Hearth Coke Bed Buoyancy in the Blast Furnace: Experimental Study with A
2006:235 CIV MASTER’S THESIS
Hearth Coke Bed Buoyancy in the Blast Furnace Experimental study with a 3-dimensional cold model
PÄR SEMBERG
MASTER OF SCIENCE PROGRAMME
Luleå University of Technology Department of Chemical Engineering and Geosciences Division of Process Metallurgy
2006:235 CIV • ISSN: 1402 - 1617 • ISRN: LTU - EX - - 06/235 - - SE Abstract
ABSTRACT
The effect of buoyancy forces acting on the hearth coke bed or the “deadman” of the blast furnace has attracted a great deal of interest during recent years of blast furnace research. This thesis presents an effort to elucidate the particle movement patterns connected to formation of a coke free layer in the hearth. In the work, the impact of different pressure distributions on the behaviour of the particle bed was studied with an experimental 3D-cold blast furnace hearth model. The bases for the work were the results from tests along with two different numerical models from a previous study, Hearth coke bed buoyancy, a preliminary investigation, made in 2004 at Bluescope Steel Research, Port Kembla, Australia. In the model, a bed of plastic particles in water were subjected to different pressure distributions, and float-sink motions induced by accumulation and drainage of the water through a valve in the bottom. The results showed that the bed was quite resistant to internal particle movements, when subjected to different linear pressure distributions along the radius. However, previous studies have suggested the downward pressure under the raceways to be severely reduced, and when going below 15:85 in pressure ratio between the peripheral and central area, it was observed that the particles moved internally. As the central load was descending in the bed, upward particle movements were observed along the walls, as well as from the centre towards the walls on the bottom. Particle movements were strongly dependent on the sink-float motions, and moved relative to one another only during drainage, when particles under the central weight moved down faster than under the peripheral reduced pressure area. This mechanism resulted in formation of a peripheral free space in the bottom of the hearth. Addition of an agglomerate of particles to the bottom of the particle bed, resulted in less particle movements and retarded formation of the peripheral free space.
Initially it was intended to carry out these tests also numerically using Bluescope Steel’s particle simulation package DPSim. Because of problems with validating DPSim for the application with float-sink motions induced by buoyancy forces, this section was constrained to a sensitivity analysis on the program. The study showed that the float-sink behaviour of the particle bed was insensitive to friction parameter adjustments in the tested range. It was also discovered that the assigned simulation time was of significant importance. This indicates that the common practise of reducing the runtime may not be valid for this application.
i ii Acknowledgements
ACKNOWLEDGEMENTS
This Thesis was carried out at Bluescope Steel Research, Port Kembla, Australia, as the final step on my way to a master’s degree in Chemical Engineering at Luleå University of Technology, LTU. First, I would like to express my sincere gratitude to Doctor Paul Zulli at Bluescope Steel Research and Professor Bo Björkman at the faculty of process metallurgy, LTU, for making this numerable experience in Australia possible for me. I would also like to thank Paul for supervising, for inspiration and encouragement, and for the freedom I have been given throughout my work.
I would like to thank Bryan Wright, David Pinson and Ian Bean. Bryan and David for supervising and support with the numerical work, and Ian for helping with the experimental equipment. Thanks to Bryan also for helping me with everything and anything from the first day of my work until the last.
Finally, I would like to thank all the others in the unit for six very rewarding months as a member in the group. I have very much appreciated the open door policy, all valuable discussions and feedback, and your longsuffering patience with my almost never ending questions.
Pajala, March 2006
Pär Semberg
iii iv Table of contents
TABLE OF CONTENTS
INTRODUCTION 1
1 LITERATURE REVIEW 3
1.1 Overview of the blast furnace 3 1.1.1 The upper zone 3 1.1.2 The cohesive zone 4 1.1.3 Force modelling in the upper- and cohesive zone 4 1.1.4 The lower zone 4 1.1.5 Force balance in the lower zone 7
1.2 Conclusion 12
2 EXPERIMENTAL 15
2.1 Introduction 15
2.2 Equipment 15
2.3 Experiments conducted 16
2.4 Uniform, central and peripheral pressure distributions 17 2.4.1 Equipment 17 2.4.2 Results 18 2.4.3 Discussion 21
2.5 Laser tracking of bed movement 21 2.5.1 Equipment 22 2.5.2 Results 23 2.5.3 Discussion 25
2.6 Tests with extreme distributions 27 2.6.1 Equipment 27 2.6.2 Results 28 2.6.3 Discussion 32
2.7 Bottom profile 33 2.7.1 Equipment 33 2.7.2 Results 34 2.7.3 Discussion 35
2.8 Faoled bed 36 2.8.1 Equipment 36 2.8.2 Results 37 2.8.3 Discussion 38
3 NUMERICAL WORK 39
3.1 Introduction 39
3.2 Method 40
3.3 DPSim Buoyancy model and modelling parameters 40
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3.4 Experimental equipment and procedure 42 3.4.1 Box test for estimating the angle of repose 42 3.4.2 Experimental buoyancy model 43
3.5 Results 44 3.5.1 Box tests 44 3.5.2 Buoyancy tests 45
3.6 Discussion 54
CONCLUSIONS AND RECOMMENDATIONS 57
REFERENCES 59
APPENDIX 1 APPENDIX 2
vi Introduction
INTRODUCTION
The blast furnace has been used for producing iron from ore since at least the 14 th century in the Nordic countries, and the process is still today responsible for the majority of the steel production in the world. In the past, “know how” of the blast furnace process most probably was limited, and obtained by practical experiences. Not until recently, during the 20th century, have efforts in terms of applied research been made. The process is capital intensive, and in order to be cost efficient the furnace must be run at long operational lifetime, high availability and high efficiency(Wright, 2002). Today there is a fairly good understanding of the general principles governing the blast furnace ironmaking process.
The blast furnace is basically a high temperature, counter current, multiphase reactor where descending iron oxides are reduced by ascending carbon monoxide gases, produced in the lower level of the vessel. The ore and coke are packed in discrete layers to maintain sufficient permeability in the bed, even after the ore loses its permeability due to softening and melting further down in the shaft. From the softening/melting zone where all the ore has smelted, only coke remains intact with the molten metal on the bottom of the vessel, which is known as the hearth. Based on temperature variations in the refractory lining of the hearth, it has been suggested that the coke bed under some conditions is floating on the molten metal and slag, and sometimes sitting on the bottom of the furnace.
During recent years, quite a lot of effort has been made to explain the principles underlying the floating/sitting state of the hearth coke bed. However, the mechanisms proposed are novel, and not yet well understood.
At Bluescope steel research, a preliminary study, “Hearth Coke Bed Buoyancy- a preliminary investigation” was carried out experimentally, and numerically in order to shed some light on the fundamental principles governing the hearth behaviour. This work was an approach to model the hearth coke bed by force balances, with results indicating that bouyancy forces, and the casting cycle possibly could explain sitting and floating behavior of the dead man.
The aim of this thesis is to use the findings from the preliminary study and take a step further towards a deeper understanding for the physical phenomenas and conditions of the blast furnace hearth. Of particular interest, is the force balance of the hearth and the importance of buoyancy forces on the proposed floating and sitting states of the hearth coke bed or “deadman”. The previous work included preliminary evaluations by both experimental and numerical methods, and both these paths will be considered in this work as well .
1
2 1 Literature review
1 LITERATURE REVIEW
1.1 OVERVIEW OF THE BLAST FURNACE
The question of whether the coke in the hearth is floating or sitting during operation can be answered by a complete force balance on the whole furnace. In order to gain some understanding of the parameters possibly affecting the state of the deadman, the different parts of the furnace are first explained.
1.1.1 The upper zone
The principal raw materials of iron ore, coke and limestone are fed from above through a chute that distributes the raw materials into discrete layers of coke and iron ore, see fig 1.1. The ore layers are blends of sinter, lump and pellets. The coke is usually fed to make the coke layer slightly thicker in the center in order to enhance productivity and obtain optimum gas utilisation.
As coke is combusted in the blast zones known as raceways in the bottom of the shaft, the bed slowly moves down as the iron oxides are reduced by the ascending CO-gases. The ore, mainly hematite, in the reduction process goes through the oxidic states magnetite and wustite before formation of iron and melting occur further down. The residence time in the upper zone is usually 4-6 hours depending on radial location in the furnace.
Fig 1.1, Schematic picture of the blast furnace
Stable composition of the raw material, high iron content of the ore, and coke with high mechanical properties as well as good size distribution are important for efficient operation. Another important property is the permeability of the bed, and
3 here both size distribution as well as mechanical and chemical properties of the raw materials should be taken into account. The latter will affect the softening temperature range, where permeability in the ore layer is strongly reduced. Generally, sinter has a wider softening range than pellets and lump, and mixed iron ore charge (pellets, sinter and lump) requires that a higher pressure drop be taken into account as compared to, for example a 100% pellets run.
1.1.2 The cohesive zone
Further down in the furnace the ore burden starts to loose shape and sticks together due to increasing temperatures. This makes the ore layers almost impermeable, which means that the ascending gas has to pass this zone mainly through the windows formed by the coke layers that cut through the cohesive zone, see Fig 1.1. Depending on how the furnace is run, the CZ from analysis of furnace dissection is known to appear V-shaped, inverted V-shaped or W-shaped.
1.1.3 Force modelling in the upper- and cohesive zone
Recently, much work has been done in order to understand how the pressure of the material in the shaft is distributed through the bed down to the hearth. Theoretical force balances using the plasticity theory as applied on granular materials, has suggested the pressure to be higher in the centre of the furnace compared to the periphery (Takahashi et al., 2002). Also results from cold experimental models (Takahashi et al., 2002) as well as measurements on a full-scale blast furnace during filling and blow in (Inada et al., 2003) agree to this. However, the pressure distribution during operation has as yet not been examined, due to the hostile physical conditions of the process.
The mechanical properties of the coke remain fairly intact through the shaft, which is essential for the gas permeability of the bed. However, the softening of the ore in the cohesive zone, as described above, changes the properties of the granular ore bed, which might imply that the plasticity theory is not more applicable. Currently, there is no knowledge to what extent the arch-like shapes of the cohesive zone may affect the pressure distribution in the shaft. If the material in the cohesive zone stick together hard enough, it is reasonable that the inverted v- and w-shape to some extent should distribute the pressure towards the walls whereas the v-shape would lead to a distribution more dense in the centre.
1.1.4 The lower zone
Included in the lower zone are the raceways, which are the blast zones from the tuyeres around the periphery of the vessel, the hearth, the coke bed, and the molten slag and iron in the bottom of the hearth, see fig. 1.1 and 1.2.
4 1 Literature review
Fig. 1.2, shematic picture of the hearth.
1.1.4.1 The raceway zone
The burden material moves slowly down towards the raceways where coke is combusted, usually together with some additional fuel such as oil or pulverized coal, PCI, injected together with pre-heated air. Depending on the angle of repose for the coke bed, a sheer plane will form between a conical shaped almost stagnant zone, the deadman, and coke sliding down towards the raceways.
The combustion zone can be described as a cavity created in front of each tuyere, the name raceway stemming from the fast movement of the coke particles within this cavity. The raceway is surrounded by lump coke having bypassed oxidation on its way down the shaft. The coke in the lower regions around the raceway is considered to periodically fall in and combust in the raceway, which causes renewal of the coke bed as this material is replaced from above.
Dissections of blown out blast furnaces as well as coke probe borings have given valuable information of the inner profile at tuyere level. A detailed analysis exists, from the quenched and dissected Kukioka No. 4 blast furnace (Kanbara et al., 1977). The general raceway profile has a small cavity next to the tuyere, surrounded by coarse coke considered to have fallen down from above after shut down. The next zone is composed of small coke particles considered to be fluidized during operation, and together these zones can be considered the raceway when the furnace is running(Kanbara et al., 1977). In front of, and under the raceway is a zone called the “birds nest” due to the shape of it resembling a birds nest. This zone is composed of slag, pig iron and fine coke of -5 mm size.
Core probing through the tuyeres give about the same picture. The probe has been classified into three zones, the raceway, the deadman and the area in between. (Helleisen et al. 1989, Negro et al. 2001). This intermediate zone is reported to have a significant content of fines and liquid, and is sometimes referred to as a “birds nest” even though the meaning here is slightly different to the one described above.
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1.1.4.2 The hearth coke bed and the deadman
Under the cohesive zone the reduced iron and slag is melting and drippling down through the bed of coke remaining on the bottom, and accumulate in separate layers in the hearth of the furnace. Saturation of carbon in the molten iron is considered to take place in the submerged part of the hearth coke bed where the iron is in close contact with the porous coke bed.
In proper terminology “the hearth coke bed” is only the part of the coke bed that is submerged in the liquids. The upper part, i.e. between the liquid surface and the shear plane formed between moving and almost stagnant coke particles, is called the deadman as this part was earlier considered to be of less importance for the chemical reactions in the hearth. For convenience, if not specified, these terms will be used as synonyms throughout this work. The deadman has a porosity of about 0.3-0.5 (Nightingale et al. 2000, Kanbara et al, 1977) with the apparent density the coke at about 900 kg/m3 compared to 6800 kg/m3 for pig iron and 2500 kg/m3 for slag. The deadman is hence lying in the bath of molten iron and slag which will exert a non-negligible buoyancy force on the coke bed. If this force matches the down pressure of the burden material and the friction forces, the deadman will float up, partly or completely in the bath.
The condition and properties of the deadman are considered to be of critical importance to the blast furnace performance, affecting the drainage when the furnace is tapped, (Fukutake, Okabe, 1976a,b), the temperature distribution in the furnace(Shimizu et al. 1990), and the refractory wear (Preuer and Winter, 1993).
1.1.4.3 Iron and slag
The molten iron and slag accumulate as two separate layers, the denser iron on the bottom, and the slag floating on top of it. As iron and slag continuously drip down into the bath, the slag layer will consist of a mix of slag and iron droplets (Desai, 1993)
As the liquid levels are rising, iron and slag are tapped intermittently through one ore several tapholes. After the taphole is opened, usually only iron is flowing out first, the slag following after the time called the slag delay. During the tap, the liquid surfaces are inclining more and more due to the viscosity of the liquids and the resistance of the dead-man. Therefore, at the end of the tap residual slag will still remain above taphole level. At the same time, due to the pressure that develops close to the taphole, the iron is sucked out and drained to levels even below the taphole (Tanzil et al.,1984).
