CONTACT TIME IN GRANULAR MEDIA

Smruti Vaidya

Reportnumber: WET 2007.09

Supervisors:

M.S.Abd-Elhady

C.C.M.Rindt

Eindhoven University of Technology

Department of Mechanical Engineering

Division Thermo Fluids Engineering

Section Energy Technology

1

Contents

1 Introduction 2

2 Experimental work 3

2.1 Experimental setup………………………………………………………… 3

2.2 Experiments performed and experiments results……………………….. 5

2.2.1 Experiments performed with soda lime glass balls………………… 5

2.2.1.A Experiments performed with rectangular bed……………. 5

2.2.1.B Experiments performed with hexagonal bed………………. 6

2.2.2 Experiments performed with glass marbles………………………... 8

3 Discussions of results 9

3.1 Results of experiments with soda lime glass balls………………………….. 9

3.2 Results of experiments with glass marbles…………………………………. 10

3.3 Comparison of contact time for glass particles and steel particles………... 10

4. Conclusions 12

Bibliography 13

Appendix A 14

2

Chapter 1

Introduction

Particulate fouling of heat exchangers is one of the major problems in the field of heat

transfer. Particulate fouling is defined as the accumulation of particles on a heat transfer

surface that form an insulating powdery layer, which reduces the rate of heat transfer and

can lead to operation failure [1]. Particulate fouling of heat exchangers is related to

particle aggregation, that is, a collection of many particles such as granular material and

powder. Removal of fouling layers by externally injected particles becomes an important

issue of study. Particle-particle collision is now fairly well understood [2], but the

mechanics of collision involving more than two particles has not yet been fully revealed

[3-4]. The removal of particles from fouling layers due to an incident particle impact can

be affected by the fluid fluctuations in industrial application if the contact time is larger

than the fluctuations time scales [8]. The contact time becomes an important parameter

when analyzing the influence of the fluid structure interaction on a fouling process.

Granular aggregates like sand, grains, rubble, ore and others, usually treated in mechanics

as continuous materials [5], but actually it is discontinuous or discrete behavior when

subjected to static or dynamic stress or strain [7]. Wave propagation in granular media

differs considerably from classical wave propagation in continuum mechanics because of

the peculiar structure of granular materials. Dynamic load transfer in granular media

occurs essentially through contact mechanism between each grain [6-7]. This

phenomenon depends inherently on micro structural packing arrangement of media. [6].

Dynamic load transfer depends on angles made by the normal at the contact points of two

adjacent granules [6]. If angle made by the normal is acute, no load transfer would take

place [6]. It is also depends on the ratio of elastic properties of granules and the filler

material and on the geometric structure [7].

The contact time for a particle hitting a bed of particles is defined as the time taken by the

incident particle to bounce off the target particle of bed. The contact time is calculated

from the instance when the incident particle reaches the bed till it ejects out of the bed. It

can be determined experimentally and numerically based on the discrete element method.

Here it is determined experimentally. The experimental setup, experiments performed

and experimental results are presented in chapter 2. Discussion of results and conclusions

are given in chapters 3 and 4.The rectangular and hexagonal beds of particle are chosen

as a preliminary step towards the understanding of the dynamic properties of randomly

arranged particulate aggregation, which is commonly found in practical granular material.

3

Chapter 2

Experimental work

2.1 Experimental setup

The set-up consists of (a) a thin transparent Perspex container that contains the bed of

particles, (b) a shooting mechanism to shoot the incident particle on the bed of particles,

and (c) a measuring system (High Speed Camera) to record the motion of the incident

and target particles. In Figure.1 a schematic presentation of the experimental setup is

presented.

(a)

(b)

Figure. 1: (a) Schematic representation of the experimental setup.

(b) Schematic representation of shooting mechanism (control valve).

The incident particle is shot on the bed particles with a fire mechanism. This mechanism

consists of a control valve, i.e. a 3-way valve, and a nozzle. The control valve is

4

connected to a compressed air connection, a vacuum connection and to the nozzle, as

shown in figure. 1.b. The vacuum connection is used to hold the incident particle against

the nozzle. When the control valve is operated the nozzle gets in contact with the

compressed air connection and the particle is shot on the bed of particles. When the

particle leaves the nozzle an air jet will travel behind the particle due to the compressed

air connection. To reduce the amount of air that travels behind the particle the control

valve is closed immediately after the release of the particle, via an electronic circuit, that

operates the control valve. The speed at which the particle leaves the nozzle is dependent

on the pressure of the compressed air. The velocity of the incident particle at the point of

impact could be increased either by increasing the pressure of the compressed air or the

height from which the particle is dropped.

The Perspex container is equipped with a movable back wall. Spacers are used to adjust

the width of the container to the diameter of the particles in the set-up. The distance

between the front and the back wall of the container are adjusted to be 0.2 mm bigger

than the diameter of the particles, to make sure that the particles can freely move after

impact.

