miller hadfield 1989
TRANSCRIPT
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J. agric. Engng Res. (1989) 42, 135-147
A Simulation Model o f the Spray Drift from Hydraulic Nozzles
P. C. H.
MILLER ; D. J. H ADFIELD?
A mod el 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 associate d w ith droplet form ation, particularly the
initial velocity and entrained air conditions; and a second phas e wher e the effects of
atmo spheric turbulence are predicted using a
“random-walk” approach. Results from the
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
oper ated conventionally. Pred icted total downwind drift deposits agre ed well with mea sured
values but the form of the vertical deposit distribution was less well predicted .
1 ntroduction
Previous work concerned with predicting spray droplet movem ent has used both
dispersion and random-w alk 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 movem ents through the air can be relatively
large. Bathe and Sayer12 and Cramer (Dum bauld et a1. 3 derived exp ressions for the
deposit distribution downw ind 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 Thom pson and Ley,’ Picot et
a l . 6
Wilson
et al . 7
and Legg and Raupauch.* Such models have been show n to provide an
acceptable description of spray deposit distributions downw ind from a defined source
given assum ed release conditions. These m odels have been used in conjunction with both
aerial and ground crop spraying systems and have examined the effects of operating
parameters on downw ind 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 assum ed 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 agricultu ral flat fan nozzles.
Such an analysis w ill 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 downw ind w here a
random-w alk approach is used.
*
Chemical Applications Group, AFRC Engineering, Silsoe, Bedford MK45 4HS, UK
7 Formerly of above address. Current address: Flat 3, 56 Ch aucer Road, B edford MK40 2A P, UK
Received 9 une 1988; accepted in revised form 6 November 1988.
Paper presented at Ag Eng 88, Paris, France, 2-6 March 1988.
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A MODEL OF SPRAY DRIFT
Notation
d droplet diameter, urn
z,
crop height, m
0, distance downw ind of nth sam- z, boom height, m
pling line, m
(Y factor indicating loss of velocity
h distance below nozzle, m correlation in successive time steps
K1 entrained air parameter,
y see Eqn (3)
dimensionless 6 constant in entrained air equation
L
Monin-O bukov length, m
rr_ L agrangian time scale, s
I, coherent length of liquid spray
At time step, s
sheet, m
Ap vapour pressure difference, P a
r see Eqn (3)
&
s
nozzle spacing on boom, m
rl
1
random variables from Gaussian
distribution with mean zero and
T, Stokesian response time, s
standard deviation of 1-O
u,
sheet velocity for fan nozzle, m/s p viscosity of air
u horizontal droplet velocity, m/s
p density of droplet, kg/m3
24, friction velocity, m/s
0”
rms horizontal velocity fluctua-
u,
entrained air velocity, m /s tions, m/s
v, droplet settling velocity, m/s
%I
rms vertical velocity fluctuations ,
w vertical droplet velocity, m/s
m s
z height above ground, m
2. Structure of the model
The model simulates a simplified spraying situation as shown in
Fig . 1
in which the
spray drift from a set of boom mounted nozzles operating above a cereal crop canopy is
measured
using ve al strings
mounted at various distances down wind. In structuring the
model the following simplifying assum ptions were made:
(1) Trajectories were considered in two dimensions only and effects due to the forward
9
W i nd d i r ec t i on
s
S a m p l i n g
l i nes
c-----D, -
.
4
Fig. 1. Simulated spraying conditions
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P. C. H. MILLER; D. J. HADFIELD
137
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.
Th e 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 + V si) + qj+lUw(l- 0 2)t - u s,+,
(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 d roplets 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
(2)
and
v,, = 3.2 x 10+d2 - 6.4 x 10+d3
for d
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A MODE L OF SPRAY DRIFT
2 .2 . Tra jecto ry ca lcu la t io n c lose to th e nozz l e
Trajectories were determined over a series of time steps using an integration routine
described by Marchan t” with drag coefficients equal to those for solid spheres. March ant
indicated that errors due to this assump tion would be less than 10% for the droplet
conditions simulated.
