained

by Achenbach (1971), Roshko (1961) and Batham (1973). It will be seen that

the présént results are in good general agreement with those of Achenbach

(971),. Thé results are also consistent among themselves except for those

obtained with k/dxlO3 = 2.66 and 3.55 for which no systematic difference

in C can be seen. This apparent inconsistency. may be due to the differences

in the spatial distribution of the roughness elements on the sandpapers as

can be seen from Fig. 3.12. A comparison of the present resúlts for k/dxlO3 =

2.66 and 3.55 with Achenbach's results for k/&d03 = 4.5 appears to indicate

that the effective surfaCe roughnesses in the present tèsts were largér than

the nominal relative roughness based on the geometric sizes of the roughness

elements. It may be remarked that Achenbach's relative roughness.values are

based on an equivalent. Nikuradse roughness obtained from duct tests. The

observed differences can, however, be partly attributed to the differences

in the length to diameter ratios lid Cf the test cylinders. In the present

tests l/d = .3.08 and in Achenbach's tests 1/d = 3.33. Similarly, it is

seen that the value of Cd obtained by Bathain (1973) for k/d = 2.17xl03 and

Re = 2.35xl05 is much lower compared with the present results for k/d

2.66x103. In Batham's tests the value of l/d was 6.67.

The effect of freestream turbulence level on the. behavior of Cd

Re curve can also be deduced from Fig. 5.1. It is seen that the critical

Reynolds-number range iñ the present tests is very narrow compared with that

in Achenbach's tests. The freestreaxn turbulence intensity jn Achenbach's

tests was 0.7% compared with 0.2% in the present tests. It is known (see,

for example, Farell (1971), or E.S.D.0 (1970) data item) that a higher

turbulence level causes a reduction in the value of the Reynolds number at

which the subcritical flow regime ends. The critical.range is consequently

wider fàr higher freestream turbulence.

AcheñbachÏ971 k/cl =. ir.1x103

Present study:

k/dx103

Osmooth

l.59

y 1.98

®2.66

O3.55

o 6.21

Re

Figure 5.1:

Drag coefficient of cylinders with distrIbuted roughness..

-(Values corrected for blockage.)

r

114

While it is difficult to estimate accurately the éffécts of

different lid ratios, and the effective values of the relative roughness

parameter, several preliminary conclusions can be drawn concerning'the efects

of surface roughness, especially at the higher Reyholds numbers, on the asis

of the results shown in Fig. 5.1. Although the present tests were limited

to a Reynolds-number range below 6x1O51 it. cän' be seen that Reynolds-

number independence was achieved completely in the tests with the larger k/d

values and very nearly in the tests with k/dxlO3 = 1.59 and 1.98. 'The

present results indicate that when the values of'both Re and k/d are large

enough, Cd becomes independent, of Re as well. as kid. However, Achenbach's

.résults with k/d = l..lxlO3 shòw that if the. relative roughness is not

large enough, Cd continues to depend upon the value 'of kid even' at large

Reynolds numbers and that.its value is lower for smaller relative roughness.

More. detailed discussiob of the aforemenioned behavior is'given in section

5.3.1.

5.1.2 Pressure distributions

The 'variation. of the, average base-pressure coefficient, C ,. andpb

the, minimum pressure coefficient, C , with Re, and k/d are depicted inpm

. .3Fig. 5.2. In the interest of clarity, only thé results for k/dxlO = 1.59

and 6.21 are shown. Included in Fig. 5.2 for comparison are the data of

Batham (1973) and curves based On Achenbach's (1971) rèsults. All the

results shown :fl Fig, 5.2 have been correctéd for blockage effects. An

xamination of. the beha\ior of these parametêrs is important not only since

they suimnarize the main characteristics of the pressure distributions but

also shed some light on the overall.effécts of surface roughness. Indeed,

it will be shown later that the difference C' C is closely conñectedpb pm

with' the characteristics of the boundary layer prior tO separation, which,

in turn, influences the pressure distribution.

I't will. e seen froth Fig.. 5.2 that both C ..and C show apb pm

systematic variation with 'the Reynolds nimber and relative 'roughness,

as did the drag coefficiént. Examination of the curves for k/dxlO3 =

1.59 shows that C becomes a minimum, ànd Ic .. j becomes a' maximum at"pb '. pmthe same Reynolds number for :Which the' òorresponding drag coefficient

Cpb

-0.5

-1.0

-1.0

-1.5

-2.0

-2.. 5

-3.0

115

b.4.5

Present study:

k/d1O smcoth

1.59

smòoth

- o 6.21 smooth

I I I- QL

Bathain 1973:

®k/d = 2.11x10

3 / Achenbach 1971-.k/dxlO 1.1_,/ (broken lines)_,

/i.

7x10 10 2 3 4 6 7x105Re

Figtare 5.2: Variation of C and C with Re, and k/d aspb. pm.

parameter.. Cylinders wïth distributed roughness.

(Values corrected for blockage)

116

curve in Fig. 5.1 indicates a minimum value ofCd..-As the Reynólds number

increases beyond this value, Ic decreases while jcIand C increase,pm pb d

until all attain nearly cónstant values asymptotically at some large Reynolds

number. While this similarityand connection between the behaviors of CbC and Cd are not very surprising, it is interesting to note the rather

marked sensitivity of the drag coefficient to the value of the minimum.

pressure coeffïcient, as revealed by the curves for k/dxlO3 1.1 taken

from. Aòhenbach (1971).. It is seen that, although thê asymptotic value of

Cb for k/dxlO3 = 1 1 is practically the saine as that for the other relative

roughnesses, the values of Cd are quite different.. Moreover, the differences

in C appear to be correlated with those in Cd .. pm

The observed variatiòn of the angle O with Reynolds number and

relative roughness is depicted in Fig. 5.3. Recall that O may be regàrded

as approximate angular location of separation. Comparison of Figs. 5.2

and 5.3 show that, as 0 decreases in the supercritical Reynolds-number

range, i.e.. as the separation point moves forward, ICbI increases and ¡C

decrease. Thi is consistent with the potential flow model of Parkinson

and Jandali. (1970). It can also be seén from Fig. 5.3 that shôws the

saine transitional changes with Reynolds number as do Cd, C and Cb

The overall effect of surface roughness on the pressure distributions

is best seen in Fig. 5.4 where. the variation of C - C with Re and k/dpb pm

is depicted. It will be seen that, in the supercritical Reynolds number

range Cb.

C decreases with increasing relative roughness for a given

Reynolds nümber. Furthermore, the incremental changes'in Cb C decrease

with increasing roughness. As wifl be discussed later on in greater detail,

the difference C - C is closely cnnected with the characteristics ofpb pm

the boundary 1aye prior to separation and therefore its strong dependence on

the relative roughness is not surprising. This quantity is also important

because it is quite insensitive to bockage effects (see Appendix 1) and

free-end effects (see Section 5.3.2 in which a comparison with cooling-tower

results is made).

130

120

110

ew

100

90

80

70

117

7x104 2 3 4 5 6 7x105Re

Figure 5.3: Variation of with Re, and k/d as parameter.

Cylinders with distributed roughness.

3.0

2.0

ç. -cpb pm

1.0

.0

118

7x104 2Re

7x10

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

Cylinders with distributed rughriess. (Symbols same

as in Fig. 5.2)

11.9

5.1.3 Boundary-layer characteristiäs

It was remarked previously that there is a döse connectiôn between

the characteristics of the boundary layer on the cylinder and the pressure

distributions In this section the boundary-layer data for the cylinder

wIth distributed roughness are examined with a view to show the nature of

this connection and a theöretical basis is advanced för the observed

relationships.

In what follows, we shall be concerned primarily with the boundary

layer behavior in the range of e lying between the location of the pressure

minimum O and that of the point of separation. Upstream of O the boúndary

layer remaIns very thin due to the severe favorable pressure gradient and

consequently accurate measurements cannot be made. In any case, for larger

surfacé roughnesses, it is doubtfúl whether the flow over the forward part

of the cylinder can be treated within the ftamework. of usual boundary-layer

theory. As can be seén from Fig. 5.5, however, the flow ver the middle

part of the cylinder, where the pressure increases from C to CPb..and the

pressure gradient is adverse, is. of the boundary layer te and the. measure-

ments reported in the previous chapter can be used to interpret the influence

of Reynolds number and surface roughness on the mean presthure distributions.

Iii order to understand the boundary-layer development in the aforementioned

region and establish its connection with the .préssure distribution it is

of course necessary to have sOme indication of the boundary layer properties

at the most. upstream station. As rarked upon earlier the boundary-layer

traversing mechanism was capable of making 'measurements uptö O = 65°, which,

fortunately, lies somewhat upstream of the location of the pressure rninimum for

the different roughness es tested..

Fig. 5.6 shows the velocity profiles measured in the neighborhood

of the pressure minimum for k/dxlO3 = 2.66 at twó different Reynolds

numbers. Also included for comparison is the profile measured by Patel '(1968)

on a smooth cylinder, fitted with trip wires at O ±450, at a higher

Reynolds number. These profiles clearly indicate the retardation produced by

the sürface ròughnéss at the two Reynolds numbers. First of all, it is seen.

that the boundary layer flow is retarded more with Re = 304000 than with Re =

l54000. It is not therefore Surprising to find in Fig. 5.5 that the boundary

layer grOws faster in the former case, and that separation takés place earlier

Re =

3.04x105

Re =

1.54x105

Figure 5.5:

Boundary layer on a cylinder with distributed roughness

(k/d = 2.66x103) at two Reynolds numbers in the super-

critical range.

1.0

0.8

0.6

0.4

0.2

121

(t-ripped)

Figure 5.6: Effect of surface roughness and Reynolds number on theboundary-layer velocity profile at or near the locationof minimum pressure coefficient.

I

Present study 2.66. 304 14.6 0.46 . -1.91

Presént study .2.66 1.54 14.1 0.59 -1.90

Patel (1968) smooth 5.01 16.Ó 1.20 -2.00

0.2 04 0.6 0.8 1.0

U/UE

k/dxlO3 Rex105 (/dX103)Om cb- C

kin --- [.4(iB2)]½ 1nC[ + 4(1-B2)

122'

(8 = 95°), than in the latter' case (where = 98°). Secondly, it is

seen from the table in Fig. 5.6 thät the pressure rise, Cb' - C, required

to séparate the boundary layer with the largest velocity defect. (Re = 304000)

is smaller (0.46) than that required to separate those with lesser defects.

Thus, the variation of the quantity Cb - Cm with kid depicted in Fig. 5.4

is consistent with the measurements of the boundary-layer developments. This

important connection between the boundary-layer characteristi at. and

the pressure rise - C. is well supported by the turbulent boundary-layer

separation mädel of Stratford (1959) and Townsend (1962).

Stratford' s (1959) model of turbulent boundary-layer development

over a smooth surface in a strong, adverse pressure gradient is based on the

division of the layer into an inner equilibrium layer and an outer layer of

almost constant total head along streamlines. According to this model

the flow in the inner layer is determined by the local shear. stress distribu-

tion, while the outer part of the flow dévelops nearly independently of

Reynolds stresses if the adverse pressure gradient is large. In particular,

the velocity in the inner layer at zero wall shear stress is shown. to be

proportional, to the square rot of the product of distance from .the wall

and local shear stress gradient normal to the wall. The model finally

leads to a simple relation between the pressure rise to separation, the pressure

gradient at separation and the properties of the boundary layer just ahead

of the region of pressure rise. Stratford assumed 'a power-law flat-plate velo-

city profile for the outer part of the boundary layer and expressed his

final result in terms of an equivalent flat-plate Reynolds number and distance.

Later on, Townsend (1962) improved the Stratford model by making use of the

'logarithmic law of the wall and refining some of the assumptions.

