Unité de Mécanique et Construction Gembloux Agricultural University 30 August, 2015 Spray Pattern Simulation Model for Standardisation of Boom Behaviour

21 April 2023

Unité de Mécanique et ConstructionGembloux Agricultural University

Spray Pattern Simulation Model for Standardisation of Boom

Behaviour TestsIr LEBEAU F

Ir BOUCHAT X

Ir RUTER R

Prof DESTAIN M-F

21 April 2023


Context

• Repartition: criterion for sprayer performance

• Quality affected by boom movements

• Need of a test methodology of the repartition in dynamic conditions

Longitudinal

Pitch Vertical

Roll

Yaw

Transversal

21 April 2023


State of the art

• Many dynamic test methodologies are used : field trials, bump tests, shakers, modal analysis, FE Analysis, Multi-body analysis...

• Spray distribution evaluation relies either on measurements or simulation

• Simulation model are often preferred

21 April 2023


Consensus on models

• The individual spray distribution of the nozzles must be taken into account

• The spray repartition can be calculated as a sum of static spray distribution

21 April 2023


Needed

• General analytical description of the model

• Global procedure description

• Validation in realistic controlled conditions

• Discussion of the limitations

21 April 2023


Static distribution measurements• 24 1-D patternator measurements at 7°30’

interval angles.

dxdysyxyxDsr ))sin()cos((),(),(

5 10 15 20 25 300

0.2

0.4

0.6

0.8

1

Gutter number

Flo

w (

ml/s

)

21 April 2023


Static distribution measurements• Results

is a sinogram

0

0.5

1

1.5

2

2.5

3

3.5

projection angle (°)

gutt

er n

umbe

r

15 30 45 60 75 90 105 120 135 150 165 180

5

10

15

20

25

30

Flow (ml/s)

21 April 2023


Static distribution measurements• 2-D distribution reconstruction using filtred

back-projection

0

))sin()cos()(,()( dyxyxDDB

21 April 2023


Static distribution measurements• Results of 2-D distribution reconstruction

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X axis (mm)

Y a

xis

(mm

)

250 500 750 1000 1250 1500

250

500

750

1000

1250

1500

Flow (ml/s)

21 April 2023


3-D Distribution matrix• The

distributions were measured at 3 heights

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

500

1000

1500

0

500

1000

1500

300

400

500

600

700

X Axis (mm)Y Axis (mm)

Z a

xis

(mm

)

Flow (ml/s.2500mm²)

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3-D Distribution matrix• Exponential decreasing law for other heights

zbeLLzL .maxmax .

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3-D Distribution matrix• Computation of the flow for 25 mm²

cells on a 6.25 square plane at 41 heights between 0 and 2 m.

• Results are stored in a 500*500*41 3-D matrix D(x,y,z) used as input to the dynamic repartition model

21 April 2023


3-D Distribution matrix

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

X axis (mm)

Y a

xis

(mm

)

500 1000 1500 2000 2500

250

500

750

1000

1250

1500

1750

2000

Flow(ml/s.250mm²)

21 April 2023


Dynamic repartition model• Release velocity caused by boom movement

and atmospheric parameters are neglected.

• Assuming y motion negligible, movement equation is expressed as

),( zxgt x

y

z

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• The time spent at a particular location is the partial derivative of the movement equation

Dynamic repartition model

xzxg

xtz

),(

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Dynamic repartition model• Repartition is a function of time spent by

the nozzle at each successive position

• Assuming the spray distribution is constant for an uniform height z, repartition is given by

dxzxgzyxD

xzxgzyxDzyxR ),(),,(),(),,(),,(

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Dynamic repartition model• The global repartition is the sum of each

height influence

0

),,(),( dzzyxRyxR

21 April 2023


Experimental procedure for model validation

1

3

4

5

2

6

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Results: Uniform speed and height

10

15

20

X axis (mm)

Y A

xis

(mm

)

500 1000 1500 2000 2500

250

500

750

10

15

20

25

Y a

xis

(mm

)

500 1000 1500 2000 2500

250

500

750

ml/m²

ml/m²

Measurements

Model output

Meas. Simul.Mean ml/m² 15.9 15.8Max ml/m² 28 23.2Min ml/m² 6.3 6.9

CV % 27.5 33.4R² 0.81

21 April 2023


Results: Variable speed, uniform height

10

20

30

40

X Axis (mm)500 1000 1500 2000 2500

250

500

750

10

20

30

40

Y a

xis

(mm

) 500 1000 1500 2000 2500

250

500

750

Measurements

Model output

ml/m²

ml/m²

Meas. Simul.Mean ml/m² 16 15.4Max ml/m² >40 >40Min ml/m² 3.7 4.4

CV % 49.7 50.2R² 0.89

21 April 2023


Results Uniform speed, variable height

0

10

20

30

40

X a

xis

(mm

)500 1000 1500 2000 2500

250

500

750

10

20

30

X axis (mm)

Y a

xis

(mm

)

2500 1000 1500 2000 2500

250

500

750

ml/m²

ml/m²

Measurements

Model output

Meas. Simul.Mean ml/m² 18.8 16.4Max ml/m² >40 36.2Min ml/m² 1.9 1.7

CV % 42.2 41.4R² 0.70

21 April 2023


Conclusions

• Alterations of the lateral spray distribution

• Nozzle speed effect on longitudinal distribution

• Height effect is well predicted but repartition measurement method shows limitations

21 April 2023


Discussion

• The model is promising (CV)

• Structure based on sound physical description

• Easy implementation using standard experimental set-up and software

• Precision needed for simulation has to be discussed

• Need of more data to propose a standard

Documents

Unité de Mécanique et Construction Gembloux Agricultural University 30 August, 2015 Spray Pattern Simulation Model for Standardisation of Boom Behaviour