The effect of turbulence on initial droplet trajectories was simulated by includin g 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
assum ed 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 ha d reached
their settling velocities after a period of approximately 4T, and so this value w as used as
the basis for changing from the ballistic trajectory to random-w alk phases of the model.
2.2.1. Spray cha rac te r i s t i cs
Spray droplets were assum ed 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 w as initially obtained from measurem ents made
using high-speed photography.”
Trajectory angles were sampled from a Gauss ian distribution with a mean of zero and a
standard deviation of O-4 times the nozzle angle. This value was determined experimen-
tally by comparing calculated volume distributions below a 110” flat fan nozzle with those
measured in patternator experiments.
The effect of the droplet size distribu tion wa s 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 maxim um
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. V olume distributions were
then determined by relating the proportion of droplets d eposited 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.
En t r a i n ed a i r ve l o ci t i e s
Studies of air entrainment in liquid sprays have shown that the velocity of entrained air
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 is a constant which
for sprays into a ir takes a value’*
of 0.4, w hile K1 is a constant defined by the width of the
spray fan at right angles to the spray sheet at a given distance from the nozzle. K1 was
determined from photographic measurem ents of a number of 80 and 110” nozzles, and a
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P. C. H. MILLER; D. J. HADFIELD
Start
139
Input nozzle
conditions
-8
Initiate droplet
flight
Fig. 2. Model
flow
chart
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140 A MODEL OF SPRAY DRIFT
mean value of 0.14 was used as input to the simulation. The entrained air velocity was
assum ed to be constant across the spray sheet.
2.2.3.
St r u c t u r e o f t h e s imu l a t i o n mode l
A flow chart for the m odel of drift from a single nozzle is shown in Fig. 2. The drift
from boom mounted nozzles w as 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 samp ling system and parameters defining the meteorological conditions. Atmos-
pheric stability w as defined in terms of the Mo nin-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 samp ling 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 fr om a 110” nozzle operating 0.5m above a cereal
crop 50mm tall . . . . . . . -, from ballistic trajectory model;
-, fr om random walk model
3. xperimental verification of the model
3.1. M ea su r emen t s o f d ow nw i n d d r i f t f r om a mo v i n g b o om
Measurem ents of the drift from three boom m ounted nozzles were made using the
techniques reported by Sharp.
l3 The nozzles (Lurmark 110015 in Kemetal) were mounted
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on a small boom and off-set from the axis of the tractor to minimise air disturbance and
wak e effects. The nozzles sprayed a 1% solution of a fluorescent tracer dye at a pressu re
of 3.0 bar in a total of 20 passes down a spray track aligned at right ang les 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 su spended in a
3 x 6 m framework. Meteorological conditions at the time of spraying were recorded
using a 10 m mast with four vane anemom eters, mean air temperature, relative humidity
and temperature difference sensors. The Mo nin-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
measurem ents. The droplet size spectrum from the nozzles was determined from data
collected from a Particle Me asuring Systems size analyser and a laboratory x-y samp ling
arrangement. l4
To simulate the drift from the boom arrangemen t of nozzles, the velocity of the liquid
sheet (and hence the initial velocity of the droplets) was estimated from d ata 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
downw ind 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 -
320-
280 -
3
f 240-
5
“
200-
C
I=
0 160-
120-
EO-
, , --*-*-.
----.
- --.-_. _
o I
I\ _ _,
_ _
I
0
2 4
6
DMance d ownw md, rn
F ig. 4. Measured and predicted downwind dri f t prof il es fr om a moving boom for two atmospheric
conditions. -,
measured in mean wind speed of 6*6m/s at a height of 1Om; - - - - - , predicted
in mean wind speed of 6*6m/s at a height of 10m; - I - i - 1-, measured i n 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
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A MODEL OF SPRAY DRIFT
of entrained air were not included in this initial simulation and model predictions
significantly over-estimated drift as expected.