Bigger furnaces are tapped almost continuously through any of the tapholes whereas smaller furnaces may be tapped from the same taphole only at certain intervals, as the production is insufficient for continuos tapping practice. Because of this, bigger furnaces can be run with lower variation in liquid surfaces and hence more smooth operation can be achieved.
6 1 Literature review
1.1.4.4 Refractory
The hearth is lined with refractory bricks to resist the high mechanical and chemical wear from the molten liquids. Still, refractory erosion is what sets the lifetime of the furnace that ultimately has to be relined, and many measures to prevent hearth wear has therefore been employed.The hearth is usually cooled with water on the sides and sometimes also on the bottom. Depending on the temperature of the metal, the metal flow rates and the rates of cooling, skull layers of solidified metal may also form on the refractory. Hence, because of refractory wear and skull layer formation, the internal shape of the hearth varies along the lifetime of the furnace.
Inside the refractory are usually built in thermocouples, which measure the temperatures at different locations around the hearth. These temperatures are then used together with other data for estimating the condition of the hearth and the blast furnace operation in general.
The theories about floating and sitting states of the deadman are partly relying on temperature variations in the hearth refractory. This phenomenon is still not well understood, although one suggestion states that higher molten metal flowrates occur between the hearth pad and the deadman during floating as compared to the sitting deadman state(Fogelpoth et al.,1985).
1.1.5 Force balance in the lower zone
In previous work it has been shown that mathematical models based on the plasticity theory are able to simulate the burden pressure distribution on the hearth with reasonable accuracy, when compared to cold experimental models with granular materials. Quite a lot of research effort has also been made to understand the state and properties of the hearth during operation. A number of furnaces have been quenched and thoroughly examined during the years, especially in Japan during the 1960’s and 1970’s, and this information is still important for today’s research. Direct measurements during operation cannot be made, given the high temperatures and hostile physical conditions in the furnace during operation. Therefore, research has to be based on secondary measurements.
Below are listed different aspects of the blast furnace hearth, and for each aspect, the effects and properties that are considered important for the force balance in an operating blast furnace.
Aspect Effect
Liquid levels and drainage * Impact on buoyancy force * Cleaning of fines
Refractory erosion and sculling * Impact on hearth geometry and thermal properties
Porosity and permeability * Impact on gas and liquid flows of the coke bed * Impact on buoyancy force
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The raceway zone * Particle consumption and deadman renewal * Dustformation * Gas drag forces 1.1.5.1 Liquid levels
The level of the liquids in the hearth sets a direct limit of the maximum buoyancy force in the furnace. The buoyancy force also fluctuates together with the liquid level heights along the casting cycle. This fluctuation might be of significance especially in small furnaces where the total liquid level fluctuations are much greater than in big furnaces. For the latter, the iron/slag interface is usually located close to the taphole level.(Nightingale et al., 2000).
Several studies of the blast furnace hearth have been conducted in cold models, based on the liquid level fluctuation as the driving force behind proposed float-sink motions of the deadman. Based on a force balance, Takahashi et al., 2002 concluded that the liquid levels being operated in typical Japanese blast furnaces would reach a critical liquid level, where the buoyancy force and wall friction would equal the downward force from the burden weight. In the previous work (Wright et al., 2004), adapted the same model to include two liquids, and applied it to Blast Furnace No. 5 at Port Kembla. The model indicated the liquid levels to be very close to the critical condition even here.
Takahashi’s model is based on plasticity theory as applied on granular materials in axisymmetrical silos and hoppers. In the model, the volume above tuyere level is divided into thin slices from the top and downward, and the average stress for the whole volume calculated. The critical state is obtained by a force balance (see equation 1) on the submerged volume in the hearth, subject to the total force from above, FE (based on an average stress coefficient), the upward friction force from the hearth wall, F1, and the buoyancy force, F2. The different forces are given by equation 2, 3 and 4(Takahashi et al., 2002).
FE= F1-F2 (1)
2 FE=πRH Y(1-ε)(ρf-ρp)g (2)
2 F1=πRH σy,av (3)
F2=2πRHτw (4) where RH is the hearth radius, Y the liquid levels relative to the hearth bottom, the pad, ε the porosity, and ρf, and ρp the liquid and coke densities respectively. σy,av and τw are the average local vertical stress and the shear stress at the wall. Takahashi et al. * * recalculated these parameters to dimensionless numbers σ y,av and τ w that permit extension of experimental data obtained by a packed bed of sand to the blast furnace.
1.1.5.2 Refractory erosion and skulling
The depth and shape of the hearth are important when calculating the buoyancy force in the blast furnace. Due to refractory erosion and skull layer formation, the geometry of the hearth will be dynamic and change throughout the campaigns. In
8 1 Literature review
order to run the furnace effectively, several models for monitoring the inner profile of the hearth during operation have been developed. Most of these are based on thermocouples embedded in the hearth refractory and aim to estimate the position of the 1150 C isotherm. This is the lowest temperature at which carbon saturated iron may exist in liquid form and usually considered the solid-liquid boundary.
The hearth profile has been studied on several quenched and dissected blast furnaces as well as at the end of campaigns on furnaces to be relined. In the latter the highest wear is frequently observed along the bottom periphery of the hearth (Vogelpoth et al., 1985), sometimes referred to as “elephant-foot” erosion.
1.1.5.2.1 Refractory erosion
Vogelpoth et al. 1985 studied temperature profiles and residence times with tracer elements in the hearth. Temperature profile changes along the furnace campaign here lead to the conclusions that a peripheral flowpattern, seen in the beginning, is changed to central flow during a three month transition period. Tracer element residency times in another furnace also indicated on a peripheral flow pattern. For the first case the buoyancy force was suggested to have increased during the campaign due to larger hearth depth produced by refractory erosion. At first, partial floating around the furnace wall produced a peripheral flow and the resulting temperature profile, but at a certain hearth depth the buoyancy force was enough to float the bed, resulting in a more uniform central flow pattern.
Based on these findings Vogelpoth et al., with a force balance model calculated the “critical bottom of the hearth depth” which would represent the hearth depth required for a certain furnace diameter to keep the dead-man floating in the metal and slag.
1.1.5.2.2 Skull layer formation
As the hearth bottom is cooled the iron at the bottom and lower wall may solidify if the metal temperature is to low, or the metal flowrate along the wall is insufficient. This should have an impact on the effective hearth geometry and thus also on the total buoyancy force as discussed above.
Skull layers have also been suggested to be the direct reason for temperature fluctuations measured by thermocouples in hearth refractory. Takeda et al. 2000 suggested a low permeability zone to form in the dead-man, changing the liquid flows so that a stagnant layer is formed. This layer then solidifies to a skull due to the low heat transfer in the stagnant layer. In the study is concluded that the temperature in the Kawasaki Mizushima No. 4 blast furnace is switching between a high and low temperature period, without falling into the intermediate range. With an unsteady- state heat transfer model, the change from the low- to high temperature period was reproduced by a change in heat transfer coeffecient from 10 to 60Wm-2K-1. However, in a previous study of heat transfer between flowing molten metal and a brick surface (Sawa et al., 1992), measured heat transfer was more than 50Wm/s even for metal flowrates of 3×10-5 m/s. Based on this, Takeda et al.concluded that a stagnant solidified layer formed on the brick surface.
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After blow out and dissection of the Kawasaki Mizushima No. 4 blast furnace, a low permeability layer composed of crystallized graphite, coke ash, coke fines and metal droplets was found. The volumetric fraction of metal here was less than 30 % (Takeda et al.2000)
1.1.5.3 Porosity and permeability
Porosity and permeability of the coke bed in the lower zone has a big impact on the operation of the blast furnace as this directly affects both the ascending gasflow and the descending metal flow. From the force balance point of view, the density of light coke or other particles will also affect the total buoyancy force exerted on the bed by the liquids. The coke down in the hearth has gone through the mechanical, chemical and thermal rigours of prior handling and is expected to dynamically reflect coke quality changes. Porosity and permeability are primarily depending on the size and size distribution of the material in the packed bed, where fines increase the fluid- solid contact area and friction forces.
The solids flow in the stagnant zone is very slow with changes in the coke bed occurring over days and weeks. This slow turnover may contribute to significant radial differences in bed permeability, as coke in the centre remain in the bed much longer than coke in peripheral areas. Radial differences have been observed both in blast furnace dissections (Takeda et al., 2000), and tracer residence time studies (Negro et al., 2001).
1.1.5.3.1 Reduction of porosity and permeability
Core probing has also shown that permeability along the furnace radius correlates with the amount of fines in the bed. High amounts have led to gas distribution more along the hearth circumference which have a deforming effect on the cohesive zone. (Kamijo et al., 1989)
Generation of fines in the furnace can be connected to three general sources (Nightingale et al., 2002). The first one, that fines are charged into the furnace with the raw materials and fines generated due to volume and surface breakage during the descent in the shaft. Also included to this is the abraded products of surface weakening on the coke due to carbon solution loss reaction.
The second source is fines generated as unfluxed oxide particles such as SiO2, Al2O3, TiO2, CaO and MgO, which are solid at deadman temperatures and which may precipitate out from dripping slags. Finally, the third source is fines generated in the raceways. This may be coke debris formed in the raceway cavity or incompletely combusted char from commonly injected pulverized coal.
It has been observed that increased amount of PCI generally lowers the deadman permeability(Kamijo et al., 1989), and also that the velocity of the raceway blast affect the amount of fines deposited on the deadman surface (Ichida et al., 1988). The fines are carried into the deadman and the active coke zone with the raceway gases, and with the lower gas velocities in the dead-man centre, especially big coal particles may be deposited here.(Nightingale et al., 2002).
10 1 Literature review
The amount of fines deposited on the deadman has been shown to correlate negatively with gas flow permeability, where high amounts have led to flow distribution more along the circumference of the hearth which have a deforming effect on the cohesive zone. (Kamijo et al., 1989)
1.1.5.3.2 Dead-man renewal
Experiments with cold models have shown that the turnover of material in the deadman occurs through new coke entering the top of the deadman in the centre of the furnace (Shimitzu et al., 1990, Takahashi et al., 1996 and Nogami et al. 2002). Coke consumption occurs through mechanisms such as dissolution and chemical reaction, and through transportation of the coke particles in the deadman region. (Nogami et al. 2002). Cold model experiments have also shown that cyclic movements of the bed caused by the casting cycle may help deadman renewal(Nishio et al 1977, Shimitzu et al.,1990, Nogami et al. 2002, Takahashi et al. 2001).
The dissolution of carbon from the deadman coke into the molten iron is considered to be important especially for the removal of coke fines. The reaction of importance is:
C(Coke) +Fe(l) - > [C](hot metal)
Reduction of unfluxed oxides in the slag will also consume some coke. Earlier the general view was that the tapped metal mostly was saturated by carbon, but it has been shown that this is most often not the case (Nightingale et al.,2002). The permeability of the deadman is directly linked to the residency time for the hot metal, and hence also to the reaction time for carburisation. At Bluescope Steel, Port Kembla, the permeability of the deadman is estimated by the Deadman cleanliness index(DCI) using the difference between the actual carbon level and the level at saturation as base for the calculation.
To be able to maintain a permeable deadman it is necessary that the metal dripping through the bed consistently dissolve carbon so that fine carbonaceous material will be consumed and removed from the bed. If the bed is clean the metal will drain fast, which means it will arrive to the metal bath with good ability to further promote carbon dissolution and coke renewal in the deadman. The other benefit of short residence time is that the liquid to a much lesser extent will damage the lump coke above the liquid surface.
When drainage is retarded by low permeability in the deadman, the retained metal causes damage to the lump coke and arrives in the hearth with low ability for carbon dissolution and fines removal Also, at slow coke bed renewal, replacement is by previously damaged coke. This means that once the deadman has lost its permeability it will be difficult and take a long time to correct, (Nightingale et al.,2002).
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1.1.5.4 Raceway impact
Except for being a source of fine material, the raceways also affect some other features relevant to the blast furnace force balance.
First, the gas buoyancy force that arises when gas flows through the packed bed has a direct effect on the force balance. It has previously been taken into account by different means in both experimental and numerical models, and theoretically by for example Ergun’s equation, (Takahashi et al., 2002). Along the hearth circumference the burden pressure is reduced by raceway gasflow, and formation of a peripheral particle free layer is reported as an effect of the particles rising faster here compared to the central area (Shibata et al. 1989, Takahashi et al. 2001, Shinotake et al. 2003). The latter also reported the initial particle bed bottom shape to be unsensitive to changes in operating conditions of the model, if gas injection from the tuyeres was not included. The conditions changed were liquid level, particle extraction rate and the application of a load on the dead-man surface.
Second, the coke consumtion in the raceways is the driving force for burden descent, but also for the deadman renewal mechanisms observed in several cold model studies. The renewal mechanisms have been investigated in both 2D-models (Shibata et al. 1989, Takahashi et al. 1996 and 2004) and in half cut 3D-models (Nogami et al 2002, Shinotake et al. 2003 and Takahashi et al. 2001). In these studies both raceway particle consumption, as well as sink-float deadman movements were included in the models.
Two main renewal paths can be considered(Takahashi et al. 1996 and 2001, Nogami et al 2002). The first one is particles that enter the deadman in the centre, descend deep down into the stagnant bed, and then, with the up-and-down movements of the bed gradually turn to move towards the raceways. The other is discharge of the particles close to the shear plane of the deadman. At accumulation the bed is lifted up and these particles are then moved out to the main stream towards the raceways, and either joining that stream or going back to the stagnant layer when the bed sinks.
In the studies mentioned above the liquid level fluctuation was one of the components in the renewal mechanisms. However, Nouchi et al., in 2003, experimentally and numerically showed a particle free layer to form based on buoyancy force and particle extraction only, ie. Without the impact of liquid level changes. In a model with wooden beads in water, it was also shown that a particle free layer was formed only when the particle extraction was placed under, or at the same level as the water surface. When the outlet was placed a little above the water level(the bottom of the outlet opening 10mm above the water surface), at steady state, no particle movements under the outlet level occurred, and the coke free layer was limited.
1.2 CONCLUSION
In this literature review, the blast furnace hearth and the different aspects of importance for particle movements are considered. Especially, the conditions and mechanisms that would govern the dynamics between floating and sitting states of hearth coke bed have been studied.
