A Numerical Study for Air Flow from Ejector Nozzle of Sorting
Machines Using Smoothed Particle Hydrodynamics
Tomoyuki Miyamoto 1, So Noguchi 1, Shinya Matsutomo 2121

Graduate School of Information Science and Technology, Hokkaido University, Japan

Department of Electronic Control Engineering, Niihama National College of Technology, Japan

Introduction

In this paper, we discuss the fundamental simulation data ofa Sorting Machine for optimum planning, effective designingand cost-reduction. Accurate sorting of particulates is afundamental problem in the Sorting Machine. Providing theaccurate sorting is of high quality, sorted products command aconsiderably higher price than unsorted ones. In the sortingmachine, a camera with high-detection capability and an ejector
to exactly remove undesired particles are required. However, it
should be avoided that the ejector removes a good particle inorder to provide high sorting ratio. We would like to understandthe behaviour of air flow ejected from an ejector nozzle in theSorting Machine for effective designing. In this study, anumerical simulation was carried out with the three-dimensional
Smoothed Particle Hydrodynamics (SPH) in order to highly
accurately reproduce the behaviour of the air flow ejected fromthe ejector nozzle in the Sorting Machine.

including symmetry of forces and conservation of momentum.
The reference [2] also solves the problem related with the SPH.
Using particle-based simulation simplifies the solution ofNavier-Stokes equations. The reason is that the number and themass of particles are constant and the mass conservation isguaranteed. Therefore the mass conservation equation can beomitted.
Based on the simplified Navier-Stokes for the accelerationof particle i we can get:

22.2

Smoothed Particle Hydrodynamics Approach

2.1

Modelling Fluids Using Particles
The SPH is an interpolation method for fluid motion
simulation [1]. The SPH deals with field quantities defined onlyat discrete particle locations and can evaluate them anywhere inspace. In the SPH the field quantities are distributed in a local
neighbourhood of the discrete locations with sphere symmetricalsmoothing kernels.
A scalar value A is interpolated at location r with a weighted
sum of contributions from the particles:A ( r )= ∑ m jja i=where ⃗v i is the velocity of particle i, fi and ρi are the force
density field and the density field at the location of particle i,respectively.
Modelling Force Fields
Instead of an equation described by the SPH rule a modified
solution is used for pressure force because it guarantees thesymmetry of forces:
f pressure=− ∑ m jij

ρ ( r )=∑ m j W ( r −r j ,h ) .
jWith the SPH approach the derivatives affect only thesmoothing kernel. A problem of the method is that theseequations are not guaranteed to satisfy some physical rulesρ2iPj+ρ 2j)∇ i W ( ri −r j ,h ) .

p=kρ
where k is the gas constant that depends on the temperature.
Applying the SPH rule to the viscosity term also yields toasymmetric forces because the velocity field varies. The idea ofsymmetrizing the expression applies the velocity differences:( )(f viscosity=μ ∑ m jij∫ W ( r ) dr= 1 .
Because mi = m (constant) in our case, we can evaluate thedensity at every step using a modified equation based on [2]:(PiThe pressure at particle location has to be computed first, it
can be computed via the ideal gas equation:

AjW r−r j ,h )ρj (where j represents the number of all particles in the scene, mj is
the mass of particle j, rj the position, ρj the density, and Aj thefield quantity at rj, respectively. The function W(r,h) is calledsmoothing kernel with core radius h. The kernel is normalized
withd ⃗v i f i=dt
ρi

33.1v j −v iρi ρ jr j −r i∣r j −r i∣2)

∇ i W ( ri −r j ,h ) .

Agenda DetailsSorting Machine
A rice processing equipment commonly has an Sorting
Machine. The Sorting Machine is the machine that sorts
discolored rice and foreign material like a stone and a glass byrecognizing with a high-performance camera, and blows away
the foreign particle with an ejector like an air-gun. Fig. 1 shows
the schematic view of the Sorting Machine. There are three
processes in the equipment. First, the material is supplied with achute. Second, good particles or bad particles are recognizedwith the high-performance camera. Third, the unwanted
particles are sorted with the ejector.
The evaluation points of Sorting Machine are the quality ofproducts, the amount of throughput, and yield rate. High-quality
products are sellable at high price. Increase in the amount ofprocessing increases the production and reduces the runningcost. The high yield rate reduces the product loss.

References[1]

R.A. Gingold, J.J. Monaghan, Kernel estimates as a basis forgeneral particle methods in hydrodynamics, Journal ofComputational Physics, Volume 46, pp.429-453, 1982
M. Müller, D. Charypar, M. Gross, Particle-Based Fluid
Simulation for Interactive Applications, SIGGRAPH/Eurographics
Symposium on Computer Animation, pp.154-159, 2003

[2]

OFFMaterial Hopper

ON

Compressed Air2mm

Chute

Measuring Point ofPressure Sensor

FeederLamps
CoilEjector Nozzle

EjectorCamerasExperiment System

Signal Processor

Ejectors
Rejects Accepts

Compressed AirahbicjdkelfmgnFig. 1. Schematic View of Sorting Machine.
3.2

Subject Outline
In the Sorting Machine, a higher value can be added toexisting impressive machines if there are ways to 1) increase theamount of throughput by raising particle packing density andspeed, 2) reduce to wrongly reject good particles with theejector. To achieve both 1) and 2), the air flow ejected from theejector nozzle should be improved. It requires a straight flow, asharp ON-OFF switching and an adequate pressure.
3.3

Simulation Model
As a simulation model for validation in order to reproduce
the behaviour of the air flow from the ejector nozzle in Sorting
Machine with the SPH, we have simulated a characteristic event(shown in Fig. 2). Fig. 2 shows the images captured with aschlieren photography and the waveform measured with apressure sensor. It was clarified that one jet operation on theejector produced twice the air flow from the ejector nozzle.
Incidentally, we will be able to understand the mechanism of
this behaviour. It will be a very valuable knowledge to develop a
new Sorting Machine efficiently.
4

Experimental Result by Schlieren Photography

Conclusiona b c d e fg h i j k lmn

In this study, the numerical simulation was carried out withthe three-dimensional Smoothed Particle Hydrodynamics basedon the characteristic event for validation in order to highlyaccurately reproduce the behaviour of the air flow from theejector nozzle in the Sorting Machine. We will figure out that
the SPH is effective in the development of the Sorting Machine.
Moreover, the details of the results will be represented in the fullpaper.
In future prospects, we will discuss an effective designing toimprove the behaviour of the air flow from the ejector nozzle inthe Sorting Machine.
Acknowledgements
We appreciate that SATAKE Corporation has suggested thesubject of this research and provided the valuable information of
the air flow from the ejector nozzle.

Flow from
Ejector Nozzle
ON-OFF of
Ejector00.001

0.002

0.003

0.004

0.005

0.006

0.007

Time[sec]

Experimental Result by Pressure Sensor
Fig. 2. Simulation Model.

0.008