A Rapid Method of Calculating the Downwind Distribution from Aerial Atomisers

Cranfield

August 1982

A Rapid Method of Calculating the Downwind Distribution from Aerial Atomisers

TECHNISCHE HOGESCHOOL DELFT b y J.J. SpiUman LUCHTVAART- EN RUIMTEVAARTTECHNIEK

BIBLIOTHEEK

KIuyverweg 1 - DELFT

College of Aeronautics Cranfleld Institute of Technology

Cranfield, Bedford, UK

A Rapid Method of Calculating the Downwind Distribution from Aerial Atomisers

by J.J. Spillman

College of Aeronautics Cranfield Institute of Technology

Cranfield, Bedford, UK

ISBN 0 902937 77 4 £7.50

'The views expressed herein are those of the authors alone and do not necessarily represent those of the Institute."

FROM AERIAL ATOMISERS.

J.J.SPILLMAN

INTRODUCTION

The effects of wind on spray from an aircraft are regarded as the basis of legal action by some people yet by others as the only possible way of doing a

satis-factory job. In many parts of the world the ideal spray condition is in a complete calm whilst elsewhere spraying is delayed until the wind speed is at least three metres per second. When the 'calm air' operators have to spray in a slight wind then the droplets are 'ideally' greater them SOQam. in diameter whilst the 'wind using operators' want the drop sizes to be less than lOO/m. in diameter.

In California herbicides are applied in large droplets to ensure their near vertical descent to the target whilst in Western Australia they are 'drift sprayed' using 50 metre lane separations.

Clearly there are reasons for these diverse views. The still air,big droplet group are concerned with avoiding damage outside their target area at all cost, and as a result their operations are inefficient and costly relative to those who can use the wind to increase lane separation because they have a mono-culture situation. However, for most situations damage can be done outside the target area but economic considerations are also importêmt. A proper \inderstanding of what is likely to happen to a particular spray would allow operations to achieve the right balance between damage avoidemce and efficient applications by choosing the right spectrum for the operational conditions under which they have to work.

BASIC PRINCIPLES

The paths of droplets released from an aircraft are going to be dominated by sedimentation cuid wind

turbulence effects once they leave the immediate vicinity of the aircraft. The effects of the aircraft are only

local provided it is not flying excessively close to the ground except for the outward and upward motion induced by the wing tip vortices. These C2ui be controlled by not placing atomisers too close to the wing tips or rotor perimeter and by fitting wing-tip sails as proposed by PARKIN and SPILLMAN (1980).

The relative iii%>ortance of sedimentation euid air turbulence on droplet destinations depends upon the size of the droplet êuid the scale of the turbulence. Turbulence is not significant when droplets are sufficiently large for their fall speed to greatly exceed the effective transport speed associated with turbulence. In general this corresponds to droplets greater than 2d>out 400 microns. The paths of very small droplets depend critically on the turbulence since their fall speed is small relative to the vertical motions of the air which surrounds them. These motions are random for any Instant

and position but can be treated in a statistical manner to give their most probable behaviour.

To do this a number of simplifications need to be made in order to obtain an analytical solution. BACHE and SAYER

(1975), ignoring the effect of the aircraft, obtained an expression for the downwind ground deposit from a crosswind line soturce by assuming a Gaussian distribution within the droplet cloud/ constant dlffusivity and mean windspeed cind total capture of the droplets on arrival at the ground.

Lawson has expressed their results in a simpler form which when re-arranged gives the following equation

HU Q D = 0.4 -j^ "2 exp 1 HU V s x i 2 xW W (1) where

D is the deposit in litre/square metre at a distamce x metres downwind of the line source

H is the height of the line source, metres

Q is the strength of the line source, litres per metre

U is the mean windspeed during the descent of the droplets, metres per second

W is the root mean square of the random vertical turbulent velocities in metres per second

V is the sedimentation velocity of the droplets in metres per second,

w

The ratio, TÏ» is a measure of the relative intensity of the turbulence £uid Lawson gives typical values associated

with windy conditions over various kinds of surface, depending upon their roughness length. Thus for a flat grass covered surface the value might be about 0.05 rising to 0.1 for

nearly mature crops like cereals or cotton and reaching values of 0.15 to 0.2 for forests depending upon the uneveness of their canopy due to ground irregularities and open areas.

Values of the relative turbulence intensity can be measured using sophisticated instruments like sensitive anemometers or hot wire devices but these tend to be rather delicate and expensive instrvunents suitable for research. Work is just

instrument for measuring relative turbulence intensity in the field.

METHOD OF CALCULATION

If a value of the relative turbulence intensity, W/y is measured or estimated, equation (1) can be used to calculate the most probeüale downwind distribution of droplets of a given size when released at a given height and windspeed. However, this must be done for the whole range of droplet sizes emitted in the spray line. This can be done using a simple programmable calculator by following the procedure outlined below if the droplet

size spectrum is known. Obviously if this has been measured at the atomiser then the distribution will only correspond to that for a non-volatile liquid.

