Wind forces and their influence on gas loss from grain storage structures

J. stored Prod. Res. 1976. Vol. 12, pp. 129-142. Pergamon Press. Printed in Great Britain

WIND FORCES LOSS FROM

AND THEIR INFLUENCE ON GAS GRAIN STORAGE STRUCTURES

P. J. MULHEARN?,

H. J. BANKS*, J. J. FINNIGANT P. C. ANNIS*

and

tDivision of Environmental Mechanics, CSIRO, Canberra, A.C.T., Australia and *Division of Entomology, CSIRO, Canberra, A.C.T., Australia (First receioed 3 January 1976. and in final form 24 February 1976)

Abstract-The wind-generated pressure coefficients likely to be encountered in a free standing cylindrical grain storage with a conical roof are presented as measured from model experiments in a wind tunnel. These take into account the turbulent flow and vertical wind velocity profile likely to be found around such structures. The influence of pulsating wind flows is discussed theoretically and the practical consequences of wind-generated gas losses are detailed for fumigation or controlled atmosphere storage of grain.

INTRODUCTION

The success of a variety of pest control measures in stored products is dependent on the retention of a definite gas composition in the storage area. Fumigations, for instance, require a toxic concentration of gas to be maintained for a set period to ensure disinfestation. Some fumigants require exposure times of a day or less for full effectiveness (MONRO,1972). However phosphine, in particular, requires much longer, 4-5 days being necessary even under tropical conditions (HESELTINE, 1973). Controlled atmosphere storage of grain using altered compositions of the atmospheric gases may take some weeks to ensure complete disinfestation at iemperatures of 20°C or less (BAILEY and BANKS, 1975). It is becoming apparent that even with compounds normally regarded as ‘contact’ insecticides gas movement can cause loss of effectiveness in some areas of a grain bulk. The effect is particularly noticeable with dichlorvos (J. F. M. DESMARCHELIER, personal communication). Knowledge of the factors leading to gas loss from commodity storage structures may lead to minimization of this loss and thus more efficient use of the pest control measures. The effects of wind, one of the factors causing gas loss, have been largely ignored in stored product pest control. No mention of wind effects on field fumigations is made by authorities such as MONRO (1972) or CHRISTENSEN (1974). WILBUR (1967) mentions wind velocity in one phrase only in an article discussing why fumigations fail. Yet in imperfectly sealed structures such as are frequently encountered in fumigations wind may be the major cause of gas loss. The effect is well known to field personnel but seldom reaches the scientific literature. COTTON et al., (1936) found wind to be a major factor leading to gas loss from mill fumigations and COTTON(1962) states that gas loss from such a fumigation is directly proportional to wind velocity. BLACKITH (1953) noted rapid loss of nicotine vapour from glasshouses under fumigation during windy periods. BROWN et al. (1968) found wind induced by a blower rapidly removed phosphine gas from a 5-ton bag stack sheeted with polythene. It was sealed with a chain around the bottom in the normal fashion. From this they concluded that wind had caused observed failures in Cyprus when bagged maize was fumigated. On theoretical grounds, external air movement was shown to be the greatest influence on gas loss from leaky freight containers under fumigation (BANKS et al., 1975). H. J. BANKS and J. H. O’KEEFE (unpublished results) observed that wind caused the virtually complete displacement of phosphine from a 2000-tonne open top cell filled with wheat. In areas outside stored product preservation the natural ventilating effect of wind on structures is well known (e.g., DICK,, 1950; ANON, 1951). YPK 13.3-*

129

130

P. J. MULHEARN, H. J. BANKS, J. J. FINNIGAN and P. C. ANNIS

However SMITH (1969), in the only available study of meteorology on grain storage systems, discounted wind as a major influence since he was largely concerned with heating and cooling phenomena. Adequate studies are available to predict the magnitude of wind induced gas loss from bluff bodies and shed-like structures (HOERNER,1965 ; BRITISHSTANDARDS INSTITUTION, 1972). However there is no published study of wind pressures on a free standing cylindrical body, dealing with turbulent flow and incorporating a vertical wind velocity profile which may be appropriately applied to a structure such as a grain storage silo. This present study treats such a situation using model bins in a wind tunnel. The models used here are of proportions corresponding to two existing 2000-tonne grain bins which are under study for use as controlled atmosphere storages and provide a basis whereby the wind component of the forces leading to gas loss from such a structure may be understood. The results of this study are to be integrated into a general model for gas interchange between grain storage structures and the atmosphere. Wind-tunnel modelling

