Wind loads on circular storage bins, silos and tanks: I. Point pressure measurements on isolated structures

Journal of Wind Engineering and Industrial Aerodynamics, 31 (1988) 165-188 Elsevier Science Publishers B.V., Amsterdam i Printed in The Netherlands

165

W I N D LOADS ON C I R C U L A R STORAGE B I N S , SILOS A N D T A N K S : I. P O I N T P R E S S U R E M E A S U R E M E N T S ON I S O L A T E D STRUCTURES

P.A. MACDONALD John Connell Group, 88 Walker Street, North Sydney, N.S. W. 2060 (Australia)

K.C.S. KWOK School of Civil and Mining Engineering, University of Sydney, N.S. W. 2006 (Australia)

J.D. HOLMES C.S.I.R.O Divison of Building, Construction and Engineering, P.O. Box 56, Highett, Vic., 3190 (Australia)

(Received June 15, 1987 )

Summary The inability to satisfy Reynolds number similarity in wind tunnel modelling of low-rise structures with circular features, and the lack of full-scale results have left designers with inadequate information for the design of circular storage bins, silos and tanks against wind loading. In this paper, wind tunnel pressure measurements on scale models of low-rise cylindrical structures carried out at Reynolds numbers > 2 X l0 b are described. Circumferential wall pressure distributions and roof pressures for a range of aspect ratios and roof configurations are presented.

1. Introduction L a r g e n u m b e r s of low-rise cylindrical s t r u c t u r e s s u c h as grain s t o r a g e silos, liquid s t o r a g e t a n k s a n d o t h e r b u l k s t o r a g e bins, h a v e b e e n d e s i g n e d a n d cons t r u c t e d w i t h little reliable d a t a for t h e design a g a i n s t w i n d d a m a g e . T h e curr e n t A u s t r a l i a n w i n d l o a d i n g code [ 1 ] o n l y p r o v i d e s a coefficient of d r a g (CD), b a s e d on s m o o t h - f l o w e x p e r i m e n t a l d a t a on wall p r e s s u r e s , a n d no details on t h e n a t u r e of t h e w i n d l o a d i n g on roofs. A l t h o u g h o t h e r design codes a n d h a n d b o o k s do c o n t a i n m o r e i n f o r m a t i o n for t h e s e s t r u c t u r e s , it is i n v a r i a b l y b a s e d on d a t a in w h i c h t h e R e y n o l d s n u m b e r a n d t u r b u l e n c e c h a r a c t e r i s t i c s of t h e full-scale n a t u r a l w i n d are i n c o r r e c t l y modelled, or it was o b t a i n e d for m u c h higher a s p e c t r a t i o s ( h e i g h t / d i a m e t e r ) t h a n t h o s e r e l e v a n t for s t o r a g e b i n s a n d silos. T h e r e h a s b e e n s o m e m o r e reliable w i n d t u n n e l a n d full-scale d a t a o b t a i n e d r e c e n t l y ( S e c t i o n 2); t h i s h a s a p p a r e n t l y n o t y e t b e e n i n c o r p o r a t e d into t h e design codes.

0167-6105/88/$03.50

© 1988 Elsevier Science Publishers B.V.

166 This lack of reliable design data has contributed to a number of wind-induced failures of such structures. There are two common modes of failures, buckling of the windward wall under positive wind pressure and overturning failure. The more common and less disastrous damage is local buckling on the windward wall, which has been found on m a n y structures including bulk storage tanks and partially or completely empty oil storage tanks. This report presents the findings of the first phase of a collaborative research programme investigating the wind loads on circular storage bins, silos and tanks. The aims of this phase were: ( 1 ) To review previous work on the subject; (2) To establish a wind tunnel testing procedure for the study of wind loads on low-rise cylindrical structures; (3) To determine circumferential wall pressure and roof pressure distributions, based on a quasi-steady assumption, for the design of isolated low-rise cylindrical structures. In the experimental part of the work, models of isolated cylindrical structures of nominal scale 1:100, with aspect ratios ranging from 0.5 to 2.0, were tested in simulated turbulent boundary layer flow in an aeronautical-type wind tunnel. Circumferential wall pressure distributions at different pressure tapping heights, and roof pressures were measured for different aspect ratios, roof configurations and Reynolds numbers. A later paper will describe the instantaneous (peak) structural loads on silo walls and the effect of grouping. More details of the work described in this paper are given by Macdonald et al. [2]. 2. R e v i e w of previous studies

Table 1 summarizes the data directly related to wind loads on circular storage bins, silos and tanks with height/diameter ratio > 0.5 published in the last 12 years. These studies have shown, for isolated silos, that there is reasonable agreement between model and full-scale mean wind pressure distributions. In all cases, the region of positive mean pressures extends up _+40 ° from the windward generator; thereafter, the mean pressures are negative. For grouped silos, the mean wind pressure distributions are significantly altered by interference effects to the flow. The region of positive mean pressure can expand to more than ± 65 ° from the windward generator. Considerable amplification of pressure magnitude can take place around the gap between silos. Unfortunately, the pressure distribution appears to be extremely dependent on the group configuration, spacing of the silos, and the angle of wind incidence, thus making the application of model test results of grouping configuration to fullscale situations difficult and unreliable. A comprehensive study of wind loads and wind-induced buckling of tanks of very low aspect ratio ( ~ 0.2) was made by Holroyd [3-5].