'Townsend's derivation can be easily extended to the case of a

boundary layer developing over a rough wall. If the initial profile in

the inner layer prior to the region of pressure rise is assumed to be given

by the suai logarithmic law of the wall for fully-rough flow and the same.

assumptions are made as in Townsend '(1962,) one obtains a simple relation

in the form

- l} + A + in Fl-B) (5.1)

123

where E shear stress gradient normal to the wall at separation,

E wall shear stress at the location of minimum pressure coefficient,C -c

=K ps pm,T 2o/pv0

K E Karman constant = 0.41,

C E pressure coefficient at separation,

A,B = known constants,

and p,v, and C are as defined previously. It may be noted that an

expression exactly similar to equation 5.1 is obtained by Townsend for the

case of a smooth wall; except in that expression, k is replaced by v/IT/p

and the value of A is different. Equation (5.1) is a relation between the

pressure rise to separation C - C , the state of the boundary layer atPS pm

the initial point (T at O = O), the surface roughness k, and the stress

gradient at separation a. The assumptions of the theory are expected to

be valid for the boundary layer of a circular cylinder in view of the large

adverse pressure gradient. The shear stress at the position of the pressure

minimum may be estimated by calculation or obtained from an experiment. The

shear stress gradient at separation, however, is more difficult to determine.

In the case of a smooth wall it is equal to the pressure gradient at separa-

tion. This is also expected to be valid for a rough wall. However, the

separation process for a circular cylinder is complicated by the overall

unsteadiness and vortex shedding, and furthermore the precise location of

separation and the pressure gradient there are difficult to determine. In

view of these difficulties the stress gradient at separation is replaced

here by an average pressure gradient in the region of pressure rise, that

is by

where O is measured in radians and the subscripts s and m denote, respectively,

the values at the location of separation and minimum pressure coefficient.

Fortunately, the error involved in this assumption is expected to be of

approximately the same order for different roughness conditions. If the

value of a is thus approximated, then a relation is obtained in the form

= function of ('V, A, B) (5.2)

2V C -c

" _2_ PS pms d O -O

s m

where

124

C -C pVkps pm odo -e.s m

This relation is plotted in Fig. 5.7 along with the experimental points

based on the measurements of Acherthach (1971) , Roshko (1961) and the present

study. (The values of C and C . used here re uncorrected for bloókage,. . ... pm. ps

except for the experiment of Roshko. ) Achenbach reported direct measurements

of shear stress and pressure distributions. In the case of Roshko, the

shear st±e was estimated from detailed boundary-layer calculations.. The

valúe ofc

for the present study was obtained from the meàsured velocity

profiles and the momentum integral equation. While the various assumptions

made in the dérivat±on of the relation 5.2 need to be verified, and although

there is some uncertainty in the valuesof t for the present experinent

and that of Roshko, the general agreement of' the thebry with the observations

is remarkable. The theory indicates that the pressure rise to separation

C - C is primarily a function of the initial stàte of the 'boundary)S ifl ' . . '

2layer at the pressure minimum, characterized by the values of k/d and T/PV

since the. value of C. - C ¡e - O. is observd to vary little 'over ,aps pm's rn . . :

wide range of roughness conditions It will be noted that the quantity

increasés as the. relative ráughness decreases. Although the vàlue of r/pV2decreases with decreasing relative roughness, this decreasé is not large.

enough compared with the increase in ., and, consequently, the 'pressure

rise to separation C . - C decreases as kid. is increased. . Furthermore,2

. ''since r/pV. is itself dependent on the relative roughness, the theory

explains the dependence of the pressure rise to separation on the value of

k/d at sufficiently large. Reynolds number. The theory also shows very.'

clearly that if the boundary layer is more retarded prior to the region of

pressure increase the resulting pressure recovery C . - C is smaller, since2 ' .

. ps pmfor the same value of T/pV the velocity profile at

0mwill have a larger

defect for a larger roughness. While most of these conclusions could as

well be reached by means of detailed calculations using either integral or

differential methods for' the'developmerit of the boundary layer In the region,

of pressure increase, the advantages of the present theory are that, firstly,

i gives a simple expression involving the important parameters, and

secondly, it Clearly denonstrãtés the inf1uenc of sürface roughness on the

'pressure rise to sepäration C - C and hence on the pressure distribution.ps pm . '

o

-2

-4

-5

I I I

k/d = 450x105, Achenbach (1971)

O k/d = 266x105, Present study

k/d = llOxlO5, Achenbaçh (1971)

c -c pVps pm o

- dO-O Ts m o

Theory (A = 3.28, B = O.18

k/d = 1x105Roshko (1961)

Q

125

Figure 5.7: Boundary-layer separation criterion for a rough-

walled circular cylinder.

o 20 30 40 50 60

K2(C -c )ps pm

in 'P

-3

126

It should be pointed out that the quantities C ,and C, are not in general

exactly the saxne for circular cylinders, whereas, for the most part, the

variations ofthe quantity C - C instead, of C - C have beenpb plu PS pm

examined in the present study. This approach has been taken in view of the

previously mentioned difficulty concerning the precise détermination of the

location of separation and also because the differences in the values of

C and: C are small. As these differences are small, the foregoing state-PS pbments about the quantity C C should also apply to. the quantity C.b - C

5.2 Effects of rib.roughness

The effects of rib roughness on the pressure distributions and

the boundary-layer development are in general similar to those of distributed

roughness. In the case of rib roughness, however, the angular spacing of

ribs e, or alternatively, the relative rib spacing s/k, appears as an

important parameter, in additionto the Reynoids.number and relative rib

height, k/d Consideration has to be given also to the local influence of

the ribs. In the following, we shall examine the various influences of

rib roughness on thé important pressure-distribution parameters and the

boundary-layer characteristics, and coimnent upon the local effects of the

ribs as far as is possible with the available data. The influence of the

width-to-height ratio of the. ribs, b/k, was not examined since it became

apparent from the study of Farell, and Maisch (1974) that this influence is

negligible fòr practical values of this parameter.

It is perhaps useful to note some of the basic differences between

distributed and rib roughness before going into a detaIled discussion of the

results. Although the general role and the effects of roughness are similar

for both types of roughness1 the .ribs act mostly as isolated agents with

little or no iflteraction of the local flow patterns around adjacent ribs,

while in the case of distributed roughness there is always a strong inter-

action of the flow around neighboring particles The isolated action of the

ribs gives rise to strong local pressure and velocity variations in their

vicinity, while the continuous interaction of the f lowbetween distributed

roughnes elements tends to smooth out such variations. This tendenc.y in

the case of distrIbuted roughness makes it possible to describe the mean

flow near the roughness elements quite adequately, wherêas it is rather

.127

difficult to characterize the flow intheregion close to the ribs. There-

fore, in àddition tó the 1balpressì.ire variations caused by the ribs,

thére is an added diffic.ilty in the theoretical treatment of the boundary-

layer development with rib roughness. In a few exceptional cases where the

rib spacing and height are small can one ecpect an approach to the conditions

observed for distributed roughness. One other important difference o.f rib

roughness is that low separation from the cylinder may be caused abruptly

by a'rib, if thé rib height is large enough.

In the following two sections, 5.2.1 and 5.2.2, we shall examine

the variations of the drag coefficient and impòrtant pressure-distribution

paiameters with thé Reynolds number and the roughness geometry parameters

k/d and O. Although the parameter s/k ïs more significant than tO, this

approach is tàken mainly for convenience in the presentation of the data.

The signIficance and the influence of the relative rib. spàcing s/k is

discussed toiards the end of section 5.2.2..

5.2.1 Drag coefficient

The variation of the drag coefficient with the Reynolds number

and the relative rib height, kid, for constant angular spacing, .O, is.

shown in Figs. 5.8, 5.9 and 5.10 for rib spacings of 50, 100 and 200,

respectively. Here again,, the values of Cd and Re have been corrected for

blockagé. The drag coefficient curve for the. smooth cylinder is included

in each figure for comparison.

The figures show that the variations in Cd are very similar to

those observed on cylinders with distributed, roughness. The same tránsi-

tional changes with Reynolds numbèr are also exhibited by the results with

rib roughness. Thus, for example, in Fig. 5.10 we see that the critical

Reynolds number at which Cd becomes a minimum for a .given k/d is smaller

for the larger roughness, and that this critical value of Cd decreases

with increasing roughness. The figures also show that a Reynolds-number

independent condition has been achieved completely or very nearly, for all

rib configurations tested. It will be seen that in the range of eyno1ds-

number independence the drag coefficient is a function only of the roughness

geometry and its value is larger for the larger roughness fOr a constant

s

s

ru

D

128

co vs.

9WTH oFa-05 IPI/D..001971 £m-05 D(/Da.003381 +AC-OS (K/D..006471 X

I I

5.8 6.0

Figure 5.8: Variation of Cd with Re and k/d for angular rib spacing of 5°.

5.0 5.2'4.8I

5.65.4LOG RE

s

129

co vs.

Figure 5.9: Variation of Cd with Re and k/d for angular rib spacing of 100.

oa+

o.

:

-

R5-U (P'/fl..00197)-10 IJÇ/D..c0338)

RC-LO IP&..Cq7JRl (IÇ/O..001971All (I'&Ø-.001971

- R2 tk'.003)

- i1L:

;

-d -II. 5.0 5.2 5.4 5.6 5.8 6.0

LOG RE

.r.

I

Dt-.)

(Do

4.8

130

co vs.

9WTh OAS-20 r/D..00197J A

-2O tI/D.0O338J +RC-20 II/Q..QQ6A47) X

Figure 5.10: Variation of C with Re and k/d for angular spacing of 20°.

6.0

-

131

angular spacing. In the case of O=5° and k/dxlO3 s 6.47, Fig. 5.8,.

however, there is a reversal in this trend. As will be discussed in detail

later on, this behavior can be attributed in part to the very small relative

rib spacing, s/k = 6 7, in this configuration The curves in Figs 5 8, 5 9,

and 5.10 a1ò show that there Is a significant influence of the rib spacing.

In particular, ït will be seen that the differences between the values of

Cä for different valués of k/a, which are small fór the smallést' angular

rib spacing, 9=5°, become increasingly pronounced' as the angular rib spacing

is incréased. This behavior is analogous to that noted' previously for

distributed rouhness in which ase thé differences in Cd' were iarqer for

smaller values of relàtivé röughness.. Increasing the rib spacing (beyond

à cetain mInimum, as' will be disáussed in section 5.2.2), therefore,

results in a decrease in the effectiveness of rib roughness. The influence

of rib spacing is further examined in the next seçtion.

5.2.2 Pressure distribution

Figures 5.11, 5.13 and 5.15 show the variations of C and Cpb pm

with Reynolds nimber 'and relative rib height k/d for constant anqular

rib spacing, O, of 5°', 10° and 20°, espectiveiy. The corresponding

variatiOns òf'C C are shown in Figs. 5.12, 5.14 and 5.16. Here again,pb pmthe valués of the Reynolds number and pressuré coefficients have been

corrected for blockage. Corresponding curves for the smooth cylinder are'

included in each' figure for comparison. The variations in the angle

were also determined from the measured distributions with rib roughness

(see Table 4.4), but have not been presented here since they are generally

similar to those observed for distributed roughness (Fig. 5.3).

It will be seen from Figs. 5.11 through 5.16 that, as in the

case of' the drag coefficient, the influeñce of Reynolds number and relative

'rib height on C , C , and C - C is in general quite similar to thatpb pm pb pm

observed for distributed roughness. The same transitional changes with

Reynolds number are exhibited and a Reynolds-number independent conditiOn

is achieved beyond sane large value of Re. A comparison of these figures

with Figs. 5.8,, 5.9 and 5.10 indicates that the variations in Cd are well

correlated with the variations in both C and C . In particular, the3

pb' pmcase of RC-05 (O=5°, k/dxl0 = 6.47) in Figs. 5.11 and 5.12 again shows

In. -C,

In

aJQ-L)0

r.

