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UDC 669.162.2 669.014
REPORT 181 STUDY ON RACEWAY
Liao Dongsheng, Mannila Paivi & Harkki Jouko
UNIVERSITY
OULU
DEPARTMENT OF PROCESS ENGINEERING UNIVERSITY OF OULU OULU, FINLAND 1996
ISBN 951-42-4371-4 ISSN 0783-7747 DISfBSMrKM OF THIS DOCUMENT IS UMtMTED DISCLAIMER
Portions of this document may be illegible in electronic image products. Images are produced from the best available original document Total model on raceway phenomena which authors are doing is a part of research project-Gas Phase Reactions in Blast Furnace, the project is from the national Finnish SULA programme. This report is a literature study on the raceway phenomena before author do the raceway model. The model will focus on the investigation of oil combution in the conditions of the raceway. The aim is to look for the way further increasing the amount of injected oil ABSTRACT
STUDY ON RACEWAY
Liao Dongsheng, Mannila Paivi & Harkki Jouko
To clarify the raceway phenomena, much research has been done. Being a literature study on the raceway phenomena, this report summarizes some research achievements which have been published. First, the dynamic condition forming raceway and the dynamics of raceway are presented, when the blast air velocity exceeds the terminal velocity of coke particle, a raceway zone will be formed in front of the tuyere. After the blast air enters the raceway, its dynamics parameters (i.e., velocity, pressure, temperature, density) change greatly along the central line of tuyere. Then, the factors influencing the formation of raceway are described, it shows that the shape and size of raceway were dependent on the blast air conditions and structure of coke burden. The dynamics characteristics of gas under injection of auxilary fuel are also described. Based on observation and measurement results on the raceway, dynamic phenomena of coke in raceway, conditions near raceway and chemical reactions taking place in raceway are presented. The last, two kinds of mathematical models simulating the raceway phenomena are introduced, one type is based on radiation strength, the other is based on chemical reaction kinetics and fluid flow. CONTENTS
Abstract
Introduction...... 1
1 Dynamic Condition Forming Raceway...... 1
2 Dynamics of Raceway Formation...... 3
3 Factors Affecting the Formation of Raceway...... 10
3.1 Effects of diameter of tuyere and velocity of blast...... 10 3.2 Effect of structure of coke burden ...... 11 3.3 Effect of comprehensive blast...... 12
4 Observation and Measurement on Raceway...... 13
4.1 Dynamic behavior of coke in raceway...... 13 4.2 Condition near raceway...... 15 4.3 Chemical reactions in raceway...... 15
5 Dynamic Characteristics of Gas under Fuel Injection...... 17
6 Mathematical Model of the Raceway...... 20
6.1 Raceway model based on radiation strength...... 20 6.2 Raceway model based on reaction kinetics and fluid flow ...... 23 6.3 Solution procedure ...... 30
References 33 Introduction
The effect of a high velocity gas jet which is submerged in a packed bed is to establish a region of high voidage (or cavity). In blast furnaces, such regions formed by the blast of hot air at velocities of 100-300 m/s are called raceway. Coke and auxiliary fuel injected into blast furnace through tuyere pyrolysis, bum and form gases in the raceway. The ascending gases transfer heat to the the descending burden, drops of molten iron and slag, and provide reducing agent for the reduction of iron oxides. Therefore, the formation of raceway in front of the tuyere will greatly affect the distribution of reducing gases, evenly descent of burden and the transfer processes of heat and mass. It is very important for blast furnace operators to have the knowledge about the phenomena in the raceway. In particularly, at present, the analysis of the combustion of supplementary fuels injected into blast furnaces requires a more detailed study of the flow in the raceway as well as the distribution of the gas flow through the raceway boundary as these determine the time available for combustion.
On the above points, the raceway has long been investigated by many research works. The studies on mechanism of the raceway formation, size and shape of the raceway have been carried out by use of cold and hot models and experimental and commercial blast furnaces. With the aid of high-speed camera and endoscope, the dynamic behavior of coke in the raceway have been studied, for example, it investigated the movement of coke, size distribution and quantity of coke particle into the raceway, speed of coke and the depth of raceway. The probes having a gas sampling hole have been used to measure the composition distribution of gases, according to the measuring results, the combustion behavior and chemical reactions taking place in the raceway have also been studied. Through dissecting the quenched blast furnace, the condition near the raceway have been analysed. All these research were based on observation and measurement. Since 1950, with the development of computational technology, mathematical model method has been widely used to investigate the raceway phenomena and many mathematical models on raceway phenomena have been published.
This report summarizes briefly the studing achievements on raceway phenomena from the following parts: First, the dynamic condition forming raceway and raceway dynamics will be described. Secondly, the factors affecting the raceway dynamics and the condition near the raceway are represented. Last, two kinds of mathematical models simulating the raceway phenomena are summaried.
1. Dynamic Condition of Raceway Formation
The raceway is a cavity in front of the tuyere, coke particles move in a form of recirculation in it, the dynamic condition for the formation of the raceway is that the velocity of blast air (ub) must exceed the terminal velocity of coke particle (ut). i.e: III
Ub>Ut
l The terminal velocity of coke particle can be calculated through the following force balance equation: III
ndl n ■(Pc ~Pg)~ Q>t^<2 —p (1.1) cmax 2
where p is density, d is diameter of coke particle, Co is resistance coefficient. Subscripts: g stands for gas, c is coke. Co is based on the motion of coke particle, therefore, Co —f(Re).