0.66:1, 0.78:1, Conical, Turbulent Open country 1.16:1 15°, 27 °, boundary layer 45 ° wind tunnel

Sabr ansky [8]

Conical, Turbulent Open country boundary (ayer 25 ° wind tunnel

0.5:1, 1:1, 2:1

1/12S

1/200

No

1.5 x 10s to Group 3 x 105 , of 3 Supercritical

1.2 x 105 1.38 x 105, 1.62 x lOS,, Supercrifical

Open country Full Scale. Supercrifical Group of 5

Finnigan and Longstaff [7]

FuH Sca(e

1.1/.:1

E6]

Cook and Redfearn

Conical, 30°

No

125 x 105, Supercritical

1/200

Turbulent Open country boundary layer wind tunnel

1.67:1, 3.07:1 Conical, :30°

Muthearn et al

[5]

No

Subcrifical

1/500

Group of Bins

1.5 x 105, Group Supercrifica= of 6

Reynolds Number

Turbulent Open country boundary layer and suburban wind tunnel

1/192

Geometric Scale

Zonica[, ill o

Open country

Approaching Terrain

0.5:1, 1:1, 3:1

Wind tunnel and wafer tunnel, with turbulence

Test Facility

Davenport and Surry [4]

Conical, 25 °

Roof

Test Program

1:I

Aspect Ratio H:D

Bin Geometry

Vickery [3]

Reference

TABLEI WiNDLOADSON STORAGEBINS, SILOSAND TANKS - A SUMMARYOF SIX PUBLICATIONS

Other Comments

speed

Bins with roof vents: Bin Eave height models sand-roughened; Static buckling tests conducted in wafer tunnel; Estimate of buckling

Reference

Mid height of wall

only

Eave height Row visualisation

Continuing project

Effect of lip at eave

Mean, standard Eave height F|ow visualisation; Drag coefficients of silos giver deviation and peak Lift coefficients of roofs given

No

Mean, standard 10m height deviation and peak

Mean

Mean, standard Eave height Lift coefficients of deviation and peak roof given

Mean

Pressures

Measurements

168 3. Experimental techniques

3.1. Wind tunnel Wind tunnel tests were carried out in the 7 × 5 ft. (2.13 × 1.52 m) wind tunnel in the Department of Aeronautical Engineering, the University of Sydney. The wind tunnel is a closed-loop concrete tunnel capable of producing wind speeds of up to 35 m s -1 in the 2.25-m-long working section. An atmospheric boundary layer flow was simulated in the relatively short working section, and the simulation technique and flow properties are described in the following sections. 3.2. Boundary layer simulation When modelling wind effects around structures in a wind tunnel, it is necessary to simulate an atmospheric boundary layer appropriate to the terrain in which the structure is typically constructed. Low-rise cylindrical structures, such as grain storage silos and other storage tanks, are predominantly found in open country terrain. For satisfactory simulation of atmospheric boundary flow in a wind tunnel, similarity between model and full-scale conditions in the following parameters should be maintained: ( 1 ) mean wind velocity profile; (2) turbulence intensity profiles; (3) Reynolds stress profile; (4) turbulence length scales and spectrum. However, in the present situation it was necessary to make some compromises between the atmospheric boundary layer simulation, particularly the turbulence length scales, to attain an adequate Reynolds number. In order to achieve a boundary layer flow in the relatively short working section of the aeronautical wind tunnel, an augmented growth method, with a combination of triangular spires and roughness elements, was employed. To generate a turbulent boundary layer flow over open country terrain, four triangular spires, 0.9 m high and 0.12 m at the base, separated by 0.45 m between centre-lines, were installed at the start of the working section, and the floor of the working section was covered in low-pile carpet, as shown in Fig. 1. The flow characteristics of the simulated atmospheric boundary layer were determined at three lateral positions 2.25 m downstream from the triangular spires, at the centre of the working section, 100 mm from the centre, and directly behind an inner spire. Hot-wire probes, mounted on the wind tunnel traversing equipment, were used to measure profiles of mean wind speed, turbulence intensities, Reynolds stress and the longitudinal turbulence spectrum. Profiles up to 1 m above the tunnel floor were measured at each of the three lateral positions. The hot-wire signals from DISA constant temperature ane-

169

Fig. 1. Simulation of turbulent boundary layer flow in the 7 × 5 ft low speed wind tunnel. mometers were linearized, low-pass filtered, digitized and processed by a microcomputer.