L).

o

o

o

4.8

132

I5.0 5.2

I5.4

LOG RE5.6

CPB VS. I

SMOOTH ORB-OS (K/Û.'.00197) £m-OS (K/Os.00333) +AC-OS ¿1(/D..OG647J X

I5.8

5.8

6.0

6.0

Figure 5.11: Variation of Cb and C with Re and k/d for angular rib spacing of 50

I I4.8 5.0 5.2 514 5.6

LOG RE

o -o

Ddtq.8

133

I I5.0 5.2 5.4

LOG RE5.6

CPS-CPM VS. FC

9WTI4 oF3-05 U/O°.O!973 L

-oS IP(/D..003381 +RC-CS tI/D..CO247) X

5.8 6.0

Figure 5.12: Variation of C - C with Re and k/d for angular rib spacing of 5°.pb pm

I I

5.0 5.2 5.11 5.6 5.8 6.0LOG RE

cre vs. cc

9t0THR3-l0 U/D..00l97)

-I0 1PIO..CQ339IRc-le IM/D..0097)Rl UUO..001971All (F/D..00l7JR2 tr/,a.00139I

134

J 1

5.0 5.2 5.11 5.6LOG RE

6.0

Figure 5.13: Variation of Cb and C with Re and k/d for angular spacing of 100.

s

s

oo

'8.8

135

J

¡

I

I I

¡p

51W TNAS-10 IK/D..0)I97)R-l0 (/O.CO338)RC-lO O(/D.CC597)RI tK/O..00197)All (IVD..00197)R? (P(/D-.003'

I

Figure 5.14: Variation of Cb - C with Re and k/d for angular spacing of loo.

CP8-CPII VS. f

o

5.0 5.2 5.85.11LOG RE

5.6 6.0

J,.o

Q-L

u,

L).

o(g

oI,,

+ ++

I

4.8

4.8

5.0 5.2

J5.0 5.2

136

5.4LOG RE

i5.4

LOG RE

cs vs. i9WTH OR3-20 IK/O'..001971 LR-2O U/D-.003381 +RC-20 1I/D..QC6q7I X

5.6 5.8

i

6.0

I ('.I

5.6 5.8 6.0

Figure 5.15: Variation of Cb and C with Re and k/d for angular rib spacing

of 200.

o.o

ti

m

o

o

'na

oo

'1.8

137

CPS-cPM VS. FC

SITII O10-20 1l/O..00I97J £

-20 1)(/D..00338) +K-20 H&D.00i47) X

6.0

Figure 5.16: Variation of Cb - C with Re and k/d for angular rib spacing of 200.

irss

I L I

5.0 5.2 5.11LOG RE

5.6 5.8

138

a trend opposite to that of the other rib configurations in the dependence

of C and C C on k/a. This behavioris similar to the reversal ofpm pb pm

trend noted in connection with the variation ofd

(F'jg. 5.8) .

Influence of rib spacing: From Figs. 5.11 tbxbugh 5.16, it is

seen thät th spacing of the ribs has a large influence on the pressure

ditributions. In order to illustrate the influence of angilar spacing

more clearly, some of the data presented in these and earlier figures are

cross-plotted in Figs. 5.Ï7, 5.18 and 5.19. In addition, the results for

the rib configuration RC-40 (k/dxlO3 6.47, te=4O°) are also included in

Fig. 5.19. Each figure shows the variation of the drag coefficient and

the pressure rise Cb - C with Reynolds number and angular rib spacing

for a constant rib height. These plots a±e particularly useful sinçe they

show that the pressure rise C - C is an excellent indicator of the overallpb pm

effect of roughness. geometry on the drag còefficint. It wilibe seen thàt,

in the supercritical regime, higher values of the drag coefficient are, in

general, associated with smaller values of C - Cpb pm

Figures 5.17 ánd 5.18 show that for k/dxlO3 = 1.97 and 3.38

there is a consistent trend in the dependenòe of C and C - C on thed pb.pm

angular rib spacing. Here we seethat larger rib spacing leads to an increase

in the critical Reynolds number and, in the Reynolds-number independent

range, to smaller values of C and larger values of C - C . The results3

d pb pmfor k/dl0 = 6.47 (Fig. 5.19) ,.however, show an opposite trend .in the

Reynolds-number independent range: C increases and C - - C décreasesd pb pm

as O is increased from 50 to 200. As discussed below, this may be partly

due to the influence of the small values of the, relative rib spacing s/k.

However, this is not the only peculiarity in thé. results for k/dxl03 = 6.47.

For example, it is seen that as the angular spacing is further increased to

40° the corresponding drag coefficient cur/e crosses the ones for O=l0°

and 20°. Furthermore, in the Reynolds-number independent range, both Cd and

C - C show anincrease over the valuesfor tO=20°. Thus, although thepb pmincrease in Cd is not large, we observe that the correlation between the

behavior of C and C C is lost iii this instance. Although the precised pb pm y. ''.'

reasons for these inconsistencies for the largest rib height are not

entirely clear, it should be noted that the cases ¿f AO=40° and A020°,

k/dxl03 = 6 47, are rather special since it appears that in these cases the

DL)

'-D

D

D

4.8

I

I

I

139

RSOS tK/Oa'.001971 OP5-10 IP(/0..00197) £R8-20 u,D..CO197J +

I - II -I t

5.0 5.2 5.4 5.5 5.8 6.0LOG RE

t

Figure 5.17 Effect of angular rib spacing on C and cb

- c for k/d =

1.97x103.p

o

DL)

(Do

t!

C

C

4.8 5.0

Figure 5.16: Effect of angular rib spacing on C and C - C for k/dd pb pm

3.38 x103.

5.2

1kO

5.4LOG RE

5.6 5.8 6.0

IyRA-05 uvO..00339JRA-10 IP/0..00338RA-20 LK/D..0033)

I t\\\i

t I I

I

a..L

th1Q-.L)D

oD I

5.0I

5.2

141

I5.4

LOG RE5.6

I5.8 6.0

Figure 5.19: Effect of angular rib spacing on C and C - C for k/d = 6.47x103.d pb pm

(1

RC-0SRC-IORC-20RC-40

iI(/D..COE47IiK/D..C47)IP/O..CC47u(/O.00647J

O£+X

142

flow separation from the cylinder is provoked abruptlyby the ribs located

at e=±92.5°(Fig. 5.25). Moreover, the rather large local effects observed.3 .

for k/dxlO = 6.47 arid a dependence of these. local effects on the rib spacing

and possibly on the Reynolds number (see section 5. 23) tènd to obscure these

results and also diminiSh the physical significance of the overall pressure

coefficients being examined here.

The variation of the pressure rise C - C with rib height and.-pb. pm

spacing in the Reynolds-number independent range is shown in Fig. 5.20. Here,

the rib spacing is represented by thé angülar separation tO as well as by

the relative circumferential distance s/k betwéen adjacent ribs. In the

latter case (Fig 5.20b), some results ôbtained by Hayn (1967) and by Farell

and Maisch (1974) on hyperbolic cooling-tower models fitted with mer-idional

ribs are àlso shown for cOmparison. The most signigicant observation to

be made from this figure is that, fcr the smaller rib heights (k/dxl03 = 1.97

and 3.38), the pressure r-ise C:b - C is mainly a function ,of s/k over the

approximate range 12 < s/k < 50. Within this range, the decrease in Cpb pm

with decreasing s/k indiôates that more closely spaced ribs correspond to

greater effective surf àce roughness. A reversal in this trend should be

expected for s/k < 12 due to a re4uction in the effective surfàce roughness

associated with the formation of 'a single. eddy in the space between adjacent

ribs in the manner shown in Fig. 5.21a. Although direct evidence of this

is lacking for k/dxl03 = 1.97 and 3. 38, and s/k < 12, the results for k/dxlO3 =

6.47 and low values of s/k appear to indicate this behavior. For values of

s/k greater than about 50, the pressure rise is again influenced by. the-

relative rib height k/a. The results for the largest cylinder 'roughness'

(k/dxlO3 = 6.47) and those for the large roughness óf k/dxlO3 = 3.99 on

cooling-tower models do not, however, comform in general with the aforemen-

tioned observatiOns. Indeed, for these caseS 'the pressure rise appears to,

be generally insensitive to variatiOns in s/k. This behavior' is most likely

due to the fact that flow 'separation is provoked abruptly by a ,rib when the

rib height and spacing are large. In addition, as-also remarked upon earlier,

the local influence of such largè ribs also tends to diminish the physical

significance of the "overall" pressure coefficients being examined here

and renders the usual boundary-layer concepts somewhat meaningless. Never-

theless, the overall agreement between the cylinder and cooling-tower results

c -cpb pm

1.2

0.8

0.4

0.0

1.2

0.8

c -cpb pm

0.4

143

(a) C - C vs. t6.pb pm

Farell and Maisch 1974,Cooling tower.

0.0

510 20 30 40 50

s/k

(b) C - C vs. s/k.pb pm

60 70 80

Figure 5.20: Effect of rib spacing on Cb - Cm in the range

of Reynold-number independence.

90

10 20 30 40

144

is significant and supports the observation of Farell and Maisch (1974)

that roughness effeôts can be optimized with a rib spacing such that s/k

is approximately 20.

Over the range of s/k and k/d where the local flow-pattern inter-

action between adjacent ribs and the local influence of the ribs are

expected to be al1 and also where abrupt boundary-layer separation does

not occur, the inflüence of rib spacing on the mean pressure distributions

and, in particular, on the pressure difference C = C can be furtherpb pm'

explained on the basis of experiments performed elsewhereon the drag of

a fence or obstacle located within a turbulent boundary layer. According

to Good and Joubert (1968) (rig. 6 of the original referencé), the drag

coefficient CdR of a singlé two-dimensional fenc o height k inmtersed in

a turbulent boundary layer at a location, where (in the absence of the fence)

the boundary-layer thickness is ô and the wall shear stress is T, is primarily

a function of the relative fence height k/6 and depends weakly on the value

of the local sheár-stress coefficient. Their experimental results can be

approximated by the 'relation

where.

CdR 0.91, + 0.37 log1, k'ô (5.3)

f = 'force per unit length of the, fence

UE = velocity'at the edge of'the boundary 'layer.

This relation is' expected to' apply over the rañgé 0.05 <'k/ô < 0.60. Al-

though there is only limited information at present on the drag coefficients

in the case of a train of fences or ribs (see Balkowski and Schollmeyer

(1974)), it is, reasonable to assumé that the drag coefficient can be estimated

by means of Eqn. 5.3 so long as the interference effects between adjacent

ribs are negligible. Th'is coñditioñ is expected 'to' be satisfied for values

of s/k greatet than about 12 (see, for exajnple, Llu, Kline and Johnston

(1966)) and for ribs with b/k 2 or less as cónsidered in 'the present study

Nöw, it can be argued that the boundary resistance of a surface with ribs

is composed of two parts: the smooth-wall shear stress between the ribs and

the drag of the individual ribs. The drag due to a single rib when "distri-

145

buted" over the area between adjacent ribs gives rise to an apparent

boundary shear-stress coefficient CfR which can be written as

f/sCfR_ 2

PUE

substituting Eqn. 5.3 into 5.4 we obtain

CfR = (0.91 + 0.37 log10 k/tS)/(s/k)

- (5.4)

(5.5)

From this we see that the apparent shear-stress coefficient CfR due to the

ribs is inversely proportional to s/k. Furthermore, the boundary-layer

measurements over the range of rib configurations tested here indicate that

kid is in the range 0.10 to 0.20, so that the dependence of CfR kid is

comparatively weak. It is also clear from Eqn. 5.5 that, for values of

s/k of the order 12 to 50, CfR is of the order 0.050 to 0.013 which is

considerably larger than the shear-stress coefficients associated with the

smooth-wall flow between the ribs. It is therefore expected that the

retardation of the boundary layer and its eventual separation, and conse-

quently the pressure rise Cb - Cm will be governed primarily by the valueof s/k. As noted earlier, these arguments apply only for configurations in

which the ribs are not large enough to give rise to significant local

effects and also in which local flow-pattern interaction between adjacent

ribs is negligible. Therefore they explain only the behavior shown in

Fig. 5.20b for 12 < s/k < 50 and the smaller values of k/d.

