Viability study of an energy-recovery system for belt conveyors

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Delft University of Technology Department Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

This report consists of 77 pages and 1 appendix. It may only be reproduced literally and as a whole. For commercial purposes only with written authorization of Delft University of Technology. Requests for consult are only taken into consideration under the condition that the applicant denies all legal rights on liabilities concerning

Specialization: Transport Engineering and Logistics

Report number: 2013.TEL.7747

Title:

Viability study of an

energy-recovery system for belt

conveyors

Author:

M.C. de Graaf

Title (in Dutch) Haalbaarheids studie van een energie-terugwin-systeem voor transportbanden

Assignment: Research assignment

Confidential: no

Initiator (university): prof.dr.ir. G. Lodewijks Initiator (company): -

Supervisor: prof.dr.ir. G. Lodewijks

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Delft University of Technology Department of Marine and Transport Technology Mekelweg 2 2628 CD Delft the Netherlands Phone +31 (0)15-2782889 Fax +31 (0)15-2781397 www.mtt.tudelft.nl

Student: M.C. de Graaf Assignment type: Research

Supervisor (TUD): Prof.dr.ir. G. Lodewijks Creditpoints (EC): 15

Supervisor (Company) - Specialization: TEL

Report number: 2013.TEL.7747 Confidential: No

Subject: Design of Energy Recovery Systems for Belt Conveyors

Materials transported by continuous conveying systems, have, depending on the speed of travel, a high – energy content. At transfer points from one belt conveyor to another, or at the discharge points from a conveyor to a storage area, or to a discontinuous conveying system, it is possible to recover most of this energy and return it to the conveying system.

An energy recovery system can be designed based on the concept of a material driven turbine. In this system, a turbine is installed at the discharge point of a belt conveyor. The material is discharged from the conveyor into the rotating turbine. The turbine converts the kinetic and the potential energy of the moving bulk material into mechanical power. To transfer the mechanical power to the conveying system a chain drive connects the turbine directly to the drive pulley of the conveyor.

The system described above has been presented on a conference by two employees of the University of Leoben in Austria and they are currently conducting measurements on a test facility. There are however some doubts about the usefulness and feasibility of this concept.

This assignment is to investigate such an energy recovery system. Insight into the purpose of the system needs to be given as well as technical problems and proper solutions. The outcome of this analysis combined with the economical viability should lead to a clear conclusion concerning the feasibility of this concept.

The report should comply with the guidelines of the section. Details can be found on the website. The mentor,

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Preface

This report is a research assignment which is a standard part of the curriculum for the master study Transportation Engineering and Logistics, and thus is conducted in the name of the Department of Transportation Engineering at the faculty of 3Me of the Technical University of Delft.

This report discusses a technical subject and is intended for engineers interested in, or involved in, the concept under consideration. Attempts have been made to write this report in such a way that also readers with a limited knowledge about these subjects can read it, but at least a basic understanding of the principles of mechanical engineering is assumed to be known.

Personally I would also like to use this opportunity to thank my supervisor Prof. dr. ir. G. Lodewijks for his guidance and advice during this thesis.

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Summary

Modern society largely depends upon conveyor belts. Men use these devices every day, often without even realizing it. They are for instance used to transport coal from mines to power plants, powering the world. This application has resulted in very large, long and powerful systems consisting of several conveyor belts. The power required to drive all these belts is however quite substantial. In order to reduce the energy required to drive these systems a new promising development was recently presented on a conference in Germany. In the paper that was presented here the possibility was investigated whether or not a solid state material driven turbine connected to the conveyor belt could reduce the power that had to be absorbed from the net.

The purpose of this report has been to investigate and determine whether or not this concept is viable. Although the idea is basically hundreds of years old dating back to the water wheel, no prior research could be found. Initially the concept seems to be very promising since for smaller conveyor systems it could save up to about 50% of the energy requirements. Not every system might be best suited for the application of this concept though. Observing the available space and the behavior of the material under the given operating conditions could indicate some issues which will lower the efficiency of the turbine. Determining the location and shape of the turbine is fairly easy with the use of several equations which have already proven their validity in other applications. The same is true for the transmission. Once the desired drive is selected the required ratio and strength (torque) can be determined either manually or with the help of DEM programs (recommended). In the ideal situation the design process would end here and the turbine is ready to be build and installed. In real life this ideal situation doesn’t exists though and problems occur when the conveyor belts operating conditions vary (even slightly). Many of these varying operating conditions can be expressed as a varying belt speed, which is the biggest problem. A varying belt speed namely result in both a different discharge trajectory, which means the turbines location has to be altered, as well as a different required transmission ratio. These problems are responsible for the fact that when a direct coupling is desired a CVT has to be used, or a detached coupling has to be used. Both of these solutions are more expensive then the simple direct coupling solutions. Nevertheless this is almost irrelevant because the price of all these systems is negligible compared to the costs of the wear tiles which protect the turbine.

The high price of these tiles combined with the little savings made by the turbine as a result of the low price for electricity lead to the conclusion that this concept is not economically viable. Companies might still want to consider this concept in order to become more sustainable and reduce their electricity usage but they have to keep in mind that this solution costs more money than it generates. Since it is a shame to immediately write off an ecologically promising concept like this because of the economical issues, it is recommended that the results regarding wear of the test facility set up by the authors of the original paper are analyzed carefully. These results should then be used to optimize the turbine shape in cooperation with a manufacturer of wear tiles so that the economical downside to this concept might disappear.

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Summary (in Dutch)

De huidige maatschappij is sterk afhankelijk van het gebruik van transportband systemen. Hoewel men dit vaak niet door heeft, maakt iedereen hier dagelijks gebruik van. Zo worden deze systemen gebruikt om kolen uit de mijn naar de energie centrale te transporteren, waar deze worden omgezet in stroom. Deze toepassing heeft geresulteerd in zeer grote, lange en krachtige systemen bestaande uit meerdere transportbanden. Deze systemen vragen echter veel energie. Om energie te besparen is onlangs een nieuw concept gepresenteerd op een conferentie in Duitsland. De gepresenteerde paper onderzocht de mogelijkheid om met een bulk materiaal aangedreven turbine verbonden met de transportband de energie opname van de transportband van het energienet terug te dringen.