3.2.1. Mean wind velocity profiles Mean wind speed profiles at the three lateral positions are presented in Fig. 2 in log-linear format. A logarithmic law with a full-scale roughness height Zo= 0.02 m is shown. A reasonably good agreement with this profile is evident in the lower part of the boundary layer, up to ~ 0.3 m.

3.2.2. Turbulence intensity profiles Longitudinal, lateral and vertical turbulence intensity profiles are plotted in Figs. 3 and 4. These turbulence intensity profiles are compared with profiles suggested by A S l l 7 0 Part 2, 1983 [ 1], the Deaves and Harris model [6], and data from the Engineering Science Data Unit E S D U 74031-[ 7]. The longitudinal turbulence intensities in the lower portion of the wind tunnel matched the models fairly closely up to a height of ~0.4 m. At a height of 0.1 m (10 m in full-scale at a linear scale of 1:100), the lateral turbulence intensity was about 80% of the longitudinal value, and the vertical turbulence intensity ~ 65%. These values are consistent with those suggested in E S D U 74031 [7]. There is a small peak in the vertical turbulence intensity profiles at a height of ~ 0.2 m which appears to be a byproduct of the spire/roughness element

170

1

zr(mI zo(m) 1 Mode[ 0.1 0.0002 -Full Scale 10 0.02 ~ o Centreline x 100turn from

100

/ cl /

/

/ ~

Centreiine

z~ Behind a Spire 0,1

ll~

10

E -

A

--

E

N

m

/_Lz/

-~

0.01 -

-

1 ~, i11

u_

0.001

0

. 0

0

0

0

1 1

~

o(z) o(zr)

2

0,01

Fig. 2. M e a n w i n d profiles at t h r e e lateral positions.

augmented growth method used in boundary layer simulation in short fetch length wind tunnels. An increase in vertical turbulence intensity may have some effect on the roof loads of structures, but the small increases observed are not expected to have a significant effect.

3.2.3. Reynolds stress profiles Reynolds stress in the atmospheric boundary layer is expected to either decrease slowly with height or remain constant with height. The measured Reynolds stress profiles in the simulated boundary layer flow, as shown in Fig. 5, reveal a peak in the Reynolds stress at around 0.2 m which, as mentioned

171 10 - ~

I

t

I !

t

I o x A

09

O8

Cenfreiine 100ram from centrelme Behind a spire

zo(m) Hodel 0 0002 Full scale 0 02

o~1~

100

I

z~lml 300

07E N

06E N

OS-

S0--\--

tm i

Oz.and Harris Model 03-U-

0.2(AS1170-Part 2. 1983) 01-

S

10

15

20

2S

0 30

u ('/.i

Fig. 3. Longitudinalturbulenceintensityprofiles. earlier, appears to be associated with the spire/roughness element augmented growth method. A similar peak was found by Standen et al. [8]. However, this peak, although having an influence on the way the flow develops downwind, should have little effect on the flow around structures of limited downwind extent, as in the present case.

3.2.4. Turbulence length scale and spectrum A longitudinal velocity spectrum of the simulated boundary layer flow is presented in Fig. 6 and is compared with the Harris-Von Karman spectrum which may be expressed as follows:

--

2

1 + 7O.8

5/6

172 1.0

I

I

I

I

I

100

Lateral Vertical Turbulence Turbulence o o Cenfreline X x lOOmm from Spire A A Behind a [entreline

09-

0.8-

E

cu~

N

0.7 E

N 0.6

~

"x.

5O %

'0.5 c c

~- 0.4

-r

03 02-

0.1-

0 5

10

15

-~U

'~

U

20

25

30

c"/,,i

Fig. 4. Lateral and vertical turbulence intensity profiles.

where Su (n) is the longitudinal velocity spectrum, n the frequency, ~ the mean longitudinal wind velocity, au the standard deviation of longitudinal wind velocity fluctuations and lux the integral length scale of turbulence. For a nominal scale of 1/100, there is a mismatch in the longitudinal velocity spectrum by a factor of ~3.5. However, Surry [9] has indicated that a mismatch by a factor of 2-3 is acceptable for the measurement of unsteady loads on low- to medium-rise structures. Lee [10] also found that the mean forces on a bluff body are not sensitive to turbulence scale provided it is significantly larger than the body dimension. 3.3. Wind tunnel models The wind tunnel models were constructed from a number of cylindrical modules of 200 mm external diameter and various lengths. The modules were manufactured from clear acrylic tube of 5 mm wall thickness. The ends of the modules were machined to allow them to be interconnected to form a continuous outer surface and allow no air leakage (Fig. 7). Two of the segments, each 25 mm in length, were fitted with pressure taps circumferentially spaced at

173 10.