5.2.3 Local effects of ribs

As mentioned previously on several occasions, the pressure

distributions on cylinders fitted with ribs are influenced locally by the

presence of the ribs. In what follows, we shall examine the extent of

these local influences for the different rib configurations tested.

Figure 5.21, adapted from Liu, Kline and Johnston (1966), shows

the two possible flow patterns in the region between two adjacent ribs:

whether the eddy behind a rib is confined to a portion or all of the region

between the ribs depends upon the rib height and spacing. In either case,

the strong curvature of the mean streamlines in the neighborhood of the

ribs results in steep local pressure gradients. These strong local effects

146

-4FLOW DIRECTION

(a) Closely-spaced ribs

FLOW DIRECTION

BACK FLOW

(b) Ribs far apart

Figure 5.21: Local influence of Ribs

[adapted from Fig. 4.2 of Liu, Kline and Johnston (1966)]

147

are of course observed only in the. forward portion of the cylinder, oütside

the wake region. Here, we shall examine the detailed pressure measurements

made by means of pressure taps located at différent positions relative tO the

ribs in the important region 500 < lOi < 1100. The "overall" or average

pressure distributions defined earlier and used in the analysis of the data

in the previous sections will be shown in the various figures. in order to

highlight thé local variations of pressuré in the vicinity of the ribs.

Figure 5.22 shows the pressure distributions obtained with

configuration RB-b (k/dxlO3 '= 1.97, s/k =4.4.2) at three, different

Reynolds nuiibers. From this we observe that thè local effects are quite

large for the smaller Reynolds-number tests and almost negligible at the

highest Reynolds numbér. Note that, for this configuration, the pressure

taps.are located at a distance 0.25s from the nearest rib,, so that s1/k =

11.05, wherel

is the distance of the first pressure tap downstream from

a rib. According to Liu, Kline and Johnston (1966), the méan length of the

separation pocket downstream of .a rib in a turbu1ent boundàry layer is

approximately 8k when the rib spacing. is large. Thus, it ïs not surprising

to find that the measurements fOr Re = 5.14x105 show very little influence

of the. ribs. For .the,smaller Reynolds numbers., however, the strong, influence

observed in the forward portion indicates that the' separation pockets are

longer than 11k This may be due to a comparatively thinner boundary layer

which is not yet fully turbulent at these. 10w Reynolds numbers '(see Section'

5.2.4). The strong dependence of the local effects of ribs on the Reynolds

number seèn here was also observed by Niemann (1971).

The détailed pressure measurements fOr configurations ÑA-lO and

R2.(k/dxlO3 =3.38,. s/k =25.8) are shown in Fig. 5.23, while those for

configuration. RA-20 (k/diclO3.= 3.38, s/k = 51.6)' are shown in Fig. 5.24..

These results clearly identify the extent of the local influence of the

ribs on the pressure distributions, and also show 'the siqnificance of the

"overall" pressure distribution It is perhaps useful here to make three

further Observations. .First, in Fig.. 5.23, there is a small difference

between the overall line deduced from the data of configuration RA-10 and

the measurements made with configuration R2 This may be attributed to the

presence of the Small discontinuity in t1e ribs i,n the ltter case.

Secondly, exazyination. of the data for e = 55° shows that the deviation of

-0.8

-1.2

-2.0

-1.2

-1.6

-2.0

-2.4-50

-0.8

-2.4

-50

-60

-60

-70

-70

148

Location of ribs

-80

9

-80

-90

RB-b

Re = 5.16x105

-100 -lic

A

\ ,,,o__ o--

o

PB-lO

Location of ribs

L) Re = 2.07x105

(0) Re = l.86x105

,;,

'-'ç,

<7

-90 -100 -110

Figure 5.22: Local influence of ribs RB-b (k/d = l.97x103, s/k = 44.2)

osi

s

I

C -1.6

p

4

I I I

-0.8

-1.2

-1.6

-2.0

-2.4 -50

Ii

I

Location of ribs for R2

(o)

o

Figure 5.23:

Local influence of ribs.

Comparison of results for R2 and

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

Re =

4.33x105.

-60

-70

-80

-90

-100

-110

-0.8

-1.2

-1.6

-2.0

-2.4

/

Location of ribs

"Overall" line

Figure 5.24:

Local influence of ribs.

Re =

3.04x105.

(Results

layer measurements, Re =

OWest points

DEast points

xEast, obtained

manually.

¿.3

RA-20 (k/d = 3.38x10

obtained manually during

2.95x105,

are also shown.

110

s/k = 51.6);

boundary

50

60

70

80

lei

90

100

Cp

-1.0

-1.4

-1.8

-2.2

-1.4

-1.8

-2.6

-1.2

-1.6

Cp -2.0

-2.4

-2.8

-50

-50

b

¡ / op / /

-60

-60

151

-70

¿/

/

-70

-80Ï

I RC-20 (s/k = 26.9)

jRe = 2.85x105

-90

PC-10 (s/k=13.5)Re = 2.87x105 -

-O - 10

Figure 5.25: Local influence of ribs. RC-lo, RC-20, and

RC-40. (k/d = 6.47x103)

-110

Cp

-2.2

-90 -100

IIo

I-80

152

the pressure coeffiôient from the overall line is larger for configuration

RA-20 (Fig. 5.24) than for configuration RA-10 (Fig. 5.23).. Since the

roughness height and the location of the pressure tàp in relation to the

rib upstream are the saine in both cases, this difference is presumably due

to the influence of rib 'spacing on the overall boundary-Ïayer characteristics,

which, iñ turn, affect the length of the separation bubble and the, magnitude

of the pressure drop behind the rib. Thirdly, Fig. 5.24 shows that the

pressure results obtained manually are in good agreement with those recorded

by the automated data-acquisition system. In Fig. 5.25 are shown the pressure

distributions for the largest rib height (k/dxlO3 = 6.47) and three different

rib spacings. it is evident that the local influence of ribs in these

cases is quite substantial. In particular, it is seen again that this influence

increases with increasing rib spacing.

While the results presented here gi*le some general indication.

concerning the local effects of ribs on the .pressùre distribution, it is

clear that much remains to be done in order to explain the observed trends

satisfactorily. It is of coürse necessary to make more.. detailed measurements

of pressure as well, as thé velocity field between adjacent ribs before a

definite quantitative evaluation, can be.. made. .However, the large. local

effects shown here raise an important practical question from the standpoint

of structural design, since the large local pressure variations can easily

offset the gains obtained .by the reduction in the mágnitude of the overall

minimum pressure coefficient. A systematic experimental study of the flow in

the vicinity of the ribs is therefore recommended.

5.2.4 Boundary-làyer characteristics

The boundary-layer development on the cylinders with distributed

roughness was examined in Sectioñ 5.1.3, and it was concluded that the

greater retardation of the bomdary-1ayer flow caused by surface roughness

results ïn lower values ofC - C . In partiòular, it was shown thatpb pm. .

there is a close connection between the value of C - C and the velocitypb pm

distribution across the boundary layer at the location of the pressure,

minimum. In this section we shall examine selected results for boundary-

layer developments on cylinders fitted with rIbs to observe the effects of

Reynolds number, rib spacing and rib he.ight. . . .

153

The development of the boundary-layer thiòkness .fôr several rib

configurations is shown in Fig. 5.26, and selectéd velocity profiles are

depicted in Fig. 5.27. The actual data points aré not shown in the latter

figure since these have already been presented in Section 4.2.2. In Fig.

5.26 (a) and (b) all the ribs are shown to scale at their proper locations.

In Fig. 5.26 Cc) only one rth, whidh is common to the three rib configura-

tions in that figure, is shown. Finally, in Fig. 5.26 Cd) one rib for each

of the three rib confïguratiôns is shown at its proper location. For

convenience, the valués of the important pressure distribution parameters

are also shown in Fig. 5.27.

Effects of Re: As séen in Fig. 5.26 (a), where thé boundary-layer

development for the rib configuration i (k/d10 = 1.97, ¿0 = 100) is.

shown for two différent Reynolds numbers, the boundary layer for Re = l.52x105

is much thinner than that for Re 2.87x105. Consequéntly, separation takes

place later at the smaller Reynolds number (0 =. 107°

Re =2.87x105), Cb - Cpm is larger, and, the pósition.

further downstì-eaxn.. °m = 78° compared with 75° for Ré

this we see. that the valué of 6/k at O = 70° for

is ofthe order.of 3., aid consequently it is not

to think of this flow in terms of boundary-layer

Reynolds number, however, 6/k is approximately 5

Of conventional boundary layers, ät leäst in the

case, Fig. 5.26(a) shOws that arguments based on

in the region between O and separation.

compared with 100° for

of the préssure minimum

= 2.87x105). The

corresponding velocity profiles at O = 70° are shown in. Fig. 5.27(a). From

the.lower Reynolds number

certain, whether it. is possible

theory. At the. higher

and the flow resembles that

outer region. In either

boundary'..layer theory apply

It is to be. expected that,if the variation of. the ov,erall pressure

distribution, parameter with Reynolds number is small, as has been observed

for larger supercritical Reynolds numbers, the chàracteristics of the boundary

layer should also show small variations. This is. illustrated in Fig. 5.26(b)

and 5 27(b) where the boundary-layer development and the velocity profiles

at O 77.5° are shown for RA-05 (k/dxiO3 =3.38) for three different

Reynolds numbers. Thia aain. demontrates the close. connection. between.

the boundary.iayer development and the. pressure distribution resulting from

its interaçtion with the external flow... .

154

Effects of rib spacing: The strong influence of rib spacing on

the pressure distribution was denstrated, in Section 5.2.3. Figs. 5.26(c)

and 5.27(c) show the boundary-layer development and the velocity profiles

near e, respectively, -for the rib configurations RA-05, RA-10 and RA-20 at

the same Reynolds number. Again, we observe a consistent váriation of

pressure distribution parämeters with the boundáry-layer characteristics.

Effects of rib height: The influence of rib height on the

development of the boundary layer and the velocity profiles in the neighbor-

hood of O is illústrated in Figs. 5.26(d) and 5.27(d). In order to isclate

the effects of rib height, only the results with similar values of s/k have

been chosen. In this instance, however, a- comparison and discussion of the

results are made difficult, especially in the case of the velocity profiles,

due to the uncertainty concerning the choice of the virtual origin for the normal

distance y and the errors in the velocity measureménts due to the proximity

of the ribs.. -Nevertheless, the relatively small values of- /k for the RC-20

configuration tend to confirm the basic differences observed between the

pressure distribution results for-that configuration and those of conf igura-

tions RA-10 and RB-05. As remarked upon in Section 5.2.2, boundary-layer

separàtion is induced by the rib at O .= 92.5° in the. case of RC-20, while

in the other two cases it is causéd by thé overall adverse pressure gradient

in the usual.sense. . . . . -

- Genéral Remarks: Owing. to the relativély large rib heights,

variable rib spacing and the special difficulties concerning the local effects

of ribs, the bounday layer data collected so far are not suitable for-

fürther detailed analysis. Thus, :for example, it is not- possible to determine

the - "equivalent" roughness in the Nikuradse sensê nor is it apprOpriate to

investigate the validity of -well known laws, süch as the -logarithiic velocIty

distribution and friction relations, established- for conventional boundary

layers for surfaces with small uniform roughness. As indicated earlier, the

st useful quantities in. the present measurements are the boundary-layer

thickness and the overall shape of the velocity profiles in the outer part

of the boundary layer, and these have been used, to the extent possible, to

explain sorne of. the gross features of the measuréd pressure distributions.