The impact of the incident particle with the bed of particles is recorded using two high-

speed camera: (1) Phantom v7.1 high speed CMOS camera, with a recording rate of 30

up to 140,000 frames per second and (2) KODAK EKTAPRO HS Motion Analyzer,

Model-450, with record rate of 30 to 4500full frames per second and 9000 to 40500

segments frames per second. The camera is positioned in front of the perspex container.

The lighting of the set-up is obtained via a light source that comes from the backside of

the set-up, in order to prevent disturbing scattering of the light in the camera. The

measuring technique used is known as the shadowgraph technique [9], where the moving

object to be tracked becomes dark and the surroundings become white.

In Figure 2 typical recorded image is represented. In recorded picture the incident

particle and the bed particle are easily distinguish.

Figure: 2. Typical recorded image of experiments. The camera used is KODAK

EKTAPRO HS Motion Analyzer, Model-450.

Incident particle

Target particle

5

2.2 Experiments performed and experimental result.

Experiments are performed with two different types of particles:(1) glass marbles with a

diameter of 25mm and (2) soda lime glass balls with a diameter of 22.2mm.

2.2.1. Experiments performed with soda lime glass balls.

An incident particle hits a rectangular and a hexagonal bed of particles. The incident

particle hits the middle particle of the bed top layer and this particle is considered as the

target particle. In the first set of experiments the incident particle hits a rectangular bed of

particles of 5×1×n particles, where n is the number of layers and it varies between 1, 3

and 5 and in the second set the incident particle hits a hexagonal bed of particles of

10×1×3 particles and 10×1×5 particles.

2.2.1.A. Experiments performed with rectangular bed.

The experimental results of an incident particle hitting a rectangular bed of particles of

5×1×1 particles are shown in Figure.3. The incident particle impact speed is 3.15 m/s.

The target particle is the middle-top particle in the bed of particles. The incident particle

and the bed particles are made of soda lime glass of diameter 22.2 mm.

The images shown are for the incident and the target particles. The scanning rate of the

camera is 47,000 frames per second and the resolution of each image is 256×128 pixels.

The time between two successive frames is 2.128e-5 s. It can be seen from fig. 3 that the

incident particle approaches the target particle from frame 11220 to frame 11233. At

frame 11233 the incident particle gets in contact with the target particle. The incident

particle stays in contact with the target particle from frame 11333 to frame 11244 and

from frame 11245 the incident particle bounces off the target particle. Therefore the

contact time is equal to (frame 11245-frame11233)/47000 i.e. 2.55e-4s.

The complete behavior of incident and target particle is mentioned below.

The incident particle approaches the bed particle in a, b, c, d. The incident particle gets in

contact with the target particle in e, The incident particle stays in contact with target

particle in f,g,h .The target particles moves downwards in i,j and k .The target particle

moves upward in l and m , and hits the incident particle in n,o and p, and from q the

incident particle bounces off the target particle. From figure 3, it look likes from frame i

incident particle bounces of the target particle but actually target particle is fluctuate from

frame i till p and bounce off the target particle from q.

6

a.Frame:11220 b.Frame:11223 c.Frame:11225 d.Frame:11230

3.2.1.B Experimen

e. Frame:11233

(Beginning contact) f.Frame:11234 g.Frame:11235 h.Frame:11236

i.Frame:11237 j.Frame:11238 k.Frame:11239 l.Frame:11240

m.Frame:11241 n.Frame:11242 o.Frame:11243 p.Frame:11244

qFrame:11245

(End of

contact) r.Frame:11246 s.Frame:11250 t.Frame:11255

ntact

Fig. 2. An incident

Figure.3 Images of incident particle hitting a target particle in a rectangular bed of

particles. The camera used is Phantom v7.1 high speed CMOS camera.

2.2.1. B. Experiments performed with hexagonal bed.

The Experimental results of an incident particle hitting a hexagonal bed of particles of

10×1×3 particles are shown in Figure.4. The incident particle impact speed is 2.8 m/s.

The target particle is the middle-top particle in the bed of particles. The incident particle

and the bed particles are made of soda lime glass of diameter 22.2 mm.

The images shown are for the incident and the target particles. The scanning rate of the

camera is 68,000 frames per second and the resolution of each image is 256×64 pixels.

The incident particle approaches the target particle from frame 24570 to frame 24583.At

7

frame 24583 the incident particle hits the target particle. The incident particle is in

contact with the target particle from frame 24583 to frame 24595, and from frame 24596

the incident particle bounces off the target particle. Therefore contact time is equal to

(frame 24596-frame 24583)/68000 i.e. 1.91e-4s.

