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Effects of ambient temperature and humidity on the controlled cooling of hot-rolled wire rod of steel
Applied Thermal Engineering 62 (2014) 148e155
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Effects of ambient temperature and humidity on the controlled cooling of hot-rolled wire rod of steel Jianguo Xue a, b, *, Min Liu a, b, *, Yafeng Deng c a
Department of Automation, Tsinghua University, Beijing 100084, PR China Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, PR China c School of Material and Mechanical Engineering, Beijing Technology and Business University, Beijing 100024, PR China b
h i g h l i g h t s We model the effect of moist air on the cooling process of hot-rolled wire rod. The cooling performance of different weather conditions is analyzed and verified. High temperature and low humidity decrease the cooling performance of steel. Low temperature and high humidity increase the cooling performance of steel. The same cooling performance can be achieved via the control of blower.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 February 2013 Accepted 11 September 2013 Available online 25 September 2013
The effects on the controlled cooling of hot-rolled wire rod of steel at different ambient temperature and humidity have been investigated. The results indicate that the convective heat-transfer coefficients and heat flux increase as humidity increase and temperature decrease. And it results in the increase of cooling rate and the decrease of phase transformation temperature of steel. According to the empirical relationship between the isothermal transformation temperature and experimental results of ultimate tensile strength with steel of SWRH82B and diameter of 12.5 mm, the maximum ultimate tensile strength (UTS) is 1206 MPa at 15 C and humidity level of 100%, and the minimum UTS is 1139 MPa at 55 C and humidity level of 0%. The predicted results agree well with the inspection results of industrial trials. And then, some references of the optimal outputs of blower have been provided for stabilizing product quality. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Controlled cooling Weather conditions Quality prediction Hot rolling
1. Introduction In hot-rolled steel production processes, controlled cooling after finishing rolling plays an important role on the final microstructure and mechanical properties of product. Stelmor air-cooling process is the most popular controlled cooling process to produce the steel wire with the sizes range from 5 mm to 20 mm. In this process, after passing through the water cooling boxes in which the temperature is reduce down to approximately 800 C, the rolled wire is placed, by means of laying head, into circle loops on the conveyor, where the forced air cooling is performed by a series of fans below. Considerable researches have been devoted to research the thermal and microstructural behaviors of steels in controlled cooling process. For instance, Nobari and Serajzadeh [1] developed * Corresponding authors. Department of Automation, Tsinghua University, Beijing 100084, PR China. E-mail addresses: [email protected], [email protected] (J. Xue). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.09.019
a mathematical model to predict temperature variations and austenite phase transformation in steel during controlled cooling. Shivpuri and co-workers [2] presented a computational approach to grain size evolution and mechanical properties of hot rolled rod. Yu et al. [3] developed an online Stelmor controlled cooling system for the stabilization of process operation. These numerical models have been successfully applied to controlled cooling process for realizing stable operation and improving product quality. Thus, in industrial practice, with more and more manipulated variables under control, the fact that the product quality varies with season and climate is more and more outstanding. But up to now, it is no available in the literature to describe the quantitative analysis on the impacts of ambient temperature and humidity upon the cooling process of hot rolled steel. Fortunately, some investigations in the similar treatment were reported. Such as, Brenn and co-workers [4] discussed the effects of ambient conditions on the drying process of liquid coatings on round metal wires. Page et al. [5] reported a model to analyze the effects of ambient
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155
Nomenclature b Bi Cp Cpa Cps Cpv D Fo g h k ka ks kv Ma Ms Mv Nu n Pr pa pv R Re r T Ti
temperature-dependent constant Biot number specific heat capacity of moist air specific heat capacity of air specific heat capacity of steel specific heat capacity of water vapor diameter of steel wire Fourier number latent heat release rate during phase transformation convection heat-transfer coefficient thermal conductivity of moist air thermal conductivity of air thermal conductivity of steel thermal conductivity of vapor average molar mass of air transformation-beginning temperature of martensite molar mass of water Nusselt number temperature-dependent constant Prandtl number partial pressure of air partial pressure of vapor molar gas constant Reynolds number radial coordinate current temperature temperature at ith time step
conditions during air treatment operations of food. These research results provide application basic for study of the effects of ambient conditions on the controlled cooling of hot-rolled wire rod of steel. In this work, an integrated model for describing the effects of ambient conditions on the cooling performance of hot-rolled steel wire after rolling is presented. The effects of moist air on heat transfer have been derived from the theoretical and empirical models with the involved ambient conditions, and the results are used to calculate the temperature evolution and phase transformation of high-carbon steel, SWRH82B, by numerical approach. Then the predicted values of ultimate tensile strength are compared with the industrial trials to validate the model. Additionally, the inverse solution of wind speed is also discussed for realizing stable production process under different ambient conditions. 2. Mathematical models In order to simplify the solution process and focus on the influence of weather, the rolled wire rod cooled on the roller conveyor is assumed as a cylinder in cross flow, which has the same heattransfer coefficient (HTC) around the surface and has no axial heat conduction. The schematic description of the process is illustrated in Fig. 1. The temperature history of steel wire is solved by heat-transfer model with the corresponding boundary conditions. The boundary conditions vary with the reference temperature due to its influence on the properties of moist air. The microstructure and latent heat of phase transformation at a specific point are determined by its timee temperature paths in isothermal transformation diagram. 2.1. Models of heat transfer Based on the following assumptions: (1) uniform initial temperature, (2) circular cross-sectional shape with the same
TN Tref Tsur Tnew Told t ti t*i Dti u X Xi xa xv ya yv
a
3s
m ma mv r ra rs rv s0 si
4av, 4va
149
fluid temperature reference temperature of fluid surroundings temperature temperature at current step temperature at previous step current time elapsed time until the ith time step virtual time of at ith time step time increment at ith time step velocity of moist air flow fraction of transformation fraction of transformation at ith time step mass fraction of air mass fraction of vapor mole fraction of air mole fraction of vapor constant for specific steel total emissivity viscosity of moist air viscosity of air viscosity of vapor density of moist air density of air density of steel density of vapor StefaneBoltzman constant incubation time at temperature Ti interaction parameter between air and vapor
boundary conditions, (3) no longitudinal temperature gradient, the heat-transfer process within steel wire in Stelmor line can be described by one-dimensional decisive differential equation [3]:
1v vT vT rks þ g ¼ rs Cps r vr vr vt
(1)
The boundary conditions can be described as follows. At the center,
Temperature of wire surface T s
Heat convection and radiation Steel wire Latent heat Heat conduction
Reference temperature T ref =(T s +T ) / 2
Surroundings temperature T sur
Fluid temperature T Air flow Fig. 1. Schematic of a cylinder in cross flow.
