A simulation model of the spray drift from hydraulic nozzles

J. agric. Engng Res. (1989) 42, 135-147

A Simulation Model of the Spray Drift from Hydraulic Nozzles P. C. H. MILLER*; D. J. HADFIELD? A model to predict the trajectories of droplets from agricultural flat fan nozzles is described. Droplet motion is considered in two phases: close to the nozzle where the trajectory is dominated by the conditions associated with droplet formation, particularly the initial velocity and entrained air conditions; and a second phase where the effects of approach. Results from the atmospheric turbulence are predicted using a “random-walk” model are compared with laboratory measurements of droplet size/velocity profiles beneath a nozzle and with field measurements of the downwind drift from boom mounted nozzles operated conventionally. Predicted total downwind drift deposits agreed well with measured values but the form of the vertical deposit distribution was less well predicted.

1. Introduction Previous work concerned with predicting spray droplet movement has used both dispersion and random-walk type models. Dispersion models have been used to study the transport of sprays both towards and within crop canopies and have been applied particularly to aerial spraying where droplet movements through the air can be relatively large. Bathe and Sayer12 and Cramer (Dumbauld et a1.)3 derived expressions for the deposit distribution downwind of a line spray source and for the airborne flux just above the crop canopy based on diffusion theory, and demonstrated some agreement with field data. Schaefer and Allsop* discuss the application of gradient diffusion theory to spray transport and demonstrate an improved prediction of deposit when compared with the linearly expanding Gaussian plume used by Bathe and Sayer and by Cramer. A number of authors have used Markov type simulation models to predict the trajectories of droplets in turbulent air flows including Thompson and Ley,’ Picot et al. ,6 Wilson et al. ,7 and Legg and Raupauch.* Such models have been shown to provide an acceptable description of spray deposit distributions downwind from a defined source given assumed release conditions. These models have been used in conjunction with both aerial and ground crop spraying systems and have examined the effects of operating parameters on downwind spray deposits. Both diffusion and “random-walk” type models have been developed that account for droplet evaporation and sedimentation by gravitational forces. However, droplet release conditions have been assumed and not related to sprayer characteristics and relatively little work has attempted to relate the conditions of droplet generation to their subsequent transport particularly in the region close to agricultural flat fan nozzles. Such an analysis will provide a basis for the design of spraying systems to minimise drift and is the subject of this paper. Droplet trajectories are described in two distinct phases: close to the nozzle where considerations of air drag and entrained air predominate, and further downwind where a random-walk approach is used.

* Chemical Applications Group, AFRC Engineering, Silsoe, Bedford MK45 4HS, UK 7 Formerly of above address. Current address: Flat 3, 56 Chaucer Road, Bedford MK40 2AP, UK Received 9

June

1988; accepted in revised form 6 November 1988.

Paper presented at Ag Eng 88, Paris, France, 2-6 March 1988.

135

136

A MODEL

OF

SPRAY

DRIFT

Notation d 0, h K1 L I, r s T, u, u 24, u, v, w z

droplet diameter, urn distance downwind of nth sampling line, m distance below nozzle, m entrained air parameter, dimensionless Monin-Obukov length, m coherent length of liquid spray sheet, m see Eqn (3) nozzle spacing on boom, m Stokesian response time, s sheet velocity for fan nozzle, m/s horizontal droplet velocity, m/s friction velocity, m/s entrained air velocity, m/s droplet settling velocity, m/s vertical droplet velocity, m/s height above ground, m

z, crop height, m z, boom height, m (Y factor indicating loss of velocity correlation in successive time steps y see Eqn (3) 6 constant in entrained air equation rr_ Lagrangian time scale, s At time step, s Ap vapour pressure difference, Pa & random variables from Gaussian rl 1 distribution with mean zero and standard deviation of 1-O p viscosity of air p density of droplet, kg/m3 velocity fluctua0” rms horizontal tions, m/s %I rms vertical velocity fluctuations, m/s

of the model

2. Structure

The model simulates a simplified spraying situation as shown in Fig. 1 in which the drift from a set of boom mounted nozzles operating above a cereal crop canopy is measured using ve&al strings mounted at various distances downwind. In structuring the model the following simplifying assumptions were made:

spray

(1) Trajectories

Wind

were considered in two dimensions only and effects due to the forward

9

direction Sampling lines

s

c-----D, .