The incident particle approaches the bed of particles in a,b and c, the incident particle

hits the target particle in d and keeps contact with the target particle until frame h, and

from i the incident particle bounces off the target particle.

a. Frame:24570 b.Frame:24575 c.Frame:24780 d.Frame:24583

(Beginning of contact)

e.Frame:24584 f.Frame:24585 g.Frame:24594 h.Frame:24595

i.Frame:24596 j.Frame:24597 k.Frame:24620 l.Frame:24630

(End of Contact)

Figure. 4: An incident particle hitting a target particle in a hexagonal bed of particles. The

camera used is Phantom v7.1 high speed CMOS camera.

The above two experiments (2.2.1A and 2.2.1.B) are repeated for beds of different

number of layers and for different particles arrangements and the results are summarized

in Table 3.1.

8

2.2.2 Experiments performed with glass marbles.

The Experimental results of an incident particle hitting a rectangular bed of particles of

5×1×3 particles are shown in Figure. 5. The images shown are for the incident and the

target particles. The scanning rate of the camera is 4500 frames per second. The incident

particle impact speed is 2.47 m/s. The incident particle approaches the target particle

from frame 2799 to frame 2801.At frame 2801 the incident particle hits the target

particle, for frame 2801 and 2802 the incident particle is in contact with the target

particle, and from frame 2803 the incident particle bounces off the target particle.

The incident particle approaches the bed of particles in a, the incident particle hits the

target particle in b and keeps contact with the target particle until frame c, and from d the

incident particle bounces off the target particle.

a.Frame:2799 b.Frame:2801 c.Frame:2802 d.Frame2803

Beginning of Contact End of Contact

Figure.5: An incident particle hitting a target particle in a rectangularl bed of particles.

The camera used is KODAK EKTAPRO HS Motion Analyzer, Model-450.

The above experiment is performed with different compressed air pressure (3 bar and 6

bar) and with different scanning rate of camera. The results are summarized in Table3. 2.

9

Chapter 3

Discussion of results

3.1Results of experiment with soda lime glass particles:

Contact time for different type of bed is shown in Table 3.1. We can say that contact time

of an incident particle hitting a bed of particles is a function of the number of bed layers

and the particles arrangement.

Table3.1: Contact time as a function of Bed Type and impact speed. (Particle: soda lime

glass)

Bed Type Impact Speed (m/s) Contact Time(s)

Rectangular Bed 5x1x1 3.15 2.55e-4

Rectangular Bed 5x1x3 2.5 4.25e-4

Rectangular Bed 5x1x5 2.38 5.74e-4

Hexagonal Bed 10x1x3 2.8 1.91e-4

Hexagonal Bed 10x1x5 2.67 1.91e-4

It is found that the contact time is proportional to the number of bed layers in case of a

rectangular bed array and independent of the number of bed layers incase of a hexagonal

bed of particles. Wave propagation in a rectangular arrangement of particles occurs in a

single chain when the impact is on the top of the target particle. Wave propagation in a

rectangular and a hexagonal bed of particles are illustrated in Figure. 6 as have been

measured and found by Shukla and Zhu [6] The incident particle bounces off the bed of

particles when the wave propagation is reflected backwards to the incident particle, so the

longer the chain is, i.e. the number of layers, the longer the contact time becomes.

However, in case of a hexagonal arrangement of particles the wave propagation occurs in

two dimensions. The load transfer in this case can be categorized by two distinct chains:

the primary chain, chains a and b in fig. 6.b, and the secondary chains which emanate due

to contact of other particles with the particles in the primary chain. The wave propagation

is transferred back to the incident particle due to the particle in the secondary chain,

irrespective of the primary chain. Therefore, the contact time for a particle hitting a

hexagonal bed of particles is independent of the number of bed layers, i.e. the length of

the primary chain.

10

(a) (b)

Figure. 6. Path of wave propagation in a rectangular (a) and a hexagonal (b) bed of

particles. Adopted from Shukla and Zhu [6].

Particles in a hexagonal bed of particles act as if they have a mass larger than their actual

mass, this could be due to their large co-ordination number that is 6, i.e. each particle is

in contact with six other particles.

3.2 Results of experiments with glass marbles:

Contact time for different compressed air pressure is shown in Table.3.2.

Table 3.2:Contact time with different pressure

Bed Type Impact Speed (m/s) Compressed Air

Pressure (bar)

Contact time(s)

Rectangular Bed

5x1x3

2.47 6 4.44e-4

Rectangular Bed

5x1x3

2.43 3 4.44e-4

From Table 3.2 we can say that contact time remains same for different pressure. For

small particles contact times get affected with different pressure but for particles, which

we used, is of diameter of 22.2mm and 25mm. Therefore for such a big particle contact

time remains same with different pressure.