150
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t > 0; r ¼ 0 : ks
vT ¼ 0 vr
(2)
At the surface
t > 0; r ¼ D=2 : ks
vT 4 ¼ hðT TN Þ þ 3 s s0 T 4 Tsur vr
(3)
An empirical correlation for the calculation of average HTC in cross flow over circular cylinders is given by Hilpert [6],
0:683Re0:466 Pr 1=3 40 Re 4000 0:193Re0:618 Pr 1=3 4000 Re 400000
In order to determine the starting time of austenite decomposition at different temperature and cooling rate, the cooling time of incubation period is divided into small time steps. Assuming constant temperature during each step, the additive reaction rule of Scheil is utilized [1], and phase transformation occurs when n X Dti ¼ 1 s Ti i i¼1
(9)
with the Nusselt number Nu ¼ hD=k, the Reynolds number Re ¼ ruD/m, and the Prandtl number Pr ¼ Cpm/k.
In order to predict austenite decomposition kinetics of the diffusional transformation under continuous cooling conditions, Avrami equation and additivity rule is employed [1]. The fraction of transformation is a function of time t at a constant temperature as follows:
2.2. Estimations of moist air properties
X ¼ 1 expðbt n Þ
Nu ¼
(4)
The thermophysical properties, including thermal conductivity, density, viscosity and specific heat capacity of moist air, should be determined to calculate the heat transfer coefficients. But it is impractical to obtain these data under different reference temperature and specific humidity from experimental measurement or molecular theory. Thus, we estimate them from the mixing rules and combining rules base on the assumption that moist air is an ideal gas mixture of two pure ideal gases: dry air and water vapor. The density of moist air can be calculated from the Dalton’s law of partial pressures [7]
r¼
pa Ma þ pv Mv RTref
(5)
The partial pressure of air and vapor can be calculated by Goffe Gratch equation [8] The specific heat capacity of moist air can be calculated as a mass-fraction average of the components [9]
cp ¼ cpa xa þ cpv xv
ma ya mv yv þ ya þ yv 4av yv þ ya 4va
(7)
The interaction parameters can be approximately expressed as
4av ¼
Mv Ma
1=2
¼ 41 va
Riblett [11] suggested an equation to calculate the thermal conductivity of a mixture of gases at low pressures, and for the binary system it can be expressed as
k ¼
1=3
þ kv yv Mv
1=3
þ yv Mv
ka ya Ma
ya Ma
When the temperature changed at next time step Dti, previous transformation is assumed as the isothermal transformation at current temperature Ti with the corresponding virtual time:
2 31=nðT i Þ 1 ln 1X i1 7 6 5 ti* ¼ 4 b Ti
(11)
So the current fraction of transformation can be updated use Eq. (10):
n Ti ð Þ X i ¼ 1 exp b T i ti
ti ¼ Dti þ ti*
(12)
The non-diffusion type transformation can be described as a function of temperature.
X ¼ 1 expð aðMs TÞÞ
(13)
(6)
A simplification of the rigorous theoretical expressions proposed by Wilke [10] is used to determine the viscosity of multicomponent mixtures, and for the binary system, it can be expressed as follows
m ¼
(10)
1=3
1=3
(8)
2.3. Calculations of phase transformation During the cooling process of hot-rolled wire rod, the austenite in steel transforms to the new phase(s), such as ferrite, pearlite, bainite and martensite, which determine the final microstructure and mechanical properties of product.
3. Input data The thermophysical properties of steam can be generated from the IAPWS Formulation. But it is not necessary to calculate them in real time with the complex computer codes. So the pre-calculated steam table was used to approximate the corresponding values with the cube spline interpolation method [12]. The thermophysical properties of air were also interpolated using the air table which is calculated from the pseudo-pure fluid equation of Lemmon et al. [13]. High carbon steel with the chemical composition given in Table 1 was studied in the present work. The thermophysical properties of steel were calculated based on the thermodynamic database, which was established by expert evaluation of experimental data using the CALPHAD (calculation of phase diagrams) method [14]. The latent heat for ferrite, pearlite, bainite, and martensite transformation is shown in Table 2 [15]. The Time-Temperature-Transformation (TTT) curves, including the critical temperatures and the constants used in Eq. (10), were generated from the thermal expansion experiment at different preservation temperatures. The ultimate tensile strength at corresponding temperature was also measured to model the relation between them [2]. The other parameters, such as blower speed (20 m/s), wire diameter (12.5 mm) and initial temperature (700 C), were determined from the industrial data. The range of air temperature studied in this work is from 15e55 C.
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155 Table 1 Chemical compositions of high carbon steel in study (wt%).