12 1 Literature review
This topic has been studied in several experimental and numerical models of the hearth. Considering the results and conclusions from these works, one of the areas that needs further investigation is the effect of the burden force distribution on the hearth. The work in this thesis is concerned with investigating this area using experimental and numerical hearth models. The models include a packed bed of particles subject to different downward force distributions. As raceway coke extraction and possibly the liquid level fluctuations can be considered the engines behind particle movement in the hearth, the work of this thesis will also aim to include these features in the models studied.
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14 2 Experimental
2 EXPERIMENTAL
2.1 INTRODUCTION
As stated in the literature survey, the pressure distribution on the hearth coke bed is one of the important unknown parameters in blast furnace hearth modelling. The aim of the experimental work in this chapter is to analyse the bed behaviour subject to different pressure distributions together with the motions induced by fluctuating liquid levels in the vessel. As in many of the previous studies, this work is concerned with clarifying the solid behaviour based on the assumption that floating and sinking of the deadman with the casting cycle occurs. In this study, particle movements were recorded in a 3D model with a force mesh applied on a bed of plastic balls in water.
The experiments were designed to evaluate the following:
• Patterns and mechanisms of particle movements in the bed (Especially mechanisms leading to the formation of a free layer, and transport of particles to the raceway zones). • The change of the bottom profile when particles are moving in the bed • The impact of different pressure distributions on particle movements and bottom profile.
2.2 EQUIPMENT
Experimentally, the blast furnace hearth was simulated by a cylindrical perspex tank that was used in a previous study (Wright et al., 2004). The vessel had a diameter of 386 mm and height of 400 mm. A series of concentric rings loaded with different amounts of sand was used to achieve the specific force distribution required for each experimental run. The rings were made of thin steel, perspex pipe and plywood. An outlet was placed in the bottom of the tank; this was connected to a pump that allowed filling and drainage of the vessel. In all experiments described below the volumetric flowrate of the pump was kept at 1500 cm3/min. Mono sized plastic balls with a diameter of 20 mm and density of 250kg/m3 were used to simulate the coke particles.
The experimental hearth was designed to simulate the geometry of Blast furnace No. 5 at Port Kembla, simplified to a cylinder with the width of the furnace taken at taphole level. With a radius of 193 mm, the vessel is 1/27 th scale, which implies a coke bed height of 234 mm according to Table 2.1.
15
Table 2.1, specification of the experimental equipment used.
To achieve the desired bed geometry, 4350 particles were used. The liquid level was set to achieve floating at a level of 15.0 cm corresponding to the general liquid level in BF 5 according to Wright et al., 2004. The burden weight applied to make this happen was obtained by trial and error, and shown to be 5.5 kg.The upward force was also calculated theoretically using Equation (2). Neglecting the friction force, and with a bed voidage of 0.37 (obtained by saturating the bed with water) a burden weight of 6.75 kg was obtained. Due to an error when preparing the equipment, the final total weight used in all experiments was 5 kg, which set onset of floating to occur at around 14.3 cm.
To obtain a reasonable range in the bed movement, the liquid level was varied between 11 and 16 cm, corresponding to a wider span than in BF No. 5, where a multiple taphole casting practice gives relatively stable liquid levels. Generally this meant a height of about 2 cm of the particle free layer at floating, and bed touch down occurring at around 12 cm during casting.
2.3 EXPERIMENTS CONDUCTED
Three main series of experiments were conducted. They are:
1 Experiments with uniform, central and peripheral pressure distributions applied over the whole bed surface area. For each distribution 10 casting cycles were conducted.
2 Laser tracking of the hearth bed throughout the casting cycle.
3 Experiments with almost all weight applied uniformly in the centre or along the periphery to simulate extreme cases. Also a distribution obtained by Takahashi et al. 2002, with almost all pressure applied on the central 2/3 of the radius was simulated. For each distribution, the weight required to stop the upward movement of a constraint applied on the open area was studied. The particle bed movement was studied during three casting cycles, and the movement of the constraint recorded.
As a special test case, a large agglomerated body of glued particles was placed in the bottom of the bed, to represent a faoled hearth.
16 2 Experimental
2.4 UNIFORM, CENTRAL AND PERIPHERAL PRESSURE DISTRIBUTIONS
2.4.1 Equipment
These experiments were carried out with concentric rings made of thin steel applied as weights. The radial pressure distributions are shown in Fig. 2.1, (for further information, see App. 1). The total weight was applied in such a way as to give the three pressure distributions shown in Table 2.2.
Table 2.2, Data for the concentric rings. Ring 1, centre 2 3 4, wall
Douter(cm) 17,2 17,2 27,2 37,3
dinner(cm) 0 8,2 18,8 18,8 2 A(cm ) 232,4 179,5 303,5 815,1
Pressure distributions for total weight of 5 kg
140
120
100 ) 2 Uniform 80 Central Peripheral 60 Wall Pressure(kg/m 40
20
0 0 5 10 15 20 Radius(cm)
Fig 2.1, Radial pressure distributions tested.
As can be seen in Fig 2.1, a gap of about 10 mm was kept in between the rings, to minimize the frictional force. In the experiments, it was shown that internal movements in the ball bed were limited, and no device was needed to guide the weights.
When the concentric rings had been applied to the bed, the bed was subject to 10 casting cycles with a water flow rate of 1500cm3/min. At the floating state of each cycle, the height of the free layer was recorded. The height was measured at one position in the centre, and as an average of four positions along the wall.
As the balls in direct contact to the wall moved a little in relation to the rest of the bed at the first movement of the bed, the tracer particles were placed about one particle diameter from the wall. The position in the centre was measured with a measuring stick inside a tube applied to the bottom of the bed as shown in Fig. 2.2.
17
At onset of floating the tube lifted with the balls, the stick still standing on the bottom of the vessel, providing a very exact measurement of the coke free layer height.
Fig. 2.2, Device used for measuring the free layer in the centre of the vessel.
2.4.2 Results
Uniform pressure distribution
Table 2.3, Heights of free layer and liquid levels at bed movement for uniform distribution. Cycle hWall ave.hCentre hWall ave.-hCentre Lift at Sink at Touch down 1 2.31 2.2 0.11 14.3 14.3 12.2 2 2.31 2.2 0.11 14.2 12.2 3 2.25 2.2 0.05 14.2 14.4 12.1 4 2.33 2.2 0.13 14.2 14.3 12.2 5 2.31 2.2 0.11 14.2 14.4 12 6 2.31 2.2 0.11 14.3 14.4 12 7 2.25 2.2 0.05 14.3 14.4 12.1 8 2.31 2.2 0.11 14.3 14.4 12 9 2.26 2.2 0.06 14.2 14.4 12.1 10 2.25 2.2 0.05 14.3 14.3 12 Averages 2.29 2.20 0.09 14.25 14.37 12.09 *All values in cm
18 2 Experimental
Free layer heights for uniform pressure distribution
2,6 2,4 2,2 2,0 1,8 1,6 1,4 Wall average 1,2 Centre
Height(cm) 1,0 0,8 0,6 0,4 0,2 0,0 01234567891011 Cycle
Fig 2.3, Heights of free layer along wall and in centre through 10 casting cycles.
Central pressure distribution
Table 2.4, Heights of free layer and liquid levels at bed movement for central distribution.
Cycle hWall ave.hCentre hWall ave.-hCentre Lift at Sink at Touch down 1 2,06 1,9 0,16 14,4 14,2 11,9 2 2,18 1,9 0,28 14,5 14,2 12,1 3 2,10 1,9 0,20 14,4 14,1 12,1 4 2,18 1,9 0,28 14,5 14,2 12,2 5 2,20 1,9 0,30 14,2 14,2 12,2 6 2,21 1,9 0,31 14,3 14,2 12,2 7 2,18 1,9 0,28 14,35 14,3 12,3 8 2,18 1,9 0,28 14,4 14,3 12,2 9 2,15 1,9 0,25 14,4 14,3 12,2 10 2,16 1,9 0,26 14,4 14,2 12,2 Averages 2,16 1,90 0,26 14,39 14,22 12,16 *All values in cm
19
Free layer heights for central pressure distribution
2,4 2,2 2,0 1,8 1,6 1,4 Wall average 1,2 1,0 Centre Height(cm) 0,8 0,6 0,4 0,2 0,0 01234567891011 Cycle
Fig 2.4, Heights of free layer along wall and in centre through 10 casting cycles.
Peripheral pressure distribution
Table 2.5, heights of free layer and liquid levels at bed movement for peripheral distribution. Cycle hWall ave.hCentre hWall ave.-hCentre Lift at Sink at Touch down 1 1,98 1,95 0,03 14,2 14,2 12,3 2 2,01 2,05 -0,04 14,3 14,2 3 2,11 2,1 0,01 14,1 14,3 12,3 4 2,03 2,0 0,02 14,2 14,1 12,25 5 2,04 2,0 0,04 14,4 14,2 12,2 6 2,08 2,0 0,08 14,3 14,2 12,3 7 2,15 2,1 0,05 14,2 14,25 12,3 8 2,08 2,1 -0,02 14,3 14,35 12,2 9 2,06 2,05 0,01 14,4 12,25 10 2,06 2,05 0,01 14,35 14,25 12,25 Averages 2,06 2,04 0,02 14,26 14,25 12,26 *All values in cm
20 2 Experimental
Free layer heights for peripheral pressure distribution
2,4 2,2 2,0 1,8 1,6 1,4 Wall average 1,2 1,0 Centre height(cm) 0,8 0,6 0,4 0,2 0,0 01234567891011 cycle
Fig 2.5, Heights of free layer along wall and in centre through 10 casting cycles.
2.4.3 Discussion
From the three charts and tables above, it is seen that the bed is stable without any indications of internal movements through the runs. The values for the free layer height are recorded at about one particle diameter from the wall. The same measurement technique was used throughout the run; nevertheless a possible error of ± 1 mm should be taken into account. It is also important to appreciate that the average height of the particles along the periphery depends on which specific particles are chosen, whereas the measuring stick in the centre measures the movement of the guiding pipe kept in place by the pressure from all particles around it. The important parameter here is therefore the change of the wall height relative to the centre.The biggest change of this parameter during 10 cycles is 0.8 mm, 1.5 and 1,2 mm for uniform, central and peripheral pressure distributions respectively.
Given the source of error for the wall average value, and the fact that no internal movements of the rings were observed, these results indicates that the hearth bed remains stable without internal distortions under the assigned conditions.
2.5 LASER TRACKING OF BED MOVEMENT
In the experiments with different pressure distributions, a hanging phenomenon could clearly be observed. This implies a delay of bed sinking from the moment water starts to be pumped out. From Fig. 2.3-2.5 (summarized in Table 2.6 below), it can be seen that the water level sinks from 16.5 to about 14.3 cm before the bed starts to move down.
21
Table 2.6, Average values for liquid levels at bed movements during the casting cycle.
Distribution Center Lift at Max. Liq. level Sink at touch down Uniform 2.20 14.25 16.50 14.37 12.09 Central 1.90 14.39 16.50 14.22 12.16 peripheral 2.04 14.26 16.50 14.25 12.26 Average 2.05 14.30 16.50 14.28 12.17 *All values in cm
2.5.1 Equipment
In order to provide a more exact picture of this phenomenon, the movement of the bed at uniform pressure distribution was tracked by means of a laser mounted above the vessel according to fig. 2.6.
Fig 2.6, Setup for tracking of the bed movement during casting.
Measures were made first on a non-flexible weight, but also for comparison, using the concentric rings and recording the movement both in the centre and along the periphery. The measurements were made on subsequent cycles on the same bed, just changing the location of the laser and the weights in between the runs.
As the ball bed was not touched in between the measurements, contrary to all the other runs, this set of experiments could be conducted without stirring the bed and wetting the balls not previously submerged. Liquid bridging has previously been suspected to affect the friction forces within the bed, and these runs thus also provided an opportunity to measure this effect, when compared to previous results. Data were collected for a cycle both before and after the cycles, when the actual laser recordings were done, to ensure stable conditions.
A final run was also performed where the setup was left for 20 hours after accumulation, to see if the bed would slowly approach a level not governed by wall friction. The results can be seen below.
22 2 Experimental
2.5.2 Results
Hearth bed movement, measured by laser
0.025
0.02
0.015
0.01 level(m) 0.005
0 00:00:00 00:01:00 00:02:00 00:03:00 00:04:00 00:05:00 00:06:00 00:07:00 -0.005 time (min)
Fig, 2.7, Laser tracking of the particle free layer with one single non-flexible weight. The black line indicates start of drainage.
Bed movement, as measured on the outermost ring
0.025
0.02
0.015
0.01 level(m) 0.005
0 00:00:00 00:01:00 00:02:00 00:03:00 00:04:00 00:05:00 00:06:00 00:07:00 -0.005 time (min)
Fig, 2.8, Laser tracking of the particle free layer measured on the outermost of the concentric rings providing the uniform force mesh. The black line indicates start of drainage.
23
Bed movement, as measured on the innermost ring
0.025
0.02
0.015
0.01 level(m) 0.005
0 00:00:00 00:01:00 00:02:00 00:03:00 00:04:00 00:05:00 00:06:00 00:07:00 -0.005 time (min)
Fig, 2.9, Laser tracking of the particle free layer measured on the innermost of the concentric rings providing the uniform force mesh. The black line indicates start of drainage.
Table 2.7, Heights of free layer and liquid levels at bed movement during laser tracked casting cycles.
Tracking with non flexible weight
Cycle hWall ave.hCentre hWall ave.-hCentre Lift at Max. liq. level Sink at Touch down 1 2,10 2,3 -0,20 14 16,5 14,6 12,2 2 2,40 2,3 0,10 14 16,5 14,6 12,25 3 2,59 2,3 0,29 13,9 16,5 12,2
Peripheral tracking
Cycle hWall ave.hCentre hWall ave.-hCentre Lift at Max. liq. level Sink at Touch down 1 2,10 2,4 -0,30 14 16,5 14,6 12,5 2 2,49 2,5 -0,01 13,9 16,5 14,6 12,7 3 2,63 2,35 0,28 14 16,5 14,6 12,2
Central tracking
Cycle hWall ave.hCentre hWall ave.-hCentre Lift at Max. liq. level Sink at Touch down 1 1,98 2,2 -0,23 13,9 16,5 14,5 12,4 2 2,31 2,3 0,01 14 16,5 14,55 12,4 3 2,60 2,5 0,10 14 16,5 14,5 12,4
Averages 2,35 2,35 0,00 13,97 16,50 14,57 12,36 *All values in cm
Table 2.8, Change of the free layer with 20 hours between readings Date Side 1 Side 2 Side 3 Side 4 Wall ave. Centre hWall ave.-hCentre Lift at Sink at Touch down Jun 1 11.53am 2.5 2.4 2.3 2.5 2.43 2.2 0.23 14.1 Jun 2 08.05am 2.5 2.45 2.3 2.55 2.45 2.2 0.25 14.5 12.1 *All values in cm
.