When testing scale models of structures in a wind-tunnel one must take into account a number of scaling laws. Firstly, the model and the prototype should be geometrically similar. For structures with curved surfaces, such as silos, the next most important criterion is that the Reynolds Number should be the same in both model and full-scale (HOERNER,1965). The Reynolds Number is the ratio Ud/v, where U is the mean wind velocity at a reference position, d is an appropriate length scale, say the diameter of the bin, and v is the kinematic viscosity of the fluid flowing around the body. In the case under study, air was used as the working fluid in the experiments, so that v could not be varied between model and full-scale. If the diameter of a full-scale grain bin is taken as 10 m, and a typical wind speed of 2 m/set is chosen, then with v = 15 x 10e6 m’/sec, one has a full-scale Reynolds Number of about 106. The wind-tunnel used for the experiments has a top speed of 30 m/set. If a model of 70 mm diameter is used, which is about the maximum possible without appreciably distorting the flow, the Reynolds Number of the model is about 105, a factor of 10 too small. However, experiments on bodies such as spheres and two-dimensional circular cylinders (GOLDSTEIN, 1952; ACHENBACH1968, 1972) show that there is a critical Reynolds Number of about lo’, above which the pressure distribution around such bodies does not vary greatly with Reynolds Number. In addition, these earlier experiments have shown that the shapes of the pressure distributions above the critical Reynolds Number differ markedly from those below and also that the critical Reynolds Number is lower in turbulent than in smooth flow. The pressure distributions obtained from the present model experiments were of the general form appropriate to Reynolds Numbers above the critical value. The full-scale Reynolds Number is always well above the critical value. In the atmosphere, the mean wind velocity increases with height and this profile of velocity must also be modelled in the wind-tunnel. In the lowest 20 to 30 m of the atmosphere, provided there is a sufficiently long fetch of uniform surface roughness upstream of the position of interest, the variation of the mean velocity, U, with height z is given by (PANOFSKY,1974) U = (u,/K) In z/zO.

(1)

K is a universal constant. z. is a constant which depends on the surface roughness and is called the surface roughness length. U* is termed the friction velocity, and is equal to (.r/p)“‘, where z is the shear stress, which is invariant with height, and p is air density. Equation (1) is true for a neutrally stable atmosphere, that is, one in which buoyancy effects, caused, for example, by heating of the air as it passes over ground warmed by the sun, are unimportant. It is desirable that the velocity profiles in the model

Wind Forces

and their Influence

131

experiments have the form of equation (1) and for the ratio z,/d to be of the same order in model and full-scale. The most important turbulence properties to reproduce are intensities and length scales. Typically, in the atmosphere (u’)“‘: (w2)ij2: u* = 2.5; 1.2: 1, where u2 and w2 are the mean square fluctuations in the streamwise and vertical velocities, respectively. Length scales are normally obtained from energy spectra s,(n) and s,(n), where these are the spectra of u and w fluctuations, respectively, and n is circular frequency. The peak in rz s,,,(n) under conditions of neutral stability generally occurs at n/U = 1/(2z) (PANOFSKY 1974). One can define a length scale L, = U/n and so L, = 22. Similarly, one can define a scale L,. L, is generally larger than L, and varies slowly, if at all, with height. Little more can be said about L, because of the large scatter in the available data. EXPERIMENTAL