151
Start
Grade
C
Si
Mn
Cr
SWRS82B
0.79e0.85
0.15e0.35
0.60e0.90
0.15e0.50
Input Data Set initial conditions
4. Solution and analysis
Calculate:pa,pv,xa,xv,ya,yv
4.1. Solution procedure A flow describing the numerical procedure is illustrated in Fig. 2. With the initial conditions, the partial pressures, mass frictions and mole frictions of air and vapor is calculated first. At every time step, the temperature of previous step (or initial temperature) is used to approximate the properties of steel and the fraction of phase transformation for calculating the corresponding latent heat, if occurs. At surface, the properties of moist air and HTC are calculated with corresponding reference temperature as well. Using the energy balance method, the forward-difference equation can be derived for any node. Iterations are performed at every time step to solve the temperatures of every node: when the temperatures of current step are solved by explicit scheme, the error between current temperature (Tnew) and previous (Told) can be obtained. If it converges to the given error, this step is followed by next time step, and if not, the temperature is recalculated in the same time step with recalculated material properties and HTC from Tnew. As a simple one-dimensional problem, the solution of discretization equations was detailed by Patankar [9], and will not be dealt with here. For the inverse calculations, the flow is similar, except the temperature model is replaced by the given cooling rate and the criteria for convergence is the error between current HTC and previous. 4.2. Sensitivity analysis
Y
T > Eutectoid temperature? N
Y
Transformation completed? N Incubation and Transformation Model
Temperature Model
N
|T new -T old|<0.001 Y
In order to analyze the sensitivity of the variance of input data, a lumped capacitance method was used with the neglect of radiation and the assumption of dry air. Two production parameters were analyzed: diameter of steel wire and velocity of air flow. Within the range of parameters values, the Biot number of wire steel can be calculated: Bi ¼ hD/(4k) z (0.01e0.05) < 0.1. It means that the lumped capacitance condition is also satisfied for the calculation. The results which have 100% pearlite transformation are shown in Table 3. It can be seen that, a half value of diameter (u ¼ 10 m/s) leads to a threefold value of cooling rate, and a threefold value of velocity (D ¼ 25 mm) leads to a double value of cooling rate. Different cooling rates determine the corresponding timeetemperature paths in TTT diagram. A variation of D from 6.25 mm to 25 mm increases the transformation time by 72.7 s and increases average transform temperature by 112.5 C. A variation of u from 10 m/s to 94.2 m/s decreases the transformation time by 67.4 s and decreases the transformation temperature by 43.3 C. In practice, the dimension of product is stable and can be measured accurately, but the turbulent wind speed of blower always fluctuates with the time and position. So it must Table 2 The enthalpy of austenite transformation. New phase
DH (108 J/m3)
Calculate:Properties of moist air at Tref, Properties of steel,Heat-transfer coefficient
Ferrite
Pearlite
Bainite
Martensite
5.9
6.0
6.2
6.5
Increase time step N Finished? Y End Fig. 2. Flow chart representing the calculation process.
be corrected with the Hilpert equation by the measured temperatures. Choice of mesh and time step are very important in numerical calculations. The effect of the variation of nods from 1(Lumped capacitance) to 11 on the cooling performance is given in Table 4. As the nodes increase from 1 to 6, the difference between surface and center can be distinguished. But increasing nodes from 6 to 11 does not cause any significant change in the results, which indicates that the discretization error is reduced to an acceptable level. Based on the comparing, 6 nodes (with mesh size 2.5 mm) were considered to be adequate. The similar analysis showed that the time step did not affect the results, thus a larger value (0.05 s) was determined from stability criterion: Fo (1 þ Bi) 1/2. Discussions of the choice of experimental correlations, including for cross flow over cylinders, for thermophysical properties of moist air, for fraction of transformation and for mechanical properties of
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Table 3 Effect of a variation of the diameter and velocity on the calculated cooling performance. D/(mm) u/(m/s) H/(W/m2/K) Incubation period
Phase transformation
Time/s Temperature/ C Time/s Cooling rate/( C/s) 12.5 12.5 6.25 25 25 25
20 10 10 10 30.7 94.2
118.6 84.9 123.0 60.0 118.6 237.2
20.9 23 16.7 35.7 26.4 20.7
4.45 3.14 9.04 1.10 2.19 4.57
17.4 25.6 11.4 84.1 38.7 16.7
614.8 632.7 543.3 655.8 643.8 612.5
steel, are also essential. As an example, there are many correlations have been suggested for the circular cylinder in cross flow. The review of exiting literature [16,17] reveal that, for the range of Reynolds and Prandtl numbers in this study, the difference of HTC between the calculated results of these correlations is less than 10%, and the results have the same trend with the variation of temperature and humidity. In the other words, maybe each of them has the bias towards “true value”, but the variance of estimated values still can explain the variance of “true values” based on the effects of ambient temperature and humidity. So, considering the inverse solution of air flow velocity, a sampler correlation, Eq. (4), is chosen. 4.3. Validity of the model For the discretization methods in this paper, which is first order accurate in space and first order accurate in time, the exact solution can be estimate from generalized Richardson extrapolation [18]. Using the results in sensitive analysis, the estimated discretization error is about 0.08 C, and relative discretization error is about 0.01%. The predictions capabilities of the model were evaluated with respect to the temperatures compared to the in-plant measured surface temperatures with the same product parameters, such as steel grade (SWRH82B), blower speed (20 m/s), wire diameter (12.5 mm), are presented in Fig. 3. The in-plant measured surface temperatures are statistical results of history data of a whole year, and the predicted temperatures are calculated under the condition of average ambient temperature (14.8 C) and dew point (3.9 C) of the same whole year. The maximum difference between average measured values (STD: 6.5 C) and estimated cooling curves is no more than 15 C. So it can be confirmed that the predicted temperatures are in good agreement with those measured. The expansibilities and validities of the model were evaluated with the comparison between the predicted volume fractions and the experimental isothermal transformation data obtained by Xu et al. [19]. The result with constant temperature of 550 C is presented in Table 5. Considering the fitting error of the temperaturedependent constants in Avrami equation, the results agree almost perfectly. Table 4 Effect of the number of grid points on the calculated cooling performance. Nodes
Incubation
1
6
11
Surface Center
Surface Center
Time/s 19.21 19.29 19.24 19.29 19.24 Cooling 6.195 6.078 5.979 6.078 5.982 rate/( C/s) Phase Time/s 13.22 12.4 14.25 12.41 14.25 transformation Temperature/ 589.16 578.92 601.80 578.84 601.75 C
Fig. 3. Comparison between the predicted temperatures and the measured surface temperatures.