Het doel van dit verslag is om te beoordelen of het hierboven beschreven concept realiseerbaar is. Hoewel het idee zelf al honderden jaren oud is, daterend tot aan het waterrad, konden er geen eerdere onderzoeksresultaten gevonden worden. Op het eerste gezicht is het concept veelbelovend aangezien de energie besparing voor kleine systemen kan oplopen tot wel 50%. Niet elk systeem is echter even geschikt voor dit concept. De beschikbare ruimte en hoe het materiaal zich in de turbine gedraagt kan namelijk het rendement van de turbine verlagen. Het bepalen van de locatie en de vorm van de turbine is vrij gemakkelijk te doen door formules toe te passen die al gevalideerd zijn in andere toepassingen. Hetzelfde geldt voor de overbrenging. Nadat een keuze voor de soort overbrenging is gemaakt kunnen de verhouding en het koppel handmatig worden bepaald, of met behulp van een EEM programma (aanbevolen). In een ideale situatie zou de ontwerpcyclus hier stoppen en de turbine gebouwd en geinstalleerd kunnen worden. In de realiteit bestaat deze ideale situatie echter niet en treden er problemen op doordat sommige parameters (lichtelijk) in grote variëren. De meeste van deze varierende grootheden kunnen worden beschouwd als een variatie van de bandsnelheid, welke het meest zorgelijk is. Een varierende bandsnelhied resulteert namelijk in zowel een veranderende baan van het materiaal, welke een andere positie van de turbine vereist, alsmede mogelijk een andere overbrengingsverhouding. Deze problemen leiden ertoe dat een directe transmissie alleen werkt met een CVT, of dat er een onafhankelijke transmissie moet worden gebruikt. Deze beide opties zijn duurder dan de simpelere directe transmissies. Dit is echter niet van groot belang aangezien de prijs van alle opties verwaarloosbaar is ten opzichte van de kosten van de slijtage-tegels die de turbine beschermen.

De hoge prijs van de slijtage-tegels vergeleken met de lage besparingen die de tubine opbrengt als gevolg van de lage electriciteits kosten leidt tot de conclusie dat dit concept niet economisch haalbaar is. Bedrijven kunnen echter nog altijd overwegen om dit concept toe te passen om zo hun ecologische

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List of symbols

Symbol Quantity Unit

a Constant -

e Eccentricity m

er Restitution factor -

f Coefficient of friction -

g Gravitational acceleration m/s2

h Height centre of mass bulk material m

hd Material height m

i Transmission ratio -

l(C/R) Idler spacing carry/return side m

m

 _{Mass flow} _kg/s

m’G Mass of belt per meter kg/m

m’L Mass of bulk per meter kg/m

m’R Mass of idler rolls per meter kg/m

m’RC Mass of idler roll carry side kg

m’RR Mass of idler roll return side kg

m”D Mass of belt rubber kg

m”Z Mass of belt carcass kg

n Constant -

q Distributed force N/m

t Time s

t(B/T) Thickness of bottom/top cover m

u Turbine speed m/s

v speed m/s

v0 Initial speed m/s

v(1/2) Speed after impact m/s

vb Belt speed m/s

ve(x/y) Speed of material after spoon (horizontal/vertical) m/s

vx(0) (Initial) Horizontal speed m/s

v(x/y)c (Horizontal/Vertical) Speed at point c m/s

vy(0) (Initial) Vertical speed m/s

x Horizontal coordinate/distance m

y Vertical coordinate m

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A Area m2

B Belt width m

C Coefficient between FN and FH -

Ci Integration constant -

D Diameter m

E Impact energy per cycle J

Ekinetic Kinetic energy J

Epotential Potential energy J

F Force N Fd Filling degree - FH Main/primary resistance N FN Side/secondary resistance N FS Special resistance N FSt Gradient resistance N H Height m Ha Hardness N/m2 K Wear constant/coefficient - L Length m M Mass kg N Number of cycles - NWB Belt wear - P Power W

PTr Power required for steady state conveyor operation W

Q Volume rate of flow m3_/s

Qm Conveyor capacity MTPH

Qt Turbine capacity kg/r

R Pulley radius m

Rc Radius of material centroid m

Rt Radius of the turbine m

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α

Inclination angle ⁰

α

d Discharge angle ⁰

α

r Angle at which slip begins to occur ⁰

β

Angle side roller ⁰

γ

Specific gravity of bulk solid kNm-3

δ

Inclination angle ⁰

ε

Angle due to shape change of belt ⁰

η

Efficiency -

θ

(1/2) Angle of impact/rebound ⁰

θ

e Angle between ve and vey ⁰

λ

Angle of repose ⁰

μ

Coefficient of friction -

μ

k Coefficient of kinematic friction -

μ

s Coefficient of static friction -

μ

b Coefficient of friction between belt and material -

ρ

Density kg/m3

ρ

r Density of rubber kg/m3

σ

a Adhesion stress kPa

σ

D Developed stress Pa

σ

n Impact pressure Pa

σ

y Yield stress Pa

ϕ

w Wall friction angle ⁰

ψ

Variable -

ω

(c/t) Rotational speed (of conveyor/turbine) Rpm

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1 Introduction

Modern society largely depends upon conveyor belts. Men use these devices every day, often without even realizing it. The reason is that belt conveyors come in so many different forms and are so well integrated that we quickly forget that they are used amongst others to work out (treadmills), to travel (luggage handling system in airports), to carry groceries past the register and to power the world (transporting coal from mines to power plants). Especially this last application has resulted in very large, long and powerful systems consisting of several conveyor belts. The power required to drive all these belts is however quite substantial. In order to reduce the energy required to drive these systems a new promising development was recently presented on a conference in Germany. In the paper that was presented here the possibility was investigated whether or not a solid state material driven turbine connected to the conveyor belt could reduce the power that had to be absorbed from the net. The conclusion of this paper was that it is technically possible to manufacture such an

energy-recovery system, but tests have to be done in order to require further insight in how the turbine operates.

The purpose of this report is to establish whether or not the energy-recovery system for continuous conveyors, with the use of a solid state material driven turbine, as proposed by Dipl.-Ing. Dr.mont. M. Prenner and Univ.-Prof. Dipl.-Ing. Dr.mont F. Kessler is a viable and (economical) efficient concept. This will be done by first verifying the findings of the original paper that such an energy-recovery system will actually work. Subsequently a look will be taken at the viability by comparing the benefits and additional costs of this system.