I o x

Centreline lOOmm f r o m c e n t r e h n e

z~ Behind a spire

08

E "

06

-

0l.

-

112 C C

ox,~

jii

/%.

A

ii 0.2

x

x

o

A

x x A o A

x~

0.005

0.01

Reyn01ds Stress Fig. 5. P r o f i l e s of R e y n o l d s stress.

7.2 ° . These segments could be inserted at various positions in the complete silo model to enable the pressure distributions at various heights to be obtained. Sufficient untapped modules were provided to enable total silo heights of 100, 200 and 400 mm to be obtained. These heights correspond to values of the non-dimensional Jensen number, h/zo, of about 500, 1000 and 2000, respectively. Zo is the roughness length defining the mean velocity profile, as discussed in Section 3.2. The nominal geometric scale of the models was 1/ 100. A flat roof, without pressure taps, was manufactured for use with any of the model configurations. In addition, two conical roofs with 25 ° pitch were manufactured. This pitch is typical of full-scale silos used for grain storage. One of these was fitted with 50 pressure taps, as shown in Fig. 8. The pressure taps were arranged so that they were at the centroid of equal area sectors. This made integration of the point pressures to give total mean drag or uplift an easy operation. All the models had a smooth surface finish, i.e. no simulated or artificial

174

I

10-l.

O{z)

10-3 ;

I illll

I

i

i

(m-I) Full Scale 10-2 irllil

10-I

I

I

i

;iiiii

I

i

l

t lIT

I

I

I Illl

/[I+70 8(n4x1215/6

i0_i O' u

Model Full Scale 10.2

~

I0 -2

i

iiiiill

i

i

0.1 10

iiiiiii

I0 -I

i

i

iiiiill

I Qiz)

10

100

(m-1) Model

Fig. 6. Longitudinal turbulence spectrum at 1/100 scale.

roughness was used. The pressure taps were 14 mm long, of 1.0 mm internal diameter and were made from stainless steel. The largest model caused a wind tunnel blockage of ~ 2.5%. The effect of wind tunnel blockage on the pressure distribution was considered to be insignificant; hence no blockage correction was applied to the results. It is noted t h a t the presence of external fittings and structures such as ladders and grain shuts can have a significant effect on the flow around a silo. However, this was not considered in this test programme. 3.4. Pressure measurement system The pressure taps on the model were connected via ~ 400-mm lengths of flexible vinyl tubing to a Type D "Scanivalve" pressure scanning switch. A " d u m m y " pressure transducer head was installed in the "Scanivalve", and a shorter length (100 mm) of tubing was used to connect it to an externallymounted Honeywell Type 163 pressure sensor. The latter tubing length had a small "restrictor" tube (10 mm long, 0.30 mm i.d. ) inserted in it, to attenuate peaks in the frequency response. The amplitude and phase responses of the system were measured using the calibration equipment described by Holmes and Lewis [11]. The amplitude response was within 5% of unity from 0 to 130 Hz, and took a value of ~ 0.5 at 200 Hz. The phase response was close to linear over this range. Although a

175

Fig. 7. Silo model showing interconnecting modules and pressure-tapped segments and roof. higher frequency response system is desirable to measure instantaneous peak pressures and suctions [12 ] the system is adequate for measuring mean and r.m.s, pressures for the present study.

3.5. Data acquisition system The signal output from the Honeywell pressure sensor was low-pass-filtered at 200 Hz to attenuate instrumentation noise of a greater frequency. The re-

176

i

{_

i

203rnm

_J

Fig. 8. Conical roof pressure tap geometry.

sulting signal was digitized by means of an eight bit analogue to digital converter, and sampled at a rate of 1000 Hz by a Tandy TRS-80 Model III microcomputer, on which all data reduction was carried out. Sample times of ~ 10 s were used, and four samples were averaged for each measurement. The sample time is equivalent to about 1000 s (17 min) in full scale, for a full-scale mean wind speed of 25 m s - 1. 4. P r e s s u r e m e a s u r e m e n t results

Nine different silo model configurations, which included three aspect ratios, 0.5:1, 1:1 and 2:1, and three roof configurations, open top, flat roof and 25 ° pitch conical roof, were tested in the wind tunnel to determine the wall pressure and roof pressure (for conical roofs only) distributions. Internal pressures were measured for open-topped silo models, and the effects of Reynolds num-

177

ber of the flow and the heights of the pressure taps were also investigated. The circumferential wind pressure distributions were found to be essentially symmetrical about the windward generator and therefore pressure readings were only taken over half the circumference of the silo model. Pressure measurement results are presented as mean, standard deviation, maximum and minimum pressure coefficients defined with respect to the mean wind velocity at wall height.