-

4

Fig. 1. Simulated spraying conditions

P. C. H. MILLER;

137

D. J. HADFIELD

movement of the sprayer and the turbulent wakes created by this forward movement were neglected. (2) The crop surface behaved as a perfect collector of spray with no movement or reflection of droplets from within the canopy. Ground spray deposits were calculated on this basis. (3) Spray droplets from adjacent nozzles on a boom acted independently. 2.1. The random-walk model The random-walk model used in the simulation was based on that developed by Thompson and Leg in which the velocity of a droplet at any time step was related to the velocity in the previous time step but with an added random component due to turbulence. The droplet velocity in the vertical direction, w, in the i + 1 th time step is given by:5 wi+l

=

(r(Wi

+ Vsi) +

qj+lUw(l-

0!2)t - us,+,

(1)

where Q = exp(-At/r,_) and 7 is a random variable. Eqn (1) is only valid if the time step At is small compared with the Lagrangian time scale, rL. The effect of droplet settling velocity, u,, is included as a direct term in the equation, and this was considered by Thompson and Ley to be satisfactory for water based droplets with diameters up to 450 urn based on data by Smith.’ Settling velocities, IJ,~,are therefore calculated using the relationships given by Thompson and Ley’ as v,, = 4.47 x 10-3d - 0.191 for d>lOOum and

(2)

v,, = 3.2 x 10+d2 - 6.4 x 10+d3 for d
=

(yui

+

U~*,+l,(l- (u) + yU”(l - “2)f

where y = 0’5rqi+l + (1 - 1’25r2)‘&i+1 and

(3) (4)

2 r=-

u* (J” G!

The trajectories of droplets over a series of time steps of At were calculated based on Eqns (l)-(4) once an effective release position for each droplet had been reached (see Section 2.2). 2.1.1. Droplet evaporation The change in droplet diameter due to evaporation was based on relationships given in Thompson and Ley” assuming that mass transfer occurred as if the droplets were of water, down to a minimum size of 1% of the original droplet volume. The change in droplet diameter was determined from Ad = - (0*358Ap/d)(2 + 0*124(v, - d)i) At The effects of droplet density or evaporation not considered in the model.

(5) of pesticide materials in the spray were

138

A MODEL

2.2.

OF SPRAY

DRIFT

Trajectory calculation close to the nozzle

Trajectories were determined over a series of time steps using an integration routine described by Marchant” with drag coefficients equal to those for solid spheres. Marchant indicated that errors due to this assumption would be less than 10% for the droplet conditions simulated. The effect of turbulence on initial droplet trajectories was simulated by including an additional vertical air velocity component term which was sampled randomly from a Gaussian distribution with a mean of zero and a standard deviation of a, and which was assumed to persist for a period equal to the Langrangian timescale, r,_. The response time of a droplet in a moving air-stream is characterised by the Stokesian response time, T, where

Initial runs with the model indicated the droplets below a spray nozzle had reached their settling velocities after a period of approximately 4T, and so this value was used as the basis for changing from the ballistic trajectory to random-walk phases of the model. 2.2.1. Spray characteristics Spray droplets were assumed to form at a distance equal to the sheet coherent length below the nozzle and have an initial velocity the same as the liquid sheet. Data relating to coherent lengths and sheet velocities was initially obtained from measurements made using high-speed photography.” Trajectory angles were sampled from a Gaussian distribution with a mean of zero and a standard deviation of O-4 times the nozzle angle. This value was determined experimentally by comparing calculated volume distributions below a 110” flat fan nozzle with those measured in patternator experiments. The effect of the droplet size distribution was accounted for by simulating the trajectories of between 500 and 5000 droplets in each of a number of size categories (depending on the required accuracy and limitations of computing time) up to a maximum of 25 size categories. Size categories in increments of 20 urn have been found convenient in applying the simulation to most agricultural flat fan nozzles. Volume distributions were then determined by relating the proportion of droplets deposited or remaining airborne in a defined area, to the total volume of spray liquid output while travelling through the sample volume and the measured droplet size/volume distribution for the spray produced by the nozzle.