(a) Effect of Re.P.1 (k/d = 1.97x103)

0=70

Effect of Re.RA-05 (k/d=3.38x10

0=70

Effect of rib spacingk/d = 3.38x103Re = 2.95x105

0=70Effect of rib heightRe = 2.95x105

80

80

155

90

90

90

80 loo

0=70 0.0 0.5 inch 1.0

Scale

Figure 5.26: Boundary layer on cylinders with ribs. (Only one rib is

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

shown in (d).)

RexiO = 2.87

RexlO5

2.952. oo

1.18

RA-05

RA-10

RA-10RB-OS

RC-2 O

I

RA-20

100

100

80 100

y(f t)

0.03

0.0

156

tO=10°)

e

77

7676

I I

0.2 0.4 0.6 0.8 1.0

U/UE

(b) RA-05 (k/d = 3.38x103, =5°)

Figure 5.27: Boundary-layer velocity profiles near the

location of minimum pressure coefficient.

0.03

(a) Rl. (k/d = 1.97x103,

RA-05. e=77.5. P.LOC=2

Rex105 Cb Cpb_ Cpm e

0.02 1.18 -1.38 0.54 982.00 -1.39 0.47 95

y(f t)

2.95 -1.40 0.45 95

0.01 RexlO

y(ft.)

0.000.0

157

(c) Effects of rib spacing

0.03

Cb Cpm O

0.36 90 76

0.55 97 76

0.56 95 75RC-2 O

Rc-io

RC

I

Ra-05

4

2

o

(d) Effects of rib height (Broken lines indicate U/UE vs y/k)

Figure 5.27: (continued)

I

Re = 2.95x105

k/dxlO3 s/k O P.LOC C

RC-20 6.47 26.9 72.5 1 -1.44RA-iO 3.38 25.8 75 0 -1.36RB-05 1.97 22.1 77.5 1 -1.31

0.2 0.4 0.6 0.8 1.0u/uE

8

6y/k

0.02

Y

(ft.)

0.01

158

.5.3 Effects of roughness at high Reynolds numbers.

5.3.1 Mean pressure distributions

The results presented so far show that the mèan pressure distributions

become independent of Reynolds númber for süfficiently high values of this

parameter.. The important pressure-distribution parameters obtained under these

conditions can then be plotted as functions Of the relative roughness height

as in Fig. 5.28. This figure includes the results of the present experiments

on cylinders with ribs as well as distributed roughness and those of a related

study on a smaller cylinder described in Appendix 1. The measurements made

by Roshko (1961) and Achenbach (1968, 1971) at large Reynolds numbers are

also shown for comparison. It should bè emphasized that the smooth cylinder

results of Roshko and Achenbach cannot be considered strictly Reynolds-number

independent. However, since the Reynolds'nimbèrs of these tests are quite6 6

large, of the order of 5x10 to 8.4x10 , and the data in the original refer-

ences indiáate only very little fùrther changes in the drag coefficient with

increasing Reynolds number, these results can be considered practically

representative of prototype conditions. It is with this understanding that

they are included in Fig. 5.28. The relative roughness values in the "smooth"

cylinder experiments of Rohko (1961) and Achenbach (1968) were estimated by

Roshko (1970). In the case of cylinders with ribs, only the, results fOr

the most effective value of rib spacing have been shown., except for the largest

rib height fo which the results for s/k = 6.7 are also included. The broken

lines in Fig. 5.28 are drawn sily to indicate the expected trends.

Although there i's some scatter in the data, Fig. 5.28 clearly

indicates that surface roughness has a significant influence. even, at large

Reynolds numbers., As the relative roughness increases, decreases and

C increases (i.e. IC lincreases and IC. I decreases).. The drag coefficientpm ' pb pm

Cd also increases with increasing ro.ughñess and reaches 'a nearly cónstant value,

of the order of 1.0, for large roughnesses. The detailed pressure distribu-

.tion reported in the previous Chapter further indicate that, for the large

values of k/d,, the position of separation moves upstream (O 95° for all

large values of kid versus = 106° for the case of Roshko), whilé. the location

of minimum presure remains substantially unaffected ('e' 72°-. 76° for large

k/d afld0m

75° for Roshko's experiment).

Cpb

-2.0

-1.2

-0.8

1.1

1.0

0.8

0.6

159

I i I 11111 I I 111111 i I I tiiji'

-...t. C

- 22.1

sie ®26.i

Cb- - 22.1

012.9

ci'

6

-Q

O Present study (distributed)

Ø Present (4-in, cylinder)

Present study (ribs)

s/k

22.1

e

12.9

26.9

-

O Roshko 1961

9 Achenbach 1968,1971

9.'1'

6.7(7

-

êI I I 11111 J I I hut I i i IIIIt

10 10k/d

Figure 5.28: Variation of C , C and C with k/d at large Re. (Thepm pb dvalue of s/k is shown next to each point for cylinders

with ribs.)

Cpm

-1.6

160

It is seen from Fig. 5.28 that the major changes with roughness

height take place upto about k/d = 2.5x103. Thereafter, further increase

in roughness height appears. to have little influence on the main pressuré-

distribution parameters. This is to be expected since the location of

separation remains nearly fixed for the larger rughnesses. Nevertheless,

further small changes in the pressure distributions may still occur due to

the influence of roughness on the boundary-layer development. The results

indicate, however, that these changes are associated with the displacement

effect of the boundary layer, rather than with gross changes in the location

of separation. These observations are also confirmed by the separation criter-

ion shown in Fig. 5.7.

It is particularly interesting to note that rib roughness appears

to be generally more effective than surface roughness of the distributed type

for a. given value of the relative roughness height k/d, provided that the ribs

are appropriately spaced (that is, with the optimum value of s/k). This is

to be expected in view of the considerations of Section 5.2.2, where it

was argued that the retardation of the boundary.iayer flow in. the case of

rib roughness was more a function of relative rib spacing than of the relative

rib height and that the effective boundary resistance was greater for rib-type

roughness for appropriaté values of s/k. It is also very likely, for similar

reasons, that rib-type roughness may be more effective than distributed

roughness also for smaller values of k/d at large Reynolds numbers provided

that there' áre a sufficient. number of ribs. More data are needed, however, to

completely clarify the effects of rib-type roughness as well as distributed-4 -3roughness at large Reynolds numbers for values of k/d between 10 and 10

5.3.2 Surface roughness and pressure rise to separation

Comparison with cooling-tower results

The variation of thé prèssure rise C C with roughnesspb pm

height k/d at large Reynolds numbers is shown in Fig. 5.29 for cylinders

as well as cooling towers. In the latter case, the pressure coefficients are

those measured at the waist. The 'îalues of s/k correspond to thé waist 'while'

the values of k/a are based on the mean diameter of thé tower. As in Fig.

5.28, only the results with the most effectivé rib spaçings are shown for the

case of rib roughness. The ôooling-tower results shown in Fig. 5.29 have

12

1.0

EOEB

0.4

0.2

0.0

10-e

k/d

Figure 5.29:

Pressure rise to separation, C

- C

, as a function of relative

pb

pm

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.)

102

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162

been reviewed in detail by Farell. and Maisch (1974). The more recent

cooling-tower result obtained by Carrasquel (1974), with k/dxlO3 =

4.0 and s/k = 12.8, is also included.

While the individual values of C and C arepb pm

for cooling towers and cylinders, it is seen from Fig. 5

rise C - C correlates remarkably well with roughnesspb pmcases. The close agreement of the cooling-tower results

quite different

.29 that the pressure

height for both

with those of the

cylinders suggests.that the pressure différence Cb - C, which is asso-

ciated with the pressure rise required to separate the boundary layer (Section

5.1.3), is insensitive to free-end effects (at least for the cooling towers

with height to mean-diameter ratios of about 2). This parameter is also

found to be quite insensitive to. wind-tunnel blockage for cylinders (Appendix

1) as well as for cooling towers (Reference. .18). The close correlation shown

in Fig. 5.29 further suggests that Ch -. C is also independent of other

effects arising from such experimental conditions as the use of open-jet

wind tunnels, where the base pressure may be influenced by the conditions

at the tunnel exit (Reference 18).

The variation of Cb - C with k/d shown in Fig. 5.29 is quali-

tatively similar to the variation of C with k/d shown in Fig. 5.28 forpm

cylinder,s and in Fig. 1 of Farell and Maisch (1974) for cooling towers.

While both C and C are individually affected by surface roughness in the.pb pmcase of cylinders, the base-pressure coeffiient Cb remains remarkably

unaffected by roughness, in the case of cooling towers due to the .f low over

the' top of the towers.. In viéw of this, the present results lend support

to the observations of Niemann (1971) and .Farell and Maisch (1974) concerning

the influence of. surface roughness on the mean pressure distribution in

general, and'on the variation of the minimum pressure coefficient C inpm

particular. '. ' '

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

The practical importance f simulating high-Reynolds-number flows

in .wind tunnels cannot be overemphasized. In this section we shall' discuss

laboratory simulation of high-Reynolds-number flows insöfar as the mean pressure

distributions are concerned. 'First we shall investigate the conditions

163

required to obtain Reynolds-number independence in the laboratory, and then

consider the question of simulating such flows by using models fitted with

surface roughness.

5.4.1 Reynolds-number independence

Since the mean pressure distributions become independent of

Reynolds number for sufficiently large values of the Reynolds number and

relative roughness height, it is of interest to identify the lowest value

of Reynolds number (denoted by Re1) at which such independence is achieved

for a given value of k/d, and to determine whether a suitable parameter can

be found to characterize this condition.

The dependence of Re1 on k/d is shown in Fig. 5.30. This is

based on the present experiments on cylinders with distributed and rib

roughness, together with the results of Achenbach (1971) for cylinders, and

of Niemann (1971) and Farell and Maisch (1974) for cooling towers with ribs.

In the case of cylinders, Re1 was determined from the variation of Cd

with Re (corrected for blockage). For cooling towers, curves of Cpm versus

Re were used. For rib roughness, only the data corresponding to the most

effective rib spacing are shown in Fig. 5.30. It should be noted that there

is some uncertainty in the determination of Re1 in this manner due to the

asymptotic nature of the curves. However, this uncertainty is not excessive.

Fig. 5.30 shows that Re1 decreases with increasing k/d. However,

Re1 is expected to level off at larger values of k/d, as shown by the broken

line drawn on the basis of the points for cylinders with distributed roughness.

Phis minimum value of Re1 is conservatively about 3x105. For smaller values

of k/d, a line can be drawn with the equation Vk/v = 1100. Thus, it appears

that the roughness parameter Vk/v can adequately describe Reynolds nuxnber-3

independence provided k/d is less than about 2x10 . Reynolds-number inde-

pendence is guaranteed if Vk/v is greater than 1100. This result is in

substantial agreement with that of Szechenyi (1974) who suggests Vk/v > 1000

for Reynolds-number independence. In view of the fact that he did not apply

any blockage corrections, thern small difference in the precise limiting

value of V k/v is not crucial.o

164 -

s/k

149.5

O Present. study (distributed)

Present -.study (ribs)

Q Achenbach 1971

Niemann 197]. (cooling tower;ribs)

V Färelj. and Maisch 1974(cooling tower; ribs)

V k/v = 1100o-

49

221 -

15

I2.9"u.....7 O12.9 V173

26.9

k/d

Figure 5-. 30 Reynolds-number independence.