PROCEDURE

The wind-tunnel used in these experiments is depicted in Fig. 1, and described in detail by WOODING (1968). The air stream is driven by a 44 kW centrifugal fan upstream of the working section. Air passes from the fan through a wide angle diffuser, a settling chamber, and contraction and working section, then recirculates through the wind-tunnel room to the fan. The working section is 1.78 m wide and 0.6 m high. The roof of the outlet diffuser was lowered to give a working section 11 m long. To generate a thick turbulent boundary layer in which to position the model silo the tunnel was set up as follows. 2.44 m from the start of the working section a piece of 50 mm angle iron was fixed to the tunnel floor normal to the flow. Immediately downstream of this was a 5.5 m fetch of roughness elements consisting of bars 3.2 mm wide and 3.6 mm high placed on the floor every 12.7 mm, normal to the flow. This was followed by 1.83 m of coated abrasive paper (40X grade). The model silos were placed 1.45 m downstream from the start of the abrasive paper section. Figure 2 shows one of the model bins in position. Two model bins were constructed of Perspex as shown in Fig. 3. Each had a diameter of 73 mm and a conical top with its surface at 30” to the horizontal. The height of the shorter model, from base to apex, was 122 mm and that of the taller, 224 mm. Many full-scale structures have a lip between the conical top and the vertical sides. This was modelled by a pair of rubber bands, one on top of the other (Fig. 2). At a scale of l/200 the shorter model corresponds to a prototype of height 24.4 m and diameter 14.6 m, while at a scale of l/123 the taller model corresponds to a protoptype of height 30 m, diameter 9.8 m. Both types are found in the Australian bulk handling system and have equivalents elsewhere. Each model was pressure tapped down one generator on the vertical sides and on another at 90” to this along the conical roof. The models were rotatable about their vertical axes to obtain pressures at any angular position. P.V.C. tubing connected the pressure tappings to a bank of manometer tubes. These measured the differences between the pressures at each tapping and a reference static pressure. Both reference static pressure, P,, and the reference dynamic pressure, @J2, were obtained from a pitot-static probe located in the same lateral plane as the model. The probe was approximately

FIG. 1. Structural

layout

of wind-tunnel.

132

P. J. MULHEAR~,H. J, BANKS,J. J. FINNIGANand P. C. ANNIS

FIG. 2. View of tall model silo with lip, showing reference pitot-static probe in position and abrasive paper on floor.

t

-rubber

bonds

--flexible polythene tube

H

‘steel

sandpaper

,

tube insert

brass hose floor

RylORbush to manometer FIG. 3. Construction of pressure-tapped

model. For short silo H = 122 mm, for tall silo H = 244 mm.

Wind Forces and their Influence

133

half the model height from the tunnel floor and 0.38 m from the centre-line. The pitotstatic probe is shown in position in Fig. 2. From these pressure readings, non-dimensional pressure coefficients C,, were obtained, where C’, = (p - P,)/($U’), and p = pressure measured at a tapping on the model. Mean velocity measurements were obtained using a standard boundary-layer pitot tube. Turbulence data were obtained with a X-configuration hot-wire probe and 2 channels of Thermo-Systems Inc. Constant Temperature Hot-Wire Anemometery Model No. 1050*. Because the output of a hot-wire anemometer is a non-linear function of velocity, the signals were linearised by analogue computer before they were recorded on a magnetic tape. The tapes were later digitised and the data processed by computer to obtain mean square values of velocity fluctuations, turbulent shear stress and velocity spectra.

RESULTS Mean velocity and turbulence

The mean velocity profile in the tunnel (with the model removed) is shown on a log-linear plot in Fig. 4. It can be seen that the velocity profile has the required logarithmic form for 5 mm < z < 254 mm. From this profile, u, = 1.26 m/set and I “0 -- 5.55 x lo-l4 m. For a model l/200 full-scale this value corresponds to a full-scale 7 of approximately 10e2 m, which is a typical value for flat or gently rolling open Eiuntry with very few obstructions (ENGINEERING SCIENCESDATA UNIT, 1972), such as is often found in grain producing areas. Profiles of mean square velocity fluctuations and of -uW are shown in Fig. 5. The shear stress z (= -puw) is seen to be approximately constant in the lowest 254 mm of the flow with (- Uw)‘I2 = 1.10 m/set. u* froni the mean velocity profile should equal -((uv#‘~ from t h e h ot wire traverse and the agreement is very good. (g)“‘, the r.m.s. of the streamwise velocity fluctuation, decreases slowly with height. In the lowest 20 to 30 m of the atmosphere all three would be constant. In the model 2.2 < (~‘/(-tlszj))~‘~ < 2.6 (wz/(-~uw))l’z 2: 1.3 In the atmosphere [u2/( - in]“’ is typically 2.5, while [w’/( -uW)]‘i2 is 1.25. The agreement, then, is quite good. Energy spectra for the u and w velocity fluctuations have also been computed. From these, time scales T, and T, have been calculated which are the inverse of that frequency below which half the turbulent energy in each component resides, that is the median frequency. From these, length scales L& and C, have been calculated such that L& = U T, and Z, = U T,,. The length scale L, has also been calculated from the frequency at which the spectrum n s, (n) reaches a maximum. Due to the scatter in the spectral results, estimates of L, are less accurate than estimates of L&. In Fig. 6 these length scales are compared with the observed distribution of L, in the atmosphere (PANOFSKY,1974). This is L,, = 22