For this reason the report is divided as follows: first off the prior art is considered in chapter 2. Chapter 3 analyses the basic principle of the material driven turbine by determining the energy content of the bulk material and the location and shape of the turbine itself is discussed in chapter 4. Chapter 5 discusses the transmission between the turbine and the conveyor belt and chapter 6 considers varying operating conditions. The economical aspects are presented in chapter 7 and are followed by the conclusions and recommendations.

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2 Prior art

As was mentioned in the introduction conveyor belts are widely used nowadays and men have used these systems for many years already. Because of this, innovation-wise these systems are very well developed. The last couple of years globally the focus has shifted to energy efficiency though, due to the greenhouse effect and the increasing price of oil. As far as conveyor belts are concerned there are a couple of ways they can be made more energy efficient. These are:

- More efficient belt. Newest development in this area is using aramid fibers in the belt which make it much lighter [1] [2]_.

- Using speed control in order to use the motors powering the conveyor as generators on downhill sections [3]_.

- Recovering energy out of the bulk itself with the use of a turbine [4].

This report focuses on this last option. Regarding this option practically no prior art was found. The principle itself however is already very old and prior art in different fields of application can be found, although their importance in the matter regarded in this report is very limited.

The oldest example that can be found is the waterwheel which has been used by humans for years in order to recover energy from falling or flowing water. The resemblance to the problem at hand basically stops here because besides this basic principle no other common ground exists. Especially the difference in powering medium, a continuous flow of a liquid (water) versus a discrete flow of solids (bulk material), limits the usefulness of this prior art. Although no equations or design specifics where found some insight can be gained from this application nevertheless. Where three different water wheel configurations have been invented through time, one model is an exact match to the solid state material driven turbine considered in this report [5]_{. This type of water wheel is known as}

the overshot type, see Figure 2.1. From these overshot wheels a number of things can be kept in mind when designing the bulk turbine. For instance the cells need to be formed in such a way so that the material can enter each cell at its natural angle of fall. The opening of each cell should also be slightly wider than the material stream so that the air can escape. Last but certainly not least, each cell should only be filled for up to 30-50% of its volume. This is done to prevent early outflow of material since the material should leave the turbine at the lowest possible point in order to subtract the maximum amount of potential energy. Efficiency’s for this type of waterwheel have been reported to range up to 85%.

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Figure 2.1 - Overshot water wheel [6]

Newer, modern versions of the waterwheel include the water turbine, impulse turbine and the Pelton wheel (which is actually an impulse turbine with a special, more efficient turbine blade shape). The water turbine is a reaction turbine. Reaction turbines are acted on by water, which changes pressure as it moves through the turbine and gives up its energy. They must be encased to contain the water pressure or they must be fully submerged in the water flow [7]_{. Since the solid material driven turbine}

doesn’t works on pressure principles the water turbine is of no further use. Because the solid material driven turbine subtracts not only the potential energy form the bulk material, but also the kinetic energy the impulse turbine (or Pelton wheel to be specific) might be of interest though. Literature [8] [9]_{shows that the force exerted on the Pelton wheel is dependent on the initial flow speed of the}

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The same principle of using a turbine to recover energy from a medium can also be found in windmills

[10]_{. This time the medium isn’t a liquid but a gas. Since a gas resembles a solid a lot less than a liquid,}

prior art regarding wind turbines supplies no useful information on any field (turbine shape, wear, etc.).

There has been some research into bulk solids driven turbines though, but never large scale. J. Liu and B. Huan investigated the use of a turbine to measure the flow rate of bulk solids [11]_{. Their tests}

were successful on a small scale with the use of small particles like sand and assuming plug flow in their experimental setup. In these tests they used an in-line turbine made from Plexiglas. Since wear of the turbine wasn’t investigated, and because of the different nature of the turbine this article is of no further interest for this viability study. If the design under consideration in this report turns out to be non-viable it is also very unlikely that the more complex turbine used by J. Liu and B. Huan will offer any improved performance. Reasons for this are the expected accelerated wear of the turbine combined with the more complex required installation.

In order to acquire some insight in the way bulk material interacts with equipment literature not directly related to energy-recovery can be consulted. For instance bucket-ladder or bucket-wheel excavators can be looked at regarding the design and wear of the turbine buckets/blades [12]_{. These}

devices differ however from the turbine under consideration by the fact that they don’t catch a stream of material but dig into densely packed material. Once this material has been severed from the earth, the relatively smooth edged chunk slides into the bucket with low velocity. Because of this these devices only need special wear resistant teeth. The solid material driven turbine however is subjected to constant impact of material and thus requires more protection. Following this reasoning, combined with the limited amount of information on the actual interaction and influence of the bulk on the wear of these devices, literature regarding dredgers, excavators and also applications of the Archimedes screw is of no further help in this study. For wear determination literature regarding wear of conveyor belts and chutes might offer a solution [13]_{. By estimating a restitution factor the equations might be}

made suitable for the turbine design. Actual usefulness of this information can’t be determined beforehand and will have to be determined later on in this study though.

The final example that was found in which recovering energy is quite common is in the transportation sector. More and more cars, trams, F1 cars and other vehicles use a so called KERS (Kinetic Energy Recovery System) in order to recover some of their kinetic energy during braking operation [14]_{. This}

principle is also referred to as regenerative braking. Crane’s can also utilize a similar system when lowering a hoist [15]_{. Articles regarding these subjects might be used for inspiration and out-of-the-box}

thinking but due to their nature are not of any direct use for the cross-flow bulk solids driven turbine under investigation in this report.

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3 Energy content

The principle of recovering energy out of bulk material which is thrown of a conveyor belt is valid in any situation. The real interesting question though is actually how much energy this bulk material contains. For that reason this chapter will first determine the energy content of the bulk material in order to establish whether or not the reason to invest in, and place such an energy-recovery system is worth the effort. In addition an analysis will investigate the amount of energy contained in the bulk material with respect to the total energy that has to be supplied to the conveying system. In this way it is possible to establish whether or not it makes sense to try to reduce the required power for a conveyor system with this solution.