4.1. Wall pressures 4.1.1. Effect of Reynolds number It was pointed out earlier that one of the most common deficiencies of experimental studies on circular structures is the inability to achieve high Reynolds number flow comparable to full-scale Reynolds number flow situations. Increasing the turbulence in the flow and artificially roughening the surface of the model have been proposed to reproduce pressure and force characteristics at effectively higher Reynolds numbers [12]. However, results of recent work by Cheung and Melbourne [ 14 ], which contain both model and full-scale measurements, suggest that modelling of full-scale structures with circular sections can be performed satisfactorily in turbulent flow with intensity > 4% provided that the test Reynolds number is in excess of 2 × 105. A series of tests were undertaken to investigate the sensitivity of the mean wall pressure distribution to variations in Reynolds number. Point pressure measurements were taken around a flat roof model silo with an aspect ratio, 1:1 at a range of test Reynolds numbers between 5.6 X 104 and 2.9 X 105 (with reference to the mean wind speed at silo model wall height). The pressure distributions at four Reynolds numbers are shown in Fig. 9. It can be seen that results from the three tests carried out at or above a Reynolds number of 1.08X 105 show very similar pressure distributions. However, at a Reynolds number of 6.59 X 104, the mean pressures near the region of maximum negative pressure are noticeably smaller in magnitude. These characteristics are consistent with the criterion proposed by Cheung and Melbourne [ 14 ] and suggest that at high turbulence intensity, the wall pressure distribution may be assumed to be independent of Reynolds number if the test Reynolds number exceeds ~ 1 X 105. Results of recent work on flow about and wind pressures on silos by Mulhearn et al. [15] and Finnigan and Longstaff [16] support this lower limit value for Reynolds number independence.

4.1.2. Effect of height of pressure taps The mean pressure distribution was measured at eight heights on a fiat roof model silo with an aspect ratio of 1:1 to determine the variation of mean pressure distribution with height. The circumferential pressure distributions are shown in Fig. 10. Generally, the distributions show the effect of the simulated

178 1.0

~ilo Aspect Ratio H:D=I:I Flat Roof o Re=6.59 x 10~" x Re=l.08 x l0s o Re=2.01 x 105 ix Re=2.9 x 10s

~ % .

Cp

0

I

,

I~t

i

I

,

30 k 6 0

I

I

,

I

90

I

I

I

120

I

I

150

,

e°

I

180

-1.0

-2.0 Fig. 9. Variation of mean pressure distribution with Reynolds number.

Silo Aspect Ratio HD:11 Flat Roof

3 0 ~

o lappin o Z~ x O v

I

I

I

60

g0

120

Cp

-10

-2.(

Fig. 10. Variation of mean pressure distribution with height.

Height z=187mm (gz.°/o) z=162mm (81%) z:138mm (69%} z-113mm (57%) z=88mm (/~/,%) z=63mm (32%) z=3Bmm (19°/o) z=13mm (7%)

I 150

180

eo

179

boundary layer flow and the three-dimensional nature of the flow around the silo. The effect is most pronounced in the lower half of the silo where there is a steady decrease in wind speed and wind pressure. Wind pressures near the top of the silo are similarly affected owing to wind flow over the top of the silo. However, at >~130 ° where complete flow separation occurs, the base pressure is essentially constant. It is important, from a structural design viewpoint, to identify regions of high positive and high negative wind pressures so that various design loads, such as local buckling loads and base overturning moments, can be accurately determined. The largest magnitude mean positive and mean negative pressures occur at between 60 and 90% of the silo height. Circumferential wind pressure distribution obtained within these heights will represent, typically, the upper bound load distribution to within a few per cent.

4.1.3. Effect of aspect ratio and roof configuration Circumferential mean wind pressure coefficients are presented in Figs. 1113 for nine different silo model configurations which included three aspect

i_~:~~ LI

~-

co

5ilo Aspect Ratio HD=O5 1 H=lOOmm o=zo0mm

"~

~

f, " 3, o

b~

TappingHeightz:62mm

o Open topped silo

, , ,

,

, i,

- 2 0 L_

Fig. 11. Mean wall pressure distributions for silos with an aspect ratio of 0.5:1.

180 20

Silo Aspect Ratio H D=I 1 H=200mm O=200rnm Tapping Height z=162mm o Open topped silo o Flat root silo zx [onical roof silo (pitch 25° )

10

30 \

-to I-

60~

~

90

/120

./J

150

180

8°

Reyoolds .°=2 9x10'

- 2 0 L_

Fig. 12. Mean wall pressure distributions for silos with an aspect ratio of 1:1. ratios and three roof configurations, It is noted that these pressure distributions were measured at between 60 and 90% silo height where maximum mean pressures (both positive and negative) occur. The test Reynolds numbers are well above the earlier proposed lower limit value of 1 × 10 ~. The pressure distributions for the open-topped silo models have been adjusted for the mean internal pressure which was found to be negative and relatively constant, at a value of about - 0 . 9 2 , within the silos. A number of significant observations are made from the pressure distributions presented in Figs. 1-13: (1) Roof configuration has little effect on the wall pressure distribution; except for open-topped silo models where the negative internal pressure has to be accounted for in order to define the overall wall loading. (2) The windward region of positive mean pressure extends to between 35 and 40 ° from the stagnation line, and decreases slightly as aspect ratio increases. When the negative internal pressure of the open-topped silo model is considered, the region of windward positive net pressure increases to up to 65 ° from the stagnation line. This is expected to have a significant effect on the local buckling critical wind speed. (3) The maximum negative mean pressure coefficient increases as aspect