5. Results and discussions 5.1. Effect on boundary conditions of heat transfer Fig. 4 shows the calculated convective heat-transfer coefficients of water vapor and dry air. As can be seen, the HTC of water vapor and dry air change with the reference temperature, this is because they have different thermophysical properties at different temperature. Similarly, the HTC of moist air would change with the reference temperature due to the changing of its thermophysical properties. Apparently, the ambient temperature affects the reference temperature, and the relative humidity (RH) affects the thermophysical properties of moist air by the rules list in Section 2.2. As shown in Eq. (3), the surface heat flux is affected by HTC, the temperature difference between wire surface and ambient, the radiation heat transfer. Fig. 5 shows the calculated heat flux changing with the surface temperature of steel wire with four different weather conditions. The heat flux decreases with the surface temperature decreasing mainly because of the decreased thermal radiation. When the ambient temperature is 15 C, there is little difference between different humidity, because the water vapor has a lower saturated pressure at low temperature. When the ambient temperature is 55 C, the heat flux of saturated moist air is higher than that of dry air, and this difference decreases as the surface temperature decreases, just as the tendency of HTC. When the humidity is 0%, there is a constant difference between different ambient temperatures, because they have the same HTC curve in Fig. 4, and this difference is mainly caused by the difference of reference temperature. 5.2. Effect on cooling performance of steel The different heat flux would result in different cooling performance of steel wire. The cooling rate and average temperature
Table 5 Comparison between the experimental data and the estimated data under isothermal transformation. Volume fraction
Experiment/s Estimation/s
1%
5%
25%
50%
99%
4.25 4.31
5.15 5.16
7.54 6.93
9.26 8.43
13.94 14.23
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155
153
Fig. 4. Calculated results of convective heat-transfer coefficients.
are the most common indexes to evaluate it. Fig. 6 shows the average cooling rate at central point of wire rod during the incubation period. Fig. 7 shows the average temperature at central point during the phase transformation period, weighted by the volume fraction of phase transformation. For the dry air, as a cumulative effect of heat transfer, the maximum difference due to variation in ambient temperature is about of 0.9 C/s on cooling rate and 10 C on transformation temperature, which is mainly because of the temperature difference between the ambient temperature and steel surface temperature. When the ambient temperature is 55 C, the maximum difference due to variation in humidity is about of 0.45 C/s on cooling rate and 6 C on transformation temperature, which is mainly because of the thermophysical properties variance of moist air. Within the range of studied weather conditions, low ambient temperature and high humidity increase the cooling performance of wire steel. 5.3. Effect on quality results of wire rods Different cooling performance determines different microstructures of product, and then determines different mechanical properties. Fig. 8 shows the ultimate tensile strength (UTS) under different weather conditions, which is evaluated from the average
Fig. 5. Calculated results of heat flux as changing with the surface temperature.
Fig. 6. Calculated average cooling rate at the center of wire rod during incubation period.
temperature during phase transformation period, according to the empirical relationship between the isothermal transformation temperature and experimental result [2]. It indicates that the UTS vary from 1139 MPa to 1206 MPa among the range of studied weather conditions. The industrial inspection results of UTS with the corresponding temperature and humidity (measured by local weather station) are also shown in Fig. 8. The ambient temperatures are binned into 5 levels to compare with the calculated UTS. As can be seen, although the measured data is endowed with various types of uncertainties, it is clear enough to distinguish the difference due to different ambient conditions, and the agreement between measurement and prediction under similar ambient conditions. With the same ambient conditions as industrial results, corresponding UTS were calculated and compared with the measured results. As shown in Fig. 9, although there is not a perfect accuracy due to complex industrial process, the predicted results also can explain 20% variance of the measured results. It means, when the ambient conditions are involved, the precision can be increased by
Fig. 7. Calculated average temperature at the center of wire rod during phase transformation period.
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J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155
Fig. 8. Calculated results of ultimate tensile strength compared with the industrial results.
20%, which is significant for product quality improving in industrial practice. 5.4. Effect on control of wind speed In the industrial process, what we need is not only to predict product quality from processing conditions, but also to control the operating conditions that can stabilize and improve the product quality. Using the inverse solution of the model, we can obtain the corresponding wind speeds, with which the products can maintain equal cooling process at different ambient temperatures and humidity. In order to simplify the solution of inverse heat-transfer, the wire rod is assumed to behave as a lumped capacity as discussed in sensitive analysis, then we can obtain from Eq. (1)
i dT g ks h 4 hðT TN Þ þ 3 s s0 T 4 Tsur ¼ dt rs Cps Rrs Cps
(14)
Set right-hand sides of the equation equal to constant (6.5 C/ s), it means that the average temperature of wire rod decreases at a constant cooling rate except phase transformation period. Then, assuming that the wind speed can be regulated continuous everywhere, we can achieve the wind speed at every time step by using the inverse method step by step.
Fig. 9. Comparison between the industrial UTS and the predicted UTS.
Fig. 10. Calculated wind speedetime curves for the same cooling process at different weather conditions.
Fig. 10 shows the calculated wind speedetime curves under three different typical weather conditions. It is evident from the figure that the wind speed varies within a wider range to acquire the same cooling effect at different conditions. Even though at the same weather conditions, the speed also varies with the surface temperature of steel, it is mainly because of the reduction of thermal radiation. Fig. 11 shows the average wind speed from incubation begins to transformation ends at different conditions. The variation range of the results is between 20 m/s to 25 m/s. Actually, the cooling conveyor is divided into several segments along the longitudinal direction, every of which has a blower with the same wind speed, so further optimization is required to determine the steady-state set-points of every blower. Considering that the blower power increases cubically as a function of wind speed, the influence of weather on energy consumptions is also significant. So integrated optimization is also required for production scheduling, such as arrange production at winter or at night as much as possible. 6. Conclusion An integrate model was developed to investigate the effect of ambient temperature and humidity on the production of hot rolled wire rod after controlled cooling process.
Fig. 11. Calculated average wind speed from the incubation begins to the transformation ends.