Divide the volxime emitted into equal increments, say 5% and determine the mid-size for each increment. Determine the sedimentation velocities for each of these sizes and express it as a fraction of the turbulence velocity, W. If this has not been measured directly it can be calculated from an estimate of the relative turbulence intensity

cuid the mean windspeed. The fraction of each increment

deposited at a specified downwind distance can be calculated using equation (1) 2md,by summing these^the total deposit can be determined.

The downwind position for the start of the deposit can be estimated for sprays containing some big droplets by taking the biggest droplet size and calculating the minimum value of x from the sedimentation relationship

If the spray spectrum consists of a significant fraction of the volume in excess of 400yum, then very close increments in x are required to determine the shape of the upwind end of the spray deposit. In this case this part of the deposit can be determined by

taking small increments in x above the minimum value, using equation (2) to calculate the extremes of values of V to which they correspond, determine the diameter associated with these sedimentation velocities cuid hence the fraction of the spray between these diameters.

EXAMPLE AND DISCUSSION

Figure 1 shows the variation in sedimentation speed of

water droplets with diameters as determined by DAVIES, (1966) .

Figure 2 shows the droplet spectrum in cumulative volume form of spray from a Micronair AU3000 spraying water at

10 litres per min,in a wind of 90knots when flat 343mm. blades set at 30° are used. From figures 1 and 2 the value of

— for the mid-size of each 5% volume increment of the spray W

was determined. Haice for the specified height and windspeed the deposit from each incremental size was calculated for a chosen downwind distance and summed to give the total deposit. Figure 3 shows the result as a full line.

In order to emphasise that turbulence is an important

factor in determining the deposit distribution the pattern has been calculated for the case of zero turbulence all other

parameters being the same, so the transport of the droplets in the vertical sense is due to sedimentation alone. The dotted curve in figure 3 shows how much greater the deposit is at the larger downwind distances under these conditions.

The reason why turbulence reduces the deposit beyond 50 metres downwind is that whilst it is moving droplets both upwards and downwards those that reach the canopy are caught and hence the number of droplets left in the air to be moved upwards and downwards decreases rapidly as the turbulence intensity increases. Of course, a few

droplets will remain airborne longer due to turbulence but their number is so small that the deposit density they create when they eveneutally reach the ground is so small that it is unlikely to do any déunage.

The deposit distribution corresponds to a line source whilst the atomisers on an aircraft are distributed across

its span. This effect can be included in the distribution by using values of line source strength for each atomiser, simply correcting the x values for their lateral spread and summing the deposits from each atomiser.

Figure 4 shows the same distribution as figure 3 but divided into 3 size groups consisting of the droplets below lOC^ttm in diameter, whose volume is 30% of the total,

droplets between lOO^m and 25C^4tn> in diameter whose volume is also 30% of the total and those greater than 25QM.m giving the remaining 40% of total volume. Figure 4 shows clearly that for droplets greater than 25Q(iim the deposit falls

rapidly with downwind distance, but that size makes far less difference below 2S0jtm., indeed, the deposit from the same voliime of droplets in the middle size class is within 4% of 75% of that from the smallest group over downwind distances of 150m.to 250m. Thus, if a rapid cut off of

deposit is required under the example conditions then droplets must be greater than about 25Q^wi. However, the rapid

decrease in deposit downwind indicates that to get a

reasonably even distribution the spacing of the atomisers, and hence of lane separations has to be small and very accurate. If a more even distribution is required then

the smaller the droplet size the better and atomiser and Icuie separations can be much greater.

Equations (1) can be written in the form

Dx

— - 0.4 Q

H

X

w

It follows that if the height, H, is halved the same value Dx

of — will be obtained at half the downstreeun distance x. Q

Fbr height of only 2.5 metres and otherwise the same conditions the distributions shown In figures 3 and 4 will

be right if the x values are halved and the deposit percentages doubled. Thus the most effective way of reducing the extent of the downwind deposit is to reduce the height of the emission

line.

It has been shown that the relative turbulence intensity is a function of atmospheric temperature gradient and type of terrain euid to a first order is Independent of the actual windspeed. If then it is assumed that the ratio ^ is

Independent of windspeed then Equation (3) shows that the deposit at a given value of x will be the same if the value of V_ remains the same. Thus as u increases so will Z

Thus the variation

w

and V must to maintain the same deposit.

of D with X will be unaltered provided the size group is Q ^s

changed to maintain constant -rr-. Figure 5 shows the effect on the example distribution of reducing the windspeed from five to one metres per second maintaining the same relative turbulence intensity, W

/ As one would deduce from equation (2)

u

to a fifth of their values. Overall the distcince the

droplets of all sizes are blown is reduced but not as much as one might expect. 20 metres downwind the deposit density is reduced to 89% of the higher wind value, at 35 metres the percentage is 50% and from 75 metres to 250 metres it only falls from 39% to 33%. Thus a reduction in windspeed reduces the peak deposit position in a mamner roughly proportional to the speed but does not reduce the deposit well downwind in a mcuiner proportional to the wind strengths. Figure 5 shows, however, that the whole of the deposit beyond 35 metres

downwind consists of droplets below lOO^jn. when the wind speed is 1 metre per second whilst the sizes were less

than 25QHm when the windspeed was 5 metres per second. Thus the lower the wind the smaller the minimtun size droplet for a

neglible deposit at a specified distance downwind.