181 20

10

f-~ 0

Silo Aspect Ratio H 0:2 1 H=L,00mm 0:200ram Tapping Height z=312mm o Open topped silo o Flat roof silo ~. Conical roof silo (25 ° pitchl

60

90

l

120

150

180 8 °

-10 Reynolds N°=3 ~xlOs

-2

Fig. 13. M e a n wall pressure distributions for silos with a n aspect ratio of 2:1.

ratio increases, from a value of about - 1.0 for an aspect ratio of 0.5:1 to a value of about - 1 . 8 for an aspect ratio of 2:1. (4) Complete flow separation occurs at ~ 130 ° from the stagnation line after which the pressures remain relatively constant. The fluctuating pressures were also measured for different silo model configurations and an example, which includes the standard deviation, m a x i m u m and m i n i m u m pressures, is shown in Fig. 14 for a flat roof silo model with an aspect ratio of 1:1. It can be seen t h a t the m a x i m u m and m i n i m u m pressure distributions are similar in shape to the corresponding mean pressure distributions shown in Fig. 12 with, as expected, much larger magnitudes. It is noted t h a t these m a x i m u m and m i n i m u m pressures are local pressures as measured at individual pressure taps and do no contain any information on their spatial correlation. In other words, they do not represent a simultaneous wind pressure loading on the silo wall.

4.2. Roof pressures Point pressure measurements were taken on a 25 ° pitch conical roof and the contours of mean pressure coefficients are presented in Fig. 15 for a silo aspect ratio of 1:1. Similar results were obtained for aspect ratios of 0.5:1 and 2:1 [2 ]. All measured pressures are negative pressures and they are nearly symmetrical

182 30 Flat roof sdo Aspect ratpo 11 Tapping height =138mrn Reynolds NO =29 = 105 Ci5 (maximum) C~ Iminimum) Cp. (standard deviahonl

o

2(

o

o o

1.0

Cp

O

01

Xl

i ""

I 30 A

~ ~

I , v60 o

,

I 90

L

~

I ~ J 120o o o o o o

~_~ o 90

I o 180

o

o o °o

°

-10

A A.A

Z~

-2.( A~A~A~

-3

Fig. 14. Fluctuating wall pressures for silo with an aspect ratio of 1:1.

about the windward axis. Two local regions of high negative pressures are readily identified. One of these is located near the centre of the roof in the form of a "dog bone" shape aligned perpendicular to the flow. The second region is located near the leading edge of the roof and is caused by a separation "bubble" and strong local vortex generation in this region. The size and magnitude of this band of local high negative pressures was found to increase with increasing aspect ratio [ 2 ]. As for rectangular buildings with low-pitch roofs, the length of the region of separated flow is directy related to the height of the structure. 5. Comparison with previous studies

5.1. Comparison of wall pressures Comparison of the mean and standard deviation wall pressures from this study can be made with a number of other wind tunnel and full scale studies. The wind tunnel tests described by Davenport and Surry [ 17 ] were carried

183 Conical Roof (25 ° pitch)

-OJ, -0.6 ,.,~..~1.0

~

-

0

.

"~

-0.6 /

.

Wind Direction

Fig. 15.Meanroofpressuredistributionforsilowithan aspectratioof 1:1. out at much lower Reynolds numbers than those used for the present tests. Unfortunately, insufficient information is given in this paper to calculate them, but they are estimated to be of the order of 2 × 104. The characteristic wall pressure distribution at sub-critical Reynolds numbers is apparent in the mean pressure coefficients which have much higher minimum pressure coefficients (i.e. lower suction coefficients) than observed in the present study and other studies at higher Reynolds numbers. However, it should be noted that the study of Davenport and Surry was intended primarily to determine roof loads, and flat roof pressures on circular silos are likely to be much less dependent on Reynolds number. Work described in refs. [15] and [16] was directed towards problems of natural ventilation and heat transfer for grain silos. However, the geometrical configurations of the models, boundary layer structure and Reynolds number used were quite similar to those in the present study. The mean pressures measured by Mulhearn et al. [15] for silos with aspect ratios of 1.7:1 and 3.3:1 can be compared with those in the present study for an aspect ratio of 2.0. The shapes of the pressure distributions with azimuth are quite similar. However, the difference between the base pressure and the minimum pressure coefficients is lower in the results of ref. [ 15 ]. This may be caused by a difference in reference dynamic pressure, but it may also be due to lower Reynolds numbers