24 2 Experimental
2.5.3 Discussion
Hysteresis or hanging It is clear that hysteresis or a hanging phenomenon occurs when the direction of the liquid flow in the tank is changed. Here the average difference in the liquid level for onset of floating to touchdown is 1.6cm. This is about the same as the difference between the level before casting and the point when the bed starts moving down, 1.9cm. In the study of different pressure distributions (see Table 2.6) these values are even closer, 2.1 and 2.2 cm respectively.
This can be explained by the force balances as illustrated in Fig. 2.10. Here, the friction forces act on the bed during both the upward and downward movement. Equillibrium in the force balance requires the buoyancy force, FB, to change by two times the wall friction, FF, when changing the direction of movement. In these tests the average delay in bed movement was 1.75 cm(see Table 2.7). When the bed is stagnant,the buoyancy force is proportional to the liquid level change. This implies the friction force to correspond to 1.75/2=0.875cm.
Fig 2.10, Force balance of the hearth for a) upward, and b) downward movement.
Fig. 2.11 shows the reconstructed bed and liquid movements for two float-sink cycles. The reconstruction is based on the average values in Table 2.7, and linear movement of the bed at the same speed as the liquid level, as confirmed by Fig 2.7- 2.9. The dashed line represents the reconstructed case when tracking a particle located at the same level as the liquid surface when the buoyancy force equals the gravitational force of the bed. This level can be roughly calculated both from the point for onset of floating (13.97-0.875= 13.095) or the point for touchdown (12.36+0.875=13.235).
It should be noted that Fig 2.11 illustrate the bed movement as function of the liquid level. In the experiments, liquid was pumped at constant flowrate which changes the liquid level speed, at the change between the moving and nonmoving state of the bed.
25
Reconstructed bed and liquid level movement
18
16
14
12
10
8 level(cm) 6
4
2
0
Fig. 2.11, Reconstructed particle free layer height and liquid level based on data from laser tracking of the bed.
Comparison with previous reports The bed movement pattern described above would be the expected for a cylinder- piston device. Hanging or hysteresis has been reported also previously (Takahashi et al., 2004, Hirsch et al., 2003). However, in most of the cases, the transfer from the hanging and moving state of the bed has not been as distinct as shown in Fig 2.7-9.
In the present preliminary tests more pronounced hanging was observed when a greater weight was applied on the bed. This trend can also be seen in the work of Hirsch et al., where a blast furnace model with both filled and half filled shaft was studied. The results here indicated more pronounced hanging and less internal distortions in the bed with the bigger load of particles in the shaft. A possible explanation to the bed behaviour in this study is therefore that the load applied on the bed strengthens friction forces within the bed that counteract internal distortions. The high size ratio of around 1:10 between particles and hearth radius in this study compared to ~1:50 and ~1:30 used by Takahashi et al. and Hirsch et al. respectively, could also contribute to higher friction and interparticular locking within the bed.
Wet or dry particle bed Comparing the results from a wet and dry particle bed (Table 2.6 and 2.7), the average bed movement delay increases from 1.75 to 2.15 cm when wetted. This is a difference of about 23 %. According to the discussion above, the frictional force is proportional to this delay, which indicates that extra friction, possibly in the form of capillary forces, are added to the bed when wet.
It was suspected that the hanging particle bed would slowly descend with creeping motions in the vessel. However, 20 hours after floating the particle bed, no movements could be detected (see Table 2.8).
26 2 Experimental
2.6 TESTS WITH EXTREME DISTRIBUTIONS
Takahashi et al. 2003 proposed through theoretical calculations and experiments in a blast furnace shaped vessel, a force distribution with almost all the pressure applied on the central area of the hearth. In Takahashi’s study, the pressure reduction at tuyere level around the hearth wall is due to the raceway zones, and the transition from the high- to low pressure area on the radius is remarkably sharp.
As the intention with this work was to provide a sensitivity analysis of the pressure distribution impact, experiments were performed to examine the hearth bed behaviour with pressure applied only on parts of the bed. The rest of the bed surface was left open without any constraint. Some preliminary test runs with the equipment showed that the bed under these conditions was redistributed, balls moving upwards at the open area, and the weight moving down. A constraint was therefore put over the open area and the experiments were designed so that more and more of the total weight was transferred over to the constraint. This was continued until the bed was moving as a whole, without internal distorsions in the bed.
As mentioned in the literature survey, the upward movement of particles towards the tuyeres due to buoyancy, has been discussed in a number of studies. However, knowledge of the impact of the pressure distributions on the hearth is limited.
Three different pressure distributions were tested:
1 Central pressure distribution with all the weight (5kg) applied on the two innermost of the concentric weights described above. This corresponds to a circular area with a radius of about 45 % of the total hearth radius.
2 Peripheral pressure distribution with all the weight (5kg) applied on the outermost ring of the rings used in the previous runs, corresponding to ca 22 % of the total radius.
3 Also, a central distribution as above according to Takahashi et al. 2003 was examined. Here the total weight (5 kg) was applied on an area corresponding to about 62% of the hearth radius.
The tests with these distributions were tracked for three cycles. Both the height of the constraint as well as the coke free layer were measured both at the sitting and floating states
2.6.1 Equipment
Due to the movements of the bed, a problem arose with a tendency of the weights to lean over, touching the wall or the constraint. This added a possible friction source, and thus made it difficult to estimate the true force distribution. Guiding the weight by glass beads rolling between the weight and guiding walls solved this problem. The beads were kept in place by a piece of double sided tape, which formed a simple low friction bearing mechanism, see Fig. 2.12.
27
Fig 2.12, Setup for guiding the weight through the descent in the particle bed.
Due to the distortion of the bed, the shape of the bottom in many of the cases was conical. This caused floating of the bed to occur at higher liquid levels. As the bed movement was shown to be critical to the distortion of the bed, the maximum height of the liquid was increased from the 160 mm used in previous experiments, to180 mm. The minimum liquid level was also changed to 110 mm to ensure the bed would be sitting on the bottom of the vessel at the end of casting. The liquid flow rate was maintained at 1500cm3/min as before.
The concentric rings used for the force mesh did not fit Takahashi’s pressure distribution. The time limits of this project did not allow manufacturing of a new cylinder, and therefore a plastic bucket with the right dimensions, reinforced by a 4 mm plywood board in the bottom was used. The bucket was not perfectly cylindrical, having a wall angle of 2.6 degrees.
2.6.2 Results
In the case of a peripheral pressure distribution, the distortion created a free layer high in the centre and low along the periphery. However, here the particles at the wall side shaded the view, making accurate measurements of the free layer height difficult. These measurements were therefore not made as in the cases of central pressure. Note also that there is no indication that a periheral pressure distribution would occur in the blast funace. Therefore, the main objective with the peripheral pressure distribution was to obtain information on the get an idea of the constraint weight needed to stabilise the bed. Each case was therefore run for only one cycle as opposed to three for the two central pressure distributions.
The results are seen in the tables and figures below.
28 2 Experimental
Peripheral pressure
Tested pressure distributions of peripheral type
120.000
100.000
) 80.000 2 112g 300g 60.000 500g 700g
Pressure(kg/m 40.000 Wall
20.000
0.000 0 5 10 15 20 Radius(cm
Fig. 2.13, Pressure distributions of peripheral type for different constraint weights used.
Table 2.9, Change of bed movement when the pressure successively is transferred over to the constraint.
Wt const. Disup at Lift at Sink Touch down Distot 0.112kg 12.2 - - - - 0.200kg 12.5 - - - - 0.300kg 13.0 - - - - 0.400kg 12.0 - - - - 0.500kg 12.5 15.7 14 14.2 1.5 0.600kg 15.4 15.9 13.5 0.8 0.700kg 13.3 15.3 15.6 13.2 0.3 *All values in cm Disup at = liquid level at first observed bed distortion at accumulation
Distot = total ascendence of constraint relative to the weight
29
Central distribution
Tested pressure distributions of central type
180.000
160.000
140.000
) 120.000 2 1400g 100.000 1550g 1700g 80.000 2000g
Pressure(kg/m 60.000 Wall
40.000
20.000
0.000 0 5 10 15 20 Radius(cm)
Fig 2.14, Pressure distributions of central type for different constraint weights used.
Bed movements for different pressure distributions of central type
30
25
20
Free layer 15 Level of constraint Height(cm)
10
5
0 0101201230123 Cycle
Fig. 2.15, Constraint level change and formation of a peripheral free layer over three float sink cycles when the pressure successively is transferred over to the constraint. From left to right the curves represent cases with constraint weights 1400g, 1550g, 1700g and 2000g.
30 2 Experimental
Takahashi’s distribution
Tested pressure distributions of Takahashi type
120.000 110.000 100.000 90.000 125g ) 80.000 2 300g 70.000 500g 60.000 700g 50.000 900g Pressure(kg/m 40.000 Wall 30.000 20.000 10.000 0.000 0 5 10 15 20 Radius(cm)
Fig. 2.16, Pressure distributions of Takahashi’s type for different constraint weights used.
Bed movements for different pressure distributions of Takahashi's type
30
25
20
Free layer 15 Level of constraint Height(cm)
10
5
0 0120123012301230123 Cycle
Fig. 2.17, Constraint level change and formation of a peripheral free layer over three float sink cycles when the pressure successively is transferred over to the constraint. From left to right the curves represent cases with constraint weights 125g, 300g, 500g, 700g and 900g.
31
Please note that for the cases in the two bed movement charts above, the tests with the biggest pressure gradients had do be interrupted before three float-sink cycles were completed. The reason for this was that the weight had descended below the guiding walls described in section 2.6.1.
2.6.3 Discussion
Bed stability In all three cases above, it is seen how transferring the weight over to the constraint stabilises the bed. The pressure ratios between the weight and the constraint for the stabilised bed with peripheral, central and Takahashi’s distribution were 0.11:0.89, 0.84:0.16 and 0.84:0.16 respectively. Given a total weight of 5 kg in all cases, the corresponding pressure gradients in absolute terms is varying more, see Appendix 1. This indicates that the ratio of the pressures on the two areas might have a greater impact on the stability of the bed than the total absolute pressure gradient. Factors such as total pressure applied, and the size of the open area under the constraint should still be taken into account.
Upward particle movements along hearth periphery Fig 2.15 and 2.17, show that the constraint moves upward quite fast in the beginning, but at a slower rate after the first cycles. These results indicate that the constraint might approach an equilibrium level, which is further discussed under the heading “Bottom profile” below. It is interesting to note that internal distortions were observed to occur when casting to a much higher degree than when accumulating. For accumulation distortion was observed mainly in the first cycle, and this happened when the difference in pressure distribution was large. For more moderate pressure gradients, distortions were observed only when the bed was sinking.
These observations are confirmed by the data in Appendix 1. The suggested explanation is that when the bed is moving up, friction between the wall and balls in contact with the wall, is acting down, as does the burden weight. During sinking, wall friction affects the balls in contact to the wall with an upward force, opposite to the force of the burden weight, which produces a significant pressure gradient between the weight and the wall, see Fig. 2.18. This makes the bed move uniformly at accumulation, but at casting the bed yields within itself under the shear forces, so that the particles in the center move down faster than those close to the wall.
Fig. 2.18, Force balance for a) upward bed movement b)downward movement.
32 2 Experimental
The results above have shown the particle movement to be quite unsensitive to the pressure distributions applied on the bed. However, if the pressure is significantly reduced over one part of the bed, internal distortions will occur. These results can also be compared to those of Shinotake et al., 2003. In this study a 3D-BF model with gas injection, particle extraction and float-sink motions was used. The conclusion made was that the bottom profile was more or less unsensitive to changes such as water level,the particle extraction rate, or the application of a load on the deadman. The addition of tuyere blasts, which is considered to strongly reduce the downward pressure from the burden materials under the raceway, caused the deadman bottom to gradually rise up towards the furnace wall.
Equipment In both the cases with central pressure the weight was observed to lean over to touch the guiding glass beads after 2-3 cycles. A gap of about 1 mm was left in between the beads and the weight when setting up the rig. The maximum angle at which the weight can lean decreases the longer the distance from the bottom of the weight to the beads. The weight can therefore increase its leaning angle when the bed is lifted. To sink the bed, the leaning angle must be reduced again when the weight slides down on the guiding beads. This should add some friction, especially with the slightly inclined walls of the bucket that was used as weight for Takahashi’s pressure distribution.
2.7 BOTTOM PROFILE
As the tapping cycles were found to be of significant importance for the bed movement, this additional series of experiments was carried out in order to gain insight in the influence of the casting cycle of the bed behaviour over an extended period.
2.7.1 Equipment
The same experimental setup was used as in the tests with extreme pressure distributions described above. Limiting factors were the total distortion allowed by the experimental equipment used. The weight used for the extreme central pressure was only 12 cm high which limited the total descent before the weight falled below the guiding walls. Therefore, the bucket used for the tests with Takahashi’s pressure distribution was used, despite the slight inclination of the bucket walls. Two cases differing only in constraint weight were tested, in order to observe one higher and one lower total bed distortion over the 10 casting cycles in question. The constraint weights were 300g and 700g. Four black balls were also placed on the bottom of the vessel, and the position continuously marked out on the transparent perspexe board during the run. As such, any movement in this part of the bed could be tracked.
33
2.7.2 Results
Fig 2.19, Constraint level change and formation of a peripheral free layer over 10 casting cycles. a) represents a case with 700g on the constraint, and b) and c) are different ways of displaying a case with a 300g constraint. b) displays the free layer formation by tracking a set of tracer particles that move up the wall, whereas the lowest particle at each measuring point is tracked in c).