It is seen that L, -Y L!;LJ, is considerably larger than C, and varies quite slowly with height. The general behaviour of the length scales therefore agrees reasonably well with atmospheric data. Reliability of pressure distribution

The pressure distributions are presented in terms of non-dimensional pressure coefficients, C,. These coefficients are estimated to be accurate to within kO.05 and are * Descriptions

of this type of

equipment are common; see for example,

BRADSHAW

(1964).

134

P. J. MULHEARN,H. 3. BANKS,J. J. FINNIGANand P. C. ANNIS

FIG. 4. Mean velocity profile.

repeatable to +_0.04. The form of the pressure variation around the circumference of the tall silo, with no lip attached, is shown in Fig. 7 at two vertical stations. 8 in this figure denotes the angular position around the silo circumference; 8 = 0” is the upstream location. The lack of bilateral symmetry in the distributions probably indicates some slight mi~lig~ent between the null position of the model and the wind direction. Contours of constant pressure coefficient on the model surface are presented in Figs. 8a-8e. Pronounced asymmetry exists in the pressure distributions on the conical roof of the silo, especially on the downwind side. The flow in this region would be very sensitive to asymmetry of the model near its apex and when the series of experiments was completed it was noticed that the plug which forms the conical top was slightly

0.3-

0.25-

x

a+

x

o+

x x

@)+

s 4B al 6 % 2

o+

0+

x

o+

x

B+

x

@2-

0.15

.P 1

J-uw@+q I)+

0.05

1

0'

"qi x

0+

0

x

+

.o + a+ I

1

x x I

2

,

3

FIG. 5. Turbulence profiles x , (?fl”;

I

4

I

5

+, (w~)“~; 0, @i#‘*.

I35

Wind Forces and their Influence

0 0

0

/

0

0.4

I

I

I

0.8

1.2

1.4

1 im) FIG.

6. Length scale profiles. x, Ew; A, from

Lw;

0,

PANOFSKY

Cu.

Dashed line indicates atmospheric (1974).

value

misaligned with the main body of the model. The main conclusions of the paper will not, however, be affected. The shapes of the pressure distributions in Fig. 7 are typical of those with Reynolds Numbers above the critical value. In subcritical flows as 6 increases, the pressure coef5 cient reaches a minimum at about 70”, increases slightly and stays constant from about 80” to 180”. Above the critical Reynolds Number, the minimum usually occurs near 80” and the pressure coefficient then increases markedly. From 140” to 180”, however,

0 360

,

,

20

40

340

320

/

!

8

t

80 280

100 260

120 240

I

140 220

160 200

180

FIG. 1. Pressure distributions around tall model with no lip at u,,,d/v = 1.15 x 105. x, C, for 0” to 180”; 0, C, for 210” to 330”. Height of measuring station is marked on each curve. Upper curve shifted 0.2 of a unit.

P. J. MULHEARN,H. J. BANKS J. J. FINNIGANand P. C. ANNIS

136

(a)

3

Expanded

0

elevationof

20

40

60

60

100

120

140

160

side

FIG. 8a. Contours of C, on the short model with no lip at U,,d/v = 9.2 x 104. FIG. 8b. Contours of C, on the short model with no lip at lJrsfd/v = 1.15 x 10’. FIG. SC. Contours of C, on short model with lip at Urerd/v = 1.15 x 105. FIG. 8d. Contours of C, on tall model with no lip at U,,rd/v = 1.26 x 105. FIG. 8e. Contours of C, on tall model with lip at Urcrd/v = 1.26 x 10”.