3.3 Comparison of contact time for glass particle and steel particles.

In Table 3.3 contact time for glass particles and steel particles [10] is summarized. From

table 3.3 we can see, for both glass particles and steel particles we get same conclusion.

Contact time is increases as number of bed layer is increases in case of rectangular bed

array, and it remains same in case of hexagonal bed array.

11

Table 3.3: Comparison of contact time for glass particles and steel particles

Glass Particles Steel Particles

Bed Type Impact

Speed (m/s)

Contact

Time(s)

Bed Type Impact

Speed (m/s)

Contact

Time(s)

Rectangular

Bed 5x1x1

3.15 2.55e-4 Rectangular

Bed 5x1x1

3.12 2.6e-4

Rectangular

Bed 5x1x3

2.5 4.25e-4 Rectangular

Bed 5x1x3

2.7 4.04e-4

Rectangular

Bed 5x1x5

2.38 5.74e-4 Rectangular

Bed 5x1x5

2.56 5.1e-4

Hexagonal

Bed 10x1x3

2.8 1.91e-4 Hexagonal

Bed 5x1x3

3 1.06e-4

Hexagonal

Bed 10x1x5

2.67 1.91e-4 Hexagonal

Bed 5x1x5

2.84 1.06e-4

12

Chapter 4

Conclusions

Experiments are performed to determine the contact time of a particle hitting a

rectangular and a hexagonal bed of particles. We can conclude that contact time of an

incident particle hitting a bed of particles is a function of the number of bed layers and

the particles arrangement .It is found that the contact time is proportional to the number

of bed layers in case of a particle hitting a rectangular bed of particles. It is also found

that the contact time of a particle hitting a hexagonal bed of particles is independent of

the number of bed layers. Particles in a hexagonal bed of particles act as if they have a

mass larger than their actual mass, this is due to their large co-ordination number, and the

whole bed acts as a massive particle.

13

Bibliography

[1] M.S. Abd-Elhady, C.C.M. Rindt, J.G. Wijers, A.A. van Steenhoven, Influence of

sintering on the growth rate of fouling layers, International Journal of Heat and Mass

Transfer, vol. 50(1-2), pp. 196-207, 2007.

[2] C. Thornton and Z. Ning, A theoretical model for the stick/bounce behavior of

adhesive, elastic-plastic spheres, Powder Technology, vol. 99, pp. 154-162, 1998.

[3] B.K. Mishra, C. Thornton, Impact breakage of particle agglomerates, International

Journal of Mineral Processing, vol. 61, pp. 225-239, 2001.

[4] D.T. Spasic, T.M. Atanackovic, A Model for three spheres in collinear impact,

Archive of Applied Mechanics, vol. 71, pp. 327-340, 2001.

[5] F. Froiio, G. Tomassetti and I. Vardoulakis Mechanics of granular materials: The

discrete and the continuum descriptions juxtaposed, International Journal of Solids and

Structures Volume 43, Issues 25-26, December 2006, Pages 7684-7720

[6] A.Shukla,C,Y.Zhu, Influence of the microstructure of granular media on wave

propagation and dynamic load transfer, Dynamic Photomechanics Laboratory,University

of Rhode Island, Kingston,RI02881

[7] H.P. Rossmanith, A. Shukla, Photoelastic investigation of dynamic load transfer in

granular media, Acta Mechanica, vol. 42, pp. 211-225, 1982.

[8] M. Lesieur, Turbulence in Fluids, Kluwer Publishers, Dordrecht, 1990.

[9] G.S. Settles, Schlieren and shadowgraph techniques – visualizing phenomena in

transparent media, Heidelberg, Germany: Springer Verlag; 2001.

[10] M.S. Abd-Elhady, C.C.M. Rindt and A.A. van Steenhoven Contact time in granular

matter. To be submitted to powder technology.

14

Appendix A

Properties of Soda Lime Glass

Thermal/ Mechanical Properties

Thermal Conductivity: 0.937 W.m/m² °C

Density (at 20º C/68 ºF): 2.44 g/cm³

Hardness (Moh's Scale): 6 - 7

Knoop Hardness: 585 kg/mm2 + 20

Modulus of Elasticity (Young's): 7.2 x 1010 Pa

Modulus of Rigidity (Shear): 3.0 x 1010 Pa

Bulk Modulus: 4.3 x 1010 Pa

Poisson's Ratio: 0.22

Specific Gravity: 2.53

Specific Heat: 0.21

Specific Weight: 2,483 g/cm³

Thermal Coefficient of Expansion (0/300 °C): 8.6 x 10 -6/°C

Softening Point: 726°C/1340°F

Annealing Range: 546°C/1015°F

Strain Point: 514°C/957°F

Failure Strength: 70 MPa/10,000 psi

Chemical Composition:

SiO2----65%, Na2O---16%, CaO---7%, Al2O3---5%, B2O3---3%, MgO---2%

15