During the 10 casting cycles, the weight descended 10 mm in the case of the 700g constraint, and 25mm in case of the 300g constraint.
34 2 Experimental
Movement of particles on the bottom of the hearth bed
20
15
10
5
300g constraint 0 700g constraint -20 -15 -10 -5 0 5 10 15 20 Hearth periphery
hearth radius(cm) -5
-10
-15
-20 hearth radius(cm)
Fig 2.20, Particle movement on the bottom of the hearth bed during 10 subsequent casting cycles
During the 10 cycle experiments, movements of the tracer particles were recorded as illustrated in Fig. 2.20. The movements were quite small, and in order to get more distinct measurements, the positions were marked every two casting cycles. For the 700g case, the particle movements were very limited, with no preferred direction of this movement. For the 300g case, the balls are clearly moving out towards the periphery, the average total movement being 16.8 mm. Movements were not observed at every reading, but occurred at different times for the different particles (see App. 1 for details).
2.7.3 Discussion
Fig. 2.19 shows that the 700g constraint is moving upwards slightly during the first casting cycle but seems to approach an equilibrium level towards the end of the run. The corresponding tracer particle movement (Fig. 2.20) is also very limited.
The two graphs of the 300g constraint case, b) and c) in Fig. 2.19 are different only in the manner in which the height of the free layer is tracked. In b) the same four particles are followed throughout the 10 cycles. However, the particles in the bottom of the vessel are moving out towards the periphery with an average of 1.7 mm per cycle (Fig. 2.20), and after about five cycles the four tracer particles selected were no longer the lowest positioned particles. Therefore the second curve of the 300g constraint case, c) in Fig. 2.19 shows the coke free layer when new particles have been chosen after the previous ones have moved up in the bed. From these two
35 graphs, and from Fig. 2.20, it is seen that the particles continue to move upward in the bed throughout the experiment whereas the free layer height and the bottom profile seem to reach equillibrium.
It has previously been shown that the inclination of the bottom on a submerged particle bed, particles being extracted at the level of the liquid surface, approach a bottom angle, which is equal to the angle of repose (Shibata et al, 1989, Nouchi et al., 2003). However, with an angle of repose of approximately 29 degrees (see Fig.3.5) for the bed in this case, theoretically the height of the coke free layer should approach a height of 107 mm for a radius of 193 mm. An explanation to this is that the bottom profile was observed to flatten out as the bed touched down every cycle. According to observations, the radius of the area touching the bottom at the minimum liquid level in all cases corresponded to a radius of at least 100 mm.
As stated earlier the constraint of the 700g case seems to reach an equilibrium level, but also the curve of the 300g graph indicates a tendency to slow down. This is reasonable as the buoyancy force on the bed is decreasing in the peripheral area when the free layer gets thicker. At the same time the weight of this zone increases by the particles transferred to the upper peripheral area when the constraint is pushed up.
2.8 FOULED BED
As discussed on page 8 and 9 in the literature survey, a fouled and impermeable bed is considered to play an important role in blast furnace operations. In this study the mechanical impact of a lump in the bottom of the bed was studied, and the results compared to one of the previous runs without the fouled part. This experiment was not planned in the original schedule, and therefore only one case was run to provide preliminary results for future studies.
2.8.1 Equipment
The experimental setup was exactly the same as in the earlier tests with extreme distributions and “bottom profile”, with a bed subject to Takahashi’s pressure distribution, and a 300g constraint over the open area along the hearth periphery.
The agglomerate of particles in the bottom of the bed was made up of 122 balls in four quadratic layers fixed together with hot glue. In the centre the device for measurements of coke free layer centre height described in section 2.4.1 was also added (see Fig 2.21).
36 2 Experimental
Fig. 2.21, Agglomerate of particles representing a fouled bed. The particles missing in the upper back corner were lost when the experimental rig was being demounted.
2.8.2 Results
The height of the coke free layer along the wall and the constraint level above the bottom of the vessel are shown in Fig. 2.22. For details, see App. 1.
Fig. 2.22, Constraint level change and formation of a peripheral free layer over 10 casting cycles. a) represent particle movements in the bed subject to Takahashi’s pressure distribution wiht a 300g constraint on the peripheral area, and with a cluster of glued particles in the bottom of the bed. b) and c) represent cases with a clean bed and constraint weights of 700g and 300g respectively.
37
2.8.3 Discussion
It is clear that the bed movement for the fouled bed is restricted compared to the equivalent case with a clean bed. The bed with a 300g constraint behaves in a manner similar to the case with a 700g constraint for a clean bed. The result was first believed to be due to experimental errors, and therefore the experiment with a 300g constraint and a clean bed was repeated in a quick 3-4 casting cycle run (not documented). The bed behaviour was observed to be consistent with the previous result (case c) in Fig 2.22).
Based on the results in section 2.4.1, it was believed that the slip planes induced by the ingot shaped lump, would help particle movement in the bed. However, these results indicate the lump to act rather like a reinforcement. Further investigations should still be carried out before clear conclusions can be drawn.
38 3 Numerical work
3 NUMERICAL WORK
3.1 INTRODUCTION
The intension with the work in this section was initially to take a step further, to be able to compare the results obtained experimentally with simulations on a numerical model. Because of problems with validating the numerical model for float-sink motions induced by buoyancy forces, this part was constrained to a sensitivity analysis on the program for this application.
Discrete particle simulation DPS is finding more and more applications as increased computer power enables larger and larger systems to be simulated, within reasonable processing times. DPS is growing in popularity especially in areas where the constitutive equations for granular flow in continum modelling techniques, are not fully developed, (Wright et al., 2004). At BlueScope Steel Research a DPS package called DPSim was developed in the late 1990’s. Since then, this package has been successfully used in a number of applications, such as transfer chutes and blast furnace solid flow (Wright et al., 2004).
In the previous study, hearth coke bed buoyancy –a preliminary investigation (Wright et al., 2004), a preliminary attempt was made to use DPSim for modelling of the blast furnace hearth. This is a system influenced by viscous and buoyancy forces, which means a new application for the program. DPSim was concluded to simulate experimental results reasonably well. However, the error margins of the experimental system used are quite large, and the trends of the results indicate a discrepancy between experimental and numerical results. Fig.3.1 shows a comparison of the change of liquid level height and a free layer as simulated by DPSim and in a validating experiment.
0.14
0.12
0.1
0.08
0.06 Height (m) Height
0.04
0.02
0 0 50 100 150 200 250 Time (s) Liquid Level DPSim Liquid Level Free Space Height DPSim Free Space Height Fig 3.1, Comparison of DPSim prediction for experimental measurements, (Wright et al., 2004).
It was believed that part of the explanation for the discrepancy could have been forces such as liquid bridging/capillary forces that are not included in DPSim, having more impact than expected.
39
The hysteresis seen on the experimental free space curve in Fig. 3.1 has also been reported previously (Hirsch et al., 2003, Shinotake et al., 2003 and Takahashi et al. 2004). The latter also reported 2D-DEM simulations where the hysteresis trend during sinking was well represented.
3.2 METHOD
In this part of the thesis, a new effort is made to validate DPSim for buoyancy simulations in the blast furnace hearth. The study was composed of a new, more comprehensive experimental study and a sensitivity analysis on the same system in DPSim. The aim was to determine appropriate values of the impact parameters for the DPSim model, to replicate the experimental results. An estimate of the friction coefficients was first made by measuring the angle of repose in a small box and a 1:1 comparison to DPSim-simulations for the same system, at different combinations of friction coefficients.
3.3 DPSIM BUOYANCY MODEL AND MODELLING PARAMETERS
DPSim models a system based on particle properties such as stiffness, coefficient of restitution and friction coefficients to calculate the position and movement of each particle at all times. The forces acting on each particle are determined and the equations of linear and rotational motion integrated to determine the particles position as time advances. The software contains a powerful pre-processor that permits the creation of complex geometries (eg the blast furnace hearth), and a post- processor for result visualisation (eg positions, velocities and forces)
In the study of Wright et al., the liquid was defined as a moving surface, and as soon as the centre point of a particle was located under that surface, a buoyancy force was added in the axial direction for the whole particle volume (Wright et al., 2004). Damping of the liquid buoyancy forces, and liquid drag forces were not considered. The free layer height was tracked measuring the lowest particle in the bed through the simulation. The only change made to the model in this study is that the buoyancy force is calculated taking into account that the particle might only be partly submerged. In the model used by (Wright et al., 2004), buoyancy corresponding to the total particle volume was applied as soon as the liquid surface reached a level above the centre of the particle. It should be noted that this improved model still remains a simplification of reality.
The file of input parameters of DPSim contains the parameters listed in table. 3.1. In this work, simulations were performed in order to investigate the effect of varying one parameter at a time. Also listed in Table 3.1 are the standard values used for the parameters that were not of interest in a specific study. An explicit explanation of these parameters is offered further down in the text.
Table 3.1, standard values for DPSim input data. Time step 2.50E-05 Stiffness 5000 Sliding friction coefficient 0.3 Rolling friction coefficient 0.05 Ds max 0.3 Coefficient of restitution 0.6
40 3 Numerical work
Timestep and stiffness
The time step is the time in between re-evaluations of the forces acting on the particles. In DPSim stiffness is represented by the linear spring model, and the stiffness coeffecient is a measure of how rigid the particle contact is and how much resultant force is applied at overlap between two particles. High particle velocities relative to the timestep may lead to significant particle overlaps, which will cause significant errors in determination of the force magnitude and direction. To prevent force propagation over particle boundaries within a single timestep, the timestep used must be smaller than some critical timestep, tc. tc depends on the particle mass, m, and stiffness, k, of the particles according to: tc=√(m/k)
The stiffness coefficient is therefore selected such that the required timestep is large enough to permit acceptable run-time performance.
Sliding friction coefficient.
The sliding friction coefficient is the dimensionless friction coefficient in Coulomb’s friction law, FFr=μ*N. Possible theoretical values hence range in between 0 and 1. In the previous study the coefficient was determined to be 0.3, and values found in the literature for experiments of the same type often lie in the range of 0.3-0.5. In this sensitivity analysis values in between 0.1 and 0.9 were tested.
Rolling friction coefficient.
The rolling friction coefficient, γr, is a measure of the resistance to rolling motion at particle-particle and particle-wall contacts due to elastic deformation of the contact surfaces. It signifies the radius of the contact circle in between two particles as illustrated in Fig 3.2. Generally the value used is less than 0.1 of the particle radius.The value used in the previous study was 10^-7, and in this sensitivity study the range of 10^-7-0.001 will be covered.
Fig. 3.2 Schematic representation of rolling friction torque for particle on a flat plane. Two particles in contact is analogous
41
Ds max
Dsmax is a measure of how tangential deformation can be stored at a contact point before slipping occurs. This value ranges between 0 and 1, the value in the previous study being 0.3. In this study values from 0.1 to 0.9 were tested
Coefficient of restitution
This parameter is a measure of how much of the energy is lost when the particle impacts and bounces off another surface. The value is hence the ratio of the speed of separation, vsep, to speed of approach, vapp, or the square root of the ratio between the height from which a particle is being dropped, hf, to the height the particle bounces after impact, hinit. e=vsep/vapp. =√(hf/hinit)
This parameter was not considered to be of big significance in the slow moving system in question, and a value of 0.6 obtained by a very simple drop-test procedure was used in all simulations.
3.4 EXPERIMENTAL EQUIPMENT AND PROCEDURE
3.4.1 Box test for estimating the angle of repose
In this experimental a 300*300*300 mm perspexe box was used to measure the angle of repose for the 20mm rigid plastic spheres used in the buoyancy experiments, see fig. 3.3. The box had one side hinged, and when this side was opened, particles flowed out, leaving a characteristic slope on the particles that remained in the box. Similar tests were also carried out in the previous study (Wright et al., 2004), however, in this study the box diameter was made twice as large to provide more exact measurements. Also, at the bottom of the hinged side, a 20 mm high lip was built to take away the effect of particles sliding out on the low friction perspex bottom.
Fig 3.3, The box tester
42 3 Numerical work
The procedure for measuring the angle of repose was as follows:
• The hinged side of the box was locked with a hook and the box filled up with 3600 balls. • The hinged side was quickly opened and the particles allowed to flow out. • A ruler was aligned with the bed surface plane on the transparent wall, and the height at the front- and backside recorded. • Five consequent runs were performed and the average angle calculated. After each test, all particles were removed from the box to ensure the same filling practice for every test
Initially it was intended to measure the angle of repose in the centre of the box tester to minimize the wall effect. In the DPSim visualisation program, slices through the bed can be made at any location allowing easy examination of any part of the box. However, experimentally no reliable method was found to measure the slope in the centre, and therefore the wall slope was chosen for the comparison.
3.4.2 Experimental buoyancy model
The first approach here was to simulate a system of the same size and simulation time used for the validation work in the previous report(Wright et al., 2004). However, for a system of around 4000 particles and a simulation time of about 250 s for a casting cycle, about 4 days of the available CPU time was required. In order to enable a sensitivity analysis with a reasonable range, the system was scaled down to 80 particles in a hearth with a diameter of 82 mm. The total simulation time was set to 25 s, of which two seconds was for filling up the system with the particles, and five seconds of constant liquid height between accumulation and tapping in each cycle.
The experimental hearth was made up of an 82 mm diameter perspex tube with a valve in the bottom. The bed movement was measured by means of a laser distance measurement device mounted on top of the tube constantly tracking the position of the bed. As it was observed that the balls on top of the bed moved internally, a piece of paper sheet was put on top of the balls to enable exact tracking of the bed, see fig. 3.4.
In the experimental, the volume of water pumped into the vessel per second was held constant, whereas the liquid surface velocity was constant in DPSim. To make the experimental and numerical simulations as similar as possible, therefore the speed of the pump was adjusted to make the filling time from the onset of floating until the coke free layer reached a height of 35mm, five seconds.
43
Fig 3.4, 80 particle experimental rig.
3.5 RESULTS
3.5.1 Box tests
The results of the experimentally obtained angles of repose for five runs and a calculated average are summarized in the table below.
Table 3.2, Angle of repose as measured in the box tester. hback(cm) hfront(cm) Anglerepose(deg) 21.2 5.2 28.07 20.7 4.6 28.22 21.7 4.1 30.40 21.3 4.6 29.10 21.1 5.1 28.07 Average 28.77
The corresponding angles of repose obtained for different combinations of friction coefficients in DPSim are summarised in the chart below.
