a discrete element model for simulation of a spinning disc fertilizer spreader

7/29/2019 A discrete element model for simulation of a spinning disc fertilizer spreader

http://slidepdf.com/reader/full/a-discrete-element-model-for-simulation-of-a-spinning-disc-fertilizer-spreader 1/38

A discrete element model for simulation of a spinning disc fertilizer

spreaderP. Van Liedekerke; E. Tijskens; E. Dintwa; H. Ramon

Departement of Agro-engineering and Economics, K.U.Leuven, Kasteelpark Arenberg 30, B-3001 Leuven; e-mail of corresponding author: [email protected]

1. introduction

In this paper, a DEM (Discrete Element Method) model is presented and a series of computer experimentsis analyzed and compared to experimental validations. Also, the simulations are compared to experimentalresults. The model uses a 3 parameter contact force to calculate impact between particles and other objectsuch as vanes. The components of the contact forces are typically modeled in terms of a scalar quantity measuring the material deformation at the contact point. In this paper we use the Hertz-Kono-Kuwabaramodel [Kuwabara ,1987] for the normal force component [Schäfer et al., 1996] experienced by the particle

:( )( )

12min 0,

N N N N Nk cδ δ δ = − +N n& . (1)

Here,N

k andN

c are the non-linear contact stiffness and damping parameter, respectively. The quantity

N sd rδ = − is termed the virtual overlap of the contacting bodies.

2. Experiments

First, an estimation of the model parameters was done. For measuring methods of particle stiffness,damping and friction, we refer to (Van liedekerke, 2006). The particles used for the experiment are from adomestic fertiliser (quite round shape), with an average radius of 1.2 mm. The model was then validated using a domestic centrifugal spreader disc of 0.15m radius with 4 vanes

which is driven by an electrical motor at 400 rpm. The feeding of the fertiliser particles was controlled by afunnel –shaped bin with a circular orifice of 0.011 m radius.

Figure 1 (left) : experimental set-up of the mini spread hall with collector tray, (right) :measured and experimental amount of fertiliser particles in each basket with the collector tray located at 1m from the disc centre.



Paul Van Liedekerke

Katholieke Universiteit Leuven (K. U. Leuven

Laboratory for Agricultural Machinery and Proces

Kasteelpark Arenberg 30, B-3001 Leuven, Belg

http://www.agr.kuleuven.ac.be/aee/amc/amc.h

DEM for centrifugal spreaDEM for centrifugal sprea



Laboratory for Agricultural Machinery and Processing

overview

Situationtomodel : frombinto field

>106particles!




overview

1. Single particlesimulations

2. Multi particlesimulations(reality)

DEM Simulations:




1.Single particlesystem

Why single particle simulations?1.Comparision of DEM contact forces withthe compone

Patterson and Reece (1962) equations

-Centrifugal force, Coriolis force, Friction,..

2.Experimental verification of the trajectory




1.Single particlesystem

DEM Contact-force description of two objects

T

N

N=C x1/2 dx/dt+N>0 (Hertz)

T=min(Kx, F)(slip-stick)

0 0.2 0.4 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

F

F=T+N function of ,C,K




1. Single particlesystem: measuringmodel pa

Measuringstifness: Compressiontests of fertilisparticles

Hertz: F=Kx3/2

break

I

forceN

-Breakagetypic




1. Single particlesystem: measuringmodel para

C=f(v1/v2) (theoretical)or

C via model parameter

optimization

v1

v2

Measuringdamping: rebounceexperimentsof fparticles

Useof High speed camera





: measuring angle (H ) of slope at consta

Useof High speed camera

H

tan (H )=





Ma=-(5/7µ)Mg + (5/7)Mω²R (rolling againstva

or

Ma= -µMg +Mω²R- 2M ω µV (sliding against

F=C x1/2 dx/dt+ Kx3/2, F>0

T= min(Kx, F)

Patersson–equationsversus DEM




Single particlesystem

forcesinvolved-rolling force

FR=?

tot

Lineis analytical sol





forcesinvolvedcentrifugal force

Lineis analytical solution





Forcesinvolved-Coriolis force

ω

V=radia

Bouncingagainstvane(dottedis lower damp





Experimental verification :

Measurintraj

of a particl





ω=470tr

o : experiment

- : DEM

Radial trajectoryplots





Particlerotation? (spin)

disc

vane

Rotational speed againstvane: a) high friction, b

->a) rolling, b) sliding





Particlerotation (spin)

Sliding onthe disc : theoretical shouldbe220->DEM simulationshows liftingof

particle,probablyduetoconservationof spperpendicular tovane

140





Conclusions:1.DEM shows a general verygoodagreemparticle situations

2.Tangential contact propertiesshouldbeverified(->liftingof particle??)