2.2.2. Entrained air velocities Studies of air entrainment in liquid sprays have shown that the velocity of entrained along the axis of a fan jet nozzle, v,, can be described by the equation:12

where u, is the sheet velocity and h the distance below the nozzle. 8 for sprays into air takes a value’* of 0.4, while K1 is a constant defined spray fan at right angles to the spray sheet at a given distance from determined from photographic measurements of a number of 80 and

air

is a constant which by the width of the the nozzle. K1 was 110” nozzles, and a

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139

D. J. HADFIELD

9

Start

Input nozzle conditions

Initiate droplet flight

-8

Fig. 2. Model flow chart

140

A MODEL

mean value of 0.14 was used as input to the simulation. assumed to be constant across the spray sheet.

OF SPRAY

The entrained

DRIFT

air velocity was

2.2.3. Structure of the simulation model A flow chart for the model of drift from a single nozzle is shown in Fig. 2. The drift from boom mounted nozzles was simulated by calculating the drift from a single nozzle and overlapping that from successive nozzles off-set by the nozzle spacing distance s. Inputs to the model in addition to those defining the spray nozzle included a description of the sampling system and parameters defining the meteorological conditions. Atmospheric stability was defined in terms of the Monin-Obukov length (L), and related to a,, a, and tr by relationships derived in Thompson and Ley.5 Simulation outputs gave the vertical distribution of airborne spray in 10 cm increments at each sampling line and the ground deposits between sampling lines. The predicted trajectories of ten 100~urn droplets released in the spray from a flat fan nozzle spraying at the rate of 0.6 l/min at a pressure of 3 bar are shown in Fig. 3.

1 Nozzle ; . ::

Crop

Fig. 3. Simulated trajectories of l&I pm droplets from a 110” nozzle operating 0.5m above a cereal from random walk model crop 50mm tall. . . . . . . -, from ballistic trajectory model; -,

3. Experimental 3.1. Measurements

verification

of the model

of downwind drift from a moving boom

Measurements of the drift from three boom mounted nozzles were made using the techniques reported by Sharp. l3 The nozzles (Lurmark 110015 in Kemetal) were mounted

P. C. H. MILLER;

141

D. .I. HADFIELD

on a small boom and off-set from the axis of the tractor to minimise air disturbance and wake effects. The nozzles sprayed a 1% solution of a fluorescent tracer dye at a pressure of 3.0 bar in a total of 20 passes down a spray track aligned at right angles to the mean wind direction so as to accumulate measurable deposits. A spraying speed of 8 km/h was used. Spray drift was captured using 2.5 mm diameter plastic tubing suspended in a 3 x 6 m framework. Meteorological conditions at the time of spraying were recorded using a 10 m mast with four vane anemometers, mean air temperature, relative humidity and temperature difference sensors. The Monin-Obukov length was derived from the Richardson number using the method described by Thompson and Ley5 for conditions above a cereal crop with Richardson number determined directly from weather mast measurements. The droplet size spectrum from the nozzles was determined from data collected from a Particle Measuring Systems size analyser and a laboratory x-y sampling arrangement. l4 To simulate the drift from the boom arrangement of nozzles, the velocity of the liquid sheet (and hence the initial velocity of the droplets) was estimated from data obtained from high speed photography of similar nozzles operating at the same pressure and with the same spray liquid.” Fig. 4 shows measured and simulated total line deposits at distances up to 6 m downwind for two different weather conditions. Simulated values were calculated using 500 droplets in 20 size categories with a 20 urn increment between categories. The effects

360 320280 3 f

240-

5 “,

C I= 02

200160120EO-

, ----. I

o 0

, --*-*-. I\!_!_,

- --.-_.