Angle of repose for different sliding and rolling friction
50
45
40 Csliding 0.1 Csliding 0.3 35 Csliding 0.5 Csliding 0.7 30 Csliding 0.9 Angle of repose(deg) of Angle
25
20 0.0001 0.01 0.05 0.10 Rolling friction coefficient
Fig 3.5, Angles of repose measured on a 50 mm slice on the wall side in DPSim.
44 3 Numerical work
Angle of repose for different sliding and rolling frictions
50
45
40 Csliding 0.1 Csliding 0.3 35 Csliding 0.5 Csliding 0.7 30 Csliding 0.9 Angle of repose (deg) of Angle 25
20 0.0001 0.01 0.05 0.10 Rolling friction coefficient
Fig 3.6, Angles of repose measured on a 50 mm slice in the centre of the box in DPSim. In the experiments it was observed that the slope in the centre was slightly less steep than close to the wall, and this effect is also clearly seen in the two charts above with slopes created in DPSim. In these simulations the same friction coefficient is used for the balls and the wall, and this might add a small error. On average for all cases, the difference is 1.05 degrees more for the slope on the wall side.
The slope continues to decrease in the centre at 1.0E-4 rolling friction, for all but the lowest sliding friction, whereas the slopes on the wall side seem to be not as sensitive to further changes of the coefficient. The two charts also show that the bed is not completely uniform and that some error margins need to be taken into account.
3.5.2 Buoyancy tests
3.5.2.1 Experimental
During the experiment, the tracking of the bed was started at the same time as the pump, which was turned off five seconds after the bed started to move. After another five seconds the pump was turned on in the reverse direction. When repeating the experiment, it was observed that the 5 s period with non-moving liquid level was sensitive to the reaction time of the operator. Below are therefore provided charts with the change of the free layer height from four different runs.
45
Experimental (1)
0.080 0.070 0.060 0.050 0.040 0.030 level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig 3.6, Laser tracking of 80 particles over one casting cycle.
Experimental (2)
0.080 0.070 0.060 0.050 0.040 0.030 level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig 3.7, Laser tracking of 80 particles over one casting cycle.
Experimental (3)
0.080 0.070 0.060 0.050 0.040 0.030 level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig 3.8, Laser tracking of 80 particles over one casting cycle.
46 3 Numerical work
Experimental (4)
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig 3.9, Laser tracking of 80 particles over one casting cycle.
In the table below, is the data of bed movement from five additional casting cycles and averages for the liquid level at onset of floating, and touch down.
Table 3.3, bed movement in five tested cases. Lift Max. liq. Level Touch down 3,80 7,35 3,00 3,80 7,40 2,80 3,70 7,60 2,80 3,90 7,70 2,60 4,00 7,60 2,60 Average 3,84 7,53 2,76 *All values in cm
The liquid level was not continuously tracked in the experiment, but the level reconstructed based on the average data in table 3.3 and the first of the four experimental cases as shown in fig. 3.10. The reconstruction uses Microsoft Excel least square trend lines to pick out the start and end of accumulation, 2.8s and 8.6s, and the start and end of the bed sinking during tapping, 14.2s and 20.6s respectively. The point where tapping starts is taken 5s after the end of accumulation, 13.5s. (For more information about the reconstruction, see App 2).
Experimental (1), with liquid level reconstruction
0.080 0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 -0.020 time(s) Free layer Liquid level
Fig. 3.10, Free layer height and reconstructed liquid level.
47
The dip at the start of casting is due to the lower volume of water per height unit in the bed compared to the coke free layer. With tapping at constant flowrate, this makes the liquid surface to move faster when the bed is stagnant. The total dip in the reconstruction is 10 mm which is in agreement with the observations.
The trend with the steep dip of the water level at the beginning of tapping was observed also in the study of Wright et al. (see Fig. 3.1) and in preliminary tests with 3600 particles in the beginning of this study, see fig. 3.11.
Preliminary buoyancy tests, 3600 particles
70
60
50
40 Liquid level 30 Free layer level(m) 20
10
0 0 100 200 300 400 500 600 -10 time(s)
Fig. 3.11, Liquid level and free layer height in preliminary buoyancy tests.
48 3 Numerical work
3.5.2.2 Sensitivity analysis of the DPSim buoyancy model.
The results from the sensitivity analysis are shown below. All charts show the liquid level (purple) and the free layer (dark blue) during a tapping cycle including accumulation, a stagnant period and tapping. The results revealed that friction coefficients had much less impact on the results than expected. Below are graphs of the free layer change and liquid surface movement for all friction coefficient combinations. In the study it was also discovered that the velocity of the liquid surface had a significant impact on the results. A series of cases only differing in the total time assigned for the casting cycle was therefore performed, and these results are also included below.
The bed movement was shown to be insensitive to the parameters time step, stiffness and Dsmax in the tested ranges. Therefore, for these parameters only one case is shown in the end of this section. For the results of the whole range tested, see App. 2.
3.5.2.2.1 Friction coefficients
Fig. 3.12 shows a case with zero friction both in regards to sliding as well as rolling(coefficient = 10^-7). Fig. 3.13-3.22 then show three cases of sliding friction, each of them tested with a set of three different rolling friction coefficients.
Zero friction, Csliding=0, Crolling=10^-7
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.12, Bed movement at zero friction
49
Sliding friction coefficient 0.1
Csliding=0.1, Crolling=0.001
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.13, Bed movement at friction coefficients 0.1 for sliding, and 0.001 for rolling.
Csliding=0.1, Crolling=0.0005
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.14, Bed movement at friction coefficients 0.1 for sliding, and 0.0005 for rolling.
Csliding=0.1, Crolling=10^-7
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.15, Bed movement at friction coefficients 0.1 for sliding, and 10^-7 for rolling.
50 3 Numerical work
Sliding friction coefficient 0.3
Csliding=0.3, Crolling=0.001
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.16, Bed movement at friction coefficients 0.3 for sliding, and 0.001 for rolling.
Csliding=0.3, Crolling=0.0005
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 0.010 0 5 10 15 20 25 time(s)
Fig. 3.17, Bed movement at friction coefficients 0.3 for sliding, and 0.0005 for rolling.
Csliding=0.3, Crolling=10^-7
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.18, Bed movement at friction coefficients 0.3 for sliding, and 10^-7 for rolling.
51
Sliding friction coefficient 0.9
Csliding=0.9, Crolling=0.001
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3,19. Bed movement at friction coefficients 0.9 for sliding, and 0.001 for rolling
Csliding=0.9, Crolling=0.0005
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.20, Bed movement at friction coefficients 0.9 for sliding, and 0.0005 for rolling.
Csliding=0.9, Crolling=10^-7
0.070 0.060 0.050 0.040 0.030 <
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.21, Bed movement at friction coefficients 0.9 for sliding, and 10^-7 for rolling.
52 3 Numerical work
3.5.2.2.2 Accumulation time
Filling at 0.008m/s Csliding=0.3, Crolling=0.05
0.070 0.060 0.050
0.040 Liquid level 0.030 Free layer
level(m) 0.020 FL at zero friction 0.010 0.000 -0.010 2 4.5 7 9.5 12 14.5 time(s)
Fig. 3.22, Bed movement at 0.008 m/s liquid level rise. The free layer change at zero friction is from Fg. 3.12 and added for comparison.
Filling at 0.004m/s Csliding=0.3, Crolling=0.05
0.070 0.060 0.050
0.040 Liquid level 0.030 Free layer
level(m) 0.020 FL at zero friction 0.010 0.000 -0.010 2 7 12 17 22 27 time(s)
Fig. 3.23, Bed movement at 0.004 m/s liquid level rise. The free layer change at zero friction is from fig. 3.12 and added for comparison.
Filling at 0.002m/s Csliding=0.3, Crolling=0.05
0.070 0.060 0.050 0.040 Liquid level 0.030 Free layer
level(m) FL at zero friction 0.020 0.010 0.000 -0.010 2 1222324252 time(s)
Fig.3.24, Bed movement at 0.002 m/s liquid level rise. The free layer change at zero friction is from fig. 3.12 and added for comparison.
53
3.5.2.2.3 Time step, stiffness and dsmax
The parameters time step, stiffness and dsmax were tested in a range according to the table below. Parameter Timestep 0.9E-5 1.25 E-5 2.5 E-5 5.0 E-5 Stiffness 1500 2500 5000 8000 Dsmax 0.1 0.3 0.5 0.9 Fig. 3.25, Tested ranges for the parameters time step, stiffness and dsmax.
Csliding=0.3, Crolling=0.05, Time step=2.5E-5, Stiffness=5000, Dsmax=0.3
0.070 0.060 0.050 0.040 0.030
level(m) 0.020 0.010 0.000 -0.010 0 5 10 15 20 25 time(s)
Fig. 3.26, Typical curve of the bed movement, seemingly independent of the parameters, Timestep, Stiffness and Dsmax over the tested range.
No significant difference could be observed in between the tested cases above, and therefore only one of the cases is shown in Fig. 3.26.
3.6 DISCUSSION
EXP-NUM comparison
It can be seen that the main parameter that influences the free layer is the accumulation time. In order to have a liquid level velocity of 0.008m/s as in the DPSim simulations, the water level should have reached ~35mm above the point for onset of floating, in about 4.5 seconds. In the four experimental cases, the actual time is closer to 6 seconds, giving a liquid level velocity of ~0.006m/s. This should still be close enough to allow a reasonable fair comparison of the coke free layer behaviour.
54 3 Numerical work
Free layer heights
In the study of friction coefficient it is clear that changing the DPSim friction coefficients does not significantly alter the height of the free layer in the buoyancy model. The box test suggests combinations such as Crolling almost 1 for Csliding=0.1 and Crolling=10^-4-0.01 for sliding coefficient 0.3 –0.9. to be used in the DPSim buoyancy model. Comparison of the friction coefficient cases shows that the results are fairly similar in all of them, and that the free layer heights remain about the same as in the zero friction case. In the box test dry particles are forming a static slope against gravity. In the buoyancy test the surface properties are altered by the presence of liquid and the dominant force becomes buoyancy. It is likely that the box test is not a good parameter estimation model for buoyancy simulations
Hanging
The experimental curves in Fig 3.6-3.9 show the same trends as the graphs obtained with the larger model with weights applied (see Fig. 2.7-2.9). The bed moves at constant velocity during accumulation and tapping, with distinct transitions between the moving and non-moving states. The data in Table 3.3 and Fig 3.10 show that there is a delay in bed movement after tapping has started. This delay implies that a liquid level drop of about 1.0 cm is required to cause bed downward movement to happen.That is the same as the difference in liquid level at onset of floating, ~3.8 cm, to touchdown ,~2.8 cm. This behaviour is the same as observed in the tests with the larger model, which is discussed in section 2.5.3. At constant flowrate and a bed porosity of 0.5, the liquid level speed for a non-moving bed would be around (0.006m/s)/0.5 =0.012m/s. This gives a 0.8 s delay in movement of the bed relative the liquid surface for the liquid drop of 1.0cm.
The experiment varied liquid at a constant volumetric flow rate, the simulations at a constant linear position of liquid interface. This results in different liquid surface positions curves when the bed is stagnant at start of tapping, and is why no liquid level dip is seen in the simulations. In all cases simulated in DPSim excluding the series of longer simulation periods, there is a delay from the time the casting starts. However, the same type of delay can also be seen after onset of floating where the bed is loosing height in comparison to the liquid surface. When accumulation stops, the bed continues to rise taking this lost height back. This effect is clearly strongly dependent on the simulation time, and when accumulation time is increased to 35 seconds, the curve goes almost parallel to the liquid level. Observations from preliminary simulations with accumulation times on around 100 seconds showed the same trend, with the bed movement almost completely aligned with the liquid level, and a very sharp transfer from moving to stagnant states.
For gravity dominated systems such as dry granular flow, the runtime are commonly shortened down to save on the CPU-time required. DPSim has been used successfully in a number of applications, and these kinds of time shortening techniques are well established. The application of systems heavily influenced by viscous and buoyancy forces is more recent, the results of this work indicating that for these systems the common practice of reducing the runtime may not be valid
55
56 Conclusions and recommendations
CONCLUSIONS AND RECOMMENDATIONS
In this study experimental work was carried out to evaluate the particle movement patterns in the hearth coke bed when subject to buoyancy induced float-sink motions and different pressure distributions applied at tuyere level. The results of this study indicated that the particle bed moved as a whole without internal particle movements, when the pressure distribution was linear along the hearth radius. When the pressure was severely reduced along the hearth periphery, internal particle movements were observed in the bed. This resulted in a net transport of particles from the centre toward the wall on the bottom, and up along the wall. A mechanism where the float-sink motions of the bed and reduced pressure along the peripheral area are the driving forces, has been proposed for these particle movements. Preliminary tests with an agglomerate of particles in the bottom of the bed indicated that the lump acted as reinforcement, retarding internal particle movements. Comparison of these results with those in other studies indicated that the relatively large particles and the load also contributed to strengthen the bed against internal distortions. Recommendations for future work are therefore to study how the hearth particle movements and renewal mechanisms are affected by the particle size and size distributions as well as different types of fouled zones.
The use of Discrete Particle Simulation software has many advantages compared to experimental work when a more complex model is to be set up and when the range of parameters to be tested is wide. In this study, an effort to validate Bluescope Steels DPS package, DPSim, for hearth modelling was made. The study showed a discrepancy between experimental and simulated results, which was not affected by the different input data tested. It was also shown that changing timescale is dangerous and results need to be tested for this. In the study, the experiment varied liquid at a constant volumetric flowrate, whereas this was simplified to constant linear position of liquid interface in the simulations. In future work, model representation could be improved by calculating liquid surface position such that constant volumetric flow is maintained.