165

The trend noted in Fig. 5.30 can be explained qualitatively in

terms of the boundary layer behavior. The necessary conditions for Reynolds-

number independence (i.e. independence from viscosity) are that: (a) the

region of laminar flow ahead of transition should be small, and (b) the

conditions downstream of transition must be such that the surface can be

regarded as fully-rough in the Nikuradse sense. The first requirement is

easily achieved not only because the Reynolds numbers of interest are large

but also because of the surface roughness. The second requirement can be

examined on the basis of the well known experimental criterion (see, for

example, Schlichting (1968)) that k/t,/p/v should be greater than 70 for

fully-rough surface conditions to be achieved. Now the direct measurements

of wall shear stress made by Acherthach (1971) on cylinders at large Reynolds

numbers show that /t/p/v increases from e = O upto about e = 50°- 55°, and

then decreases until separation takes place (see Fig. 2.2). Transition

from laminar to turbulent flow occurs at about e = 10° to 20°. These experi-

ments suggest that if the boundary layer is of the fully-rough type

immediately following transition, then it will remain so further downstream

past the position of the pressure minimum. The rapid decrease in the wall

shear stress just ahead of separation may, however, cause k/Tip/V to fall

below 70 and reestablish the influence of viscosity. Since the region over

which this is likely to occur is quite small, it can be said that Reynolds-

number independence can be achieved if the value of k/Tip/v is greater than

70 immediately after transition, that is,

k(/Tip)> 70

V

where the subscript T denotes transition, or

V k (/Tip)o T >70V

o

Using the experimental value of (/TiQ)T/V observed by Achenbach for

k/d = l.1xl03 at large Reynolds numbers, we have

Re k/d E V k/v > 1070o

which agrees well with the data shown in Fig. 5.30.

166

For larger values of k/d, the governing factor for Reynolds-

number independence appears to be transition. It is evident that Re1 cannot

decrease indefinitely as k/d increases, since there must be a certain value

of Reynolds number below which early transition cannot be induced by surface

roughness. Re1 cannot of course fall below the value at which the subcriti-

cal regime ends for a rough-walled cylinder and must be greater than that

value since, for Reynolds-number independence, transition must be sufficiently

forward for viscosity to be unimportant.

In the case of cylinders and cooling towers f itted with ribs

the boundary layer flow is affected not only by k/d but also by s/k. It

appears that, for rib-type roughness, at least for the relatively large values

of k/d for which experimental results are available, vàlues of Re1 are

generally lower than those for distributed roughness. In other words, for a

given k/d, Reynolds-number independence is adhieved at lower values of

Reynolds number, provided that the rib spacing is optimum. Conditions f r

Reynolds-number independence in the case. of rib roughness with smáll values

of k/d cannot, however, be conclusively determined until additional tests

are made using smaller k/cl and different s/k. Such information is not, avail-

able at the present time.

Finally it should be noted that if Reyñolds-number independence

is achieved, then the results 'are also expected tó be independent of free-

stream turbulence, since according to Armitt. (1968), freestréam turbulence

has no effect for Vk/v greater than 600;

5.4.2 Simulation by employing models withlargcr relative roughness

As indicated, earlier, it is desirable. to reproduce, as best as

possible, the expected mean-pressure distributions on prototype structures

such as cooling tower shells, on scaled models in the laboratory. When

Reynolds-number independence can be. achieved on the models, the 'laws of

dynamic similarity imply that the model results are applicable to geometri-

cally similar prototypes operatiñg at much larger Reynolds numbers. While

this 'appears to solve the problem of simulation,' the solution is not always.

practicable since the relative surface roughness of, prototypes of interest

is usually so small that,, given the limited capabilities of most present-

day wind tunnels, the models with the same relative roughness will not

167

exhibit the desired Reynolds-number independence. Moreover, èven the

prototypes themselves will not be operating in the Ïange of Reynolds-number

independence if the roughness Reynolds number Vk/ is not large enough

(See section 5.4.1). Additional modelling criteria are therefore needed.

A number of previous investigators (for example, Armitt (1966)

and Batham (1973)) have proposed that simulation of prototype pressure

distributions on scaled models may be achieved by further roughening of

the. model surface. Môre. recently, Szechenyi (1974) has suggested that,

provided the flow around the model is. supecritical, similarity between

model and prototype can be obtained if the value of the roughness Reynolds

number Vk/ is the same in both cases. This criterion, which is considered

to be applicable to circular òylinders with Surface roughness in the range.30.16 < k/dxlO < 2.0, is, however., based on measurements of the drag

coefficient, rather than on detailed observations of the pressure-distribution

parameters. Furthermore, Szechenyi presénted his results in the form of an

envelope (see Fig 5 31) which obscures any systematic influence of the

relative roughness k/d. The data obtainèd from the presèñt investigation

and those of Roshko (196l)and Achenbach (1971), however, show a systematic

variation of C as well as C. and C with kid. The simple modèllingd pb pmcriterion suggested by Szechenyi. cannot therefore be accepted Since Cd

as well as C.. and C are functions of both Re and k/d, it iè indeed;pb pm. ; .

unlikely that a simple product of these two parameters, namely Vk/v, can

account for botheffects. .These effects are well depicted by Fig. 5.31.

It is in fact gratifying to observe that the present data are consistent

with those of Szechenyi, and yet exhibit.the sytematic influence of the

surfàce roughness.

As indicated àbove, the scaliñg criterion of Szechenyï is based

on the drag coefficient However, ensuring the same value of Cd for the model

and the prototype does not necessarily imply that the pressure distributions

will also be similar in the two cases. Consider, for example, the measure-

ments of Achenbach.. For .Vk/v = 750,, at which the drag coefficient curves

for k/dxlO3 = 1 1 and 4 5 cross each other in the supercritical range, Fig

5.31 shows that the válues of C for k/dxlO3 1.1 and 4..5 are -1.82 andpm. .

-1.62 respectively (The corresponding vàlues of Ch are -l.0.4and -0.96).

Cd

1.2

1.0

0.8

0.6

-1.4

-1.8

-2.2

-2.6

40

I I

Achenbach 1971

/ Széchenyi 1974

4.5

Achenbach 1971

(0.16<k/dxlo3< 2.0) -

Roshko. 1961

9 .... Present study:

k/dxlO3i 1.59 (Distributed

168

k/dxlO3

D 6.21 (Distributed)

O i.97 (RB-05,s/k=22.1

ç 3.38(RA-05,s/k=12.

I I

1000

Figure 5.31: Drag coefficient and minimuxn pressure coeffi-cient as a function of roughness Reynoldsnumber, V k/v.

4Xi0100Vk/v

169

On the other hand, the high-Rey±iolds-riumber values of C, (=087) and C3

d pm(=-l.75) for k/dxlü 1.1 can be Obtained, within 2.3 percent, by means of

a test with the present cylinder with k/dxlO3 = 1.59 and V0k/\ = 350

(or Re = 2.2x105). From Fig. 52 the corresponding value of Cb for k/dxlO3 =

1.59 is -0.97 which is close to the high-Reynolds number value of Cb

3p

for k/dxlO = 1.l. It is therefOre clear that a. single parameter such as

Vk/v cannot, by itself, be üsed as a scaling parameter. A more sátisfactòry

procedure which recognizes the importance of both the Reynolds number and

the roughness size is suggested below.

Returning to the problem of simulating high Reynolds-number flow.

past a prototype, with known surface roughness.k/d, on a model with a

rougher surface, let us assume that the drag coefficient and the mean pressure

distributions on the prototype are known either from aötual tests or from

interpolation of the curves of Cä Cpm and Cb vs kid such as those given

in Fig. 5.28. The.objective is to reproduce as closely as possible, these

results. on a geometrically similar (except for súrface roughness) model in a

conventional wïnd, tünnel. In the, case of long cylindrical structurés with

distributed roughness, this may be achieved by refer.ence to Figs.' 5.1 and

5.2 where C , C and C are plotted as functïons of Reynolds number añdd pm pb

relative, roughness. .A combination of k/d and Re', in the supercritical range,

can be found, such that the prescribed values of C, C and Cb corresponding

to the prototype can be reprod.uced on the model Once this is achieved, it

is expected that the remaining characteristics of the pressure distribution,

such as the location of the pressure minimum and sepäration, will also demon

strate substantial similarity between 'the model and prototype.

This procedure assumes a previous knowledge of the conditions

which are expected to prevail on thè prototype as well as, a sufficiènt

knowledge of the variation of the aforementioned parameters, with relative

roughness and ReynOlds number obtained from model tests, in wind tunnels.

Hoqever,, as also remarked upon earlier in section 5.3.1, the available

high-Reynolds-number data for small and moderate values of relative roughness

are limited. Until such .dta are availabl,,e, the infortriation provided by Fig.

5.28 can be used as an interIm solutioñ to the expected prototype behavior.

It should also be remarked that more d'ata are also needed on the behavior f

model pressure distributions for small values of the rcLativc rouqhness to

make the proposed scaling procedure more generally usable This will Lnvolve

the use of larger wind tunnels.

170

In chos'ing the proper Reynolds number and roughness height in the

manner described here it is also necessary to give due consideration to

the problems associated with wind-tunnel testing. In particular, since the

results presented here have been corrected for wind-tunnel blockage, it is

imperative that allowances be made for blockage before selecting the size

of the model and the roughness height. It is clear that the availability of

larger wind tunnels would greatly alleviate the problems associated with

blockage. Special attention should be given also to the influences of wind-

tunnel turbulence.

In the case of modelling of short cylindrical structures, such

as cooling tower shells, for which the height to mean-diameter ratio is

about 2, a similar procedure to the one described above for long cylinders

may be followed. Here, however, the average base-pressure coefficient is

essentially independent of surface roughness and Reynolds number in the

.supercritical range and is controlled primarily by the, flow over the free

end. The latter feature .implies that the base pressure (and consequently

the pressure distribution) is' especially dependent upon the blockage and

other experimental conditions, such as the size of the base tables on which,

the models are mounted. Recent studies made at the Institute (Reference 18)

indeed show the strong influence of blockage on the base-pressure coefficient.

Extreme care must therefore be taken to avoid éxcessive wind-tunnel blockage

in chosing the model Reynolds number and surface roughness.

In the case 'of cylinders and 'cooling towérs.fitted with ribs' it

has already, been pointed out that the rib spacing s/k must be considered

in addition to the roughness height kid.. However, as 'Fig. '5.31 'shows, when

the. ribs are spaced jn an optimum manner (i.e., s/k of the order of 12 to 20),

the rib data show trends similar to those obtained with distrïbuted roughness.

The relative insensitivity in the range of Reynolds-number independenòe of

this data to variations in k/d for optimum values of s/k has already been

conented. upon earlier and attributed to the observation that the rb spacing

s/k is more important than the rèiative roughness height kid. The problem of

modelling structures fitted with ribs will of course require more experimental

'data. Such data areespecially needed for structures fitted with small

ribs with optimum as well as other-than-optimum spacings. However,

considerable insight can be gained by the information available to date and

this infOrmation can -be used profitably until such data are. obtained.

l7l

(See also the studies Of Niemann (1971) and .Farell and Màisch (1974)

in connection with cooling towers fitted with fibs).

Finally, it is perhaps useful to emphasizé once more that the

mean-pressure distributions (as well as the pressure fluctuations) on cylin-

drical structures are influenced not only by the Reynolds number and 'surface

roughness as well as the geometry of the structure but also by a number of

other factors enumerated previously. It is evident that much remains to

be investigated in order to completely understand th influence and the

relative importance of each of these factors so that satisfactory design

and modelling criteria can be established. However, the Reynolds number and

surface roughness appear to be among the most important of these factors. It

is therefore hoped that the present stùdy will serve as another step towards

a better understanding of the aerodynamics of large cylindrical structures.