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155
A quantitative analysis of heat transfer, cooling performance and mechanical property in the production of hot rolled wire rod has been demonstrated with different ambient temperature and humidity. The integrate model can be effectively applied to predict products quality, stabilize operating conditions and optimize production schedule. Acknowledgements This work was supported by the National Key Basic Research and Development Program of China (2009CB320602), the National Natural Science Foundation of China (61025018, 61021063, 60834004) and the National Science and Technology Major Project of China (2011ZX02504-008). The authors are grateful to Xingtai Iron & Steel Corp., LTD, China for providing technical supports and test samples. References [1] A.H. Nobari, S. Serajzadeh, Modeling of heat transfer during controlled cooling in hot rod rolling of carbon steels, Appl. Therm. Eng. 31 (2011) 487e492. [2] S. Phadke, P. Pauskar, R. Shivpuri, Computational modeling of phase transformations and mechanical properties during the cooling of hot rolled rod, J. Mater. Process. Technol. 150 (2004) 107e115. [3] W.-H. Yu, S.-H. Chen, Y.-H. Kuang, K.-C. Cao, Development and application of online Stelmor controlled cooling system, Appl. Therm. Eng. 29 (2009) 2949e 2953. [4] K. Czaputa, G. Brenn, The convective drying of liquid films on slender wires, Int. J. Heat Mass. Transfer 55 (2012) 19e31.
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[5] J.-F.L. Page, C. Chevarin, A. Kondjoyan, J.-D. Daudin, P.-S. Mirade, Development of an approximate empirical-CFD model estimating coupled heat and water transfers of stacked food products placed in airflow, J. Food Eng. 92 (2009) 208e216. [6] T.L. Bergman, A.S. Lavine, F.P. Incropera, D.P. DeWitt, Fundamentals of Heat and Mass Transfer, seventh ed., Wiley, Hoboken, 2011. [7] M.J. Moran, H.N. Shapiro, D.D. Boettner, M. Bailey, Fundamentals of Engineering Thermodynamics, seventh ed., Wiley, Hoboken, 2011. [8] D.M. Murphy, T. Koop, Review of the vapour pressures of ice and supercooled water for atmospheric applications, Q. J. R. Meteorol. Soc. 131 (2006) 1539e 1565. [9] B.E. Poling, J.M. Prausnitz, J.P. O’Connell, The Properties of Gases and Liquids, fifth ed., McGraw-Hill, New York, 2004. [10] W.D. Monnery, W.Y. Svrcek, A.K. Mehrotra, Viscosity: a critical review of practical predictive and correlative methods, Can. J. Chem. Eng. 73 (2009) 3e40. [11] J. Gosse, Technical Guide to Thermal Processes, Cambridge University Press, Cambridge, 1986. [12] W. Wagner, H.J. Kretzschmar, International Steam Tables Springer-properties of Water and Steam Based on the Industrial Formulation IAPWS-IF97, second ed., Springer, Berlin, 2008. [13] D.R. Lide, CRC Handbook of Chemistry and Physics, 90th ed., CRC Press, Boca Raton, 2010. [14] J.-O. Andersson, T. Helander, L. Höglund, P. Shi, B. Sundman, ThermoCalc&DICTRA, computational tools for materials science, Calphad 26 (2002) 273e312. [15] B. Buchmayr, J.S. Kirkaldy, Modeling of the temperature field, transformation behavior, hardness and mechanical response of low alloy steels during cooling from the austenite region, J. Heat Treat. 8 (1990) 127e136. [16] S. Sanitjai, R.J. Goldstein, Forced Convection Heat Transfer from a Circular Cylinder in Crossflow to Air and Liquids, 2004. [17] J.P. Holman, Heat Transfer, tenth ed., McGraw-Hill, 2009. [18] W.L. Oberkampf, C.J. Roy, Verification and Validation in Scientific Computing, Cambridge University Press Cambridge, 2010. [19] J.Q. Xu, Y.Z. Liu, S.M. Zhou, Computer simulation of microstructure evolution of 82B rod at different cooling rates, J. Iron. Steel. Res. Int. 15 (2008) 56e59.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Effects of ambient temperature and humidity on the controlled cooling of hot-rolled wire rod of steel Jianguo Xue a, b, *, Min Liu a, b, *, Yafeng Deng c a
Department of Automation, Tsinghua University, Beijing 100084, PR China Tsinghua National Laboratory for Information Science and Technology, Beijing 100084, PR China c School of Material and Mechanical Engineering, Beijing Technology and Business University, Beijing 100024, PR China b
h i g h l i g h t s We model the effect of moist air on the cooling process of hot-rolled wire rod. The cooling performance of different weather conditions is analyzed and verified. High temperature and low humidity decrease the cooling performance of steel. Low temperature and high humidity increase the cooling performance of steel. The same cooling performance can be achieved via the control of blower.
a r t i c l e i n f o
a b s t r a c t
Article history: Received 16 February 2013 Accepted 11 September 2013 Available online 25 September 2013
The effects on the controlled cooling of hot-rolled wire rod of steel at different ambient temperature and humidity have been investigated. The results indicate that the convective heat-transfer coefficients and heat flux increase as humidity increase and temperature decrease. And it results in the increase of cooling rate and the decrease of phase transformation temperature of steel. According to the empirical relationship between the isothermal transformation temperature and experimental results of ultimate tensile strength with steel of SWRH82B and diameter of 12.5 mm, the maximum ultimate tensile strength (UTS) is 1206 MPa at 15 C and humidity level of 100%, and the minimum UTS is 1139 MPa at 55 C and humidity level of 0%. The predicted results agree well with the inspection results of industrial trials. And then, some references of the optimal outputs of blower have been provided for stabilizing product quality. Ó 2013 Elsevier Ltd. All rights reserved.