3.1 Energy content of the bulk material

As the original paper by Prenner and Kessler [4]_{correctly stated the energy content of the bulk}

material can be divided into kinetic energy and potential energy. This means that the energy content can be calculated with the use of equation 3.1.

2

(0,5

) (

)

kinetic potential

P



E



E



 

m v

  

m g H

[3.1] In this equation

m



is the mass flow per second, v is the belt speed in m/s, g is the gravitational acceleration and h is the height difference (a.k.a. elevation change) between the end and start of the conveyor belt. To indicate how much energy is actually involved a simple example will be given. Assume a conveyor belt transporting coal. For this application a conveyor belt travelling at a speed of 6 m/s, carrying 3600 t/h is taken, which are quite common values. Taking a height difference of 3 m the power in the bulk equals:

2

3600 1000

(0,5

6 ) (

9,81 3)

47, 43

3600

P









 

kW

3.2 Energy content of the conveying system

The power that was calculated in the previous section and thus could theoretically be subtracted from the bulk material is a substantial amount of energy. Saving such an amount would be beneficial. Before an entire installation is purchased though, it might be smart to analyze whether or not this amount of energy is a substantial part of the total energy in the system. If the energy in the bulk is for instance only 1% of the total amount of energy that has to be supplied to the conveyor belt, it is probably smarter to start saving energy on another part of the conveyor system. For that reason now the power that has to be supplied to a conveyor belt will be calculated so that this supplied power can be compared to the energy that can be recovered out of the bulk material.

Note that what follows now are basic power calculation. They offer no detailed insight and don’t take effects of for example rubber into account. This isn’t important though for this analysis since the purpose is only to obtain a comparable power number.

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In order to calculate the required power (in steady state operation) first the required force has to be determined. This force is dependent on the motional resistances and according to DIN 22101 consists of the main or primary resistance FH, the side or secondary resistance FN, the gradient resistance FSt

and the special resistances Fs[16] [17]. This can also be seen in equation 3.2.





H N St S

F



F



F



F



F

[3.2]

All these individual terms need to be determined separately. The primary resistance can be seen as the force that is necessary to overcome the friction in the motion of direction of the material, see Figure 3.1. The value of FH can be determined according to equation 3.3.

Figure 3.1 - Primary resistance [17]

H Z

F

 



F

 



M g



[3.3]

In the belt conveyor world the friction coefficient μ is replaced by the letter f. The mass M consists of the mass of the belt m’G, the mass of the bulk material m’L and the mass of the rotating rolls m’R.

Since m’G, m’L & m’R are given per meter belt length the entire mass M follows out of equation 3.4.





' ' '

2 cos

R G L

M



L m



_

 

m



m







_

[3.4]

In this equation L is the belt conveyor length and δ the inclination angle. These mass per length values all need to be determined independently again.

The mass of the rotating rolls per meter belt length is given by equation 3.5.

' ' ' RC RR R C R

m

l





[3.5]

Here lC stands for the carry idler spacing and lR for the return idler spacing. This spacing should must

be known and can be quickly measured otherwise. The mass of the individual rolls can be found in tables, see Figure 3.2.

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The mass of the belt is normally given but if this one happens to be unknown it can be found in a graph (see Figure 3.3) combined with equations 3.6 and 3.7.

Figure 3.3 - Mass of belt carcass [17]





' " " G Z D

m



m



m



B

[3.6]





" D r T B

m







t



t

[3.7]

In these equations m”z is the mass per meter length of the carcass [kg/m], m”D is the mass per meter

length of the rubber carcass cover [kg/m], B is the belt width [m], ρr is the density of the rubber cover

[kg/m3_{], t}

T is the thickness of the top cover [m] and tB is the thickness of the bottom cover [m].

The third unknown mass per length parameter, the mass of the bulk material, depends on the capacity of the conveyor belt according to equation 3.8. In this equation v is the belt speed and Qm is

the capacity of the conveyor belt, in tons per hour.

'

3, 6

m L th

Q

m

A

v



 





[3.8]

Equation 3.3 can be rewritten and the primary resistance therefore is:







' ' '



2 cos

H R G L

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Figure 3.4 - Graph of coefficient C versus conveyor length L [17]

Figure 3.5 - Table of conveyor length L and coefficient C [17]

The gradient resistance is given by equation 3.11. In this equation H is the height difference between the beginning and end of the conveyor belt.

'

St L

F

 

H m



g

[3.11]

The final resistances that have to be overcome in order to drive the conveyor belt at a constant speed are the special resistances. This are however as the name suggests special cases and thus these forces aren’t always present in the system. In the example in this paragraph these forces won’t be considered.

This means that the total motional resistance is:







' ' '



'

2 cos

R G L L

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With this driving force known the required basic power can be calculated with equation 3.13. Tr

F v

P







[3.13]

Now is known how to determine the required power this can be done for a relatively simple example, see Figure 3.6. A number of parameters need to be chosen or assumed though. First of all the speed, capacity and height difference logically need to be the same as for the calculation of the energy content of the bulk material in the beginning of this chapter, thus:

v = 6 m/s Qm = 3600 MTPH

H = 3 m

The other values that need to be set are given below. f = 0,012 L1 = 2200 m L2 ≈ 300 m C = 1,04 δ1 = 0⁰ δ2 = 0,57⁰ B = 1,4 m Roll diameter = 0,133 m

lc = 4 m (spacing between a three roll carry idler set) lr = 8 m (spacing between a two roll return idler set) m”z = 25 kg

ρr = 950 kg/m3

tT = 0,008 m

tB = 0,003 m

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Thus the total mass '



' '



'



' '



1 R

2

G L

cos

1 2 R

2

G L

cos

2

M



L m

_



 

m



m





_





L

_



m

 

m



m







_

Substituting the masses just calculated gives:









2200 9, 2

2 50 167 cos(0)

300 9, 2

2 50 167 cos(0,57)

690.500 M



_



 





_





_



 







_



kg

With this mass and equation 3.12 the total resistance force becomes:

'

1, 04 0, 012 690.500 9,81 3 167 9,81 89,5

L

F

  

C f M g

  

H m

 

g



 





kN

This means that according to equation 3.13 the required steady state driving power is:

89.500 6

548 0,98

Tr

F v

P

kW









1

Comparing this required driving power with the previous calculated energy content of the bulk material it can be seen that almost 9% of the driving power is stored in the bulk material.