160

I?7

Wind Forces and their Influence

it varies very slightly (GOLDSTEIN, 1952). The curves of Fig. 7 obviously correspond to the supercritical situation. However in order to assess more accurately the effect of the lack of Reynolds Number similarity referred to earlier, the behaviour of C, with increasing Re was investigated and the results presented in Fig. 9. For the short model with no lip the pressure coefficient at 180” appears to be approaching a constant value as the maximum available Reynolds Number (that used for most results) is approached, while that at 90” is still decreasing. It is probable therefore that on a full scale silo, pressures in this region will be lower than our results would indicate. Figures 8a, 8b, show the overall pressure distributions on the short model with no lip at two different Reynolds Numbers. It can be seen that the shapes of the distributions on the vertical sides of the model are very similar. The main difference is that the values of the pressure coefficients near 80” and at about two-thirds height are slightly lower at the higher Reynolds Number. This is clearly shown in Fig. 10 where the pressure distributions of one height and different Reynolds Numbers are compared for the short silo with and without lip. On the conical roof the disparity is more pronounced and again there is a slightly lower pressure coefficient at about 90” for the higher Reynolds Number. Figure 8c presents the overall pressure distribution on the short model with a lip for the higher Reynolds Number and only minor differences are apparent. For these three runs the reference pitot-static tube was 59.2 mm above the floor. It is apparent that the test Reynolds Number is not quite high enough to have achieved complete Reynolds Number independence at least in the case of the short model. The regions where the pressure coefficients have not stabilized are however small in content and confined to the regions of highest negative pressure and we can be confident that the main features of the pressure distributions have been modelled correctly. The main features of interest for the shoot model are the high positive pressure regions on the front at about two thirds height and the regions of large negative pressure (suction) on the sides and on the roof around 90”. Note also that for angles greater than 40” the pressure coefficients are negative. Figure 9b illustrates the variation of pressure coefficient with Reynolds Number for the tall model and in this case the coefficient has become constant before the maximum Reynolds Number is reached.

8i

x

x

180°

x x

x

L 0

/ 05

IO Ud

x lo+

I5

--OIS

xx

--~ IO

Ud 7 I lo-'

FIG. 9. Variation of C, with Urerd/v.0, 90”; x, 180”. (a) short model, no lip 71 mm above floor (b) tall model, no lip 163 mm above floor.

I’5

P. J. MULHEARN,H. J. BANKS J. J. FINNIGANand P. C. ANNIS

138

Z-O-

1.0.

O-

CP

-1-O

-2.0

c

20

40

60

80

100

120

140

160

180

FIG. 10. Comparison of pressure distributions 84 mm above floor on short model. 0, no lip U,,d/v = 9.2 x 104; x, no lip U,,,d/v = 1.15 x 105; 0, with lip U,,d/v = 1.15 x 10’.

The pressure distributions on the tall model with and without a lip (Fig. 8) show only minor differences from each other. For these runs the reference pitot-static tube was mounted 113 mm above the floor. As with the short model there is a region of large positive pressure on the front at about two thirds height and the pressure coefficients are negative for angles greater than about 40”. However, the region of largest negative relative pressure is now on the conical roof and there are two negative relative pressure peaks on the sides at approximately 90”. Note also that the whole of the roof is a region of negative relative pressure (Fig. 8d). Due to an oversight this is the only case for which pressures were obtained on the front half of the roof. However we expect to find a similar distribution for all configurations. EATON and MENZIES (1974) report that the roofs of houses with pitches of less than 35” have negative pressure coefficients. As the model roof has a-pitch of 30”, it is not surprising that it also is a region of suction. Near the base of the tall model for heights below about 16 mm the region of maximum pressure is not at 0” but at about 20”, and the pressure coefficients are low. This effect is no doubt due to a down-wash vortex which is known to form on the front of bodies in shear flows (HUNT, 1971). The size of this vortex would have been smaller for the short model silo and apparently had little effect on the pressure readings in that case. DISCUSSION

Effect of a steady wind on gas retention

The pressure differences generated by a steady wind will cause air to flow into the structure in regions of positive pressure and gas to flow out where pressures are negative.

