Influence of Structure on Thermal Conductivity of Insulation Board Used during Ingot Casting
2017 年 58 巻 4 号 p. 668-672
詳細
2017 年 58 巻 4 号 p. 668-672
In order to improve heat prevention property of insulation board used in hot top during casting of steel ingot, thermal conductivities of insulation boards of solid structure and porous structure with different porosities were investigated using numerical simulation and calorimetric techniques. A heat transfer model used to calculate the thermal conductivity of insulation boards was developed, and the accuracy of the model was verified by calorimetric experiment. A series of porous insulation boards made of floating beads with different porosities were designed and effect of porosity on thermal conductivity of porous insulation board was investigated by numerical simulation. It was found that porous insulation board performs a better heat prevention property than insulation board of solid structure. Thermal conductivity of porous insulation board decreases notably with the increase of porosity. By contrast, the sizes of pores almost have no influence on the thermal conductivity of porous insulation board.
During casting of a steel ingot, shrinkage pipe and shrinkage holes always form in the top of an ingot due to gravity and solidification shrinkage. In view of this, hot top is adopted to compensate the shrinkage and is widely used in ingot production. Figure 1 is a schematic of heat transfer in hot top of a steel ingot during solidification. In general, the depth of shrinkage pipe and shrinkage holes depends on feeding effect of the hot top mostly. For hot top with insulation boards, utilization of high-property of heat preservation material has a great benefit for decreasing the depth of shrinkage pipe and improving metal yield.
Schematic of heat transfer in hot top of a steel ingot during solidification.
Usually, insulation boards have two different structures, namely, solid structure and porous structure. At present, insulation boards with solid structure are widely used in hot top during casting of steel ingots. However, porous insulation boards that have a better heat preservation property are not so popular. Many researchers have investigated the thermal physical properties of porous materials1–5). The thermal conductivity of porous materials is closely related to the parameters of pores. Dos Santos6) investigated the effect of moisture and porosity on the thermal conductivity of a conventional aluminous refractory concrete. He found that there was a linear dependence of the thermal conductivity with the porosity. Rafael Barea et al.7) measured the thermal diffusivity of highly porous mullite materials with pores of about 30 μm in diameter. They found that the thermal conductivity of materials with porosities ≥45% is almost constant with temperature and about 75% lower than that of the dense mullite. In addition, the thermal conductivity is also related with the size and distribution of the pores8).
Floating beads are wastes generated from coal-burning power plants, which have many characteristics such as high strength, good hardness, low density and low heat conductivity. Therefore, insulation boards made of floating beads would have good heat prevention properties. Furthermore, the consumption of floating beads can simultaneously make contribution to utilization of waste resources. However, there are few reports about porous insulation boards made of floating beads. In this paper, by combination of numerical simulation and calorimetric techniques, thermal conductivities of insulation boards with solid structure and porous structure with different porosities were investigated. And heat prevention properties of insulation boards with different structures were discussed. Based on the results, further investigation will focus on influence of thermal conductivity and thickness of insulation boards on shrinkage pipe and macro-segregation under hot top of steel ingots.
There are insulation boards with solid structure and porous structure. The insulation board with solid structure mainly consists of silica sands, clays and paper fibers, among which, silica sands act as aggregates, clays and paper fibers act as adhesives. Figure 2 shows photographs of insulation board with solid structure. The porous insulation board mainly consists of floating beads and clays, in which floating beads act as aggregates, clays act as adhesives. Figure 3 shows photographs of porous insulation board made with floating beads. The floating beads are hollow spherical shapes with different sizes as shown in Fig. 3 (c) and (d). Composition of the floating bead is shown in Table 1. It can be seen that the main composition of floating beads is similar to that of clays.
Photographs of insulation board with solid structure, (a) no magnification; (b) 7 times normal magnification.
Photographs of porous insulation board made with floating beads, (a) Porous insulation board with no magnification, (b) Porous insulation board with 7 times normal magnification, (c) Floating beads with 7 times normal magnification, (d) Floating beads with 50 times normal magnification.
| Composition | SiO2 | Al2O3 | Fe2O3 | CaO | MgO |
|---|---|---|---|---|---|
| mass% | 55.4 | 32.85 | 3.38 | 1.38 | 1.1 |
In order to measure the size of the floating beads statistically, 50 floating beads were sampled randomly from the porous insulation board and observed under 100 times normal magnification using a microscope. It was found the average size of the floating beads was about 0.1 mm.