184

used than the present tests (by a factor of 3 or 4). It appears that Reynolds number independence had not been reached, at least where the aspect ratio was 1.7:1, in their tests. More recent work by Sabransky and Melbourne [18] was, to some extent, taken as the starting point for the present tests. Mean and standard deviation wall pressures were measured for a range of aspect ratios from 0.66 to 1.16. The Reynolds numbers were slightly lower than those in the present study. A disadvantage of this work, however, was the wide angular resolution (22.5 ° ) used, which limited the ability to determine the peaks in the mean pressure distribution. W h e n a comparison is made with Sabransky and Melbourne's mean wall pressures for the cases of aspect ratios of 0.78:1 and 1.16:1, with a 27 ° roof pitch, and the present results with an aspect ratio of 1 and 25 ° roof pitch, excellent agreement is shown. However, the standard deviation and peak pressures are slightly larger in Sabransky and Melbourne's tests. The reasons for this are not clear, as the turbulence intensities and frequency response of the pressure measurement systems were quite similar in the two cases. Perhaps the most important work for comparison with the present studies is that of Cook and Redfearn [ 19 ] who measured pressures on full scale isolated and grouped silos with an aspect ratio of 1.14:1. A comparison between their isolated silo mean and standard deviation pressures is made in Figs. 16 and 17, respectively. The full-scale pressure coefficients were computed using a dynamic pressure based on the mean wind speed at a height of 10 m. To convert this data to that based on the mean speed at the top of the wall ("eaves" height) a factor of 1.35 was applied. Conica( Roof S,Ios

0

J t

c~ I 0

~"~O ~

~ I'hq 30

Height/Oiameter 1 11L,

Present studies Cook and Redf . . . . (1980)

~,

Roof p*tch Z5° 30°

z/H 0.81 /', ~ to ~6 o.• On either sides tCompostte of windward

results) gener=tor

t

I

I

I

60

90

120

150

I 180

•C3

Fig. 16. Comparison of mean wall pressures around conical roof silos.

. 9°

185 Conica| Roof Silos

Height/Diameter

Present studies Cook and Redfearn (1980)

O'S r ICp.O't' --. / °

1

111.

30°

z/H 0 81 ,~. ~] to ~ O.II On either sides (Composite results)

•

o o

Roof pitch 25 e

of vindvard generator

a •

a

•

•

o

~

01

0

30

60

90

120

1S0

180

e°

Fig. 17. Comparison of fluctuating pressures around conical roof silos.

The mean pressures in Fig. 16 agree well in both positive and negative pressure regions. This is encouraging as it indicates that Reynolds numbers used in the wind tunnel were high enough to ensure that full scale conditions were adequately modelled. (The Reynolds number for the full-scale tests was 2.5×106). The comparison of standard deviation pressures is not so good with considerably higher values occurring in full scale. Presumably this is related to a higher turbulence intensity in full scale, but there is insufficient information in the report on the full-scale work to confirm this.

5.2. Comparison of roof pressures Of the studies described in the previous section only those of Mulhearn et al. [ 15 ] and Sabransky and Melbourne [ 18] included roof pressure measurements for a conical roof of the same or similar pitch as that used in this study. The roof measurements of Mulhearn et al. [15] on a 25 ° conical roof can be compared with the case for aspect ratio of 2:1 in the present work. Similarly, Sabransky and Melbourne's data for a pitch of 27 ° and aspect ratio of 1.16:1 can be compared with the present results for an aspect ratio of 1:1. Generally, excellent agreement is shown in both magnitude and distribution of the mean pressure coefficients. However, in the case of Mulhearn's study there were, apparently, insufficient pressure taps in the vicinity of the leading edge of the roof. Also, Sabransky and Melbourne's data do not show such high suctions in the vicinity of the apex as found in this study. Again this is likely to be related to the distribution of pressure taps chosen, as the pressure coefficients vary rapidly in short distances in this region.

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7. Conclusions T h e m a i n conclusions f r o m this s t u d y of p o i n t pressures on isolated cylindrical silos are as follows. ( 1 ) In t u r b u l e n t b o u n d a r y layer flow where t h e t u r b u l e n c e i n t e n s i t y is high, the wall pressure d i s t r i b u t i o n s are i n d e p e n d e n t of R e y n o l d s n u m b e r , p r o v i d e d it is greater t h a n 1 X 105. (2) M a x i m u m m a g n i t u d e m e a n pressures occur at 60-90% of t h e height of a silo. Below 50% of the height, the m a g n i t u d e of the m e a n pressures reduces noticeably. (3) I n c r e a s i n g the silo aspect ratio ( h e i g h t / d i a m e t e r ) increases the magnitude of the m a x i m u m m e a n suction f r o m a b o u t - 1 . 0 at an aspect ratio of 0.5:1 to - 1.8 at an aspect ratio of 2.0:1. (4) T h e m e a n r o o f p r e s s u r e d i s t r i b u t i o n s show high suctions occurring n e a r the leading edge, a n d n e a r t h e conical apex of the roof. (5) Generally, excellent a g r e e m e n t in b o t h m e a n wall a n d r o o f pressures with o t h e r high R e y n o l d s n u m b e r full-scale a n d model studies is shown. H o w ever, the s t a n d a r d deviation p r e s s u r e s in the p r e s e n t tests are s o m e w h a t lower.

