ISSN 09670912, Steel in Translation, 2011, Vol. 41, No. 5, pp. 407–409. © Allerton Press, Inc., 2011. Original Russian Text © A.N. Smirnov, A.Yu. Tsuprun, E.V. Shtepan, V.V. Kislitsa, V.M. Pil’gaev, 2011, published in “Stal’,” 2011, No. 5, pp. 19–21.
Thermal Analysis of Mold in Continuous SlabCasting Machine A. N. Smirnova, A. Yu. Tsuprunb, E. V. Shtepana, V. V. Kislitsac, and V. M. Pil’gaevd a
Donetsk National Technical University, Donetsk, Ukraine b NPO DONIKS, Donetsk, Ukraine cOAO MK Azovstal’, Mariupol, Ukraine d AO NKMZ, Kramatorsk, Ukraine
Abstract—The factors affecting the thermal state of mold walls in continuous slabcasting machines are ana lyzed. On the basis of the proposed method and model, the design parameters of a radial mold with slot chan nels and the parameters of the coolant (water) flow may be calculated. DOI: 10.3103/S0967091211050160
where δmw is the wall thickness; λmw is the wall’s ther mal conductivity. The resistance due to the heat transfer at the sur face of the cooling channel is Rco.ch = 1/α, (5) where α is the heattransfer coefficient to the water from the surface of the cooling channel. Analysis of Eqs. (2)–(5) shows that two values required for calculation of the temperature field have Mold coating
Mold coating
(2)
where δcr is the crust thickness; λcr is the crust’s ther mal conductivity. 407
TB Tm
Water
Solid crust
SFS
Gap
Tw
Tg T Tco. co ch Tmw
Tsl Tcr
Tco Tcr Tco.ch Tmw Tsl Rmw Rcr Liquid steel Rco. ch Rsl Rco
(a)
SFS
Liquid steel
Solid crust
Mold
Mold
(1)
where q is the heatflux density; Tm, Tw are the tem peratures of the liquid metal and cooling water, respectively; Rcr, Rsl, Rco, Rmw, and Rco.ch are, respec tively, the thermal resistances of the crust, slagform ing mixture, mold coating, and mold wall and the resistance due to the heat transfer at the surface of the cooling channel. Consider the thermal resistances in Eq. (1). The thermal resistance of the crust is Rcr = δcr/λcr,
(3)
where δco is the coating thickness; λco is the coating’s thermal conductivity. The thermal resistance of the mold wall is Rmw = δmw/λmw, (4)
Water
Tm – Tw q = , R cr + R sl + R co + R mw + R co.ch
The thermal resistance of the mold coating is Rco = δco/λco,
Gap
The mold plays an important role in determining the rational operation of continuous casting machines and the optimal quality of the continuouscast slab. In mold design, the geometric parameters and coolant (water) flow rates selected must, on the one hand, ensure the required crust thickness at the mold exit and, on the other, ensure reliability and durability of the mold walls. To calculate the thermal field in the mold of a con tinuous slabcasting machine, we consider the heat transfer from liquid steel to the coolant. In the lower part of the mold, when a gas gap forms on account of shrinkage, the heat transfer from the mold is as shown in Fig. 1a; in the upper part, it corresponds to Fig. 1b. Obviously, the operating conditions of the plates are more challenging in the second case. Consequently, in what follows, we will consider the upper part of the mold, which determines the overall operating condi tions of the walls. Analysis of Fig. 1 shows that the system consisting of the liquid steel and the cooling water may be described by the equation [1]
Tm
(b)
Fig. 1. Heat transfer in mold: Tm, Tcr, Tsl, Tg, Tco, Tmw, Tco.ch, and Tw are, respectively, the temperatures of the liquid metal, the crust, the slagforming mixture (SFS), the gap, the mold coating, the mold wall, the surface of the cooling channel, and the cooling water; Rcr, Rsl, Rco, Rmw, and Rco.ch are defined in the text.
408
SMIRNOV et al.
Comparison of plant data and calculations of the heatflux density Eq.
Mean heatflux density, W/m2
Formula* qint = (0.76v + 0.34) × 106 qint = 1.9 × 106exp(–0.365L) – 1.93 × 106exp(–2.69v) qint = 7.3t–0.5 qloc = 1.12 × 106exp(–3.13t) + 0.503 × 106 qloc = [exp(–3.26 + 4t) + exp(0.921 – 2.24t)] × 106 qloc = v0.46668exp(14.689 + L((–4.3376 + L(5.5939 –3.1608L2)) + 0.007815/L/v – 5.71 × 10–8L–5)
(1*) (2*) (3*) (4*) (5*) (6*)
1024000 1196558 942425.9 801305 1539478 933087
Note: *Here v is the casting speed; L is the distance from the meniscus.