Keywords: Controlled cooling Weather conditions Quality prediction Hot rolling
1. Introduction In hot-rolled steel production processes, controlled cooling after finishing rolling plays an important role on the final microstructure and mechanical properties of product. Stelmor air-cooling process is the most popular controlled cooling process to produce the steel wire with the sizes range from 5 mm to 20 mm. In this process, after passing through the water cooling boxes in which the temperature is reduce down to approximately 800 C, the rolled wire is placed, by means of laying head, into circle loops on the conveyor, where the forced air cooling is performed by a series of fans below. Considerable researches have been devoted to research the thermal and microstructural behaviors of steels in controlled cooling process. For instance, Nobari and Serajzadeh [1] developed * Corresponding authors. Department of Automation, Tsinghua University, Beijing 100084, PR China. E-mail addresses: [email protected], [email protected] (J. Xue). 1359-4311/$ e see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.applthermaleng.2013.09.019
a mathematical model to predict temperature variations and austenite phase transformation in steel during controlled cooling. Shivpuri and co-workers [2] presented a computational approach to grain size evolution and mechanical properties of hot rolled rod. Yu et al. [3] developed an online Stelmor controlled cooling system for the stabilization of process operation. These numerical models have been successfully applied to controlled cooling process for realizing stable operation and improving product quality. Thus, in industrial practice, with more and more manipulated variables under control, the fact that the product quality varies with season and climate is more and more outstanding. But up to now, it is no available in the literature to describe the quantitative analysis on the impacts of ambient temperature and humidity upon the cooling process of hot rolled steel. Fortunately, some investigations in the similar treatment were reported. Such as, Brenn and co-workers [4] discussed the effects of ambient conditions on the drying process of liquid coatings on round metal wires. Page et al. [5] reported a model to analyze the effects of ambient
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155
Nomenclature b Bi Cp Cpa Cps Cpv D Fo g h k ka ks kv Ma Ms Mv Nu n Pr pa pv R Re r T Ti
temperature-dependent constant Biot number specific heat capacity of moist air specific heat capacity of air specific heat capacity of steel specific heat capacity of water vapor diameter of steel wire Fourier number latent heat release rate during phase transformation convection heat-transfer coefficient thermal conductivity of moist air thermal conductivity of air thermal conductivity of steel thermal conductivity of vapor average molar mass of air transformation-beginning temperature of martensite molar mass of water Nusselt number temperature-dependent constant Prandtl number partial pressure of air partial pressure of vapor molar gas constant Reynolds number radial coordinate current temperature temperature at ith time step
conditions during air treatment operations of food. These research results provide application basic for study of the effects of ambient conditions on the controlled cooling of hot-rolled wire rod of steel. In this work, an integrated model for describing the effects of ambient conditions on the cooling performance of hot-rolled steel wire after rolling is presented. The effects of moist air on heat transfer have been derived from the theoretical and empirical models with the involved ambient conditions, and the results are used to calculate the temperature evolution and phase transformation of high-carbon steel, SWRH82B, by numerical approach. Then the predicted values of ultimate tensile strength are compared with the industrial trials to validate the model. Additionally, the inverse solution of wind speed is also discussed for realizing stable production process under different ambient conditions. 2. Mathematical models In order to simplify the solution process and focus on the influence of weather, the rolled wire rod cooled on the roller conveyor is assumed as a cylinder in cross flow, which has the same heattransfer coefficient (HTC) around the surface and has no axial heat conduction. The schematic description of the process is illustrated in Fig. 1. The temperature history of steel wire is solved by heat-transfer model with the corresponding boundary conditions. The boundary conditions vary with the reference temperature due to its influence on the properties of moist air. The microstructure and latent heat of phase transformation at a specific point are determined by its timee temperature paths in isothermal transformation diagram. 2.1. Models of heat transfer Based on the following assumptions: (1) uniform initial temperature, (2) circular cross-sectional shape with the same
TN Tref Tsur Tnew Told t ti t*i Dti u X Xi xa xv ya yv
a
3s
m ma mv r ra rs rv s0 si
4av, 4va
149
fluid temperature reference temperature of fluid surroundings temperature temperature at current step temperature at previous step current time elapsed time until the ith time step virtual time of at ith time step time increment at ith time step velocity of moist air flow fraction of transformation fraction of transformation at ith time step mass fraction of air mass fraction of vapor mole fraction of air mole fraction of vapor constant for specific steel total emissivity viscosity of moist air viscosity of air viscosity of vapor density of moist air density of air density of steel density of vapor StefaneBoltzman constant incubation time at temperature Ti interaction parameter between air and vapor
boundary conditions, (3) no longitudinal temperature gradient, the heat-transfer process within steel wire in Stelmor line can be described by one-dimensional decisive differential equation [3]:
1v vT vT rks þ g ¼ rs Cps r vr vr vt
(1)
The boundary conditions can be described as follows. At the center,
Temperature of wire surface T s
Heat convection and radiation Steel wire Latent heat Heat conduction
Reference temperature T ref =(T s +T ) / 2
Surroundings temperature T sur
Fluid temperature T Air flow Fig. 1. Schematic of a cylinder in cross flow.
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t > 0; r ¼ 0 : ks
vT ¼ 0 vr
(2)
At the surface
t > 0; r ¼ D=2 : ks
vT 4 ¼ hðT TN Þ þ 3 s s0 T 4 Tsur vr
(3)
An empirical correlation for the calculation of average HTC in cross flow over circular cylinders is given by Hilpert [6],
0:683Re0:466 Pr 1=3 40 Re 4000 0:193Re0:618 Pr 1=3 4000 Re 400000
In order to determine the starting time of austenite decomposition at different temperature and cooling rate, the cooling time of incubation period is divided into small time steps. Assuming constant temperature during each step, the additive reaction rule of Scheil is utilized [1], and phase transformation occurs when n X Dti ¼ 1 s Ti i i¼1
(9)
with the Nusselt number Nu ¼ hD=k, the Reynolds number Re ¼ ruD/m, and the Prandtl number Pr ¼ Cpm/k.