57
58 References
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61
APPENDIX 1
1.1 PRESSURE CALCULATIONS FOR THE DIFFERENT PRESSURE DISTRIBUTIONS TESTED
Data for the concentric weights representing the force mesh for uniform, central and peripheral pressure distributions on the experimental hearth Ring 1, centre 2 3 4, wall
Douter(cm) 17,2 17,2 27,2 37,3
dinner(cm) 0 8,2 18,8 18,8 A(cm2) 232,35 179,54 303,47 815,12
Uniform distribution Radial press.- 1 1 1 1 distribution P(kg/m2) 51,69 51,69 51,69 51,69 Weight(kg) 0,199 0,928 1,569 2,304
Central distribution Radial press.- 4 3 2 1 distribution P(kg/m2) 114,59 85,94 57,30 28,65 Weight(kg) 0,441 1,543 1,739 1,277
Peripheral distribution Radial press.- 2 3 4 5 distribution P(kg/m2) 24,64 36,96 49,28 61,60 Weight(kg) 0,095 0,664 1,496 2,746
Data for the weight and constraint representing the force mesh for extreme peripheral pressure distribution Ring 1, constraint 2, weight Ring 1, constraint 2, weight
Douter(cm) 27,20 37,30 Douter(cm) 27,20 37,30
dinner(cm) 0,00 28,70 dinner(cm) 0,00 28,70 A(cm2) 581,07 445,79 A(cm2) 581,07 445,79 weight(kg) 0,112 4,888 weight(kg) 0,300 4,700 P(kg/m2) 1,93 109,65 P(kg/m2) 5,16 105,43
P/(P1+P2) 0,02 0,98 P/(P1+P2) 0,05 0,95
Ring 1, constraint 2, weight Ring 1, constraint 2, weight
Douter(cm) 27,20 37,30 Douter(cm) 27,20 37,30
dinner(cm) 0,00 28,70 dinner(cm) 0,00 28,70 A(cm2) 581,07 445,79 A(cm2) 581,07 445,79 weight(kg) 0,500 4,500 weight(kg) 0,700 4,300 P(kg/m2) 8,61 100,94 P(kg/m2) 12,05 96,46
P/(P1+P2) 0,08 0,92 P/(P1+P2) 0,11 0,89
1
Data for the weight and constraint representing the force mesh for extreme central pressure distributions Ring 1, weight 2, constraint Ring 1, weight 2, constraint
Douter(cm) 17,20 37,30 Douter(cm) 17,20 37,30
dinner(cm) 0,00 18,80 dinner(cm) 0,00 18,80 A(cm2) 232,35 815,13 A(cm2) 232,35 815,13 weight(kg) 3,600 1,400 weight(kg) 3,450 1,550 P(kg/m2) 154,94 17,18 P(kg/m2) 148,48 19,02
P/(P1+P2) 0,90 0,10 P/(P1+P2) 0,89 0,11
Ring 1, weight 2, constraint Ring 1, weight 2, constraint
Douter(cm) 17,20 37,30 Douter(cm) 17,20 37,30
dinner(cm) 0,00 18,80 dinner(cm) 0,00 18,80 A(cm2) 232,35 815,13 A(cm2) 232,35 815,13 weight(kg) 3,300 1,700 weight(kg) 3,000 2,000 P(kg/m2) 142,03 20,86 P(kg/m2) 129,11 24,54
P/(P1+P2) 0,87 0,13 P/(P1+P2) 0,84 0,16
Data for the weights and constraints representing the force mesh for Takahashi’s pressure distributions Ring 1, weight 2, constraint Ring 1, weight 2, constraint
Douter(cm) 24,30 37,30 Douter(cm) 24,30 37,30
dinner(cm) 0,00 26,30 dinner(cm) 0,00 26,30 A(cm2) 463,77 549,46 A(cm2) 463,77 549,46 weight(kg) 4,875 0,125 weight(kg) 4,700 0,300 P(kg/m2) 105,12 2,28 P(kg/m2) 101,34 5,46
P/(P1+P2) 0,98 0,02 P/(P1+P2) 0,95 0,05
Ring 1, weight 2, constraint Ring 1, weight 2, constraint
Douter(cm) 24,30 37,30 Douter(cm) 24,30 37,30
dinner(cm) 0,00 26,30 dinner(cm) 0,00 26,30 A(cm2) 463,77 549,46 A(cm2) 463,77 549,46 weight(kg) 4,500 0,500 weight(kg) 4,300 0,700 P(kg/m2) 97,03 9,10 P(kg/m2) 92,72 12,74
P/(P1+P2) 0,91 0,09 P/(P1+P2) 0,88 0,12
Ring 1, weight 2, constraint
Douter(cm) 24,30 37,30
dinner(cm) 0,00 26,30 A(cm2) 463,77 549,46 weight(kg) 4,100 0,900 P(kg/m2) 88,41 16,38
P/(P1+P2) 0,84 0,16
2
1.2 EXPERIMENTAL DATA FOR UNIFORM, CENTRAL AND PERIPHERAL PRESSURE DISTRIBUTIONS
Uniform hwall.av.- Cycle hSide 1 hSide 2 hSide 3 hSide 4 hWall ave. hCentre hCentre Lift at Sink at Touch down 1 2.4 2.35 2.2 2.3 2.31 2.2 0.11 14.3 14.3 12.2 2 2.4 2.35 2.2 2.3 2.31 2.2 0.11 14.2 12.2 3 2.3 2.25 2.2 2.25 2.25 2.2 0.05 14.2 14.4 12.1 4 2.35 2.3 2.3 2.35 2.33 2.2 0.13 14.2 14.3 12.2 5 2.35 2.3 2.3 2.3 2.31 2.2 0.11 14.2 14.4 12 6 2.35 2.3 2.2 2.4 2.31 2.2 0.11 14.3 14.4 12 7 2.3 2.25 2.15 2.3 2.25 2.2 0.05 14.3 14.4 12.1 8 2.3 2.3 2.25 2.4 2.31 2.2 0.11 14.3 14.4 12 9 2.3 2.3 2.15 2.3 2.26 2.2 0.06 14.2 14.4 12.1 10 2.3 2.2 2.2 2.3 2.25 2.2 0.05 14.3 14.3 12 Average: 2.34 2.29 2.22 2.32 2.29 2.20 0.09 14.25 14.37 12.09
Central hwall.av.- Cycle hSide 1 hSide 2 hSide 3 hSide 4 hWall ave. hCentre hCentre Lift at Sink at Touch down 1 2.0 2.15 1.9 2.2 2.06 1.9 0.16 14.4 14.2 11.9 2 2.2 2.25 2.0 2.25 2.18 1.9 0.28 14.5 14.2 12.1 3 2.0 2.1 2.1 2.2 2.10 1.9 0.20 14.4 14.1 12.1 4 2.15 2.2 2.1 2.25 2.18 1.9 0.28 14.5 14.2 12.2 5 2.15 2.2 2.15 2.3 2.20 1.9 0.30 14.2 14.2 12.2 6 2.2 2.25 2.15 2.25 2.21 1.9 0.31 14.3 14.2 12.2 7 2.1 2.25 2.1 2.25 2.18 1.9 0.28 14.35 14.3 12.3 8 2.1 2.2 2.15 2.25 2.18 1.9 0.28 14.4 14.3 12.2 9 2.1 2.15 2.1 2.25 2.15 1.9 0.25 14.4 14.3 12.2 10 2.1 2.2 2.1 2.25 2.16 1.9 0.26 14.4 14.2 12.2 Average: 2.11 2.20 2.09 2.25 2.16 1.90 0.26 14.39 14.22 12.16
Peripheral hwall.av.- Cycle hSide 1 hSide 2 hSide 3 hSide 4 hWall ave. hCentre hCentre Lift at Sink at Touch down 1 2.1 1.9 1.8 2.1 1.98 1.95 0.03 14.2 14.2 12.3 2 2.05 2.0 1.85 2.15 2.01 2.05 -0.04 14.3 14.2 3 2.2 2.05 1.9 2.3 2.11 2.1 0.01 14.1 14.3 12.3 4 2.1 2.0 1.8 2.2 2.03 2.0 0.02 14.2 14.1 12.25 5 2.1 2.05 1.8 2.2 2.04 2.0 0.04 14.4 14.2 12.2 6 2.15 2.0 1.9 2.25 2.08 2.0 0.08 14.3 14.2 12.3 7 2.2 2.1 2.0 2.3 2.15 2.1 0.05 14.2 14.25 12.3 8 2.2 2.0 1.85 2.25 2.08 2.1 -0.02 14.3 14.35 12.2 9 2.1 2.0 1.9 2.25 2.06 2.05 0.01 14.4 12.25 10 2.1 2.0 1.9 2.25 2.06 2.05 0.01 14.35 14.25 12.25 Average: 2.13 2.01 1.87 2.23 2.06 2.04 0.02 14.30 14.25 12.26
* Here “h“ is the height of the free layer, and “Lift at“, “Sink at“ and “Touch down“ the liquid levels for the bed to lift at accumulation, onset of bed sinking at drainage, and bed touch down at drainage, respectively.
*All values in cm
3
1.3 EXPERIMENTAL DATA FROM LASER TRACKING OF THE HEARTH BED MOVEMENT
Central tracking hSide hSide hSide hSide hWall hWall ave.- Lift Max. liq. Sink Touch Cycle 1 2 3 4 ave. hCentre hCentre at level at down 1 2.4 2.3 2.2 2.4 1,98 2,2 -0,23 13,9 16,5 14,5 12,4 2 2.5 2.4 2.35 2.5 2,31 2,3 0,01 14 16,5 14,55 12,4 3 2.55 2.45 2.4 2.55 2,60 2,5 0,10 14 16,5 14,5 12,4
Peripheral tracking hSide hSide hSide hSide hWall hWall ave.- Lift Max. liq. Sink Touch Cycle 1 2 3 4 ave. hCentre hCentre at level at down 1 2,45 2,55 2,4 2,45 2,46 2,4 0,0625 14 16,5 14,6 12,5 2 2,7 2,65 2,6 2,7 2,66 2,5 0,1625 13,9 16,5 14,6 12,7 3 2,6 2,5 2,4 2,65 2,54 2,35 0,1875 14 16,5 14,6 12,2
Tracking with non flexible weight hSide hSide hSide hSide hWall hWall ave.- Lift Max. liq. Sink Touch Cycle 1 2 3 4 ave. hCentre hCentre at level at down 1 2,6 2,45 2,35 2,6 2,50 2,3 0,2 14 16,5 14,6 12,2 2 2,6 2,5 2,5 2,55 2,54 2,3 0,2375 14 16,5 14,6 12,25 3 2,55 2,5 2,3 2,6 2,49 2,3 0,1875 13,9 16,5 12,2 Here h is the height of the free layer, and Lift at, Sink at and Touch down the liquid levels for the bed to lift at accumulation, onset of bed sinking at drainage, and bed touch down at drainage, respectively. The height was measured on a particle located at one particle diameter from the wall of the model.
*All values in cm
4
1.4 EXPERIMENTAL DATA FOR EXTREME PRESSURE DISTRIBUTIONS
Extreme central pressure distribution C y c l Touch Wt const. ehSide 1 hSide 2 hSide 3 hSide 4 hAve hSide 2 hSide 3 hSide 4 hSide 4 hAve Disup Lift at Disdown down 1.400kg 1 00000.00 22.3 22.5 22.2 22.3 22.33 2.5 2.2 1.9 2.5 2.28 25.3 25.25 25.7 25.05 25.33 14.2 15.0 16.8 15.5 2 2.5 2.8 2.15 1.7 2.29 25.35 25.4 24.8 25 25.14
1.550kg 1 00000.00 22.5 22.2 22.4 22.5 22.40 2 2.3 2 1.8 2.03 24.9 24.6 24.9 24.8 24.80 15.0 15.0 15.8 13.3 2 1.6 1.5 1.4 1.4 1.48 24.15 24 24 23.9 24.01 2.85 3 3.1 3 2.99 25.8 25.5 25.7 25.55 25.64- 16.3 14.9 15.0 3 2.85 2.8 2.7 2.9 2.81 25.5 25.2 25.3 25.3 25.33
1.700kg 1 00000.00 22.3 22.2 22 22.2 22.18 2.85 3 3.1 3 2.99 25.8 25.5 25.7 25.55 25.64 13.0 14.8 16.5 12.0 2 0.65 0.7 0.5 0.4 0.56 23 22.85 22.3 22.75 22.73 2.6 2.85 2.7 2.75 2.73 25.4 25.25 24.7 25.1 25.11- 15.0 15.6 12.0 3 0.6 0.9 0.4 0.55 0.61 23.05 23 22.4 22.8 22.81 2.5 3.15 2.8 2.85 2.83 25.5 25.4 24.8 25.25 25.24- 15.4 14.7 12.0 4 0.7 1 0.5 0.6 0.70 23.1 23 22.5 22.85 22.86
2.000kg 1 00000.00 22.5 22.5 22.2 22.3 22.38 2.4 2.3 2.15 2.35 2.30 25 25 24.6 24.6 24.8 15.0 15.0 15.7 11.8 2 0.6 0.25 0.3 0 0.29 23.2 22.8 22.3 22.5 22.70 2.9 2.6 2.5 2.4 2.60 25.6 25.4 24.8 25 25.2- 15.0 16.0 3 0.75 0.3 0.3 0 0.34 23.8 22.85 22.3 22.5 22.86 2.7 2.6 2.6 2.5 2.60 25.7 25.4 24.8 25 25.2- 15.1 14.8 11.8 4 0.9 0.25 0.3 0 0.36 23.4 22.9 22.4 22.55 22.81 Here h is the height of the free layer, and Lift at, Sink at and Touch down the liquid levels for the bed to lift at accumulation, onset of bed sinking, at drainage and bed touch down at drainage, respectively. hAve. Disup and Disdown are the liquid levels where bed distortions first occurred at accumulation and at drainage respectively.