2. Multi particlesystem

-Difference with 1-particle :- Conical disc

- 2 or more vanes

- Vanes with border are nee

- Multiple collisions involved

- Feeding of the spreader (b





- Conical disc

- 2or more vaneswithborder

Cylinders on the vane edges to incorporate random





- Multiple collisions

Computationtime#Particles

Useof efficientcontact detectionalgorithmsis requ




2.Multi particlesystem

Feeding : fill-up of a beam

In steadof a bin, the particlesstart froma beamwhichhasthe sameshapeonitsbase asthe orificeof the bin




2.Multi particlesystem

Feeding : adjustableinput flow(kg/s)

Gravity

No Gravity

Constant speed V

Randomvelocitycomponentsadded

Flow(kg/s) = V x (particledensity) x

orifice




2.Multi particlesystem: measurement

Model validation:1. Spread patternmeasurements




2.Multi particlesystem: measureme

Summaryof the experimentDomestic fertilizer

Domesticcentrifugal spreader

Disc radius : 0.15m

Discspeed : 400rpmBasket resolution : 0.25m X 0.25m

Number of baskets : 14

Amountof fertiliser per basket-line: 1.5kg

Particleflow : 0.1kg/s




2.Multi particlesystem: measureme

0.5m

1m

1.5m

spreader




2.Multi particlesystemsimulationresu

Longitudmeasurement

simulations0.5m,1m and 1

disc




Multi particlesystem

2. Mini tester bin

Collector tray




0°

90°

vanes270°

Particlefeedingarea


collector





Cilindrical plots




simulation





Conclusions-Thereis a goodagreementof Dsimulationswithexperiments




steel plate



When the particles are released on the disc, they are thrown away by the vanes and collected by a tray of baskets, which is 3.5m long and consists of 14 baskets of 0.25m x 0.25m. This collecting tray can bereplaced to obtain information about the spread pattern at different locations from the disc (see figure1,left).

Each experiment consists of releasing 1500g of fertiliser on the spinning disc. The flow rate of the particlesthrough the bin is constantly kept at 0.1 kg/s. This experiment is repeated for 3 times for 3 differentdistances (1.5m, 1m and 0.5m) from the disc in order to have an idea of the static spread pattern.

3. Simulations

In the simulations, 10000 spherical particles are used with the same particle distribution, representing atotal mass of 150g and using the same flow rate. Although the total particle mass is 10 times less than inthe experiment, it was investigated that introducing more particles in the simulation has little effect on theresult. The trajectory through the air was calculated by simple ballistics, using an air resistancecoefficient of 0.5.Using an efficient contact detection algorithm, one simulation typically takes 30.000 seconds andrepresents 1 second of real time.

4. Conclusions

Figure 1 (right) shows a reasonable agreement between simulation and experiment, especially in aqualitative way. Anyway, a discrete element model might provide interesting information about how aspread pattern behaves when different geometry is introduced for the spreader without having to do any experiments. It might also be used as an optimization tool to obtain better spread patterns.

5. References

Kuwabara G; Kono K (1987) Restitution coefficient in a collision between 2 spheres. Japanese Journal of

Applied Physics 26(8):1230-1233

Schäfer J; Dippel S; Wolf D E (1996). Force Schemes in simulations of granular materials. Journal dePhysique (France), 6, 5-20

Van Liedekerke P; Tijskens E; Ramon H (2006). A discrete element model for centrifugal spreaders. I:single particle simulations. Powder Technologie (in press)

a discrete element model for simulation of a spinning disc fertilizer spreader

Documents