The terminal velocity of coke particle under different conditions has been calculated through equation(l.l). Fig. 1.1 shows that the maximum terminal velocity of coke particle does not exceed 36 m/s (ut < 36 m/s) under modem blast furnace operation. In fact, the hot blast enters the furnace through the tuyere at a velocity (tit,) of 200-300 m/s. i.e: /!/
Ub»Ut
Therefore, the dynamic condition for the formation of the raceway cavity is fully attained.
0.02 0.04 0.06 0.08 de »® pg - density of fluid
Fig. 1.1 Relationship between the terminal velocity ut and particle diameter dc /!/.
2 2. Dynamics of Raceway Formation
The blast jet entering the raceway has the characteristics of a limited jet besides the common characterics of free jet, momentum decreases gradually and pressure increases in the direction of proceeding of blast jet. The change of pressure and the effects of resistance and inertia make the blast flow move entraining coke lumps in form of recirculation. Fig. 2.1 shows the distribution of static pressure at theboundary of raceway. Inside the raceway, due to the hurtle of blast with coke, an intensive turbulency is generated, a part of momentum of blast air is transfered to static pressure, thus the static pressure coefficent increases from 130 to 160 at the boundary of the raceway 111.
P- static pressure, p- density of gas
Fig. 2.1 Distribution of static pressure at the boundary of raceway /2/.
Viewing the axis of tuyere as the circulating axis of raceway, 0 is the initial circulatlating angle. A relationship between distribution coefficent of static pressure and 9 can be seen from Fig. 2.2, a static pressure peak occurs near the position of 0=160 °C. At the same time, some relationships between the peak and depth of raceway exist, the velocity of gas decreases as the increase of depth of the raceway at the hurlting position of the blast, and, the peak decreases also. Considering the position of peak, the axis of the raceway is above the horizontal line of the raceway. Ill
C,=(P-P0)/(x>o 2/2)
Fig. 2.2 Distribution coefficent of static pressure venus angle Z2Z
3 According to momentum law, decrease of momentum per unit time should be equal to thesum of pressure and resistances. For a limited jet, the following equation is valid 737.
(2.1)
Where m0. p0 are mass,velocity and pressure of blast at entrance cross section respectively, Uj, pi are velocity and pressure of blast at exit cross section. R is energy lose of jet flow due to diffuse and entrain coke.
Fig. 2.3 shows the change of velocity of blast air in the direction of axis of tuyere, a transitional zone exists between the initial and main flow zone, the velocity of blast decreases quickly along the axis of tuyere due to the circulating motion of coke lumps in the raceway. It is apparent that the turbulent boundary consists of pure gas phase keeping the velocity of exit and gas-soild two phase entraining coke lumps. Thus, the thickness of boundary layer along the central line of tuyere should be the depth of raceway (Lr), the width of flow field should be the width of raceway ( Br ). 74/
Fig. 2.3 (a) Diffusion and (b) velocity change of blast in raceway /4/.
Fig. 2.3 shows also that boundary layer thickness depends mainly on the terminal velocity of the largest coke lump and the change of blast velocity at the exit. According to the dynamic condition of raceway formation, at the position of Ub =ut, the distance from the tuyere nose at the tuyere axis is the theoretical depth of raceway
4 ( Lt). If thechange of gas velocity in front of the tuyere were known, the depth (Lt) can also be found.
According to momentum law and calculation results on boundary layer, under insulation, the relationship between the maximum velocity of blast (Umax ) and the thickness of boundary layer (yb) can be expressed as 151:
Wo (2.2) 0.336r BJpg/p a
rB =[C"(Mmax-«,)/(ttmax+Mf) + C0](x + x0) (2.3)
where y0u0are radius of tuyere and initial velocity respectively, p& pmareaverage density of gas phase and gas-soild two phase flow in front of tuyere. C is experimental coefficient and x0 is intial position ofmain flow.
Equations (2.2) and (2.3) are derived under insulation flow and the pressure gradient which is not taken into account. In feet, under blast furnace operation, the gradents of pressure and temperature of gases are very big along the axis of tuyere. Therefore, the average temperature Tg and pressure Pg are often used and they can be expreesed by the following equations: 151
r2 = r„[i+/,(*)] (2.4)
Pg — + f2 (x)] (2.5)
where f(x) and f2(x) are functions of distance x. TB and PB are temperature and pressure of blast.
Then, the following relationships are derived:
I + /2OO Pg - P b (2.6)
l + /l(*) UB — Us (2.7) l+/2(*)
5 Thus, the maximum velocity is:
(2.8)
(2.9)
where dB. uB are diameter of tuyere and velocity of blast air at exit respectively.
The change of velocity of main flow can be expressed by the following equation:
(“maxAf ~ 1/3)3 -(lA2 -2J? + l/3)(«max/z/, -1/3)
(2.10)
where Z = [Cpcj2d,m (1 -f) /
S = ^0.5(1-f)(p>8 )
C1$ experimental coefficent
While Um« = ut, the theoretical depth of raceway can be calculated as:
(2.11)
Or (2.12)
Where GB is the mass flow rate of blast at the tuyere nose.
Equation (2.12) denotes that the depth of raceway increases as the mass flowrate increases, depth also decreases while the diameter of tuyere and coke lump increase, decrease of porosity decreases the depth of raceway. As the above equations show, the Lr.t is not the function of pressure and temperature, while temperature increases and the pressure decreases, the density and the velocity of gases will increase according to the continuity equation: 76/
pgug = constant (2.13)
6 Fig. 2.4 shows the change of velocity along the axis of tuyere. Z=xZLr.t represents the relative distance from the nose of tuyere. Curves 1,2, 3 show ut=f(Z, B), curves 4, 5, 6 show Umax/ut=/(l/Z, B). The velocity decreases along the central line of raceway with increase of Z and B. The porosity of coke and thedepth of raceway do not change the velocity with a certain value of Z. Model experimental results 161 show that the streamlines are stable when the flow is fully turbulent. The distribution of static pressure is also stable with the maximum depth of raceway.
2 4 e 8 z* ‘
Fig. 2.4 Change of velocity along the axial of tuyere /6/.
These curves can be appromixately represented by the following explicit functions /6/:
^ = --0.1155-0.95 xb Where x'b = 13.665d BJp~G B / {c^Jpc(l - g)\S561G B + 0.97d3Bp cJdcmxx (1 - g)p B/Pg +115cf=V^».xPcPb ]> 1.272Gb Cp cdB Jdcwx (1 -s) (0.070715 + 5.567) B is the function of the ratio of density ofsolid and gas phases 7 At the same conditions, the radius of raceway cavity can be represented by the following equations: 1 - (0.0922 + 1.S6)Z 1-(0.0922-0.04)2 ** x'b (4.56 - 0.070712)(l-Z2)2cr x0 < x < Lrj (2.17) (3.2052+ 58.46)Z 2 -0.070712 + 2.56 where xb. rb are the position and radius of initial zone of raceway. Analysing the above equations, while Gb>1.5 kg/s, the radius of cavity begins to increase, while x=Xn,„ the radius will reach its maximum, while x>xmix, the radius begins to decrease, and the Xm« can be expressed by the following equation: 22.57Gj[l-(0.0575B+0.975)" “s] CpBdB^dctm(\-S)(2ZB-\) In thesame way, r^ can be also derived. The minimum diameter of cavity depends on the maximum coke lump, then, the actual depth of raceway can be derived with assumptions rp=0.5d^,v Lr.t=x. 4. +0.707WC„ !Cf(B)LR, -L2RI = 0 (2.19) where Lr_„ is the actual depth of raceway 2.2663^/(1 -s)p c/p g +58.46 f(B) = 1.38 >/(l-e)pc/pg (4.56 - 0.05)^(1- e)p c/p g The calculated results are indicated in Fig. 2.5, we can see that the shape of raceway depends on porosity of coke burden, mass of blast, size of coke lump and so on. The effect of diameter of tuyere on size and shape of raceway is shown through Fig. 2.6. Fig. 2.7 shows the effect of coke lump on shape and size of raceway. 8 = 0.07 m 0.05 m Cb» kg/s Fig. 2.5 Amount of blast venu actual depth ofraceway ( Lr.„) /6/. Fig. 2.6 Effect of amount of blast and diameter of coke on shape ofraceway /6/. -0.2! Fig. 2.7 Relationship between shape of raceway and diameter of tuyere /6/. 9 Above calculations do not involve in the effect of drops of molten iron and slag entering the raceway on the moving process of gases and particles, thus, results shown are not completely accurate in the calculation above. In order to ensure a proper distribution of gas flow and the uniform distribution of temperature, every operating furnace has an its own ideal raceway structure. Researchers have done many experimental works about it. The most ideal depth of raceway may be calculated briefly by the following empirical equations: 111 Lrt = 0.3/? (2.20) or Lrj = 0.814 +1.403 * 10-3 j, (2.21) Where R is diameter of hearth, Vu is Volume of furnace The width can be represented by the following equation: — = 2 cot 30° (1+x- 45-)05 (2.22) dB dB Where bR, LR are width and depth of raceway, k is a coefficent. 3 Factors affecting the formation of raceway The size and shape of raceway greatly affect the initial distribution of gases flow and the formation of cohesive zone /8/. An important means-bottom adjustment in blast furnace operation is to form a proper raceway through controlling the parameters of blast. In order to meet the requirements of blast furnace operation, the composition and amount of injectant must be also controlled, the structure of coke burden (grade size, porosity ect) should be adjusted. 3.1 Effect of diameter of tuyere and velocity of blast While the diameter of tuyere is fixed, increasing the amount of blast will result in increase of velocity of blast (Table 3.1), but, the width of raceway does not change, the volume of raceway increases and the shape of raceway is approximate ellipse. 191 10 Table 3.1 Relationship between the amount of blast and the shape of raceway/9/ toms types max 1 2 3 /min diameter of tuyere, m 0.036 0.036 0.036 velocity of blast, m/s 22.0 28.0 37.4 1.7 depth of raceway, m 0.072 0.084 0.105 1.45 Height of raceway, m 0.108 0.143 0.175 1.62 width of raceway, m 0.082 0.087 0.094 1.15 volume of raceway, m3 638*10-* 1045*10"* 1727*10"* 2.7 Decrease of the diameter of tuyere can increase the velocity of blast, but, in order to keep uniform distribution of gases at the cross section, the decrease must be limited. For improving the distribution of gases, FHlnft is proposed to determine the diameter of tuyere (FH is cross area of hearth, n is numbers of tuyere, /t is exit cross area each tuyere). The value can be chosen from 100 to 120.710/ 3.2. Effect of structure of coke burden The size and porosity of coke lump also affect the size and shape of raceway, Fig. 3.1 shows the experimental results, while the velocity of blast is fixed, the depth L& decreases as the increase of coke lump size, while the porosity decreases, the depth of raceway decreases due to the increase of the resistance. . iso m m Fig. 3.1 Effect of size ofcoke lump on depth of the raceway // It. 11 Effect of average diameter of coke lumps on shape of raceway can be seen from Fig. 3.2. It shows that the length and height of raceway decrease gradually with increasing the average diameter of coke lump, but the width does not change. The diameter of coke decreases only about 50 % of initial size when the coke descends to raceway, this is one of the reasons resulting in increase of static pressure in raceway./!!/ I I 1 Fig. 3.2 Effect of diameter of coke lump on depthfLu), width(bR)and height(H R) ofraceway/ll/. 3.3 Effect of comprehensive blast Lately, most blast furnaces adopt high temperature, oxygen enrichment and injecting auxiliary fuel to reduce thecoke consumption, theses result in changes of volume and dynamic conditions of gases in raceway. Increasing temperature of blast makes the volume and velocity of blast increase, the raceway will be expanded. On the other hand, it speeds up the oxidation of carbon thus, it makes the raceway contract. Therefore, the effect of high temperture on raceway depends on the effects of interaction. Oxygen enrichment can increase the volume of combustion gases, but due to the decrease of nitrogen in blast, the total volume of gases decreases. Thus, the change of volume of gases depends on the two effects also. In general, the raceway contracts in oxygen enrichment operation. Literature /12/ shows that depth decreases 0.1 m and width decreases 0.025 m under oxygen enrichment 1 %. 12 Coal injection is useful for developing the centre gases flow. Fig. 3.3 shows that depth of raceway increases with increasing coal amount injected, but combustion ratio and replacement ratio decrease. Amount of injected coal Wc kg/THM. Fig. 3.3 Relationship between depth of racerway and amount of coal injected /12/. Oil injection can increase the depth of raceway, because the H2 in gases improves the transisability, but if the oil can not bum fully, solid soot may be formed, it will damage the gas permeability and result in contract of the raceway /12/. In general, the effects of comprehensive blast on raceway are very complicated. 4.0bservation and Measurement on Raceway The extreme difficulty of taking measurements in raceways, has resulted in only a few measurements having been reported. The first quantitative study on the raceway was conducted by Wagstaff and co-worker A 3/ in 1950. Afterwards reseachers conducted various measurements and observations on blast furnace by use of cold and hot models in experimental and commercial blast furnace, for example, the physical depth of raceway has been probed, the coke movement has been observed by use of endoscopes and the axial gas composition has been measured. 4.1 Dynamic behavior of coke in raceway Inatani A 4/ built a cold experimental model to simulate the movement of coke particles in raceway, with the aid of high-speed camera the dynamics behavior of coke in raceway has been studied. Fig. 4.1. shows the routs of tracer particles. According to different movement state, the raceway can be divided into five sections A-E. Section A is the area at the tuyere nose, where the particles have the highest speed as they are blown in by the blast, thesupply of coke particles is carried out from a limited area in 13 the upper part of tuyere nose. In section B, particles are more scattered than in other sections, this section is thought to be the widest because there is a high possibility for particles disappearance from the field of view. In section C, particles falling toward the tuyere nose move laterally toward tuyere before falling. In section D, the particles circulate densely and slowly round point P. Section E is a boundary between the bed of stationary particles near the raceway and the particles in the raceway, in this section, the packing density of particles is high and a layer with a thickness of three or four particles moves slowly upwards. 714/ In view of the above experimental results, the particles and gases at the raceway boundary is in a state of semi-static dynamic balance. 714/ THE RACEWAY 54 I Tuyere Fig. 4.1 Coke movement in model raceway /147. The velocity of coke particle in raceway was measured. Fig. 4.2 shows the relationship between the size and velocity of coke particles in the raceway which was determined by Kase et al 7157. The smaller the coke size and the larger the blast volume, the higher the coke velocity. Fig. 4.2 Relationship between the size and speed of coke particle in raceway/15/. 14 4.2 Condition near the raceway Fig. 4.3 shows the condition near the raceway observed on dissection of a blast furnace. In general, large coke lumps which are considered to have been fallen from above after end of operation are found just in front of the tuyere, and these are surrounded by round small coke particles. Beyond and below this area of small coke particles there is a space of a low voidage made up of coke breeze of 5 mm or less, slag and pig iron particles. Only large coke particles exist at the centre of the furnace. 716/ THE RACEWAY Fig. 4.3 Horizontal section at tuyere level /16/ Theresults of observation show that the packing density of coke in the upper part of the raceway was very low. Small coke particles were found fluidized by upward flows of gas and thatthe process of small coke particles escaping from the combustion zone remaining around the edge of the raceway and then being blowing back into the combustion zone. Experimental results also show that the raceway expands as the particle size decreases. The raceway shrank horizontally when very small coke powder was generated in raceway. At this time theamount of gas flowing near the furnace wall increases. 4.3 Chemical reactions in raceway Because the raceway is not symmetrical, gas composition measurments along the axis are difficult to interpret. However, a consistent pattern can be seen from the measurements in Fig. 4.4. A decrease in O2 concentration along the raceway is 15 associated with an eventual increase in CO concentration. The CO2 profile have a maximum near the where CO initiating. According to the distribution profile of gases, the loss reaction of coke seems to take place mainly at the boundary between thecoke- filled bed and the raceway space. The point where the reaction occurs is depending on the coke reactivity and surface area and affects the temperature distrebution in the furnace. Injection of a fuel with the blast results in a more rapid decay in O2 with an earlier decreases of C02 -peak. At the same time the position of CO2 approaches the tuyere nose and the increasing of CO. concentration occurs near the tuyere. /IT/ a without injectirtt' b with injectam in blast Fig. 4.4 Illustrative gas composition measurements reported along tuyere axis/1 7/ Kodama measured the effect of humidity and oxygen in blast on state of combustion zone. The measured result, Fig 4.5, shows that the temperature near the raceway decrease with the increasing moisture in the blast. The oxidation zone expands and the value of raceway increased markedly. 718/ However, because the raceway is not symmetrical and the difficulty of measurment, the measuring results along the tuyere axis are difficult to interpret. These remain the only data with which prediction from combustion models can be compared. 16 to) 1 lb1 I V'lm1 mm * r* I M !-• *•»•#» M O 31 2 33,, Oi 2.0*/. IV) II 0 100 200 0 100 200 0 100 700 to I I 5Nm 1/mm lb I l SN<" */#*.. n l<"l I SMm* m»n I HfO 16 lg> ! M/O 31 7 31q «' O, 2.0*/. HjO II 7g 300 - | lo" only! | 200 ■ 0 100 200 0 100 200 0 100 200 Dislonce from tuyere Imml (oMbllct ! lines of equol temperatures fa'I fb'lIc'f I lines of equal COz conlcnls Fig.4.5 Effect of humidity and oxygen in blast on state of combustion zone /18/ According to the measured results, the major reactions in raceway as following: C+1/2 02 = C0 PC C + CO2 = 2C0 C + H2CNCO + H2 Soild-Gas chemical reaction — C + 1/2 O2 = CO Coke C + C02 = 2CO Reaction c+h2o = co+h2 Gas- Liquid Oil O2 + CHb Gas-Gas CO +1/202= C02 5. Dynamic characteristics of gas under injection of fuel It is useful to study the kinetic characteristics of gases under injection of fuel for improving the economy effect and production target. It is important to determine the amount of injectant for improving kinetic conditions of bottom gases. All the reactions 17 can be concentrated on the theoretical flame temperature which can be as a suitable index to determine the proper amount of injectant. The theoretical flame temperature can be calculated by the following equation /19/: t 09341 tB + 8208c?-g>(2402- 1.2178^ >-(1932 + 2,235%)- / + to+2$) + (0.0012 + 0.0013^j«Sj + -0.39 + 2.2175% - 2673S g +94.76 40.00055, + 2.026Sg (51) where, a is percentage of oxygen in blast, q t is heat capacity of liquid fuel burned, SI, S2, S3 are the amount of soild, liquid, gasous fuel in blast (m3/m3) respectively, Cs is component content offuel (Kg/Kg), the coefficents in front of tB. co, (pare heat capacity,weight or volume of per unit oxygen and evaporation. The effect of injectant on kinetics condition should be determined by Atr and Atg (fluctuate of theoretical flame and gas temperature ). Fig. 5.1 shows the effect of Atr and original temperature on productivity and coke rate. The effect of injection will be improved with increase of m. The productivity will increase with decrease of Atr. In general, the reason thatincreasing tr results in decrease of productivity is the change of zone of heat exchange, the zone of heat exchange moves toward the top of blast furnace and the temperatures of escaping gases increases, thus, it increases the consumption of coke and decreases the productivity. 719/ o 1.001 itT. c a 't. V 6 Fig. 5.1 Effect of tTon coke rate and productivity /19/ 18 Where IJ is productivity per day; 02 is oxygen content in blast; AP is increase ratio of productivity; AK is increase ratio of coke rate; The fluctuation of blast amount in different tuyeres results in unstable injection. The distribution of theoretical flame temperature is non-uniform in different tuyeres and different dynamics conditions are generated in different raceways. So it is important that theblast can be adjusted under injection. Under combined injection, the propriate proportions of different injectant must be payed attention. Oxygen enrichment can reduce the whole volume and velocity of gases. The opposite effect is generated under oil and natural gas injection. Combined injection in a proper propotion can compensate for each other. For example, oil-coal combined injection experiment shows that adjusting the proportion can control the depth of raceway and distribution of gases. In general, the dynamic conditions can not be damaged under fuel injection. Therefore, in order to obtain an ideal effect of injection, some auxiliary steps should be taken, for example, while oil is injected , these steps which increasing the temperature of blast, decreasing the moisture in blast, enriching oxygen should be taken. On the other hand, due to increase of volume of gases, it provides the conditions for generating fluidization and liquilization, about the point, enough attentions should be payed. 19 6. Mathematical Model of the Raceway The phenomena in the raceway are very complicated because of the highly turbulent, recirculating flow of gas, the spatial variation of the raceway wall temperature and composition, and the descent of coke bed causing coke particles to enter the raceway. All these factors are strongly dependent on the raceway shape and size. Further complications may arise in the form of molten metal trickling into the raceway. The extreme complexity of phenomena in the raceway has resulted in a few comprehensive mathematical models describing the phenomena having been reported. Due to the differences of studing methods on the the raceway, different mathematical describtions about raceway phenomena have been presented, which can be divided into the following two kinds : 6.1 Raceway model based on radiation strength Radiation strength was viewed as a major objective index in mathematical model. Based on the studing results on combustion reactions in raceway, researchers thought that a statistical relationship exists between radiation strength and heat state in the hearth, especially, between the silicon content in the iron and the radiation strength. Through thesemodels, some effects of blast conditions on the radiation strength can be predicted. The major factors affecting radiation strength are temperature and components of gas-phase, 717/ Construction of model Basic assumptions (1) Only 02 and N2 exist in blast. (2) Shape factor of coke particle is cj> =1. (3) All the reactions are first-order irreversible. (4) Coke component is pure carbon. (5) Forms of heat exchange: coke-gas convection coke-coke radiation (6) Chemical reactions: C + 02 = C02 + Q1 (6-1) 2C + 02 = 2CO + Q2 (6-2) C + C02 =2CO - Q3 (6-3) 2CO + CO = 2C02 + Q4 (6-4) Continuity equations: For gas: £ = ^ ^ (?/*«** ) + r> + > (6.1) 20 A A 2 i For coke: +------jc(cic-cn +—- ctjx) (6.2) dx 8x Pg where rR is radius of cavity of raceway, ug _R is velocity of gas flaw, jc, jx are mass of carbon and volume combined generated per unit carbon bumded respectively, jx can be decided by the following: jx=jxi +jx2 +jx3 (6.3) where jxx = -kxSp gcx -0.363Sk\f (cx ,c2,p g ) (6.4) jx2 = \.2129k3Sp gc3 - 0.6365^f(cx ,c2 ,p g ) (6.5) jx3 = l.315k xSp gcx - k3Sp gc3 + k'4f(cx,c2 ,pg ) (6.6) where ki_ k3 are reaction coefficents of reactions (6-1) and (6-3) m/s, k4 is reaction speed coefficent of reaction (6-4). clr c3 are relative concentration of 02r CO., C02 respectively kg/kg, S is surface area of raceway m2/rtf , XiX2x3 are reactive amounts of 02, CO., C02 2 recpectively, uc is average mass velocity of coke, ------Jc(cic ~ ct) combustion rate of rRpg coke. Heat balance equations: For coke: J.rJc(r,r)]-ac ^ [rTc(rxx,0)\ (6.7) l(cpTg) = -uK^cpTg)% *pMcpT'-cpTg) . C,T. For gas: Pg —a r(Tc - Tg)+—f(c\’c2>P,)Q4 (6.8) Pg Pg Boundary condition: For coke Tc ir, x,0) = TCO(x) 0 Initial conditions (%,0) — Pg(o) (x) Tc(r ,x,0) — Tco^xy (6.11) 21 A difficulty exists in deciding the boundary condition, it is how to calculate the radiation heat exchange between the coke particles in the raceway and the wall of raceway, because the boundary temperatures are various, it is a function of position and time. In order to overcome the difficulty, an average temperature is introduced, then the heat balance equation of coke particle can be expressed as: /18/ -aT ( Tc - Tg ) - 0-^ (T* - T* ) + kxpgcxq x - k3p^c3q 3 (6.12) Where Ac is heat conduction coefficient, Therefore, the model consists of a set of semi- empirial equations describing the phenomena of raceway, but it is very difficult to solve these equations. In order to avoid the problem solving these queations, the following additional assumptions should be included. 719/ (1) Coke particles movement is in semi-steady state. (2) The volume of CO is not considered. (3) Combustion rate of coke should be equal to gasfication velocity of coke and can be expressed as: uc = -(% = A)(W, +t,C3/?3) (6.13) Pc Where /?;, ff arechemical calculation coefficents of reactions (6-1) and (6-3). and the temperature grandient at radial can be represented by the following equation: A-c (~jp) - UcCcPc (TB.C - Tc.O ) (6.14) Where TB,c is surface temperature of coke particle at the boundary of raceway, cc is speciflcl heats of coke, Tc.o is initial temperature of coke entering the raceway. Therefore, th temperature can be obtained through solving the heatbalance equation: Discussion: The change of radiation strength reflects theheat exchange effect between gases and coke, liquid, therefore, it is useful in researching the heat state in raceway. But the model has some highly strict limitations, it can not meet the demends of modem blast furnace operation, it assumpts the flow of coke is semi-steady, in fact, the moving state is very complex and greatly affects the processes of mass and heat transfer.Therefore the distribution of composition and temperature of gases calculated are not fully accurate, and due to the limitation of assumptions, it can not be used in 22 comprehensive blast conditions. Thus, further development and application in mordera blast furnace operation are restricted. At present, few people develop raceway mathematical model based on this theory. 6.2 Raceway model based on reaction kinetics and fluid flow Based on reaction kinetics and fluid flow, the balance equations of mass, heat, momentum and chemical species are built. There are two main features in this kind of model, one is that it includes rate expressions for essential reactions, another typical feature is that loss of pressure is included in momentum equation. The accuracy of this kind of model is principily based on presupposing the knowledge of the mechanisms of basic chemical reactions. Many papers on such model have been published, but its details have not been disclosed, kinetics models also need empirical data, at least rate and equilibrium coefficents for heat and mass transfer. The coefficents are determined by theFrossling equations based on conservation principle. All the models develpoed have two common assumptions. /20/ (1) All reactions are viewed as first-order irreversible. (2) The gas film diffusion determines the rate of coke combustion reactions. We can see above, this kind of raceway model consists of equations of motion and continuity of gas and coke particles, and heat balance. By solving these equations, the distribution of components and tempeature of gas and coke , and the moving state and pressure field can be obtained. All these kinetics models which have been developed can be divided into One-dimensional and two-dimensioal. Three-dimesional kinetics model about raceway phenomena has not been reported yet. One-dimensional model Most models developed about the raceway phenomena are one-dimensional in form , withsimple treatments for the reaction kinetics. Construction of model As has been said above, the phenomena of raceway is extremely complicated, it is difficult to build accuratly a set of equations describing the phenomena. Thus, first, many cold model experiments were performed to investigate the gas flow patterns. Fig 6.1.(a) shows the gas streamlines visualized, in this case, gas flow patterns can be presented by the following equations /21/. divF = 0 (6.15) gradP- -(/i 4-/2 F)F (6.16) 23 Where F is molar flux vector of gas; P is gas pressure; ft, f2 are Ergun's coefficients. Fig. 6.1(b) shows the calculated streamlines and isobars. From it, some agreements between the predicted and the experimental streamline can be seen. THE RACEWAY Fig. 6.1 Streamlines and isboars of gas: (a) visualized streamlines; (b) calculated streamlines and isboars /21/. Szekely and Kajiwayra 1221 built a cold model to observe the liquid flow patterns near the tuyere combustion zone, in terms of a continuity theory of approximation and holdup theory, a set of equations simulating the liquid flow patterns were built, the equations are the same as above except for £2=0 and the gravity was taken into account. By use of the equations to estimate the effect of gas flow on the liquid holdup. The experimental and theoretical results revealed that the liquid triking down through the bed behaves as a continuity and the effect of distribution of holdup on the gas flow pattern in the bed is comparatively small. Based on observing results to a blast furnace with the aid of an endoscope, Greuel et al /23/ identfied jetting space in which many coke particles were involved. Then , one dimensional model describing raceway phenomena was built. Fig. 6.2 shows the physical configuration of the space. In the construction of model, the following assumptions were made: (1) Raceway zone is a cylindrical jetting space which as the same diameter as the tuyere, the depth is fixed. (2) The combustion zone is a loosely packed bed. 24 Fig.6.2 Schematic view ofcombustion zone in front of tuyere /23 /. The same a set of equations (6-13), (6-14) were used in the model, the gas molar flow rate is given by the average flow rate: 723/ Before combustion /•„ =F6[lOOO(l + ^2)/22.4 + ITa /18] (6.17) After combustion: F02 = Fb{1000[0.79 + 2(021 + Wo2)]722.4 + 2WSlllB + 11) (6.18) The average flowrate of gas based on the cross-section of the hearth is: ^=2(^.1 +Fm)!nDl (6.19) Where Fb is blast volume, Wo2is the oxygen enrichment, W^i is the fuel oil injection rate, WSt is the blast humidity and is the mass fraction of hydrogen in oil, Dh is hearth diameter. Fig. 6.3 shows the predicted results, it is found that the majority of blast flows out of the tuyere zone through its upper boundary, and a relationship between the upperward component Fy and the horizontal component Fx were found and the relationship between them can be expressed as: 723/ (6.20) 25 radius (m) -i. |o Fig. 6.3 Gas streamlines around the combustion zone /23/. One -dimensional kinetics model: Chemical rate process: Basic reactions (Under fuel injection, the reaction equations will be added) c+o2=co2 R* i (6-5) C + C02=2C0 R*2 (6-6) c+h2o=h2+co R*3 (6-7) h>+\o,=h2o R*4 (6-8) Where R*, is overall reaction rates (i=l,2,3,4),Ci is molar concentration is molar fractiona reactive gas component, rjs rate of dissipation of the reactive gas component, r, can be expressed as follows : f) = -edCjfd9- -ed(Pyi fRTg)/d9 (6.21) r\ = Ri + r2 = ~Ri + K r3 ~ R3 ~ R4 r4 ~ —2-^2 — R$ Where s is voidage of combustion zone, R is gas contant and6 is time. 26 Calculation of reaction rate According to assumption, all the reactions are first- order irreversible, the rate can be represented as follows: 724/ R*=kjCi (i=l,2,3) (6.22) Ki is the overall rate contant covering the following three parts (1) Gas film diffusion resistance. (2) Combination of pore resistance. (3) First- order chemical reaction. Under loosely packed bed, k; can be written as follows: = 1/(1/kna +1 / JJikmiPbc) fl= 1-3) (6.23) Where Kjjis mass transfer coefficent, a-is special surface area, ijris effectiveness factor, K„ is chemical rate constant According to convective principle, mass transfer coefficient can be werriten as follows /25/ — (A jQdp)Sh (6.24) Sh = 1.5 Re0-55 (6.25) Where Z), is the diffusivity ofreactant gas, tj> is the shape factor, dp is the particle diameter of coke, and Sh is the Sherwood number. Chemicalrate constant: 1261 ^ =6.53*10 5(a//)k)V^"exp(-22140/r„) (6.26) km2 = 8.31 *10 9 exp(-30190/ Tm) (6.27) Arm3 = 13.4rmexp(-17310/rm) (6.28) ^4 = r3 ( >yl) K =° ( yi Where Tm is average temperature of gas and coke. 27 Heat and mass balances Assumptions: (1) Heat and mass transfer processes are steady state (2) One-dimensional flow The combustion zone is illustrated as Fig. 6.2., mass balance can be represented as follows: Total gas: 5 dFx/dx = 4 Fy%! D + ]£/; (6.29) 1=1 element component: 5 efyi/dx = O,-ri)Fx (6.30) i=i Heat balance: Heat exchange: convective gas-coke heat of reaction. ~d(CJgFx)Jdc = 4F,fCtTg /DT - CcTc ^ (-Aff,)+hgc (7^ - Tc) 1=1 1=1 Where Cc and Cg are the specific heats of coke and gas, Tc and Tg are the temperatures of coke and gas, -AHt is the heat of reaction, and hgc is the heat transfer coefficent between gas and coke. Assumption: Tc=0.8Tg Boundary condition: (1) FxQ — / ( 7tDTn / 4) (6.31) (2) JlO — (1— J^O )(0.21 + W02 ) / (1 + Wo2) (6.32) (3) y20 - ^40 - -VsO — 0 (6.33) (4) J'ao = K [Wst +1000(1 + Wo2)/1.244] (6.34) (5) II (6.35) Where the subscript 0 represents the situation at the tuyere nose. Consumption rate of coke 5 = 2X (636) i=i Numerical computation was carried out , the distribution of gas component and temperature can be obtainedt under various blast conditions. 28 Discusion: In order to simplify the numerical treatment and the Ergun equation can be used in the model, the model views the racyway as a loosely packed bed of 60 % porosity through which the hot blast flows as cylindrical nonspreading jet with gas leaving the main flow zone through th eroof of cylindrical path, the assumption is conflict with the well accepted phenomena of coke circulation in the raceway, and the fact that the raceway is a cavity. Two-dimensional model Construction of model Basic Assumptions: 1211 (1) The pressure loss equation for a packed column may be applied at the outside region ot the raceway. (2) Coke and gas movement in the raceway may be determined by the interaction forces. (3) The boundary of the raceway may be defined as a certain critical value /c Basic equations (1) Equations of motion (N-S) For gas (u .grad)u = ——gradP+—£?u +—/ (6.37) Pg Pg Pg For coke (uc. grad)uc = —A2uc - —/ + g (6.38) Pc Pc (2) Equations of continuity For gas: div(epg ug)-0 (6.39) For coke div(pcuc ) = 0 (6.40) (3) Equation of interaction force between gas and coke / = a(u c -ug ) +b(uc - ug).|uc - ug | (6.41) Coefficents in thisequation are as follows, after Ergun „ = iso (6.42) £ dl s3 d. where dp is the diameter of coke particle, pc is the apparent density of the coke, Pbcis coke density, eis the coid ratio. (4) Heat and mass transfer in raceway. Equation of mass transfer: div(spgug Where Equation of heat transfer. Up + Hcol $ col + Hco+co (6.44) CpN2 Where Ho. H^Hco standard heat of components, Cp„ is heat capcity of components. 6.3 Solution procedure A difficulty exists in solving theequations of motion of gas and coke, it is the unknown pressure field, in order to simulate accuratly the actual phenomena of raceway, the Ergun ’s pressure loss equation as in one dimensional can not be used. So, in order to solve the equations, the following three methods are adopted: Vorticity-based methods.(The stream function and vorticity co are introduced) /28/ psu = roty/,rotu = co The velocity and pressure in the motion equations (6.37)-(6.40) can be instead by the *¥ and to. By use of the stream function , the continuity incidentaly satisfied. Through vector analysis, these equations can be insteaded by the following: Motion equations Pc Pg div(----- grachf) = -co (6.47) div(—grades) = -co (6.48) Pc The distributions of co and xg for gas and coke are numerically solved by a finite difference method. Fig. 6.4-Fig. 6.7. are some calculated results: 30 The SIMPLE Algorithm /28/ The method stands for Semi-Implict Method for Pressure -Linked Equations, it has been used widely to solve the motion equations for pressure-linked. The important operations, in the order of their exection, are: (1) Guess the pressure field P. (2) Solve the motion equations , such as equations to obtain velocity field u,v. (3) Solve the pressure p correction equation. (4) Solve the velocity corretion equation. (5) Solve the descrization equation. (6) Theat the corrected pressure p as a new guessed pressure, return to step 2, and repeat the whole procedure until a converged solution is obtained. Penalty function formulation In order to eliminate the pressure term, the penalty function formulation is introduced and used the equation of continuity /29/, namely: div(eugpg ) = y (6.49) where X is the penalty parameter. When appling the penalty function formulation the equation of continuity is no longer satisfied exactly. However, sufficiently large value of X, enforces the equation to be almost equivalent to the original continuity equation. Therefore, the equation can form a expression for the pressure and this is then substituted into pressure gradient terms of the motion equation, the pressure term is eliminated and thefinal equations can be solved. But, the method has never been used in solving the equations describing the phenomena of raceway. 31 w w fig, Fig.6.5 h eig h t(m ) 6, 4 Effect blast Effec of air of oxygen oxygen 0.5 COz 02 enrichment enrichment . : : 18% 8% on HzO: N on 2 temperature coke : 62% 12% consumption distribution >1111 / 27,'/ Fig. 6.7. Fig.6.6. Effect o Effect of coal raceway of injectionon coal In injection boundary raceway on temperature profde o mark and distribution gas streamlines. /2?/ References 1. An, Y. Blast furnace process aerodynamics. 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