5.5 Use of external ribs on cooling tower shells

The experiments reported here and thöse performed earlier by

Niemann (1971) and Farell and Maisch (1974) suggest that external ribs on

cooling tower shells considerably reduce the magnitude of the overall minimum

pressure coefficient. This reduction is particularly marked when th rib

spacing is. such that the ratio s/k is of the order of 20. From the availäble

results shownin Fig. 5.29, it is seen that a relative rib heIght k/d of aboût

4x1&3 will lead to maximum reduction. in thé maximum suction. However,

the practicality of such a large relative rib height is questionable as

discussed below.

As a typical practical situàtion, we shall consider the Weisweiler

cooling tower (Niemann, 1971). Measurethents on the prototype were made by

Niemann and scaled models of this, tOwer have been tested in wiñd tunnels by

Niemannas well asFarell and Maisch. This towér has-a height of l0'5.lm

arid a mean diameter of S2.5m. . The diameter at-the waist, or throat,is 44.6m

and the shell thickness is about lO cm In order to obtain kid t 4x103 and

s/k = 20 on this particular tower, 33 ribs (O = 10 90) with a height of

2lcmare required.. It isseen that, insofar as the mean préssùre loading

is cOncerned, the optimum height is about twice thé shell' thickness. Such

.a size is. of course, likely to pose structural .problem for the designer

and consideration must also be given to the possible .locàl effects o the

ribs discussed in section 5.2.3. - .

From the prototype tower at Weisweiler, which has 52 ribs (tO =

6 90) of height 1 8cm, so that k/d.xlO3 = 0 34 and s/k = 149 5, Niemann

.30. and C = -0.41±0.02. From the discussions .presentedpb

that the large value of Ic. .1obtained in these tésts

pmto the rather.. small relative rib height and especially

the rather large relative rib spacing. It.will be seen from Table 5.1

that the magnitude of the minimum pressure coefficient can be reduced well

below 1.30 if larger and more closely spaced ribs are usted suáh thät k/d

is of the order of 1-2x103 and s/k is about 20. As remarked above, it

may also be possible to obtain substantial reductions in Ic even with3

pmvalues of k/d less than 1.Ox.lO provided, that the optimum rib spacing is

obtained C = -1pm

so far it appears

can be attributed

172

Substantial reductions in le I can still be attained, however,pm

with smaller ribs. Using the Weisweiler tower as a typical case, severà]..

possible rib configurations with s/k = 20 have been examined. The relevant

information is given in Table 5.1. The expected values of C. have been= pm

deduced from Fig 5 29 using C = 0 43 (18) The minimum pressure coeffi-p

cients given in Table 5.1 for k/dxlO = 0.5 and 1.0, however, may be in.

error since, as also remarked upon in Section 5.3.1, the available data in

thé range l0 < kid < 10 shown in Fig. 5.29 were obtained with very

large values of s/k. Since the ribs are most effective with the optimum

value of s/k of about 20, it is likely that the magnitude of the minimum

pressure coefficients (i.e. IC I) could be even smaller than those quoted

in the table for k/dxl0 = 0.5 and 1.0.

Table 5.1: Use of extérnal ribs on a cooling tower shell. s/k = 20.(Weisweiler tower mean diameter d = 52 5m, diameter atwaist s 44.6m, height = 105.lm, shell thickness t s 10cm.)

Case k/dxlO3 k (cm). k/t. NumberÓf ribs

e .

(degrees)

Cpm

1 0.5 .2.63 0.26 266 1.4 -1.20

2 1.. 0 5.25 0.53 133 2.7. -1.05

3 2.0 10.5 ï. b5 66 5.4 -0.90

4 4.0 21.0 2.10 33 10.8 -0.75

173

employed. Additional experiments are needed to. investigate this possibility.

It should be recognized, however, that, even if this possibility is proved

to be true, a very large number of ribs would be required for the smaller

valués kid, as can be. seen from Table 5.1. It appears, therefore that rib

configurations with k/dxlO3 betweén 1.0 to 2.0 and with the corresponding

number of ribs between 130 . and 66 would probably prove to be the most

practicable.

VI. SUNMAY AND CONcLUSIONS

The main objectives of the present study were: 1) to investigate

te influence of external ribsand distributed roughness on the mean

pressure distributions on ircular. cylinders at large Reynolds ñumbers;

2) to study the feasibility Of simulating prototype conditions in wind-

tunnel experiments.; 3) to. determine the relative merits of the exterñal

roughness elements for use on large circular structures; and 4.) to.clar.ify the

physical mechanisms responsible for the observed roughness effects and

elucidate the various observations by theoretical analysis. The study was

prompted by an immediate need for a .better understanding of the róughness

effects on the mean pressure distributions on hyperbolic cooling-tower shells.

and was conducted with a view to apply the findings towards reducing the

mean wind loads on such cylindrical structures. The effects of several

different configurations of external ribs and of different sizes of roughness

of the distributed type on the mean pressure distributions and boundary-layer

development were investigated by: systematic experiments. The results have

been analyzed in the light of boundary-layer concepts and other data

obtained by previous investigators The main conclusions from the present

study are summarized belOw:

Surface roughness has a strong influente on the méan pressure

distributions on circular cylinders At sufficiently large Reynolds numbers,

the pressure distribution becomes independent of Reynolds number and,

other factors being the same, it is determined by the chaacteristics of

the surface roughness. .

In the' Reynolds-number independence.range, an increase in the

relative roughness siz (k/d), leads tö'a reduction ir'the .mágnitüde, of the

174

minimum pressure coefficient (JCJ) and an increase in the magnitude of

the base-pressure coefficient (jC b' as well as the overall drag coeffïcient

(Cd). The major éffects of roughness size are, however, óbserved with k/dxl03

less than about 25 to 4. For larger values of kid, additional changes in the

drag coefficient and the pressure-distribution parameters are relatively

small.

The effects of external ribs are generally similar to those

of distributed roughness. There are, however, strong local influences of

ribs which need to be studied further Ribs appear to be generally more

effective than distributed roughness with similaÉ rèlàtive heights k/d,

provided the relative rib spacing s/k is chosen in an appropriate manner.

The relative rib spaóing s/k is an important parameter.

The maximum roughness effect is obtained when s/k is in the range of 12-20.

An optimum value of s/k = 20 is suggested on the basis of the present

experiments on cylinders and previoús tésts on cooling-tower models

performed by Fareil and Maisch (1974).

For values of s/k about 12 to 20 and k/d > l0, pressuré

distributions at large Reynolds numbers appear to depend more on s/k than

on k/d. There äre indications that this may also be true for values òf

kid smaller than l0. Further studies are needed to confirm this possi-

bility.

The pressure rise to sepáration, cb - C, for cylinders

as well as cooling towers. is primarily a function of the surface roughness

at large Reynolds numbers, and independent of blockage (for blockage ratios

less than 15% for cylinders) and free-end effécts. While the individual

values of Cpb and Cpm are quite different for cooÏïng towers and cylinders,

the pressure rise C - C correlatés well fór both cases. The dependencepb pm

of Cb - C on k/d at large Reynolds numbers is supported by a theory

extending Townsend's (1962) separation model to cylinders with distributed

roughness.

A close connectjon is indicatedbetween the thicknéss and

vélocity profiles of the boundary layer and the value of Cb C.Lower values of C - C are associated with thicker and more retarded

ph pmboundary layers. Earlier transition and larger wall shear-stresses asso-

175

dated with large surface röughness result in a thicker and more retarded

boundary layer, and therefore lead to a lower value of C - C and earlierpb pm

separation.

For a given relative roughness k/d, there is an upper limit

to the Reynolds number, Re]1 beyond which the drag coefficient and the

mean pressure-distribution parameters become independent of Reynolds nwnber.

The available data indicate that Re is a function of kid. Over a range

of values of. k/d, the product of these two parameters, namely the roughness

Reynolds number Vk/v, appears to remain constant. In particular, for

cylinders with distributed roughness and k/d lèss than about 2x103,

Reynolds-number independence can be achieved if Vk/v is greater than 1100

(i.e., Re1 = fl00/(k/d)). For much larger relative roughnesses, with k/d

greater than 4x103 say, Re1 becomes independent of k/d and attains a nearly

constant value of the order of. 3x105.. In. the case of cyliñders with ribs.

spaced in an optimum manner (see item 4 above), Re1 is somewhat lower than

that for distributed.roughness of same relative height kid. This is due to

the greater effectiveñess of ribs referred to earlier in item .3.

it has been shown that a given prototype mean-pressure

distribution can be reproduced in a wind tunnel at a much lôwèr Reynolds

number by employing models with larger surface roughnesses. A modelling

procedure based on the experimental results has been outlined. .A previous

suggestionof Szechenyi (1974), that prototypé conditions can be modelled

if the roughness Reynolds number V k/v is the same in the model as in the,

prototype, has been found tobe an oversimplificätion. Indeed, it has

been shown that the influences àf the Reynolds ñumber and the relative

roughness must be considered separately in order to obtain the .proper scaling.

If prototype hyperbolic cooling-towers aré to bé fitted

with the optimum rib configurations indicated by thïs study (i.e., k/a

4xiO3 and s/k l2-2O), two problems are likely to arise: (a) the rib

heights become large compared with the shell thickness, thus posing a

structural design problem, and (b). the local .effècts of such large rIbs will

most probably offset the. gains made by reduding the magnitude of the overall

minimum pressure-coefficient Nevertheless, this study indicates that the

magnitude of the minimum pressure coefficient can be reduced substantially

from, its value on unroughened shélls by the use ò ribs which are somewhat

176

larger and more closely spaced than those employed by some manufacturers

at the present time. It appears that a choice of rib configurations with

the values of k/dxlO3 between 1.0 to 2.0 and with the corresponding number

of ribs between 130 to 66 would prove to be the most practicable for

cooling towers with a mean diameter of the order of 50 meters and a shell

thickness of about 10cm.

177

REFERENCES

Achenbach, E. (1968) "Distribution of local pressure. and skin6friction around a circular cylinder in cross-flow up to Re=5x10 ,"

J. Fluid Mech., Vol. 34, pp. 625-639.

Achenbach E. (1971) "Influence of surface roughness on the ôross-f low around a circular cylinder," J Fluid Mech , Vol 46.pp 321-335..

Allen, H.J., and Vincenti, W.G. (1944) "Wall interférence in a two-dimensional flow wind-tunnel with consideration of the effect ofcompressibility," N.A.C.A., TR 782, 1944.

Armitt, J. (1968) "The effect of surface roughness and free streamturbulence on the flow around a model cooling tower at criticalReynolds numbers," Proceedings of a Symposium on Wind Effects onBuildings and Structures, Loughborough University of Technology,England.

Balkowski, M., and Schollmeyer, H. (1974) "Untersuchungen ZumWider standsverhalten hintereinander Liegender Wandfester Storkorker,"Abhandlungen aus dem Aerodynainischen Institut der Rhein -WestfTechnichér Hochschule Aachen, Heft 21, pp. 20-24.

Batham, J.P. (1973) 1'Pressure distrïbutions On cirOular cylindersat critical .Reyñoids numbers," J. Fluid Mech., Vól. 57, pp.. 209-229..

Bearman, P.W. (1969) "On vortex shedding from a circular cylinderin the critical Reynolds number range," J Fluid Mech Vol 37,pp. 577-585. . .. . .. .

Carrasquel, S.C. (1974) "Effect of wind tunnel walls on the flowabout circular cylinders and cooling towers," M S Thesis, TheUniversity of Iowa.