Watt (198 2) has proposed a 300m. buffer zone between the most downwind application cmd possibly sensitive areas. Clearly, such a procedure is extremely desirable. If the droplet size spectra, wind and turbulence ccnditions are known the metJiod outlined herein would allow the size of such a buffer zone to be calculated more accurately^ so reducing the risk of damage or the extent of untreated target areas.

10. CONCLUSIONS

1) A method of estaimating downwind spray deposits using a simple programmable calculator has been derived from the original work of BACHE and SAYER (1975) and LAWSON (1978).

2. The effect of turbulence in the air is to significantly reduce the downwind movement of the majority of the smaller droplets cUid as a consequence deposits well downwind are far smaller than a sedimentation theory would predict.

3) The effect of halving the height of emission is to produce the same form of downwind distribution. It can be obtained by halving the downwind distances and doubling the deposit levels.

4) To ensure that the deposit level is below a specified value at a given distance downwind of the source the spray must be in sizes above a critical value. This critical

value depends upon emission height, windspeed and relative turbulence intensity. Below this critical size the downwind distribution is almost insensitive to droplet size.

5) The critical size of droplet decreases with decrease in windspeed and increase in relative turbulence intensity.

6) A reduction in windspeed reduces proportionately, the distance downwind at which the peak deposit of big droplets occurs

but the deposit levels well downwind do not reduce so rapidly.

7) The method can be used to determine the size of a buffer

zone between the most downwind spray line and a sensitive ground area if the spray spectrum, windspeed and relative turbulence intensity are known. The size of the buffer zone will reduce proportionately to the spray emission

height-8) The accuracy of the above conclusions depends upon the accuracy of the assun^tlons which have had to be made in the analysis. Clearly these results should be used as a guide to field trials under real crop conditions In order to assess tJieir usefulness in spraying operations.

BachefD.H. Sayer, W.J.D.

(1975)

Transport of Aerial Spray,

Pt.I A Model of Aerial Dispersion Agricultural Meteorology,15 (1975) 257-271

Davies,C.N. (1966)

Deposition from a Moving Aerosol 'Aerosol Science' (C.N.Davies, ed.) pp 393-446 Academic Press,London

Lawson,T.J. (1978)

Particle Trcmsmission and Distributions in Relation to the Crop.

'Aerial Application of Pesticides' Short Course Notes. Sept. 1978. Cranfield Institute of Technology.

Parkin, C.S. Spillman, J.J.

(1980)

The use of wing-tip sails on a Spraying Aircraft to reduce the eunount of

material carried off-target by a crosswind.

J.Agrtc.Engng.Res.(1980) 26,pp.65-74

Watt, J. (1982)

Drift Mcunagement and Observations. Short Course on Application Technology Queensland Agricultural College,1982.

100

1 10 100

EFFECT OF SPHERE DIAMETER ON TERMINAL

ACCUMULATIVE y TOTAL VOLUME »l / /

Y

FLOW RATE OF V^I^TER 10 I/MIN

BLADE SETTING 30o

BLADE TYPE FLAT 13-5." 90KNür5

MICRONS

100 200 300 400 500 600 700 800 900 1000

DROPLET SPECTRUM USED IN EXAMPLE

160 170 180 190 200 DISTANCE DOWNWIND METRES

DOWNWIND SPRAY DEPOSIT DISTRIBUTION WITH AND WITHOUT TURBULENCE

FIGURE 3

100-250>im — O - DEPOSIT OF NEXT 30*U OF SPRAY VOLUME

250-90QMm A- DEPOSIT OF BIGGEST AO*/. OF SPRAK VOLUME

lr±-r

CONDITIONS AS FOR FIGURE 3.

O 10 20 80 100 120 140 160

DISTANCE DOWNWIND METRES

180 200 220 240

DOWNWIND DEPOSIT OF DIFFERENT SIZE GROUPS

UJ

5 ' / » ^ p f - i P ^ K § - 3 7 9

OfA

DISTANCE DOWNWIND ^ METRES

130 140 150 160 170 180 190 200

DISTANCE DOWNWIND METRES

210 220 230 240 250

DOWNWIND SPRAY DEPOSIT DISTRIBUTION IN DIFFERENT WINDSPEEDS

FIGURE 5