Wind Forces and their Influence

139

The flow achieved will depend on the wind strength and the location and dimension of the holes. The difference in C, values, AC,, shows where holes in the structure are likely to be important and thus where attention should be given if natural ventilation is to be reduced. Taking the tall model with lip as an example (Fig. 8e) the maximum AC,, 2.4, occurs between 0 = 0” and 80” at about three-quarters of the structure’s height. A vertical difference, in C, values, AC, = 1.6, occurs between the base, 6’= 0 - 40”, and the apex of the roof. A horizontal difference occurs at the roof-wall joint between 0 = 0” and 80” of AC, N 2.2. The first large difference noted above is not likely to be important as silos are less prone to structural imperfections in their walls than in their joints. However, the two latter differences are important from the point of view of gas movement. They both occur in areas where there is a high risk of leakage. The apex and base contain inspection hatches and handling gear which are often difficult to seal while the wall to roof joint is an area prone to thermal movement which causes cracks. In concrete silos the joint marks an area between two separate concrete construction units. The horizontal difference will tend to ventilate the head space while the vertical difference will give a tendency for an upward movement of gas through the stored commodity. The pattern of pressure coefficients on the short models is similar to that on the tall but with only one low pressure peak at about 8 = 80”. The upwind pressure areas extend relatively further down the wall in the shorter models. The vertical component of pressure difference is increased in this case to ACp 2: 2.2 (Fig. 8c) but the other components are similar. It should be emphasised that the results given here are for single free standing structures. PONSFORD'S (1970) study illustrated the qualitative changes occurring in a linear group of closely spaced silos and high-lighted the unpredictable effects of structures such as elevator towers and inloading equipment on the bin roof. The effects of ribs or substantial corrugations on the walls as found in some grain storage structures have not been investigated either. HOERNER (1965) presents some data for gas storage tanks which show that the mean suction on the sides around 80” is substantially reduced by relatively small vertical ribs. To illustrate the importance of the vertical pressure difference (ACp 2: 1.6) we can calculate the flow rate between two holes-at the roof and at the apex-with cross-sectional areas of 4 x 10e4 m2 and orifice coefficients, 0.6. For an empty silo of the proportions of the tall model with lip, a wind speed of 5 m/set will result in a volume flow of 93 m3/day between the two holes. This figure is probably not significantly modified when the silo is filled with grain. The air space will then comprise about 407; of the total volume (JONES, 1943) and for a 2000 tonne storage this will correspond to about 1200 m3 of air. Thus about 8% of the air will be exchanged daily with the atmosphere by a leak of this magnitude. This percentage value will be larger in silos of smaller volume and reduced by incomplete filling. nze efSect of pressure jluctuations Although the importance of modelling the turbulent nature of the atmospheric wind was stressed in an earlier section, only time mean pressure has been measured. However the instantaneous pressure coefficients fluctuate over a wide frequency range. Steady pressure differences of course can only remove gas from the structure when two holes are present but in certain circumstances gas interchange through a single hole can be effected by a pressure pulsation. MALINOWSKI (1971) summarised the ways in which gas exchange could take place through a single hole in a building under the influence of wind. His results are not directly interpretable under practical circumstances because he did not specify the frequency of pulsation used. Clearly if the mean pressure difference is always larger than the fluctuating one, the Auctuations will not be important, as gas cannot then be drawn backwards and forwards out of the storage. If the static pressure within is equal to atmospheric pressure, then the pressure coefficients (C,) presented above (Fig. 8) may be regarded as representing