The densities of the insulation boards with solid structure and porous structure are 1547.6 kg･m−3 and 762.6 kg･m−3, respectively. Both the main materials of the two kinds of insulation boards are SiO2, thus the porosity of the porous insulation board can be regarded as 50.7%, which was calculated according to the densities.
The thermal conductivities of the two kinds of insulation boards were measured using calorimetric techniques9) as shown in Fig. 4. Samples of the insulation boards with dimensions of Φ180 mm × 20 mm were prepared. The upper and lower faces of the samples were smooth and parallel. Before the experiment, the samples and thermal spreader were dried at 110℃. The thicknesses of the samples were measured with vernier calipers to an accuracy of 0.02 mm. Germanium thermocouples were placed on center of the upper face and thermal spreader below the lower face to measure the temperatures of the hot surface and the cold surface of the samples.
Schematic of calorimetric techniques.
After the sample was placed into the heating furnace, temperature on the hot surface of the sample was raised to 1100℃ at a heating rate of 80℃･min−1. Water flow rate of the calorimeter was 70 g･min−1–90 g･min−1 to make sure the temperatures of the cold surface and the hot surface were 830℃ and 1100℃, respectively.
When the temperatures were stable for 120 min, the water flow rate and temperatures were recorded every 10 minutes for 3 times and took the average values. The thermal conductivities were calculated using eq. (1).
| \[\lambda = \frac{Q \cdot \delta}{A \cdot \Delta T}\] | (1) |
Where λ is the thermal conductivity of the sample, W･m−1･℃−1, Q is the amount of heat transferred through the sample per unit time, W, δ is thickness of the sample, m, A is area of the sample, m2, ΔT is the difference in temperatures of the cold surface and the hot surface, ℃.
The measured conductivities of the insulation boards with solid structure and porous structure were 0.447 W･m−1･℃−1 and 0.163 W･m−1･℃−1, respectively.
2.2 Heat transfer model of insulation boardInsulation boards with different structures have different thermal conductivities. In order to make clear the influence of structures on thermal conductivity of insulation board, heat transfer models of insulation boards with different structures were developed based on Fourier's equation as shown in eq. (2). Effects of porosity and pore size on thermal conductivity of insulation board were investigated by numerical simulations.
| \[\rho c \frac{\partial T}{\partial t} = \frac{\partial}{\partial x} \left( \lambda \frac{\partial T}{\partial x} \right) + \frac{\partial}{\partial y} \left( \lambda \frac{\partial T}{\partial y} \right) + \frac{\partial}{\partial z} \left( \lambda \frac{\partial T}{\partial z} \right)\] | (2) |
Where ρ is density, kg･m−3, c is specific heat J･kg−1･℃−1, λ is thermal conductivity, W･m−1･℃ −1.
Assumptions were made as followings:
Geometric models with dimensions of 1.0 × 1.0 × 0.5 mm3 of insulation boards with solid structure and porous structure were developed as shown in Fig. 5. According to the assumption 2), pores were of uniform size and distributed evenly in the porous insulation board.
Geometric models of insulation boards with solid structure and porous structure, (a) solid structure, (b) porous structure.
The insulation board with solid structure mainly consists of silica sands and clay, whose main composition is SiO2. The porous insulation board mainly consists of floating beads, whose main composition is also SiO2 as shown in Table 1. Therefore, assumption that materials of the insulation boards all have the same thermophysical properties is reasonable. The thermal conductivity and density of the insulation board with solid structure which are 0.447 W･m−1･℃−1 and 1547.6 kg･m−3, respectively, can be regarded as the thermal conductivity and density of the materials. The specific heat of the materials was calculated according to database of FactSage software. FToxid databases in FactSage software contain thermodynamic data for pure oxides and oxide solutions of Al2O3, SiO2, CaO, Fe2O3, MgO, MnO, and so on10,11). Interior of the floating bead is almost vacuum state, which only consists of gas such as N2, H2 and CO2 in trace amounts. Therefore heat conduction of the gas inside the floating beads can be neglected12).
Side faces of the insulation board were of adiabatic condition. Temperatures on bottom face and top face were 830℃ and 1100℃, respectively, which was in conformity with calorimetric experiment. The finite element mesh of the insulation boards was 0.02 mm, which was selected based on several mesh refinements.