3.3 Comparison

Since the analysis of paragraph 3.2 only considers a single situation it isn’t fair to base a conclusion on only these numbers. For that reason it is interesting to see how the percentage of drive power that is stored in the bulk material (and thus can be recovered) changes with varying conveyor lengths, elevation changes and belt speeds. This paragraph will perform these three analyses and shortly discusses their results.

First two more drive powers will be calculated for respectively a very short and a very long conveyor belt. All parameters remain the same except for the following. For the short conveyor L1 = 200 m; L2

≈ 50 m; C = 1,38 and δ2 ≈ 3,4⁰. For the long conveyor these parameters change into L1 = 9900 m; L2

≈ 100 m; C = 1 and δ2 ≈ 1,7⁰. This results in a mass, force and power of about 69.000 kg, 16,1 kN

and 98,6 kW for the short conveyor and 2.762.000 kg, 330 kN and 2,02 MW for the long conveyor. This means that the percentage of energy stored in the bulk material with respect to the energy that has to be supplied to the entire system decreases as the length of the conveyor belt increases. This can be seen in the following table:

Table 1 - Bulk material energy content versus conveyor length Conveyor

length [m]

Required drive power [kW]

Energy content bulk material [kW]

Percentage of supplied energy stored in bulk material

250 98,6 47,43 48

2.500 548 47,43 9

10.000 2.020 47,43 2

1_{Note that motor powers are standardized. Since it is not the purpose of this example to select an}

entire electrical drive for a conveyor belt the calculated value will be used. In reality probably a motor of 550 kW will be selected though.

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This percentage drop with increasing conveyor length can be explained by the increase in friction losses for longer conveyors (longer conveyor means more idler rolls and thus more losses) while the energy content of the material remains the same. From the table above it can be clearly seen that the proposed idea of energy recovery out of the bulk material with the help of a turbine thus has the most potential with relatively short conveyor belts. Conveyor belts of these lengths are quite common within factories or bulk terminals like for instance the EMO terminal in the port of Rotterdam.

The second variable that is of direct and huge influence on the energy content in the bulk material with respect to the energy in the system is the elevation change that the belt realizes. Just like was done before with the conveyor length a short analysis will be performed with 3 different elevation changes. For this the short conveyor (length of 250 m) will be used as the basic configuration. Again also all other parameters will be kept the same. Since this analysis uses the same equations as before only the final answers will be shown in Table 2. The only difference with the first analysis is that although the belt speed is kept constant (and thus the kinetic energy) the elevation is varied and thus the potential energy changes. For this reason not only the required drive power has to be recalculated every time but also the energy content of the bulk material. The first row assumes the same

configuration as before, so with H = 3 m, L2 ≈ 50 m and δ2 ≈ 3,4⁰. The other two configurations have

these parameters changed in respectively H = 8 m, L2 ≈ 50 m and δ2 ≈ 9⁰ and H = 15 m, L2 ≈ 50 m

and δ2 ≈ 16,7⁰.

Table 2 - Bulk material energy content versus conveyor elevation change Conveyor elevation

change [m]

Percentage of supplied

energy stored in bulk material

3 98,6 47,43 48

8 148,8 96,48 65

15 218,6 165,15 76

This second table shows some interesting data. Apparently the energy content of the bulk material increases faster with increasing elevation change then the required drive power. This would imply that the maximum elevation change that can be achieved should be chosen. However due to practical reasons like increased costs of the construction and required space (not only vertically but also horizontally since the bulk material is thrown further away from a higher conveyor) all existing systems are generally build as compact (and low) as possible.

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power as well as the energy content of the material have to be recalculated. Filling in the correct equations results in the data given in the table below:

Table 3 - Energy content bulk material versus belt speed Conveyor belt

speed [m/s]

Percentage of supplied

energy stored in bulk material

2 60,5 31,43 52

4 79,6 37,43 47

6 98,6 47,43 48

From this table it can be concluded that the belt speed is almost irrelevant regarding the percentage of supplied energy that is stored in the bulk material. This is explained by the fact that as the speed decreases the kinetic energy of the material decreases, and thus the total energy content, but also the power that has to be supplied to the system decreases. Since these two energies apparently decrease at almost the same rate, the percentage remains almost constant regardless of the belt speed.

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4 Turbine design

Normally when people think of a turbine they have a picture of a jet engine or water turbine in mind. The geometry of such a turbine however isn’t suited to be used with bulk material. The turbine that will have to be used is a cross flow type and looks more like a Pelton wheel or like the wheel of a bucket wheel excavator. In the original paper [4]_{both the placing and the design of the turbine were}

done with the aid of the discrete element method (DEM). Since this report only intends to establish whether or not the idea itself is viable the focus lies on the conceptual phase. DEM normally is used later on in the design process and thus won’t be used here. This chapter instead provides more information about the turbine in an analytical way. For this first different methods for determining the materials trajectory are compared, followed by the turbine placement with the help of the material trajectory. Finally the turbines shape is analyzed in section 4.3.

4.1 Material trajectory determination methods

Being able to predict the material discharge trajectory is very important in the field of conveying techniques because many machines require an accurate placing (like chute’s, impact plates, etc.) in order to function properly. Because of this importance many different approaches and methods have been developed over time. These different methods differ slightly from each other though, resulting in different trajectories. These different methods will briefly be discussed here.

C.E.M.A. [18]_:

The Conveyor Equipment Manufacturers Association has released six editions of the C.E.M.A. guide, ‘Belt Conveyors for Bulk Materials’ since 1966. The first five editions follow the same procedure for determination of material trajectory with only slight adjustments to various values in reference tables. In the 6th Edition of the C.E.M.A. guide (from 2005), there is a change to how the time interval is

calculated for high-speed belts for determining the trajectory profile, now being calculated based on the belt speed rather than the tangential velocity. For all other conditions the time intervals are calculated as per the previous editions. The C.E.M.A. guide also establishes a sort of ground rule as to what classifies as low or high-speed. This rule is summarized in Table 4. In this table Vs represents the

tangential velocity of the material at the discharge point, Rc stands for the radius of the materials

centroid and α is the belt inclination angle.