2

4 DMance

_

!_!_

downwmd,

I

6 rn

Fig. 4. Measured and predicted downwind drift profiles from a moving boom for two atmospheric measured in mean wind speed of 6*6m/s at a height of 1Om; - - - - -, predicted conditions. -, in mean wind speed of 6*6m/s at a height of 10m; - I - i - 1-, measured in mean wind speed of 1_9m/s at a height of 10m; - * - ’-, predicted in mean wind speed of 1_9m/s at a height of 10m

142

A MODEL

of entrained air were not included in this initial simulation significantly over-estimated drift as expected. 3.2. Droplet size/velocity

OF SPRAY

DRIFT

and model predictions

profiles below a nozzle

Measurements of droplet size and velocity were made 0.5 m below the central axis of a flat fan nozzle (Lurmark 110015 in Kemetal) spraying water plus 0.1% Agral (ICI plc) using a Particle Measuring Systems size analyser,14 and the results are plotted on Fig. 5. Data are for six replicated scans of the spray produced by the nozzle. Also plotted on Fig. 5 are the droplet size/velocity profiles calculated using the ballistic trajectory routine in the model and on the following assumptions: (1) a constant entrained air velocity between nozzle and sampling point equal to the mean measured velocity of droplets in the 40-80 pm size range, and (2) entrained air velocities defined by Eqn (7), and with values for the constants as given in Section 2.2.2 (i.e d2/2K1 = O-57). Velocities of the larger droplet size are more variable because of the relatively small number of droplets of this size in the spray sample. The results show that the velocities predicted using the trajectory routine in the model were some 2-5 m/s above those measured and indicate that the initial (or liquid sheet) velocity used in the simulation at 17.0 m/s was too high. It was also expected that the theoretical plot in Fig. 5, based on a constant entrained air velocity between nozzle and measuring point, would under-predict droplet velocities, and the fact that this was not the case except above 450 pm also indicated that the release velocity was less than that assumed.

0 Droplet

size, pm

Fig. 5. Measured and predicted droplet velocities below 110” nozzle. *, measured values; -, predicted using trajectory routine in model with entrained air velocity determined from Eqn (7,); ----, predicted assuming a constant entrained air velocity

P. c.

H. MILLER;

143

D. J. HADFIELD

14-

12-

0

I 100

0

I 300

I 200 Droplet

sue,

I 400

5

pm

Fig. 6. Measured and predicted droplet velocities below a 110” nozzle with different entrained air conditions. -, 62/.2KI in Eqn (7) = O-57; *, measured values; -. - . -, Sz/2K, in Eqn (7) = O-95; - - - - - , 6 ‘/2K, in Eqn (7) = 1.25

350-

300Ti g 250b $ D E L z t

200150IOO50-

0:

0.5

I

I.5

I

2.5 Distance

I

3.5 downwmd,

I

1

4.5

5.5

c 5

m

Fig. 7. Measured and predicted downwind drift profiles. *, measured; -, predicted as Fig. 4; ---, predicted with entrained air, sheet velocity = 17.0 S2/2K, = 0.57; - . - . - , predicted with entrained air, sheet velocity = 15.0 6 2/2K, = 0.95

144

A MODEL

OF

SPRAY

DRIFT

200 180-I

180 160

60. 40.

i$,,, I

>

20. 0:

0

0. 2'0

4b

6b

Line deposit,

8b

Id0

I;

.