*All values in cm
5
Takahashi’s pressure distribution C y c l Touch Wt const. ehSide 1 hSide 2 hSide 3 hSide 4 hAve hSide 2 hSide 3 hSide 4 hSide 4 hAve Disup Lift at Disdown down 0.125kg 1 0000 0.00 22.8 22.5 22.4 22.7 22.60 1.751.15 1.65 1.8 1.59 25.6 25.1 24.6 25.2 25.13 13.2 15.1 16.5 13.0 2 0.4 0.7 0.7 0.4 0.55 24.7 24.6 23.9 24 24.30 1.752.6 2.5 2.3 2.29 26.6 26.6 25.75 25.8 26.19- 15.4 15.8 13.0 3 0.4 1.6 1.8 0.8 1.15 25.5 25.8 25 24.6 25.23
0.300kg 1 0000 0.00 22.3 22.5 22.6 22.9 22.58 32.9 2.65 2.9 2.86 25.3 25.6 25.5 25.8 25.55 14.3 15.0 15.7 13.5 2 1.7 1.7 1 1.4 1.45 24.5 24.6 24 24.5 24.40 43.8 3 3.8 3.65 26.7 26.8 26.3 26.8 26.65- 15.2 15.6 13.3 3 2.4 1.9 1.7 2.2 2.05 25.5 25.9 25.2 25.3 25.48 43.7 3.7 4.1 3.88 27.3 27.8 27 27.1 27.30- 15.6 15.7 13.6 4 3.5 2.7 2 1.3 2.38 26.5 26.8 25.9 26 26.30
0.500kg 1 0000 0.00 22.7 22.3 22.3 22.3 22.40 2.72.7 2 2.7 2.53 25.425252525.10- 14.8 15.5 12.0 2 1.3 0.6 0.4 0.3 0.65 23.6 23.1 22.8 23 23.13 43.2 2.9 3.1 3.30 26.2 25.7 25.55 25.8 25.81- 15.2 15.5 12.0 3 1.7 0.75 0.5 0.6 0.89 23.8 23.2 22.9 23.2 23.28 4.23.45 3 3.2 3.46 26.35 25.8 25.6 25.8 25.89- 15.3 15.9 11.9 4 1.8 0.85 0.5 0.6 0.94 23.9 23.2 23 23.4 23.38
0.700kg 1 0000 0.00 22.5 22.4 22.2 22.22 22.33 2.42.4 2.2 2.4 2.35 25 25 24.8 24.8 24.90 14.8 15.0 15.5 11.5 2 0.8 0.4 0.3 0.3 0.45 23 22.9 22.6 22.8 22.83 3.32.9 2.7 2.8 2.93 25.6 25.4 25.1 25.3 25.35- 14.7 15.4 12.3 3 1.3 0.8 0.4 0.5 0.75 23.7 23.2 22.7 23.1 23.18 3.73.2 2.7 2.9 3.13 26.2 25.8 25.2 25.6 25.70- 15.0 15.0 12.0 4 1.5 0.9 0.4 0.5 0.83 24 23.3 22.7 23.2 23.30
0.900kg 1 0000 0.00 22 22.1 22.2 22 22.08 2.62.5 2.5 2.7 2.58 24.8 24.7 24.9 24.8 24.80- 14.8 15.4 11.8 2 0.5 0.2 0.3 0.2 0.30 22.3 22.3 22.6 22.35 22.39 32.8 2.7 2.75 2.81 25 25 25.3 25.1 25.10- 14.8 15.0 11.8 3 0.75 0.3 0.4 0.25 0.43 22.4 22.3 22.7 22.4 22.45 3.23 2.9 3 3.03 25.15 25.1 25.5 25.2 25.24- 15.0 14.7 11.9 4 0.9 0.4 0.4 0.3 0.50 22.6 22.35 22.8 22.5 22.56 Here h is the height of the free layer, and Lift at, Sink at and Touch down the liquid levels for the bed to lift at accumulation, onset of bed sinking at drainage, and bed touch down at drainage, respectively. . hAve. Disup and Disdown are the liquid levels where bed distortions first occurred at accumulation and at drainage respectively.
*All values in cm
6
1.5 BOTTOM PROFILE
Tracking of bottom profile of the hearth bed subject to Takahashi’s pressure distribution, with a 700g constraint Free layer heights Level of constraint Cycle side 1 side 2 side 3 side 4 Average Cycle side 1 side 2 side 3 side 4 0 0 0 0 0 0.00 0 0 000 0.5 2.4 2.3 2.1 2.5 2.33 0.5 2.4 2.3 2.1 2.5 1 0.9 0.5 0.5 0.3 0.55 1 0.9 0.5 0.5 0.3 1.5 3.15 2.6 2.45 2.6 2.70 1.5 3.15 2.6 2.45 2.6 2 1.1 0.6 0.5 0.35 0.64 2 1.1 0.6 0.5 0.35 2.5 3.3 3 2.75 2.8 2.96 2.5 3.3 3 2.75 2.8 3 1.2 0.75 0.5 0.4 0.71 3 1.2 0.75 0.5 0.4 3.5 3.55 3.15 2.8 2.9 3.10 3.5 3.55 3.15 2.8 2.9 4 1.3 0.8 0.5 0.45 0.76 4 1.3 0.8 0.5 0.45 4.5 3.6 3.3 2.9 2.95 3.19 4.5 3.6 3.3 2.9 2.95 5 1.25 0.8 0.5 0.4 0.74 5 1.25 0.8 0.5 0.4 5.5 3.55 3.2 2.8 2.8 3.09 5.5 3.55 3.2 2.8 2.8 6 1.3 0.85 0.5 0.4 0.76 6 1.3 0.85 0.5 0.4 6.5 3.65 3.2 2.85 2.85 3.14 6.5 3.65 3.2 2.85 2.85 7 1.45 0.85 0.5 0.4 0.80 7 1.45 0.85 0.5 0.4 7.5 3.75 3.25 2.8 2.9 3.18 7.5 3.75 3.25 2.8 2.9 8 1.5 0.85 0.5 0.45 0.83 8 1.5 0.85 0.5 0.45 8.5 3.8 3.2 2.8 2.9 3.18 8.5 3.8 3.2 2.8 2.9 9 1.55 0.9 0.5 0.5 0.86 9 1.55 0.9 0.5 0.5 9.5 3.85 3.2 2.7 2.9 3.16 9.5 3.85 3.2 2.7 2.9 10 1.6 0.85 0.5 0.5 0.86 10 1.6 0.85 0.5 0.5
Tracking of bottom profile of the hearth bed subject to Takahashi’s pressure distribution, with a 300g constraint Free layer heights Level of constraint Cycle side 1 side 2 side 3 side 4 Average Cycle side 1 side 2 side 3 side 4 0 000 00.00 0 000 0 0.5 2.2 2.4 2.5 2.45 2.39 0.5 2.2 2.4 2.5 2.45 1 1.5 1.5 0.8 1.2 1.25 1 1.5 1.5 0.8 1.2 1.5 3 3.7 3 3.3 3.25 1.5 3 3.7 3 3.3 2 2.15 2.2 0.9 1.5 1.69 2 2.15 2.2 0.9 1.5 2.5 3.6 4.1 2.8 3.1 3.40 2.5 3.6 4.1 2.8 3.1 3 2.4 2.3 1.1 1.9 1.93 3 2.4 2.3 1.1 1.9 3.5 3.8 4.3 2.9 3.7 3.68 3.5 3.8 4.3 2.9 3.7 4 2.2 2.6 1.3 2.4 2.13 4 2.2 2.6 1.3 2.4 4.5 3.75 4.4 3.1 4.4 3.91 4.5 3.75 4.4 3.1 4.4 5 1.8 2.45 1.5 3 2.19 5 1.8 2.45 1.5 3 5.5 3.7 4.35 3.3 4.8 4.04 5.5 3.7 4.35 3.3 4.8 6 2 2.6 1.7 3.3 2.40 6 2 2.6 1.7 3.3 6.5 3.8 4.6 3.4 3.5 3.83 6.5 3.8 4.6 3.4 3.5 7 2.1 3.3 1.85 2 2.31 7 2.1 3.3 1.85 2 7.5 3.8 3.45 3.6 3.7 3.64 7.5 3.8 3.45 3.6 3.7 8 2 2.1 1.8 2.1 2.00 8 2 2.1 1.8 2.1 8.5 3.8 3.9 3.5 3.8 3.75 8.5 3.8 3.9 3.5 3.8 9 2.1 2.8 1.8 2.1 2.20 9 2.1 2.8 1.8 2.1 9.5 3.6 4.5 3.3 3.6 3.75 9.5 3.6 4.5 3.3 3.6 10 2 3 1.7 2 2.18 10 2 3 1.7 2 *All values in cm
7
Tracking four tracer particles touching the wall on the bottom of the hearth bed subject to Takahashi’s pressure distribution, with a 300g constraint Tracer particle levels Level of constraint Cycle side 1 side 2 side 3 Cycle side 1 side 2 side 3 Cycle side 1 side 2 0 0000 0000 00 0.5 2.2 2.4 2.5 0.5 2.2 2.4 2.5 0.5 2.2 2.4 1 1.5 1.5 0.8 1 1.5 1.5 0.8 1 1.5 1.5 1.5 33.731.5 33.731.5 33.7 2 2.15 2.2 0.9 2 2.15 2.2 0.9 2 2.15 2.2 2.5 3.6 4.1 2.8 2.5 3.6 4.1 2.8 2.5 3.6 4.1 3 2.4 2.3 1.1 3 2.4 2.3 1.1 3 2.4 2.3 3.5 3.8 4.3 2.9 3.5 3.8 4.3 2.9 3.5 3.8 4.3 4 2.2 2.6 1.3 4 2.2 2.6 1.3 4 2.2 2.6 4.5 3.75 4.4 3.1 4.5 3.75 4.4 3.1 4.5 3.75 4.4 5 1.8 2.45 1.5 5 1.8 2.45 1.5 5 1.8 2.45 5.5 3.7 4.35 3.3 5.5 3.7 4.35 3.3 5.5 3.7 4.35 6 22.61.7 6 22.61.7 6 22.6 6.5 3.8 4.6 3.4 6.5 3.8 4.6 3.4 6.5 3.8 4.6 7 2.1 3.3 1.85 7 2.1 3.3 1.85 7 2.1 3.3 7.5 3.8 5 3.6 7.5 3.8 5 3.6 7.5 3.8 5 8 2 3.7 1.8 8 2 3.7 1.8 8 2 3.7 8.5 3.8 5.6 3.5 8.5 3.8 5.6 3.5 8.5 3.8 5.6 9 2.1 4.5 1.8 9 2.1 4.5 1.8 9 2.1 4.5 9.5 3.6 6.2 3.3 9.5 3.6 6.2 3.3 9.5 3.6 6.2 10 2 4.6 1.7 10 2 4.6 1.7 10 2 4.6 *This table represents the same experimental case as the previous table. Only the values in blue are different, and represent the case when the tracer particles moved up in the bed, not more located on the bottom particle-coke free layer boundary.
*All values in cm
8
Tracking of the horizontal particle movement in a bed subject to Takahashi’s pressure distribution, by four tracer particles in the bottom of the bed. 300g 700g Side x y Cycle x y Cycle 1 0 11.7 1 0 3.2 1 0 12.3 3 0.3 3 2 0.4 12.85 7 0.7 12.9 11
2 93.61 3 0 1 9.4 4.05 4 2.35 0.6 2 9.8 4.6 7 2.1 0.4 3 10.35 4.45 9 10.85 4.45 11
3 0.25 -10.15 1 -0.2 -3.1 1 0.6 -10.4 5 -0.6 -2.4 9 0.75 -11.1 7 -0.3 -2 5 1.2 -11.45 9 1.4 -11.6 11
4 -10.1 -2.1 1 -3 -0.55 1 -10.4 -2.3 3 -2.8 -0.35 5 -10.8 -2.1 5 -11.3 -2.25 7 -11.7 -2.4 9 -11.85 -2.4 11 *Here origo is taken at the centre of the circular bottom on the experimental vessel
*All values in cm
9
1.6 FOULED BED
Tracking four tracer particles touching the wall on the bottom of the hearth bed subject to Takahashi’s pressure distribution, with a 300g constraint and a cluster of glued particles in the bed. Free layer heights Level of constraint Cycle side 1 side 2 side 3 side 4 Average Centre side 1 Cycle side 1 side 2 side 3 0 0 0 0 0 0.00 0 23.1 0 00 0 0.5 2.7 2.95 3 2.8 2.86 2.9 25.9 0.5 2.7 2.95 3 1 0.1 0.35 3 0.5 0.99 0 23.45 1 0.1 0.35 3 1.5 2.8 3.2 3 3.2 3.05 2.75 26.35 1.5 2.8 3.2 3 2 0.1 0.5 3 0.6 1.05 0 23.5 2 0.1 0.5 3 2.5 2.9 3.2 3 3.2 3.08 2.75 26.25 2.5 2.9 3.2 3 3 0.1 0.6 3 0.5 1.05 0 23.6 3 0.1 0.6 3 3.5 2.9 3.3 3 3.3 3.13 2.75 26.3 3.5 2.9 3.3 3 4 0.1 0.6 3 0.5 1.05 0 23.7 4 0.1 0.6 3 4.5 2.95 3.3 3 3.25 3.13 2.8 26.5 4.5 2.95 3.3 3 5 0.15 0.65 3 0.5 1.08 0 23.6 5 0.15 0.65 3 5.5 2.9 3.3 3 2.75 2.99 2.75 26.5 5.5 2.9 3.3 3 6 0.1 0.7 3 0.6 1.10 0 23.75 6 0.1 0.7 3 6.5 2.9 3.4 3 3.4 3.18 2.75 26.55 6.5 2.9 3.4 3 7 0.1 0.8 3 0.6 1.13 0 23.9 7 0.1 0.8 3 7.5 2.8 3.4 3 3.4 3.15 2.7 26.6 7.5 2.8 3.4 3 8 0.2 0.9 3 0.7 1.20 0 24 8 0.2 0.9 3
*All values in cm
10
APPENDIX 2
LIQUID LEVEL RECONSTRUCTION FOR THE VALIDATING EXPERIMENT IN SECTION 3.5.2.1.
Experimental (1), with liquid level reconstruction
0.080 0.070 0.060 0.050 y = 0.0002x + 0.0343 0.040 0.030 y = 0.0062x - 0.0167 y = -0.0059x + 0.1217 2 2
level(m) 0.020 R = 0.9952 R = 0.9963 0.010 0.000 -0.010 0 5 10 15 20 25 -0.020 time(s) Free layer Liquid level
The liquid level reconstruction uses Microsoft Excel least square trend lines to pick out the start and end of accumulation, and the start and end of the bed sinking during tapping. The trend lines are based on the data intervals 2.9-8.5s, 9.5-13.5s and 14.5-20.5s. The intersections points of the trendlines and average data from additional experiments in Table 3.3 gives the data points for the liquid level in the table below. In the experiments, the liquid level was held stagnant 5s after the end of accumulation. In the reconstruction, the point where tapping starts is therefore simply taken 5s after the end of accumulation, 13.5s.
1