Table 4 - C.E.M.A. classification

Low-speed Medium High-speed

Horizontal 2

1

s c

V

g R





N/A 2

1

s c

V

g R





Inclined 2

cos( )

s c

V

g R







2

1

s c

V

g R





2

1

s c

V

g R





2

cos( )

s

1

c

V

g R







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As can already be concluded form Table 4 the C.E.M.A. method is based on the centroidal path. To plot the trajectory, a tangent line is drawn from the point at which the material leaves the pulley. At regular time intervals along this tangent line, vertical lines are projected down to fall distances supplied in the C.E.M.A. guide. A curve is then drawn through these points to produce the centroid trajectory. The upper and lower trajectory limits can also be plotted by offsetting from the centroidal curve the distance to the belt and to the load height. It is evident from this procedure that a constant width trajectory path results. C.E.M.A. notes that for light fluffy materials, a high belt speed will alter the upper and lower limits with both vertical and lateral spread due to air resistance.

M.H.E.A. [18]_:

The Mechanical Handling Engineer’s Association guide from 1977, ‘Recommended Practice for

Troughed Belt Conveyors’ addresses both low-speed and high-speed belts via centripetal acceleration. It uses the same speed classification as C.E.M.A. but instead of the material centroid the pulley diameter is used. This results in the determination of the lower trajectory. This method also provides an approximation for the outer trajectory of the material by first determining the angle at which the upper surface of material starts its trajectory. The M.H.E.A. released a second edition of the guide in 1986 which is identical to the C.E.M.A. method up to and including the 5th Edition. However it uses metric rather than imperial units and the conversion results in minor differences, ultimately causing minor variations to the trajectory curves.

Booth [18]_:

In 1934 Booth found that while using available theory, a large discrepancy was present between the theory and that of the actual trajectory. After careful investigation Booth concluded that, for one, the effects of the material slip were not being addressed as material discharged over the head pulley. This led to an analytical analysis to develop a more representative theory. Booth’s method begins by determining the angle at which the particle will leave the head pulley, using the same classification conditions described by the C.E.M.A. method. The equations and method to solve these equations can be found in the referred to literature but are left out of this report because Booth himself

acknowledged that this method was tedious and complicated. As an alternative he developed a chart to minimize the time required to analyze a particular belt conveyor geometry still with a reasonable accuracy.

Golka [18]_:

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divergent coefficients have been introduced for the lower and for the upper trajectory, which takes into account variables such as air resistance, size distribution, permeability and particle segregation. Unfortunately no explanation is given as to how they are determined though. Since it is unknown how these divergent coefficients are determined explaining the method any further is of no use. Nevertheless it is possible to solve a series of Cartesian coordinate based equations for pre-selected time steps with all these variables, resulting in the trajectory.

Korzen [18]_:

Korzen’s method which dates back to 1989 is the most complex in its approach of all the methods addressed here, addressing the issues of adhesive materials, inertia, slip and air drag in its calculations. There is also a distinction between static friction (μs) and kinematic friction (μk) used in

the determination of the discharge velocity and discharge angle (αd).

For high-speed belts the discharge angle equals the belt inclination angle and the discharge velocity equals the belt speed. For low-speed belts the angle of discharge will have to be calculated with equations 4.1 and 4.2. Equation 4.1 calculates the angle at which material begins to slip on the belt before discharge. This value can be used in equation 4.2 to determine the integration constant (Ci) by

setting V(ψ) = vb and ψ = αr. Once the integration constant is known equation 4.2 can be used to

determine the discharge angle with the relationships V2_{(ψ) = R}

c g cos(ψ) and ψ = αd.





2

1 1 1

tan (

) sin

sin tan (

)

b

2

a

r s s c d

v

R g

h









 















_



_

 

_

_











[4.1] 2 4 2 2

(4

1) cos( ) 5

sin( )

( )

2 (1 16

)

k k k c i k

V



g R









C e

 



 





 





   

_

_

 





[4.2]

The detailed numerical analysis developed by Korzen is achieved by a series of successive approximations which incorporate ‘corrected’ air drag coefficients based on particle shape and a proportionality factor for air drag. Using the x-displacement for any given position of the trajectory, the y-displacement, trajectory angle and resultant velocity can be obtained.

The first approximation is for a free falling particle in a vacuum, which is used as the initial trajectory estimate, where air drag is neglected, for all other approximations air drag is applied. The analysis is continued until the differential error between successive approximations has deviations no greater than 1% or 2%. Once the analysis has been completed for a suitable range of x-displacements, the x and y coordinates are plotted to produce the trajectory for the central path.

The discharge angle and discharge velocity calculated above are for the centre height of the material stream. Korzen also allows for calculation of the upper and lower trajectory limit discharge velocities. For high-speed belts the upper and lower discharge velocities are the same as that for the centre height trajectory but for a low-speed belt, the discharge velocities are calculated based on ratios of the radius of the lower and upper trajectories. Although the discharge velocity for the lower and upper trajectories can be determined, there is no method described for the determination of the

corresponding trajectories.

For particles over 1g in mass, Korzen dismisses the effects of air drag. This being the case, only the first approximation is performed and the trajectory is plotted from those values. As a last side note it

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is worth mentioning that this method does not include the belt thickness when determining the trajectory curves.

Goodyear [18]_:

The ‘Handbook of Conveyor and Elevator Belting’ from Goodyear out of 1975 is quite simplistic in its approach to determining material trajectory. Using the principles of projectile motion, equation 4.3 and 4.4 are used to determine the x and y coordinates of the trajectory. The discharge angle is determined according to the C.E.M.A. method for the material centroid. There is no reference to the determination of the discharge angles or trajectories for the lower or upper trajectories. The

assumption has been made that all discharge angles are of equal value, thus resulting in parallel trajectory streams. b

x

 

v t

[4.3] 2

2 g t

y





[4.4]

The Goodyear method actually uses the same classification as the C.E.M.A. method with the only difference that for high-speed inclined conveyors the division needs to be larger than the cosine of the inclination angle instead of being larger than one. Once the x and y coordinates and the discharge angle have been determined, producing the trajectory curve is straight forward.