3.2. D r oplet size/velocity prof i l es below a nozzle
Meas urements of droplet size and velocity were m ade 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 M easuring Systems size analyser,14 and the results are plotted on F ig. 5.
Data are for six replicated scans of the spray produced by the nozzle. A lso plotted on F ig .
5
are the droplet size/velocity profiles calculated using the ballistic trajectory routine in
the model and on the following assum ptions:
(1) a constant entrained air velocity between nozzle and samp ling point equal to the
mean m easured 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 d2/2K 1 = O-57).
Velocities of the larger droplet size are more v ariable because of the relatively sm all
number of droplets of this size in the spray sample.
The results show that the velocities predicted using the trajectory routine in the mod el
were some 2-5 m/s above those m easured 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
F ig. 5,
based on a constant entrained air velocity between nozzle and
measuring point, w ould 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.
Droplet size pm
0
F ig. 5. Measured and predicted droplet velociti es below 110” nozzle. * , measured values; -,
predicted using trajectory r outine in model with entrained air velocity determined from Eqn (7,);
-----
,
predicted assuming a constant entr ained air veloci ty
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H MILLER; D J HADFIELD
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14-
12-
0
I I
I
I
0 100 200
300 400 5
D r op l e t sue , pm
F ig. 6. Measured and predicted droplet veloci ties below a 110” nozzle with dif ferent entr ained 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-
300-
Ti
g 250-
b
D 200-
E
L
z 150-
t
IOO-
50-
:
I I
I I 1
0.5 I.5 2.5 3.5
4.5 5.5 c
D i st a n c e d o w n w m d , m
5
Fig. 7. Measured and predicted downwind dri ft profi les. * , measured;
-, predicted as Fig. 4;
----
, predicted with entrained ai r, sheet velocity = 17.0 S2/2K, = 0.57; - . - . - , predicted with
entr ained air , sheet velocity = 15.0 6 2/2K, = 0.95
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P. C. H. MILLER; D. J. HADFIELD
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value of 6’/2K1 close to unity gave an improved agreement with both m easured
dow nwind drift and size/velocity profiles below the nozzle. Orig inal values of the
entrained air parameters were derived from photographic measurem ents 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
dow nwin d drift values are not overestim ated. 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 drop lets. Further work needs
to examine the interaction between the spray sheet and surrounding air movem ents and
to improve the definition of entrained air effects.
4.2. Change fr om trajectory to random walk rout ine
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 w ith downw ard velocities greater than the settling
velocity.
4.3. General discussion
The agreement between measured and predicted drift profiles from 3 boom mou nted
nozzles was relatively good particularly in view of some of the assumptions made relating
to nozzle movement. With entrained air, predicted downw ind profiles, show n in Fig. 7,
4oo
t
,/._..__...........
.
01
’ ’ ’ ’ ’ ’ ’ ’ ’
I 2 3 4
5 6 7 8 9 IO
Time in trqectory routine nT
F ig. 9. Effect of increasing time in trajectov routi ne on the total airborne dri ft up to 6m from a
boom with three 110” nozzles. -, dri f t at 6m; - . - * -, drif t at 3 m; - - - - , drif t at 2m;
. . . . .
9
dri ft at 1 m
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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 compon ent in the “random-w alk” model.
Further work has now examined this feature of such models, e.g. Walklate,” and
incorporating an improved description of ‘heavy’ particle trajectories downw ind should
improve model predictions.
Work is being conducted to compare the model predictions with measurem ents 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 assum ptions made regarding droplet retention and
reflection were too simplified.
All the calculations assum ed that droplets behaved as spherical particles. This
assum ption 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 m easured and predicted downw ind drift
profiles.
Further work is required to extend the range of conditions for which the model h as
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 d ue 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.
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a
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