140

P. J. MULEEARN,H. J. BANKS, J. J. F~NNIGAN and P. C.

ANNIS

the pressure differences across the bin walls. * BATHAM(1973) presented pressure coefficients for both mean and fluctuating pressures around a long circular cylinder at critical Reynolds Numbers. From his results it can be seen that on the vertical sides the fluctuations are only large enough to change the sign of the pressure difference for 8 = 30 + lo”. In this region the r.m.s. pressure coefficient is 0.15. Because this value is low compared to the mean pressure differences, which occur elsewhere, pulsations here will be relatively unimportant. Using the same values for the leak as in the steady pressure example above, this pressure coefficient corresponds to gas loss of 6 m3/day. This small value represents a maximum and in practice it will be reduced by incomplete mixing during a pulsation. As detailed by MALINOWSKI(1971) a reduction in the actual interchange achieved will occur since part of the fresh air entering during the positive pressure phase of a pulsation will be removed in the negative phase. Unfortunately we have no information at all about the size of the ~uctuations near the roof or at the base of the silo but the abrupt change from positive to negative pressures around the lip of the roof between 0 = +30” suggests that the pulsations here could be large. This of course is one of the regions most prone to cracking in concrete structures as was pointed out earlier. This area is to be studied on full scale bins. Finally, the presence of a vortex, the horseshoe vortex, which typically forms at the junction of the silo and the ground probably means that the fluctuations are enhanced here too. The mean velocities and pressures in this region however are generally smaller than near the roof and the fluctuations should be proportionately less severe. Practical

eflects of wind

In the Introduction the practical consequences of gas loss from structures under fumigation or controlled atmosphere storage conditions were detailed. In the example above a steady wind velocity of 5 mjsec was used. This value is the approximate annual average speed for some grain storage areas and will be frequently exceeded for extended periods. Table 1 gives annual average wind speeds for a number of such localities. Gas loss will be proportional to the wind speed if the leaks in the structure act as orifices when the through flow is proportional to the square root of the pressure drop, since this is also proportional to the wind velocity. Where the flow through a leak is directly proportional to the pressure across it, flow will be proportional to the square of wind velocity. The first situation corresponds to that observed by COTTON (1962). Both types of imperfection and intermediate ones have been observed in concrete grain storages and effective orifices greater than those used in the example are frequently encountered in apparently sound untreated concrete bins (H. J. BANKSand H. C. ANNIS, unpublished results). It will be noted that wind effects will decrease in significance as the structure becomes less leaky. There will be a degree of sealing, depending on the structure, where the effects will be minor compared with more long term effects not dependent on the size of the leak such as thermal expansion of the internal gas or changes in atmospheric pressure. CONCLUSIONS The model experiments presented in this paper have provided data about the pressure fields generated by wind on the surface of single cylindrical wheat bins. A theoretical estimate of the importance of pressure fluctuations resulting from atmospheric turbulence and the turbulent boundary layer which forms on the walls of the silo has been given. With the results of the model studies and plausible values for wind speeds and * It should be noted that the mean pressure difference between parts of the bin and atmosphere may be modified by gas density effects, induced either thermally or by differing gas composition. This may be allowed for in calculation and will shift the area where pressure pulsations are important but will not alter the general conclusions below.

Wind Forces and their Influence

141

TABLF. I. ANNUAL AVFKAG~WIND SPEEI)DATA FOR A SI~LECTION OF (;KAIU STOKAW LOCALITIES

Observations Times (hrs) Reference

Annual

Place

average speed m/set

Period

Alma-ata, USSR

1

1971

0000,0600,1200,1800

ANON (1971b)

Avonmouth, UK

5

1970

Continuous

METEOROMGICAL (1970)

Basel, Switzerland

1

1970

0000,0900,1800

SCHNEIDER (1970)

Nakuru, Kenya

3

1970-1972

1200

EAST AFRICAN METEOROMGICAL DEPT. (1972/74)

New Delhi, India

2

1968

0000,0600,1200,1800

INDIA METEOROLOGICAL DEPT. (1969)

Wagga Wagga, Australia

3

1970.1971

Continuous

ANON (1970/71a)

Wichita, USA

6

1970.1971

?Continuous

U.S. DEPT.

OFFICE

COMMERCE

(1971/72)

the size of typical leaks in the storage fabric it was demonstrated that about 8% per day of the gas in a full silo can be replaced by atmospheric air. The effect of pressure fluctuations w&s seen to be small in comparison. Finally some observations were made on the practical consequences of these results in a field situation. Acknowlrdyements-We this project.

are grateful to the Australian Wheat Board who provided part of the finance for

REFERENCES ACHEINBACH. E. (1968)

Distribution of local pressure and skin friction around a circular cylinder in cross-flow up to Re = 5 x 106. J. Fluid. Mech. 34, 625-639. ACHENBACH.E. (1972) Experiments on flow past spheres at very high Reynolds numbers. J. Fhrid Me& 54, 565-575.

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