not been determined: the heattransfer coefficient α to the water from the surface of the cooling channel; and the heatflux density q. Various methods are used to determine the heat transfer coefficient. In the present work, we employ empirical methods to determine the heattransfer coefficient—in particular, the formula for a liquid moving at more than 5 m/s (the Shaker formula) α = 3380Vw(1 + 0.014Tw),
(6)
where Vw is the velocity of the water. This method adequately describes the heat transfer from the mold to the water, as we see by comparing the results obtained from Eq. (6) with literature data [2, 3]: 38592 and 35000 W/(m2 °C), respectively. The integral heat flux is determined experimentally from the difference in water temperatures at the mold input and output and the water flow rate [4] q = ρwgwcwΔTw,
(7)
where ρw is the density of the water, kg/m3; gw is the water flow rate in mold cooling, m3/s; cw is the specific heat of water, J/kg K; ΔTw is the difference in water temperatures at the mold input and output, K. Геометрия каналов Количество каналов для расчета
9
Расстояние от края до центра канала, мм
№ канала
(соотношение глубины каналов и расстояния между ними рекомендуется выбирать в пределах 1–1.5) Количество типов каналов 3 Ширина Глубина Ширина Глубина Количество каналов Расход воды Расход воды на канал, м3/ч Тип канала, мм канала, мм канала, мм канала, мм на стенку на тип 20 5 20 2 3.996 5 7.992 1
1
26
2
63.5
5
18
2
5
18
2
3.5964
7.1928
3
80.5
5
16
3
5
16
5
3.1968
15.984
4
97.5
5
16
Подача воды
Верхняя
Нижняя Давление на входе в канал, МПа
0.527188549
Условия разливки
0.4
Общий расход воды на стенку, м3/ч
31.1688
600
Скорость разливки, м/мин:
1.2
Температура воды на входе, °C
35
500
Температура воды на выходе, °C
38
Рабочая длина кристаллизатора, м
0,9
Теплоемкость воды, Дж/(кг К)
4180
Скорость воды, м/с (рекомендуется не менее 5 м/с)
11.1
400
Температура разупрочнения материала стенки
Температура разупрочнения материала покрытия
300 Управление проектом
Свойства стенки кристаллизатора Теплопроводность материала стенки, Вт/м. град Температура разупрочнения, С
365 500
БрЦр(холоднодеформ Выбор материала стенки Свойства покрытия кристаллизатора Теплопроводность материала покрытия, 80 Вт/м. град 400 Температура разупрочнения, С Выбор материала покрытия
Давление на выходе из канала, МПа
выберите покрытие
Начать счет
200 Температура насыщения
шаг по оси x
50
шаг по оси y
100
100
Сохранить снимок экрана
Геометрия стенки кристаллизатора Ширина стенки, мм
229
Толщина стенки, мм
45
Толщина покрытия, мм
0.55
Количество перестрожек
0
Глубина перестрожки, мм
1
Расстояние от мениска, м
0.04
Температура покрытия
Температура меди
Температура стенки канала
Fig. 2. Thermal state of the narrow wall of a slab mold.
For continuous casting machines from different manufacturers, the integral and local heatflux density has been studied, and empirical formulas have been derived for specific conditions [5–10]. The choice of formula largely depends on the specific continuous casting machine; experimental research is required here. At OAO MK Azovstal’, in casting lowcarbon, low silicon steel (at a rate of 0.9 m/min; slab thickness 220 mm), we have studied the heat transfer from the mold in the following conditions: 24/250 Water flow rate at narrow/broad walls, m3/h Water heating at narrow/broad walls, °C 7/6.5 Mold width, mm 2100 Metal temperature in mold, °C 1550 Specific heat of water, J/kg K 4180 Heat removed in unit time 194091.33/1877371.5 from narrow/broad walls, J/s Mean heatflux density at narrow/broad 945864.2/979327.87 walls, W/m2 Maximum heatflux density at 1713577.5 0.9 m/min, W/m3
The table compares experimental data for the heat flux density with results from the formulas in [5–10]. Analysis shows that Eq. (3*) best describes the data for OAO MK Azovstal’. On the basis of the results, we have developed a method for calculating the thermal state of mold walls and corresponding Mould software. This software allows us to take account of the mold geometry, the parameters of the cooling water, and the properties of the wall. An example of the calculation is shown in Fig. 2 for the narrow wall of a slab mold (thickness 220 mm). Analysis of the mold wall’s thermal state by Mould software draws attention to the following factors. (1) The channel temperature on the wall side must be 5°C below the saturation temperature. Note the pressure dependence of water’s boiling point. Equally STEEL IN TRANSLATION
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THERMAL ANALYSIS OF MOLD IN CONTINUOUS SLABCASTING MACHINE
important is the water speed, determined by the ratio nal channel geometry and the pressure created. This speed must ensure sufficient heat transfer at the chan nel walls and prevent film boiling of the water (Fig. 2). (2) The temperature of the mold wall and the mold coating must be less than the softening temperature of the wall material (Fig. 2). (3) The mean water temperature in the channels must prevent the formation of deposits. (In other words, it must be above 45°C.) Correspondingly, the water speed must be at least 6 m/s. (4) Variation in channel width in the range 5–10 mm has practically no influence on the heattransfer rate. Design and technological considerations may be employed to make a selection within that range. (5) The ratio of the channel depth and the distance between channels must maximize radiation and is selected by the designer in the range 1–1.5. Below 1, the temperature of the mold wall and mold coating tends to rise; above 1.5, the useful wall thickness for reconstruction is reduced. Thus, on the basis of the experimental data and cal culation results, we have developed a method for cal culating the thermal state of mold walls for a continu ous slabcasting machine. The method permits selec tion of the mold’s geometric parameters and the wall material. REFERENCES
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