In order to predict austenite decomposition kinetics of the diffusional transformation under continuous cooling conditions, Avrami equation and additivity rule is employed [1]. The fraction of transformation is a function of time t at a constant temperature as follows:
2.2. Estimations of moist air properties
X ¼ 1 expðbt n Þ
Nu ¼
(4)
The thermophysical properties, including thermal conductivity, density, viscosity and specific heat capacity of moist air, should be determined to calculate the heat transfer coefficients. But it is impractical to obtain these data under different reference temperature and specific humidity from experimental measurement or molecular theory. Thus, we estimate them from the mixing rules and combining rules base on the assumption that moist air is an ideal gas mixture of two pure ideal gases: dry air and water vapor. The density of moist air can be calculated from the Dalton’s law of partial pressures [7]
r¼
pa Ma þ pv Mv RTref
(5)
The partial pressure of air and vapor can be calculated by Goffe Gratch equation [8] The specific heat capacity of moist air can be calculated as a mass-fraction average of the components [9]
cp ¼ cpa xa þ cpv xv
ma ya mv yv þ ya þ yv 4av yv þ ya 4va
(7)
The interaction parameters can be approximately expressed as
4av ¼
Mv Ma
1=2
¼ 41 va
Riblett [11] suggested an equation to calculate the thermal conductivity of a mixture of gases at low pressures, and for the binary system it can be expressed as
k ¼
1=3
þ kv yv Mv
1=3
þ yv Mv
ka ya Ma
ya Ma
When the temperature changed at next time step Dti, previous transformation is assumed as the isothermal transformation at current temperature Ti with the corresponding virtual time:
2 31=nðT i Þ 1 ln 1X i1 7 6 5 ti* ¼ 4 b Ti
(11)
So the current fraction of transformation can be updated use Eq. (10):
n Ti ð Þ X i ¼ 1 exp b T i ti
ti ¼ Dti þ ti*
(12)
The non-diffusion type transformation can be described as a function of temperature.
X ¼ 1 expð aðMs TÞÞ
(13)
(6)
A simplification of the rigorous theoretical expressions proposed by Wilke [10] is used to determine the viscosity of multicomponent mixtures, and for the binary system, it can be expressed as follows
m ¼
(10)
1=3
1=3
(8)
2.3. Calculations of phase transformation During the cooling process of hot-rolled wire rod, the austenite in steel transforms to the new phase(s), such as ferrite, pearlite, bainite and martensite, which determine the final microstructure and mechanical properties of product.
3. Input data The thermophysical properties of steam can be generated from the IAPWS Formulation. But it is not necessary to calculate them in real time with the complex computer codes. So the pre-calculated steam table was used to approximate the corresponding values with the cube spline interpolation method [12]. The thermophysical properties of air were also interpolated using the air table which is calculated from the pseudo-pure fluid equation of Lemmon et al. [13]. High carbon steel with the chemical composition given in Table 1 was studied in the present work. The thermophysical properties of steel were calculated based on the thermodynamic database, which was established by expert evaluation of experimental data using the CALPHAD (calculation of phase diagrams) method [14]. The latent heat for ferrite, pearlite, bainite, and martensite transformation is shown in Table 2 [15]. The Time-Temperature-Transformation (TTT) curves, including the critical temperatures and the constants used in Eq. (10), were generated from the thermal expansion experiment at different preservation temperatures. The ultimate tensile strength at corresponding temperature was also measured to model the relation between them [2]. The other parameters, such as blower speed (20 m/s), wire diameter (12.5 mm) and initial temperature (700 C), were determined from the industrial data. The range of air temperature studied in this work is from 15e55 C.
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155 Table 1 Chemical compositions of high carbon steel in study (wt%).
151
Start
Grade
C
Si
Mn
Cr
SWRS82B
0.79e0.85
0.15e0.35
0.60e0.90
0.15e0.50
Input Data Set initial conditions
4. Solution and analysis
Calculate:pa,pv,xa,xv,ya,yv
4.1. Solution procedure A flow describing the numerical procedure is illustrated in Fig. 2. With the initial conditions, the partial pressures, mass frictions and mole frictions of air and vapor is calculated first. At every time step, the temperature of previous step (or initial temperature) is used to approximate the properties of steel and the fraction of phase transformation for calculating the corresponding latent heat, if occurs. At surface, the properties of moist air and HTC are calculated with corresponding reference temperature as well. Using the energy balance method, the forward-difference equation can be derived for any node. Iterations are performed at every time step to solve the temperatures of every node: when the temperatures of current step are solved by explicit scheme, the error between current temperature (Tnew) and previous (Told) can be obtained. If it converges to the given error, this step is followed by next time step, and if not, the temperature is recalculated in the same time step with recalculated material properties and HTC from Tnew. As a simple one-dimensional problem, the solution of discretization equations was detailed by Patankar [9], and will not be dealt with here. For the inverse calculations, the flow is similar, except the temperature model is replaced by the given cooling rate and the criteria for convergence is the error between current HTC and previous. 4.2. Sensitivity analysis
Y
T > Eutectoid temperature? N
Y
Transformation completed? N Incubation and Transformation Model
Temperature Model
N
|T new -T old|<0.001 Y
In order to analyze the sensitivity of the variance of input data, a lumped capacitance method was used with the neglect of radiation and the assumption of dry air. Two production parameters were analyzed: diameter of steel wire and velocity of air flow. Within the range of parameters values, the Biot number of wire steel can be calculated: Bi ¼ hD/(4k) z (0.01e0.05) < 0.1. It means that the lumped capacitance condition is also satisfied for the calculation. The results which have 100% pearlite transformation are shown in Table 3. It can be seen that, a half value of diameter (u ¼ 10 m/s) leads to a threefold value of cooling rate, and a threefold value of velocity (D ¼ 25 mm) leads to a double value of cooling rate. Different cooling rates determine the corresponding timeetemperature paths in TTT diagram. A variation of D from 6.25 mm to 25 mm increases the transformation time by 72.7 s and increases average transform temperature by 112.5 C. A variation of u from 10 m/s to 94.2 m/s decreases the transformation time by 67.4 s and decreases the transformation temperature by 43.3 C. In practice, the dimension of product is stable and can be measured accurately, but the turbulent wind speed of blower always fluctuates with the time and position. So it must Table 2 The enthalpy of austenite transformation. New phase
DH (108 J/m3)
Calculate:Properties of moist air at Tref, Properties of steel,Heat-transfer coefficient
Ferrite
Pearlite
Bainite
Martensite
5.9
6.0
6.2
6.5
Increase time step N Finished? Y End Fig. 2. Flow chart representing the calculation process.