Heat transfer process was calculated using ProCAST 2013.0 until distribution of temperature in the insulation board was stable. ProCAST is a commercial finite element software for numerical simulation of casting and heat transfer. Then heat flux through the insulation board could be obtained. With combination of the heat flux and difference in temperature of cold surface and hot surface, the thermal conductivity of the insulation board could be calculated. The calculated thermal conductivity of the porous board with porosity of 51.2% is 0.170 W･m−1･℃−1, which is close to the measured value (0.163 W･m−1･℃−1) of the porous board with porosity of 50.7% as mentioned before. Therefore, it can be said that the model is reliable.
In order to investigate the influence of porosity and pore size on thermal conductivity of insulation board, a series of insulation boards with different porosities and pore sizes were designed as shown in Table 2. Considering the computational load, dimensions of geometric models for different designs were different. For each design, pores were of uniform size and distributed evenly in the porous insulation board. Material properties and boundary conditions for calculations were the same as mentioned above. Thermal conductivity of each design was calculated.
| Design# | Porosity | Pore size, mm | Dimensions of geometric models, mm3 | Thermal conductivity, W･m−1･℃−1 |
|---|---|---|---|---|
| 1# | 0 | 0 | 0.50 × 0.50 × 0.30 | 0.4500 |
| 2# | 0.512 | 0.099 | 0.50 × 0.50 × 0.30 | 0.1696 |
| 3# | 0.702 | 0.099 | 0.45 × 0.45 × 0.27 | 0.1003 |
| 4# | 0.385 | 0.099 | 0.55 × 0.55 × 0.33 | 0.2332 |
| 5# | 0.233 | 0.099 | 0.65 × 0.65 × 0.39 | 0.3102 |
| 6# | 0.187 | 0.099 | 0.70 × 0.70 × 0.42 | 0.3366 |
| 7# | 0.152 | 0.099 | 0.75 × 0.75 × 0.45 | 0.3542 |
| 8# | 0.104 | 0.099 | 0.85 × 0.85 × 0.51 | 0.3891 |
| 9# | 0.088 | 0.099 | 0.90 × 0.90 × 0.54 | 0.3943 |
| 10# | 0.296 | 0.099 | 0.48 × 0.48 × 0.36 | 0.2760 |
| 11# | 0.125 | 0.099 | 0.48 × 0.48 × 0.32 | 0.3600 |
| 12# | 0.521 | 0.087 | 0.44 × 0.44 × 0.26 | 0.1726 |
| 13# | 0.524 | 0.062 | 0.31 × 0.31 × 0.19 | 0.1723 |
| 14# | 0.519 | 0.112 | 0.56 × 0.56 × 0.34 | 0.1726 |
| 15# | 0.512 | 0.124 | 0.63 × 0.63 × 0.38 | 0.1755 |
| 16# | 0.512 | 0.149 | 0.75 × 0.75 × 0.45 | 0.1761 |
| 17# | 0.512 | 0.496 | 2.50 × 2.50 × 1.50 | 0.1755 |
| 18# | 0.512 | 0.993 | 5.00 × 5.00 × 3.00 | 0.1760 |
| 19# | 0.512 | 1.985 | 10.0 × 10.0 × 6.0 | 0.1760 |
| 20# | 0.512 | 4.963 | 25.0 × 25.0 × 15.0 | 0.1763 |
Effect of porosity on thermal conductivity of porous insulation board based on the calculations under pore conditions of #2–#11 in Table 2 is shown as squares in Fig. 6. It can be seen that thermal conductivity of porous insulation board decreases with the increase of porosity. Due to the interior of the floating bead is almost vacuum state and heat conduction of the gas inside the floating beads is neglected, the presence of porosity in insulation board reduces the cross-section area for heat carrying severely.
Effect of porosity on thermal conductivity of porous insulation board according to the calculations and literatures.
According to the relationship of porosity and thermal conductivity of porous material from Loeb13), the relationship of porosity and thermal conductivity of the porous insulation board can be expressed as
| \[\lambda = \lambda_{\rm s} - \alpha \cdot V_{\rm p} \cdot \lambda_{\rm s}\] | (3) |
Where λ is thermal conductivity of the porous insulation board, W･m−1･℃−1, λs is thermal conductivity of the insulation board with solid structure, W･m−1･℃−1, α is coefficient and Vp is porosity.
The thermal conductivity of the insulation board with solid structure is 0.447 W･m−1･℃−1 according to the calorimetric measurement. Namely, λs is 0.447 W･m−1･℃−1. The coefficient α is obtained as 1.19 using a regression analysis of the calculated data. The thermal conductivity of the porous insulation board can be written as λ = 0.447–0.5332 × Vp, which is shown as the line of Loeb's relation in Fig. 6.