Dunlop [18]_:

The Dunlop Conveyor Manual from 1982 uses a graphical method to determine the material trajectory leaving the conveyor for low-speed belts and an analytical method for speed belts. For high-speed belts, material again leaves the belt at the point where the belt is at a tangent to the pulley. To calculate the x and y coordinates the same equations are used as for the Goodyear method. Dunlop states that the mathematics behind the trajectory for low-speed conveyors is complex and so developed a graphical method. For this graphical method only the belt speed and pulley diameter need to be known. If the graphical method however doesn’t happen to include the combination of these two parameters the method for high-speed belts should be used. The resulting trajectory is a prediction of the lower boundary.

What can be concluded from the different methods described above is that determining the exact trajectory is very difficult. As can be seen in Figure 4.1 different methods lead to different trajectories. It basically depends on the kind of system under consideration (for declined conveyors only C.E.M.A., M.H.E.A. and Goodyear offer solutions), the amount of parameters that are known and the amount of

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Figure 4.1 - Different discharge trajectory methods [19]

4.2 Turbine placement

The placement of the turbine causes several problems which need to be solved, or at least

considered. The placement is most and formally determined by the trajectory of the particles coming from the conveyor belt. In order to recover as much energy as possible out of this stream of material the turbine has to be placed in this stream so that it can intercept all the material. The turbine however also needs to be placed in the material trajectory in such a way that when the material leaves the turbine again it does so at the lowest possible point so that the maximum amount of potential energy is subtracted from the material.

For the determination of the trajectory a method comparable with the Goodyear method will be used. Although not an official method like those discussed in the previous section it has the same simple approach as the Goodyear or Dunlop methods. The material trajectory will be determined with

simplified elementary physics equations which describe the motion of a projectile [13]_{. Using this simple}

approach means a number of assumptions are made, these include: - The influence of air drag is negligible

- Material lifts off at the tangent of the drive pulley - No belt sag occurs in the transition

- There is no cohesion

- Acceleration due to transition is neglected

These assumptions are reasonable to make considering the fact that the trajectory has to be

determined in general without any further knowledge of the system or material under consideration. Also note that many of these (if not all) of these assumptions are also made by the official methods for determining material discharge trajectory presented in the previous section.

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These assumptions simplify the equation for the discharge trajectory. The equation of the path (based on projectile motion and in terms of the horizontal position x) is given by equation 4.5.

2 2 2 0

tan(

)

2 cos (

)

g

y

x

V

 



 

 





[4.5]

In this equation α represents the conveyor inclination angle [⁰] and ε is the angle [⁰] that results from flattening the belt at the pulley from its troughed shape, see Figure 4.2. “g” is the gravitational acceleration as always and V02 is the initial speed of the material [m/s]. Applying this equation to the

example in the previous chapter: a conveyor with a total length of 250 m, inclination angle over the last 50 m of 3,43 degrees rising to a height of 3 m, belt speed of 6 m/s and assuming that ε is zero, a material trajectory as shown as in Figure 4.3 is obtained. Note that the material height is not included in the trajectory equation. The upper and lower trajectory can be obtained by shifting the y-coordinate accordingly, resulting in parallel trajectories like in the C.E.M.A. method. Also in general slip may occur before lift-off takes place. Hence, the acceleration and inertia force are included. However, it is

unlikely that slip will be significant so it may be neglected.

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With the materials trajectory known the placing of the turbine can be determined. For this the desired location along the trajectory has to be selected. Whether the turbine is placed close to the conveyors head pulley or far away, high or low doesn’t matter since the energy content of the material remains the same. Further along the trajectory the potential energy is converted into vertical speed. Although technically speaking placing of the turbine is irrelevant, factors like accessibility for maintenance and potential surrounding systems can influence this decision. With the selected point along the trajectory as well as the turbine design (see next section) the coordinates of the turbines axle can be obtained.

Although the entire trajectory is specified by equation 4.5, this trajectory is measured from the point where the material leaves the belt, as can be seen in Figure 4.4. With inclined (high speed) conveyors this point has a little offset with respect to the centre of the conveyors head pulley, known as the eccentricity e. Since it is a lot easier to measure from the pulleys axle when installing the turbine the eccentricity has to be calculated so that this offset can be compensated. Due to the estimative nature of the trajectory determination the choice can also be made to neglect the eccentricity because it normally is relatively small. Nevertheless below it is shown how this offset can be calculated with the help of Figure 4.4 and equation 4.6.

(

) sin( )

e



R h

 



[4.6]

Figure 4.4 - Material trajectory and hood location [13]

In this equation R is the radius of the pulley and h will be determined below with the help of equation 4.7 up and until 4.11, and Figure 4.5.

2

A U b

 

[4.7]

C

r

B



[4.8]

2 b

  

B

C

[4.9]

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



2

2 2

1 tan( )

sin( ) sin(2 ) 1 4 cos( ) 2 1 cos(2 )

(1 2 ) 2 6 r U r r r r       _ _   _       _     __   _ _ [4.10]



A



h

B C





[4.11]

Figure 4.5 - Load profiles at discharge [13]

In the equations above B and C are the dimensions of the idler rolls, β is the angle the side idler roll makes and λ is the angle of repose. Now that it is possible to select the location of the turbine along the path of the trajectory also the speed of the material can be determined when it comes into contact with the turbine. In order to determine the speed the following equations can be used. In these equations v0 is the speed of the material at the point where it leaves the belt, and thus equals

the belt speed. Further t is the time in seconds.

0 0

cos( )

x

v

 

v



[4.12] 0 0

sin( )

y

v

  

v



[4.13] 0 x x

v



v

[4.14] 0 y y

v



v

 

g t

[4.15] since

x



v

_x₀



t

[4.16] then 0 x

x

t

v



[4.17] thus ₀ 0 y y x

g x

v







[4.18] 2 2 c xc yc

v



v



v

[4.19]

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Particle size/weight distribution: In an ideal situation all particles would be of the same size and weight and thus follow the same path, which is the path described by equation 4.5 to be precise. In reality though, no two particles are the same. Because of this also not all the particles will follow the same trajectory. This leads to the fact that every kind of material and every application needs to be analyzed separately. Depending on the particle size and weight distribution a segregated trajectory could form with on one side the very light and fine particles (dust and sand like), and on the other side the heavy large lumps. Such a segregated material can already be detected on the conveyor, see Figure 4.6. If this would occur in a severe form not all the material can be intercepted by the turbine and the particle size and weight distributions need to be used to determine whether it is better to place the turbine in the path of the fine particles or the lumps. Whichever of the two has the most mass thus also holds the most energy and will be most beneficial to recover energy from. The downside of a segregated material like this is obviously that only part of it can be captured in the turbine and thus only a fraction of the energy content of the material can be recovered, lowering the efficiency substantially.