20

/II

40

6b

80

Id0

I

Line deposit, ~1

Fig. 8. Measured and predicted airborne spray profiles at 1 m (left) and 6m (right) downwind of a

predicted with no entrained air sheet velocity = 17aOm/s, boom sprayer. *, measured; -, - - - - , predicted with entrained air sheet velocity = 17.0 6 ‘/2K, = O-57; - . - . -, predicted with entrained air sheet velocity = 15.0 6 ‘/2K, = O-95

Fig. 6 shows the same experimental data but with velocity profiles predicted assuming a sheet velocity of 15.0 m/s and values of 6’/2K1, in Eqn (7) of O-57, O-95 and l-25. Using a value of O-57 gave predicted droplet velocities up to 3-5 m/s above measured values, and some variation in the values of 6’/2K1 was considered justified because of the practical difficulties in measuring K, from photographic records. Values of O-95 and l-25 gave an improved fit to the measured data although the form of the measured relationship was still not well predicted.

3.3. Revised simulation

of measured

results

The simulation of the field drift measurements was re-run with an initial droplet velocity of 15-O m/s. Fig. 7 shows the effects of using revised velocity and assumed entrained air conditions on the predicted downwind drift with the equivalent vertical airborne spray profiles at distances of 1 and 6 m downwind shown in Fig. 8. The inclusion of entrained air reduced drift volumes as expected with the best agreement between measured and predicted drift obtained with an entrained air parameter of O-085 corresponding to a value of d2/2K1 in Eqn (7) of O-95.

4. Discussion of results 4.1. Entrained

air effects

The results indicate the importance of the correct definition of sheet velocity and entrained air conditions close to the nozzle. The use of entrained air parameters giving a

P. C. H. MILLER;

145

D. J. HADFIELD

value of 6’/2K1 close to unity gave an improved agreement with both measured downwind drift and size/velocity profiles below the nozzle. Original values of the entrained air parameters were derived from photographic measurements of the spray section and were probably inaccurate due to the difficulty in identifying spray boundaries on such photographs. Further work is needed to define the effects of entrained air conditions for a range of nozzle types and sixes and in different parts of the spray structure. It can be seen from the results in Figs 5 and 6 that with an entrained air parameter of 0.085 (i.e. S2/2K1 = O-95) the model underestimates the vertical velocities of droplets below 150 pm in diameter and yet it can be seen from Figs 7 and 8 that downwind drift values are not overestimated. The droplet size/velocity profiles were measured in the laboratory at a relatively low horizontal scanning speed of O-05 m/s, and this velocity difference may affect the trajectories of drifting droplets. Further work needs to examine the interaction between the spray sheet and surrounding air movements and to improve the definition of entrained air effects. 4.2. Change from trajectory to random walk routine This was examined by examining the airborne drift volumes at distances up to 6 m from the nozzle when simulating drift with different integer increments of the Stokesian response time, T, in the trajectory routine of the model, and the results are shown in Fig. 9. With values of less than 4, drift values were lower indicating that droplets entered the random walk routine of the model with downward velocities greater than the settling velocity. 4.3. General discussion The agreement between measured and predicted drift profiles from 3 boom mounted nozzles was relatively good particularly in view of some of the assumptions made relating to nozzle movement. With entrained air, predicted downwind profiles, shown in Fig. 7,

4oo

,/._..__........... ..................................................... .... t

01

’

I

2

’ 3 Time

’ 4

’ 5

in trqectory

’

6

’ 7

’

’

’

8

9

IO

routine, nT,

Fig. 9. Effect of increasing time in trajectov routine on the total airborne drift up to 6m from a boom with three 110” nozzles. -, drift at 6m; - . - * -, drift at 3 m; - - - - , drift at 2m; . . . . . 9 drift at 1 m