David S.Smith et al.14) investigated effect of pore volume fraction on thermal conductivity of porous ceramics. They found that when pore volume fraction (Vp) is smaller than 0.65, the Maxwell-Eucken's relation15) for closed porosity and Landauer's relation16) for open porosity give good agreement to experimental data on tin oxide, alumina and zirconia ceramics. When pore Vp is larger than 0.65, the thermal conductivity of kaolin-based foams and calcium aluminate foams was well described by the Hashin Shtrikman upper bound17) and Russell's relation18). Equation (4) and eq. (5) express the Maxwell-Eucken's relation and Russell's relation of porosity and thermal conductivity of the porous insulation board, respectively.
| \[\lambda = \lambda_{\rm s} \frac{2 - 2V_{\rm p}}{2 + V_{\rm p}} = 0.447 \times \frac{2 - 2V_{\rm p}}{2 + V_{\rm p}}\] | (4) |
| \[\lambda = \lambda_{\rm s} \frac{1 - {V_{\rm p}}^{2/3}}{1 + V_{\rm p}} = 0.447 \times \frac{1 - {V_{\rm p}}^{2/3}}{1 + V_{\rm p}}\] | (5) |
Thermal conductivity of the insulation board as a function of porosity according to literatures of Loeb's relation, Maxwell-Eucken's relation and Russell's relation as well as the calculated results are all shown in Fig. 6. It can be seen that the calculated results are close to that from Maxwell-Eucken's relation. Maxwell-Eucken's relation assumes that pores are spherical and distributed evenly without any interaction with each other in the matrix. However, Russell's relation assumes that pores are cubic instead of spherical. In simplified Loeb's relation, porosity and thermal conductivity are of liner relation, which is not suitable for a wide range of porosity. In fact, the floating beads in the porous insulation board are spherical and distributed evenly without any interaction with each other. So, it's reasonable that Maxwell-Eucken's relation can describe thermal conductivity of the insulation board as a function of porosity best.
Effect of pore size on thermal conductivity of porous insulation board based on the calculations under pore conditions of #12–#20 in Table 2 is shown as squares in Fig. 7. It can be seen that pore size has little influence on thermal conductivity of porous insulation board. Generally the diameter of floating bead is smaller than 0.5 mm. Therefore the sizes of floating beads almost have no influences on the thermal conductivity of porous insulation board.
Effect of pore size on thermal conductivity of porous insulation board.
In situ strength of porous insulation board has a negative relationship with the porosity19). Therefore, the decrease of the in situ strength of porous material should be taken into consideration when method of increasing porosity to decrease the thermal conductivity is adopted. Insulation boards are used in hot top to prevent heat transfer there during casting of a steel ingot, which does not require high strength of insulation boards. In addition, the floating beads themselves are of high strength. Therefore proportion of floating beads can be adjusted in a wide range to meet the demand of heat prevention property of porous insulation boards.
Conclusively, insulation boards with solid structure have a better heat prevention property than that of porous structure. The thermal conductivity of insulation boards made of floating beads has a close relation with the porosity and little relation with the sizes of floating beads. Insulation boards made of floating beads, which are wastes generated from coal-burning power plants, can not only improve metal yield during ingot casting but also turn the waste materials into a benefit.
In this paper, thermal conductivities of insulation boards with solid structure and porous structure with different porosities were investigated using numerical simulation and calorimetric techniques. It was proved that insulation board with porous structure has a much better heat prevention property than that of solid structure. Effect of porosity on thermal conductivity of porous insulation board made of floating beads was studied, which can provide guidance for manufacture of porous insulation board.
(1) Thermal conductivity of porous insulation board with porosity of 50.7% is 0.170 W･m−1･℃−1, which is 63.5% smaller than that of insulation board with solid structure.
(2) Thermal conductivity of porous insulation board decreases notably with the increase of porosity. By contrast, there is little influence of the sizes of pores on the thermal conductivity of porous insulation board.
(3) Porous insulation boards made of floating beads can not only improve metal yield during ingot casting due to the perfect heat prevention property, but also make contribution to the utilization of waste resources.
This work was supported by the National Natural Science Foundation of China under Grant No. 51274029 and the State Key Laboratory of Advanced Metallurgy Foundation No. 41614014. The authors are thankful to ANSTEEL for the support on the field test.