Cowdrey, C.F., nd O'Neill, P.G.G. (1956) "Reports of tests on amodel cooling tower for the C.E.A. Pressure measurements at highReynolds numbers," National Physical Laboratory, NPL/Aero/316a

Davenport, A.G.,, and Isyumov, N. (1966) "The dynamic and staticaction of wind on hyperbolic cooling towers," University of WesternOntario, Canada, Engineering Science Research Report, BLWT-l-66

Dryden, H.L., and Hill, G.C.. (1930) "Wind pressure on circulärcylinders and chimneys," U S Bureau of Standards, Journal ofResearch, Vol. 5, pp. 653-693.

Ebnér H. (1968.) "Untetuchungds' Einflusses der Kräftwerksgebudeuf die Windbelastung des Balcke-NaturzugkUhlturms Kraftwerk Mengede(GBAC), "Technische Hochschule Aachen, Lehrstuhl Fir Leichtbau,Bericht Nr. 21/1968. . . .

178

E.S.D.U. (1970) "Fluid forces acting on circular cylinders forapplication in general engineering," Engineering Sciences DataItem, No. 70013. Enginèering Sciences Data Unit, 251-259 RegentStreet; London, WIR 7AD, England.

Fage, A., arid Falkner, V.M. (1931) "Further experiments on the flowaround a circular in er" Aerö. Res. Comm., London, Reports andMemoranda No. 1369.

Fage, A., and Warsap, J.H. (1929) "The effects of turbulence andsurface roughness on the drag of a circular cylinder," Aero. Res.Coima., London, Reports and Memoranda No. 1283.

Farell, C. (1971) "On the modeling of wind loading on large coolingtowers," Proceedings, Second Annual Thermal Power Conference andFifth Biennial Hydraulics Conferénce, Washington State University,Pullman, Washington, pp. 139-166.

Fa.rell, C., and Maisch, E.F. (1974) "External roughness effects onthe mean wind pressure distribution on hyperbolic cooling towers,"UHR Report No. 164, Iowa Institute of Hydraulic Research, TheUniversity of Ïowa.

Farell, C., Carrasquel, S.,. and úven.;Q. "Effects of wind tunnelwalls on flows about circular cylinders and model hyperboliccooling towers," journal article in preparation at the Iowa Instituteof Hydraulic Research, Thé University of Iowa, Iowa City, Iowa.

Farell, C., Patel, V.C., and GTiven, 0. (1974) "Aerodynamics of hyper-bolic cooling towers," IOwa Institute of Hydraulic Re5eaìch, ProgressReport suiitted to the National Science Foúndatjon.

Goldstein, S. (1938) Modern devé1oiénts in fluid mechanics, Vols. 1and 2, Oxford University Press, Oxford also Dover Publications,NewYork (1965). '

2i. Golubovic, G. (1957) "Etude a&rodynamigue.d'une tour réfrigéranteen forme dhyperbolöide de révolution," Pub. Int Ass. Br. and Str.Eng., Vol. 17, pp. 87-94.

GOod, M.C. and Joubert, P.M. (1968) "The form drag of two-diminsjonalbluff plates immersed in turbulent boundary layers," J. Fluid Mech.,Vol. 31, pp. 547-582.

Hayn, F. (1967) "Druckverteilungsmessuñgen am Modell des Kraftwerks:Scholven," Deutsche Versuchsanstált für Lüft-und Raumfährt E.V.,institut fûr angewandte Gasdynamik, Port-Wahn, Bericht AM 511.

Liu, C.K., Kline, S.J.,and Johnston, J.P. (1966) "An experimentalstudy of turbulent boundary layer on rOugh wails," ThermòsciencesDivision, Report 'No. l'ID-15, Stanford University, Stanford, California.

25 Maisch, F (1974) "Wind loading on hyperbolic cooling towers," M SThesiS, The University f Iowa

179

Mor.sbach, M. (1967) "ober die Beding ngen fr eine Wirbeistrassen-bildung. hinter Kreiszylindern" Dissertation, T.H. Aachen, 1967.

Naudascher, E. - (1964) "Effect of density oñ air-tunnel measùrernents,"J. Royal Aeron. SOC.., Vol. 68, p. 419..

Niemann, H.J. (197-1) "On the stationary wind loading of axisyinmetricstructures in the transcritical Reynolds number region," Institut fùrKonstruktiven Ingénieurbau, Rihr-Universitt Bochum, Report Ño. 71-2.

Parkinson, GV., and Jandali, T. (1970) "A Wake source model forbluff body pOtential flow," J. Fluid Mech. Vol 40, pp. 577-594.

Patel, V.C. (1968) "The effects of curvature on the turbulent boundarylayer," A.R.C. R.& M.No. 3599.

Patel, VC., Nakayaxna, A., and Dainian, R. (1973) "An experimentalstudy of the thiòk turbulent boundary layer near the tail of a bodyof revolution," uHR Report No. 142, Institute of Hydraulic Research,The University. of Iowa.

Pris, M.R. (1959) "Etudes aodynarniques I: Tour de rcfrigerationhyperbolique," Annales de i 'Institute Technique du Bâtiment et desTravaux-Publics, No.134, pp. 147-167.

Rogers, P.K., and Cohen, E.W. (1970) "typerbolic coo..ing towers,development and practice," Journal of the Power Division, ASCE, Vol 96,No. Poi, Proc. Paper 7030, pp. 117-128.

34.. Roshko, A. (1961) 'Expèriments òn the mean flow past a circular cylinderat. very high Reynolds number," J. Fluid Mech., Vol. 10, pp. 345-356.

Roshko, A. (1970) "Oñ the. äerodynami drag of cylindérs at .highReynolds number," U.S.-Japan Research Seminar on Wind Loads on Structures,Honolulu.

Schlichting, H. (1968) Boünday-Layer Theory, McGraw-Hill BOok Co.,1968, 6th Ed -

.. :

Scranton, D.G., and Manchester, E.G. (1973) "The use of Simplotter,a high level plotting system," Research and Development Report,November 1973, Document No 4, Revision No 2, Aines Laboratory,USAEC Iowa State University, Aines, Iowa.

38 Stratford, B S (1959) "The prediction of separation of the turbulentboundary layer,'! J. Fluid .Mech., Vol'.-5,pp.i-l6.

Szechenyi, E. (1974) "Simulation of high Reynolds ntmibers on a cylinderin wind tunnels tests" La Recherche Aerospatiale, May-June 1974,pp. 155-164. . - . .... -.

Townsend, A.A. (1962) "The behaviour of a turbulent boundary layerhear separation," J. Fluid Mech., Vol. 12, pp. 536-554.

180

APPENDIX 1

Effects of wind-tunnel blockage

In order tò determine the effects of wind-tunnel blockage on the

values of the mean pressure coefficients and the drag coefficient, a series

of tests were made in the large low-turbulence wind tunnel of the Institute

with the. circular cylìnder described by Carrasquel (1974). The cylinder

surface was roughened by Norton-Co. #36 sandpaper (k = 0.535 mm), and the

cylinder diameter,. includIng the thickness of the sandpaper and tape, was

d = 4.094 in. A high value of relative roughness, k/d 5.14 x 10, waschosen so as to eliminate any Reynolds-number dependence of the results.

Different blockage ratios òf 6.82%, 9.90%, 11.28%, 14.11%, 16.37% were öb-

tamed by means of movable side walls éxtending 8 ft downstream from the be-

ginning of the 9 ft-long test section. The cylinder axis was located at the

same position as the larger cylinder désòribed in Section 3.2, and the same

experimental set-up as descri.bed in the text was employed.

The results are suarized in Table A-1. As can be seen from Table

A-1, Reynolds-number independence was achieved. The threè larger Reynolds-

number experiments for each blockage ratio are chosen for presentation and

discussion in the following.

The variations of C, jCj, C

Jand C -C with the blockaged. pm pb. pbpm

ratio d/w, where w is the tunnel width, are plotted in Fig. A-1. Also plotted

are the corrected values obtained by the blockage-correction procedure describedbelow.

It can be seen that the correction probedure yields horIzontal lines

for all the parameters considered, namely Cd,. C, and Cb and thatthe corrected

values are close to the extrapolated zero-biòckagevalues. This correction

procedure, therefore, can be considered reliable, at least for the Reynolds-

number-independent f lows past circular cylinders..

It can also be seen that while both C and Cb are affected by blockage,the difference pb_C is almost independent on the blockage ratio, at least

in the range of blockage ratios of these tests.

181

Table A.1: Effects of wind-tunnel blockage

Summary of results

d/w(percent)

Re x l0 Cd IcpmI ICpbI Cpb-Cpm

16.17 2.17 1.135 1.76 1.28 0.482.16 1.132 1.76 1.26 0.502.14 1.093 1.76 1.23 0.521.86 1.108 1.76 1.26 0.501.66 1.074 1.75 1.23 0.521.46 1.058 1.74 1.21 0.53

14.11 2.19 1.096 1.70 1.23 0.472.19 1.100 1.67 1.23 0.442.19 1.093 1.70 1.23 0.471.89 1.072 1.69 1.22 0.471.69 1.037 1.67 1.16 0.511.47 1021 1.68 1.15 0.53

11.28 2.22 1.032 1.59 1.13 0.462.22 1.046 1.61 1.14 0.472.22 1.049 1.62 1.14 0.481.89 1.030 1.59 1.12 0.471.70 1.017 1.58 1.10 0.481.49 0.990 1.56 1.09 0.47

9.90 1.51 0.959 1.54 1.03 0.511.72 0.993 1.54 1.06 0.482.24 1.025 1.57 1.10 0.472.24 1.029 1.56 1.11 0.452.24 1.022 1.55 1.10 0.451.94 0.996 1.54 1.07 0.47

6.82 1.52 0.976 1.50 1.02 0.481.73 0.984 1.50 1.02 0.481.98 1.012 1.47 1.06 0.412.26 1.034 1.47 1.08 0.392.26 1.027 1.47 1.07 0.402.26 1.017 1.49 1.06 0.43

2.5

2.0

Cpm

J 1.5

cpb

J

Cpb-Cpm1.0

0.5

0.0

® Experimental

Values

A Corrected Values

Figure A.1:

Effect of wind tunnel blockage on Cd, Cpb, Cpm and Cpb-Cpm.

0.0

0.05

0.10

d/w

0.15

0.20

Carrasquel (1974), who made a similar and more comprehensive study

in the smaller wind tunnel of the Institute, came to the same conclusions.

The values of iCI, ICbI obtained by Carrasguel are, however, consistently

larger (by about 0.24) than the ones obtained in these tests in the larger

wind tunnel with the same model and the same relative roughness for the same

blockage ratios. The differences can be attributed in part to the different

span-to-diameter ratios (See, for example, Achenbach (1968)). (l/d = 8.03

in the large tunnel, l/d = 5.86 in the small tunnel).Correction Procedure. The correction procedure employed in this

study is the same as that used by Roshko (1961). It is based on two formulas

of Allen and Vincenti (1944) (Eqns A-1 and A-2), and a formula proposed by

Roshko (Egn. A-3):

V=1+¼c +0.82 d2

dw (;:)

o

-½C i-2.46 d2Cd

1 dw (;)

V-C -1= 02

PC ( ) (C -1)V p

C

183

Here, the subscript c denotes corrected values. Other symbols have already

been defined. The corrected Reynolds number is that based on the corrected

velocity.

184

APPENDIX 2

Meaw-pressure-distribution plots and tables

(under separate cover)

This appendix contains the computer plots and tables of the

mean-pressure-distribution data obtained for smooth and rough-walled cylinders

as described in the text. The results presented here have not been corrected

for blockage effects. The plots and tables are presented in groups corres-

ponding to each of the differetit roughness configuratIons investigated.

Each plot is presented on an even-numbered page followed by the corresponding

table on the odd-numbered page facing the plot.

Owing to its length (617 pages), Appendix 2 is produced under

separate cover. It can be obtained from the Iowa Institute of Hydraulic

Research upon request.