Figure 4.6 - Material segregation on conveyor [17]

Space: The problem just discussed in the previous section (particle size/weight distribution) offered the solution of placing the turbine in only a part of the trajectory. This could lead to a different problem though since existing systems are normally build as compact as possible. As can be seen in Figure 4.7 the construction can be kept either small by placing the turbine under the flow of material, or a large system is obtained when the turbine is placed further away. This last option also has the disadvantage of having an oncoming flow of material resulting in a direction of rotation opposite to that of the conveyor. If the turbine is directly coupled to the conveyors pulley as proposed by the authors of the original paper [4]_{the latter option is less desirable. The reason is that for direct coupling}

the opposite direction of rotation requires an increase of the engineering effort by including a system to change the direction of rotation. This extra system however inevitably also leads to an increase of the losses of the energy recovery system.

The available space can also lead to another problem concerning the path the material follows after it leaves the turbine. Normally this function is fulfilled by a hood and spoon. Placing the turbine could

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take up so much space that the hood and spoon don’t fit any more. Removing these guidance parts has an effect on the subsequent systems, more on this can be found below.

Figure 4.7 - Potential turbine locations

Surrounding systems: Now as just has been said it might not be possible to place both the turbine and the hood and spoon because of the limited space. This isn’t a problem when the material is transferred from a conveyor to a stockpile (since a hood and spoon configuration isn’t used here anyway) but it might be problematic in the other possibilities (which are transfer from conveyor to conveyor, conveyor to perpendicular conveyor & conveyor to discontinuous conveyor).

Since the turbine intercepts the material flow a hood isn’t required anymore, although maybe a plate feeding material that has overshot the turbine back into it will be necessary. The spoon however fulfills a totally different function which the turbine can’t take over. Normally this part directs the flow of material onto the subsequent belt at the right speed so that the wear of the second belt is

minimized (as well as the required power for accelerating the material). This is not the case with the turbine. In this case the material is just dropped vertically onto the second belt. The fact that the material has to be accelerated by the second belt again doesn’t matter since the energy that this costs is mainly stored in the material as kinetic energy and can be recovered out of the material again with the same turbine principle. The speed difference between the belt and the material does lead to accelerated wear of the belt though. The wear can be calculated with the following 3 equations. All terms in these equations are explained in Figure 4.8 except for ρ, which is the density of the bulk material, and μb, which is the coefficient of friction between the belt and the material.

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Figure 4.8 - Spoon feeding a conveyor [13]





2





3 a b n b ex b ey b ex b b WB

W



 



v



v



 

 

v



v



v



 

  

v

N

[4.20]





2 3

sin( )

cos ( )

R e WB e R

v

N

v









[4.21] b R e

v



[4.22]

By calculating both the wear with and without the spoon the additional wear can be determined. An analysis of the extra costs due to the earlier replacement of the second belt versus the energy savings due to the turbine will have to show whether or not application of the turbine is economically

beneficial.

A compromise would of course be to install a spoon under the turbine. In this way the turbine

recovers energy out of the bulk material and the second conveyor has no additional wear or additional power requirements. Logically this solution is only possible when there is enough space (height) to install such a system (see Figure 4.9) and obviously some potential energy remains in the material since it leaves the turbine at a certain height (the height of the spoon).

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4.3 Turbine shape

Although quite a lot of attention was paid to this subject in the original paper, a detailed analysis is beyond the scope of this report. The reason is that this report only analyzes the viability of the idea in general and doesn’t attempts to find the optimal shape of the turbine itself.

The shape of the turbine itself is however an important but also a complex and contradictive problem. In order to transfer a maximum of the kinetic energy of the moving bulk material into turbine power, it is necessary to contain as much as possible of the bulk material in the turbine buckets. Ideally the slowed down bulk material should be totally contained in the mashed turbine buckets and should be totally discharged at the lowest position of the turbine buckets. To convert the kinetic energy into power it is also necessary to slow down the bulk material in the turbine buckets.

The analysis performed by the authors of the original paper [4]_{showed that these criteria were best}

met by a complex shape of the turbine blades. As the authors stated themselves as well though, the solution isn’t as simple as that. The reason for this is that the turbine blades are subjected to extreme wear and because of that need protection. This can best be done by applying techniques that are already proven. In this case that would be the use of wear plates which are currently being used in most hood and spoon designs, see Figure 4.10. These plates are expensive though and are being produced in relatively normal and simple shapes. This means that they can’t be used to form a complex shape and as a result of that the shape of the turbine blades will have to be considerably simplified.

Figure 4.10 - Wear tiles in chute [20]

The result is a turbine as is shown in Figure 4.11, consisting out of 3 straight panels connected to each other at certain angels. An optimization process should be performed to determine the optimal angles to connect the panels and the number of buckets created by these panels. As has been said before though this is beyond the scope of this report.

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Figure 4.11 - Example of a turbine design [4] Impact analysis

Although an entire optimization process won’t be performed, an analysis has been performed

nevertheless regarding the angle under which the turbine blade should intercept the material stream. For this the impact model shown in Figure 4.12 with a restitution factor (er) is used [13]. The restitution

factor has a value between zero and one with zero being a completely inelastic impact, meaning no rebound, and one being a completely elastic impact, meaning no loss in energy.

Figure 4.12 - Impact model [13]

This impact model results in the following equation for determining the materials speed after impact with the turbine blade.





1 0

cos( )

1 k

(1

r

) sin( )

1

v

 

v







 

e





[4.23]

Note that the initial speed (v0) of the material in this equation equals the materials velocity at the

selected point of impact along the discharge trajectory (thus v0 = vc from section 4.2).

The analysis results can be found in Table 5. As can be seen the analysis has been performed for every possible restitution factor (with steps of 0,05) and every possible impact angle (with steps of 5 degrees). The initial speed was set at 8 m/s and the kinematic coefficient of friction is taken to be 0,46, which is a reasonable value for the friction coefficient between coal and metal.

Viability study of an energy-recovery system for belt conveyors

Specialization: Transport Engineering and Logistics

Report number: 2013.TEL.7747

Title: