Heat exchange in molten pool in liquid-phase melting of ore-coal pellets.
Combination of all processes, occurring in the furnace, represents for the time being irresolvable task and can not be described mathematically.
For real conditions and mathematical description construction of the model is simplified, if one takes into account a number of issues, characteristic of melting of metallized pellets in the arc furnace at different types of charging.
One may assume that for melting with application of the metallized pellets process of their dissolution in the molten pool is of a subordinate character in comparison with melting, because temperature of the molten metal is higher than melting point of the pellets. Among all questions of interest is determination of peculiarities of the process, stipulated by thermal physics characteristics of the material, because they are different in the pellets and the scrap.
The assigned task may be solved first of all by the model of heat exchange between a pellet being heated and the molten metal (the slag). Kinetics of heating and melting of a pellet may be considered on basis of the model of heat transfer by heat conductivity in the body of spherical shape under boundary conditions of third kind, i.e. at constant temperature of the metal (the slag).
Duration of the pellet melting, heated in the course of the convection heat transfer, depends upon thermal physics properties of the material and coefficient of heat exchange at the interface between the body and the medium. Heat exchange between the body and the medium, characterized by heat exchange coefficient a, may vary under real conditions within much wider range than physical properties. In the arc furnace heating and melting of the metallized pellets occurs both in the slag and at the slag-metal interface.
The investigations showed that values of coefficient of heat exchange between the metal and the melting in it scrap or a metallized pellet change within a narrow range. So, in melting of slag in a converter values of the heat exchange coefficient achieve [alpha] = 58-62 J/([m.sup.2] x s x [degrees]C) .
Investigation of melting of cylindrical steel specimens and metallized pellets in the induction furnace showed that heat exchange coefficient at a relatively low intensity of mixing equaled 13 J/([m.sup.2] x s x [degrees]C); at maximum power (intensive mixing) its values were within 139-220 J/([m.sup.2] x s x [degrees]C).
Taking into account somewhat overstated latter values, one may assume that the heat exchange coefficient in melting of a pellet in the molten metal may constitute 11-146 J/([m.sup.2] x s x [degrees]C) . Because of a lower heat conductivity, density and increased viscosity of the slag in comparison with the molten metal, its heat exchange coefficient may be by several orders lower than in the molten metal-pellet system.
As a rule, heating and melting of the metallized pellets is accompanied by release of gases, stipulated by reaction between carbon and iron oxides. It is found  that noticeable release of gases (mainly CO) starts at 800 [degrees]C. As rate of a pellet heating increases, maximum of gas release shifts in direction of high temperatures. Recalculation of intensity of the CO release into rate of decarburization at heating rate 250 [degrees]C/min will give intensity 0.2 % C per minute, and share of carbon, which entered into reaction,--more than 1 %. High level of the gas release intensity from surface of a pellet in heating in slag or at the slag-metal boundary stipulates significant intensity of mixing of the melt layers, which directly contact with the pellet and, as a result, increased heat exchange.
Under real production conditions at continuous loading of pellets into the pool conditions of heat exchange between the medium and a pellet in the process of heating and melting change in direction of the heat exchange increase. This is explained by change of mean density of the pellets (due to which they move from the slag lower to the slag-metal interface) and development of the decarburization reaction in the pellet, which intensifies heat exchange owing to increased degree of turbulence of the slag or the molten metal flows, which wash the pellet.
[FIGURE 1 OMITTED]
At correctly organized pellet melting technology heat exchange in the slag and at the slag-metal boundary is characterized by values [[alpha].sub.sl] = 3.6 J/([m.sup.2] x s x [degrees]C) and [[alpha].sub.sl-m] = 3.6 J/([m.sup.2] x s x [degrees]C) .
At the heat exchange coefficient value less than 3.6 J/([m.sup.2] x s x [degrees]C) and typical for the pellets size of the sphere, values of the Biot criterion constitute 0.5-2.0. At this ratio of internal and external heat flows heating of a pellet occurs in such way that by the time of the melting point achievement, temperature gradient on its surface gets insignificant over its radius.
In Physical-and-Technological Institute of Metals and Alloys (FTIMS) of the NAS of Ukraine heat exchange in melting of the ore-coal pellets in motionless and boiling slag were investigated.
Goal of this work was investigation of heat exchange in the pool in liquid-phase melting of the ore-coal pellets. The investigations were carried on experimental installation (Figure 1), the design of which included Tamman furnace, a frequency converter (FR-5520-0.4K), an electric motor, and a graphite crucible. By rotation of the crucible with slag intensity of the slag boiling in melting of the ore-coal pellets was simulated.
In the experiments lime-silica slag (55.5 % CaO, 44.5 % Si[O.sub.2]) was used with melting point 1475 [degrees]C. Mass of the slag in all experiments was constant--0.3 kg.
For manufacturing of the ore-coal pellets an iron-ore concentrate, a carbon-containing reducer and the grade 400 cement, which functioned as a binder in formation of the pellets, were used. Content of the cement constituted 15 % of total mass of the ore concentrate and the reducer.
Electrode scrap, containing 86 % C, was used as the reducer. Consumption of the reducer exceeded by 30 % its quantity, theoretically necessary for full reduction of iron in a pellet. Weight share of components in the mixture was as follows, %: are concentrate--66.7; reducer--19.0; cement--14.3.
The pellets were produced by ramming the mixture in a specially made mould. In center of the pellet the VR-20/5 tungstenrhenium thermocouple was placed. For protection of the thermocouple junction against direct contact with iron and its oxides protective elec-trocorundum coating was applied on the surface. The pellets were subjected to hardening drying at room temperature within 7 days and then to low-temperature (300 [degrees]C) drying in the drying chamber.
Mass of a pellet was 0.009 kg, density--2150 kg/[m.sup.3]. Chemical composition of the ore-coal pellets was as follows, wt.%: 1.33 FeO; 58.6 [Fe.sub.2][O.sub.3]; 7.34 Si[O.sub.2]; 0.82 [Al.sub.2][O.sub.3]; 10.92 CaO; 0.6 MgO; 0.02 Ti[O.sub.2]; 16.34 C; 0.34 [K.sub.2]O; 0.06 [P.sub.2][O.sub.5]; 0.63 S.
At the beginning of the experiment the crucible with slag was installed in isothermal zone of the furnace, the furnace was turned on, and the slag was melted. The slag temperature was measured by the tungstenrhenium thermocouple, junction of which was protected by a quartz tip. Readings of the thermocouple were registered by the Ml 108 portable millivolt-ammeter.
After melting of the slag and its overheating up to (15550 [+ or -] 5) [degrees]C the crucible with the slag was imparted rotational movement at a preset speed, and the pellet was immersed into the slag. In process of the experiments speed of the crucible rotation equaled 0; 0.01; 0.02 and 0.04 m/s.
Temperature of the pellet center from the instant of its immersion into the slag was registered by the UPIT portable universal instrument, developed by FTIMS of the NAS of Ukraine and designed for periodic measurements of temperatures by means of the converters. Error of the temperature measurement equaled [+ or -] 1 [degrees]C. Time interval between previous and subsequent measurements of the pellet center temperature was constant and equaled 5 s. Time of the pellet heating was registered by a stop-watch.
[FIGURE 2 OMITTED]
Duration of a pellet heating was determined by its stability. Failure of the specimen being heated was detected at high temperatures; it was stipulated by intensive gas release of the iron reduction reaction products in internal layers of a pellet and swelling and loss of strength of a pellet because of phase and structural transformations during heating .
Change of the pelt surface temperature and coefficient of convective heat exchange between the pellet surface and the slag depending upon intensity of the slag boiling and time of heating were determined using data presented in Figures 2 and 3. These graphs are built according to calculated values of the Fourier criterion and analytical solution results of differential equation of heat conductivity in case of heating of bodies of spherical shape under non-stationary conditions in the constant temperature environment . They are applicable for this case because mass of the slag is 30 times higher than that of the pellet.
The graphs are drawn in the form of the following equation:
[theta] = f (Bi, Fo, r/R)
[theta] = f ([alpha]R/[lambda], a[tau]/[R.sup.2], r/R)
where [theta] is the dimensionless variable temperature; Bi is the Biot criterion, which determines character of temperature distribution within volume of the pellet being heated; Fo is the dimensionless time; r/R is the dimensionless coordinate; r is the current value of the pellet radius, m; R is the pellet radius; [lambda] is the pellet heat conductivity, J/([m.sup.2] x s x [degrees]C); a is the pellet heat diffusivity coefficient, characterized by its heat inertia properties, [m.sup.2]/s.
[FIGURE 3 OMITTED]
Heat diffusivity coefficient is determined from the expression
[alpha] = [lambda]/c[rho],
where c is the pellet heat capacity, J/(kg x [degrees]C); p is the pellet density, kg/[m.sup.3].
Presented in Figures 2 and 3 dependences are drawn for two values of the dimensionless coordinate: r/R = 0 and r/R = 1, which correspond to the pellet center and its surface.
Heat exchange coefficient a and the pellet surface temperature were determined according to the calculated Fourier criterion and dimensionless temperature of the pellet center for each instant of the time, at which temperature of the pellet center was measured. In calculation of the heat diffusivity coefficient heat capacity and heat conductivity of the pellet material were assumed to be constant and represent mean values of mentioned thermal physics properties within temperature range of 0-1200 [degrees]C.
Necessary for calculation of the heat capacity and heat conductivity values were taken from .
Dimensionless temperature of the pellet center [[theta].sub.c] was determined from the expression
[[theta].sub.c] = [T.sub.c] - [T.sub.0] / [T.sub.sl] - [T.sub.0],
where [T.sub.c] is the measured temperature of the pellet center, [degrees]C; [T.sub.0] is the pellet temperature prior to its immersion into the slag, [degrees]C; [T.sub.sl] is the slag temperature, [degrees]C.
Using found values of dimensionless temperature of the pellet center and the Fourier criterion value, the Biot criterion was found with application of the data, presented in Figure 2.
Heat exchange coefficient a was determined from the expression
[alpha] = Bi[lambda]/R [J / (mxsx[degrees]C)].
Dimensionless temperature of the pellet surface was determined using data of Figure 3.
Temperature of the pellet surface [T.sub.s] was determined from the expression
[T.sub.s] = [[theta].sub.s] ([T.sub.sl] - [T.sub.0]) + [T.sub.0] [[degrees]C]
where [[theta].sub.s] is the dimensionless temperature of the pellet surface.
Experimental and calculated values of parameters of the pellet heating process in molten slag are presented in Tables 1-4.
It follows from the presented data that initial period of heating of the pellets is characterized by increased values of the Biot criterion. At this period change of temperature field significantly differs from initial thermal state of the body. That's why character of mentioned process is not determined unambiguously by conditions of heating and properties of the pellet. Later at Fo [greater than or equal to] 0.3, value of the Biot criterion remains practically constant. This proves establishment of regular heating conditions, at which distribution of temperatures over volume of the pellet does not depend upon initial conditions and is determined by conditions of heating and thermal physics properties of the pellet material.
Presented data also show that character of temperature distribution within the pellet volume is determined by the Biot criterion, i.e. conditions of external heat exchange, when intensity of internal heat exchange or internal heat resistance of the pellet does not change in the process of heating. As speed of the slag rotation increases, i.e. as intensity of the slag boiling gets higher, intensity of heat exchange between surface of the pellet and molten slag increases. So, when speed of the slag rotation increases from 0 to 0.04 m/s, the Biot criterion increases from 0.366 to 0.715 and coefficient of heat exchange from 73 to 143 J/([m.sup.2] x s x [degrees]C) (Figure 4).
As intensity of heat exchange in the pool increases, rate of the pellet heating gets higher (Table 5).
Data, presented in Table 5, prove that heating of a pellet in the rotating slag reduces time, necessary for achievement of the preset temperature of the pellet center. So, at speed of the slag rotation 0.01 m/s time, necessary for achieving by center of the pellet of temperature 900 [degrees]C, reduces in comparison with immobile slag by 6.8 %, and if speed of the slag rotation increases up to 0.04 m/s it reduces by 60 %. So, results of the investigations allowed establishing dependence of the heat-transfer coefficient upon intensity of the slag mixing.
[FIGURE 4 OMITTED]
[1.] Goldfarb, E.I., Sherstov, B.I. (1975) Heat-mass-exchange processes in bath of steelmaking units. Moscow: Metallurgiya.
[2.] Trakhimovich, V.I., Shalimov, A.G. (1982) Use of direct-reduced iron in melting of steel. Moscow: Metallurgiya.
[3.] Kachula, V.V., Fofanov, A.A., Antonova, S.M. (1978) About influence of natural properties of concentrates on strengthening of pellets and their behaviors during reduction. Izvestiya Vuzov. Chyorn. Metallurgiya, 8, 25-28.
[4.] Kitaev, V.P., Yaroshenko, Yu.G., Suchkov, V.D. (1957) Heat exchange in shaft furnaces. Sverdlovsk: Metallurgizdat.
[5.] Kitaev, V.P., Yaroshenko, Yu.G., Lazarev, B.P. (1966) Heat exchange in blastfurnaces, Moscow: Metallurgiya.
V.N. KOSTYAKOV (2), E.B. POLETAEV (2), G.M. GRIGORENKO (1), S.N. MEDVED (2), E.A. SHEVCHUK (2), A.A. YASINSKY (2)
(1) E.O. Paton Electric Welding Institute, NASU, Kiev, Ukraine (2) Physical-and-Technological Institute of Metals and Alloy, NASU, Kiev, Ukraine
Table 1. Values of absolute and dimensionless temperatures of pellet center and surface, and Fourier and Biot criteria in case of pellet heating in immovable slag [pi],s [T.sub.c], [degrees]C [[theta].sub.c] Fo 5 81 0.040 0.064 10 116 0.063 0.129 15 173 0.100 0.193 20 248 0.149 0.257 25 322 0.197 0.320 30 395 0.245 0.386 35 465 0.290 0.450 40 530 0.333 0.515 45 597 0.377 0.580 50 664 0.421 0.640 55 726 0.460 0.700 60 784 0.500 0.770 65 843 0.538 0.840 70 894 0.571 0.900 75 941 0.602 0.965 [pi],s Bi [[theta].sub.c] [T.sub.c], [degrees]C 5 -- -- -- 10 0.550 0.217 353 15 0.405 0.246 396 20 0.385 0.277 444 25 0.370 0.325 517 30 0.360 0.368 583 35 0.355 0.405 640 40 0.355 0.445 701 45 0.355 0.483 759 50 0.365 0.515 808 55 0.370 0.544 852 60 0.373 0.575 900 65 0.375 0.595 930 70 0.380 0.627 979 75 0.387 -- -- Note. Here in all cases [Bi.sub.av] = 0.366, [[alpha].sub.av] = 73.26 J/([m.sup.2] x S x [degrees]C). Table 2. Value of absolute and dimensionless temperatures of pellet center and surface, and Fourier and Biot criteria in case of pellet heating in rotating slag (speed of rotation [[upsilon].sub.sl] = 0.01 m/s) [pi],s [T.sub.c], [degrees] C [[theta].sub.c] Fo 5 81 0.040 0.064 10 110 0.059 0.129 15 211 0.125 0.193 20 290 0.176 0.257 25 375 0.232 0.320 30 456 0.285 0.386 35 532 0.330 0.450 40 604 0.380 0.515 45 669 0.424 0.580 50 728 0.462 0.640 55 784 0.500 0.700 60 836 0.533 0.770 65 890 0.568 0.840 [pi],s Bi [[theta].sub.s] [T.sub.s], [degrees] C 5 -- -- -- 10 0.520 0.219 355 15 0.510 0.276 442 20 0.455 0.315 502 25 0.445 0.367 582 30 0.435 0.413 652 35 0.415 0.455 717 40 0.420 0.495 111 45 0.415 0.535 839 50 0.415 0.565 884 55 0.420 0.595 930 60 0.410 0.625 976 65 0.410 0.653 1019 Note. Here in all cases [Bi.sub.av] = 0.425; [[alpha].sub.av] = 85 J/([m.sup.2] x s x [degrees]C). Table 3. Value of absolute and dimensionless temperatures of pellet center and surface, and Fourier and Biot criteria in case of pellet heating in rotating slag (speed of rotation [[upsilon].sub.sl] = 0.02 m/s) [pi],s [T.sub.c], [degrees]C [[theta].sub.c] Fo 5 81 0.040 0.064 10 133 0.074 0.129 15 226 0.140 0.193 20 327 0.207 0.257 25 427 0.266 0.320 30 519 0.326 0.386 35 604 0.380 0.450 40 688 0.436 0.515 45 762 0.485 0.580 50 828 0.528 0.640 55 884 0.565 0.700 60 930 0.595 0.770 [pi],s Bi [[theta].sub.s] [T.sub.s], [degrees]C 5 -- -- -- 10 0.655 0.250 402 15 0.565 0.315 502 20 0.545 0.375 594 25 0.515 0.425 670 30 0.500 0.470 739 35 0.500 0.515 808 40 0.510 0.555 869 45 0.510 0.593 927 50 0.505 0.625 976 55 0.510 0.655 1022 60 0.500 0.697 1086 Note. Here in all cases [Bi.sub.av] = 0.51; [[alpha].sub.av] = 102 J/([m.sup.2] x s x [degrees]C) Table 4. Value of absolute and dimensionless temperatures of pellet center and surface, and Fourier and Biot criteria in case of pellet heating in rotating slag (speed of rotation [[upsilon].sub.sl] = 0.04 m/s) [pi],s [T.sub.c], [degrees]C [[theta].sub.c] Fo 5 75 0.036 0.064 10 169 0.097 0.129 15 298 0.180 0.193 20 430 0.268 0.257 25 550 0.346 0.320 30 650 0.410 0.386 35 741 0.470 0.450 40 825 0.526 0.515 45 922 0.590 0.580 [pi],s Bi [[theta].sub.s] [T.sub.s], [degrees]C 5 -- -- -- 10 0.870 0.321 511 15 0.725 0.402 635 20 0.760 0.483 759 25 0.750 0.548 858 30 0.695 0.583 912 35 0.685 0.630 984 40 0.685 0.670 1045 45 0.715 0.705 1099 Note. Here in all cases [Bi.sub.av] = 0.715; [[alpha].sub.av] = 143 J/([m.sup.2] x s x [degrees]C) Table 5. Influence of slag rotation speed on rate of pellet heating Time of heating (s at T in center of pellet, [[upsilon].sub.sl] [degrees]C 500 600 700 800 900 0 36.5 45.0 53.0 61.5 70.5 0.01 33.0 40.0 47.5 56.5 66.0 0.02 29.0 35.0 41.0 47.5 56.5 0.04 23.0 27.5 33.0 38.5 44.0
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|Title Annotation:||ELECTROMETALLURGY OF STEEL AND FERROALLOYS|
|Author:||Kostyakov, V.N.; Poletaev, E.B.; Grigorenko, G.M.; Medved, S.N.; Shevchuk, E.A.; Yasinsky, A.A.|
|Publication:||Advances in Electrometallurgy|
|Date:||Jan 1, 2008|
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