Acknowledgements T h e a u t h o r s acknowledge t h e p e r m i s s i o n of the H e a d of D e p a r t m e n t of Aeronautical E n g i n e e r i n g , U n i v e r s i t y of S y d n e y , to use t h e 7 X 5 ft wind tunnel. T h e research p r o g r a m m e is s u p p o r t e d b y C S I R O / U n i v e r s i t y of S y d n e y Collaborative R e s e a r c h F u n d .

References 1 Standard Association of Australia, SAA Loading Code Part 2 - - Wind Forces, AS1170, Part, 2, 1983. 2 P.A. Macdonald, K.C.S. Kwok and J.H. Holmes, Wind loads on isolated circular storage bins, silos and tanks: point pressure measurements, Research Rep. No. R529, School of Civil and Mining Engineering, University of Sydney, July 1986. 3 R.J. Holroyd, On the behaviour of open-topped oil storage tanks in high winds. Part I. Aerodynamic aspects. J. Wind Eng. Ind. Aerodyn., 12 (1983) pp. 329-352. 4 R.J. Holroyd, On the behaviour of open-topped oil storage tanks in high winds. Part II. Structural aspects, J. Wind Eng. Ind. Aerodyn., 18 (1985) 53-73. 5 R.J. Holroyd, On the behaviour of open-topped oil storage tanks. Part III. A structural dynamic instability mechanism, J. Wind Eng. Ind. Aerodyn., ( 1985 ) 339-341. 6 D.M. Deaves and R.I. Harris, A mathematical model of the structure of strong winds, CIRIA Rep. 76, 1978. 7 Engineering Sciences Data Unit, Characteristics of atmospheric turbulence near the ground, Part II: single point data for strong winds (neutral atmosphere), Data Item ESDU 74031, 1974.

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10 11 12 13 14

15 16 17 18 19

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N.M. Standen, W.A. Dalgleish and R.J. Templin, A wind tunnel and full-scale study of turbulent wind pressures on a tall building, Proc. 3rd Int. Conf. on Wind Effects on Building and Structures, Tokyo, 1971, pp. 19-209. D. Surry, Consequences of distortion in the flow including mismatching scales and intensities of turbulence, in Wind Tunnel Modelling for Civil Engineering Application, Cambridge University Press, Cambridge, 1982, pp. 137-186. B.E. Lee, Some effects of turbulence scale on the mean forces on a bluff body, J. Ind. Aerodyn., 1 (1976) 361-370. J.D. Holmes and R.E. Lewis, Optimization of dynamic-pressure measurement systems, I - single point measurements, J. Wind Eng. Ind. Aerodyn., 1988, submitted. J.D. Holmes, Effect of frequency response on peak pressure measurements, Wind Eng. Ind. Aerodyn., 17 {1984) 1-9. J. Armitt, Wind loading on cooling towers, J. Struc. Div., A.S.C.E., 106 (1980) 623-641. J.C.K. Cheung and W.H. Melbourne, Turbulence effects on some aerodynamic parameters of a circular cylinder at supercritical Reynolds numbers, J. Wind Eng. Ind. Aerodyn., 14 (1983) 399-410. R.J. Mulhearn, H.J. Banks, J.J. Finnigan and P.C. Annis, Wind forces and their influence on gas loss from grain storage structures, J. Stored Product Res., 12 (1976) 129-142. J.J. Finnigan and R.A. Longstaff, A wind tunnel model study of forced convective heat transfer from cylindrical grain storage bins, J. Wind Eng. Ind. Aerodyn., 10 (1982) 191-211. A.G. Davenport and D. Surry, The pressures on low rise structures in turbulent wind, Proc. Canadian Structural Engineering Conf., 1974. I.J. Sabransky and W.H. Melbourne, Design pressure distribution on circular silos with conical roofs, J. Wind Eng. Ind. Aerodyn., 26 (1987) 65-84. N.J. Cook and D. Redfearn, Full scale wind presure measurements on cylindrical silos: a preliminary report, Dep. Environment Note No. N103/80, Building Research Establishment, September 1980. B.J. Vickery, An investigation of the failure due to wind action of a group of six silos at Boggabri, N.S.W., Investigation Rep. No. S152, School of Civil Engineering, University of Sydney, April 1974.