146

A MODEL

OF SPRAY

DRIFT

decayed more rapidly than those measured, and this is probably related to the method used for incorporating a settling velocity component in the “random-walk” model. Further work has now examined this feature of such models, e.g. Walklate,” and incorporating an improved description of ‘heavy’ particle trajectories downwind should improve model predictions. Work is being conducted to compare the model predictions with measurements of the drift from single static and boom mounted nozzles to eliminate the effects of movement and any nozzle interactions. The predicted drift profiles differed from those measured directly above the crop/ground surface indicating that the assumptions made regarding droplet retention and reflection were too simplified. All the calculations assumed that droplets behaved as spherical particles. This assumption was probably valid for droplets up to 350 urn in diameter, but it can be seen from the results in Figs 5 and 6 that the velocities of larger droplets are underestimated because of the effects of shape distortion. 5. Conclusions and proposals for future work The model provides a useful description of the spray drift from agricultural hydraulic nozzles, with reasonable agreement between measured and predicted downwind drift profiles. Further work is required to extend the range of conditions for which the model has been validated. Work is also required to improve the description of entrained air effects, to include the effects of forward speed including the generation of turbulent wakes from the boom and spray vehicle, and to improve the calculation of “heavy” particle trajectories. Acknowledgements Thanks are due to Mr A. P. Chick and Mr J. E. Pottage for assistance with the field experiments and to Mr C. R. Tuck for assistance with the laboratory measurements of droplet size/velocity profiles.

References ’ Beche, * a 4 5 ’

’

*

D. H.; Sayer, W. J. D. Transport of aerial spray, I. A model of aerial dispersion. Agricultural Meteorology 1975, 15: 257-271 Bathe, D. H.; Sayer, W. J. D. Transport of aerial spray. II. Transport within the crop canopy. Agricultural Meteorology 1975, 15: 371-377 Dumbauld, R. K.; Rafferty, J. E.; Bjorkland, J. R. Prediction of spray behaviour above and within a forest canopy. USDA Forest Service Report, 1977, TR-77-308-01 Schaefer, G. W.; Allsop, K. Spray droplet behaviour above and within a crop. Proceedings 10th International Congress of Plant Protection 1983, 3: 1057-1065 Thompson, N. J.; Ley, A. J. Estimating spray drift using a random-walk model of evaporating drops. Journal of Agricultural Engineering Research 1983, 28: 418-435 Picot, J. J. C.; Kristmanson, D. D.; Basak-Brown, N. Canopy deposit and off-target drift in forestry aerial spraying. The effects of operational parameters. Transactions of the ASAE 1986, 29: 80 Wilson, J. D.; llmtell, G. W.; Kidd, G. E. Numerical simulation of particle trajectories in inhomogeneous turbulence. IV: Comparison of predictions with experimental data for the atmospheric surface layer. Boundary Layer Meteorology 1981, 21: 443-463. Legg, B. J.; Ranpach, M. R. Markov chain simulation of particle dispersion in inhomogeneous

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flows. The mean drift velocity induced by a gradient in Eulerian velocity variance. Boundary Layer Meteorology 1982,24: 3-13 Smith, F. B. The turbulent spread of a falling cluster. In: Advances in Geophysics 6, Atmospheric Diffusion and Air Pollution. London: Academic Press 1959, pp. 193-210 Mar&ant, 1. A. Calculation of spray droplet trajectory in a moving airstream. Research Note. Journal of Agricultural Engineering Research 1977, 22: 93-96 Lake, J. R. Sprays, physical properties and deposition on cereals and weeks. PhD Thesis, University of London, 1982 Briffa, F. E. J.; Dombrowski, N. Entrainment of air into a liquid spray. American Institute of Chemical Engineers Journal 1966, l2(4): 708-717 Sharp, R. B. Comparison of drift from charged and uncharged hydraulic nozzles. British Crop Protection Council, Proceedings of Conference on Pests and Diseases, 1984, pp. 1027-1031 Lake, J. R.; Dix, A. J. Measurements of droplet size with a PMS optical array probe using an x-y nozzle transporter. Crop Protection 1985, 4(4): 464-472 Walklate, P. J. A Markov-chain particle dispersion model based on airflow data: Extension to large water droplets. Boundary Layer Meteorology 1986, 37: 313-318