be corrected with the Hilpert equation by the measured temperatures. Choice of mesh and time step are very important in numerical calculations. The effect of the variation of nods from 1(Lumped capacitance) to 11 on the cooling performance is given in Table 4. As the nodes increase from 1 to 6, the difference between surface and center can be distinguished. But increasing nodes from 6 to 11 does not cause any significant change in the results, which indicates that the discretization error is reduced to an acceptable level. Based on the comparing, 6 nodes (with mesh size 2.5 mm) were considered to be adequate. The similar analysis showed that the time step did not affect the results, thus a larger value (0.05 s) was determined from stability criterion: Fo (1 þ Bi) 1/2. Discussions of the choice of experimental correlations, including for cross flow over cylinders, for thermophysical properties of moist air, for fraction of transformation and for mechanical properties of
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Table 3 Effect of a variation of the diameter and velocity on the calculated cooling performance. D/(mm) u/(m/s) H/(W/m2/K) Incubation period
Phase transformation
Time/s Temperature/ C Time/s Cooling rate/( C/s) 12.5 12.5 6.25 25 25 25
20 10 10 10 30.7 94.2
118.6 84.9 123.0 60.0 118.6 237.2
20.9 23 16.7 35.7 26.4 20.7
4.45 3.14 9.04 1.10 2.19 4.57
17.4 25.6 11.4 84.1 38.7 16.7
614.8 632.7 543.3 655.8 643.8 612.5
steel, are also essential. As an example, there are many correlations have been suggested for the circular cylinder in cross flow. The review of exiting literature [16,17] reveal that, for the range of Reynolds and Prandtl numbers in this study, the difference of HTC between the calculated results of these correlations is less than 10%, and the results have the same trend with the variation of temperature and humidity. In the other words, maybe each of them has the bias towards “true value”, but the variance of estimated values still can explain the variance of “true values” based on the effects of ambient temperature and humidity. So, considering the inverse solution of air flow velocity, a sampler correlation, Eq. (4), is chosen. 4.3. Validity of the model For the discretization methods in this paper, which is first order accurate in space and first order accurate in time, the exact solution can be estimate from generalized Richardson extrapolation [18]. Using the results in sensitive analysis, the estimated discretization error is about 0.08 C, and relative discretization error is about 0.01%. The predictions capabilities of the model were evaluated with respect to the temperatures compared to the in-plant measured surface temperatures with the same product parameters, such as steel grade (SWRH82B), blower speed (20 m/s), wire diameter (12.5 mm), are presented in Fig. 3. The in-plant measured surface temperatures are statistical results of history data of a whole year, and the predicted temperatures are calculated under the condition of average ambient temperature (14.8 C) and dew point (3.9 C) of the same whole year. The maximum difference between average measured values (STD: 6.5 C) and estimated cooling curves is no more than 15 C. So it can be confirmed that the predicted temperatures are in good agreement with those measured. The expansibilities and validities of the model were evaluated with the comparison between the predicted volume fractions and the experimental isothermal transformation data obtained by Xu et al. [19]. The result with constant temperature of 550 C is presented in Table 5. Considering the fitting error of the temperaturedependent constants in Avrami equation, the results agree almost perfectly. Table 4 Effect of the number of grid points on the calculated cooling performance. Nodes
Incubation
1
6
11
Surface Center
Surface Center
Time/s 19.21 19.29 19.24 19.29 19.24 Cooling 6.195 6.078 5.979 6.078 5.982 rate/( C/s) Phase Time/s 13.22 12.4 14.25 12.41 14.25 transformation Temperature/ 589.16 578.92 601.80 578.84 601.75 C
Fig. 3. Comparison between the predicted temperatures and the measured surface temperatures.
5. Results and discussions 5.1. Effect on boundary conditions of heat transfer Fig. 4 shows the calculated convective heat-transfer coefficients of water vapor and dry air. As can be seen, the HTC of water vapor and dry air change with the reference temperature, this is because they have different thermophysical properties at different temperature. Similarly, the HTC of moist air would change with the reference temperature due to the changing of its thermophysical properties. Apparently, the ambient temperature affects the reference temperature, and the relative humidity (RH) affects the thermophysical properties of moist air by the rules list in Section 2.2. As shown in Eq. (3), the surface heat flux is affected by HTC, the temperature difference between wire surface and ambient, the radiation heat transfer. Fig. 5 shows the calculated heat flux changing with the surface temperature of steel wire with four different weather conditions. The heat flux decreases with the surface temperature decreasing mainly because of the decreased thermal radiation. When the ambient temperature is 15 C, there is little difference between different humidity, because the water vapor has a lower saturated pressure at low temperature. When the ambient temperature is 55 C, the heat flux of saturated moist air is higher than that of dry air, and this difference decreases as the surface temperature decreases, just as the tendency of HTC. When the humidity is 0%, there is a constant difference between different ambient temperatures, because they have the same HTC curve in Fig. 4, and this difference is mainly caused by the difference of reference temperature. 5.2. Effect on cooling performance of steel The different heat flux would result in different cooling performance of steel wire. The cooling rate and average temperature
Table 5 Comparison between the experimental data and the estimated data under isothermal transformation. Volume fraction
Experiment/s Estimation/s
1%
5%
25%
50%
99%
4.25 4.31
5.15 5.16
7.54 6.93
9.26 8.43
13.94 14.23
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155
153
Fig. 4. Calculated results of convective heat-transfer coefficients.
are the most common indexes to evaluate it. Fig. 6 shows the average cooling rate at central point of wire rod during the incubation period. Fig. 7 shows the average temperature at central point during the phase transformation period, weighted by the volume fraction of phase transformation. For the dry air, as a cumulative effect of heat transfer, the maximum difference due to variation in ambient temperature is about of 0.9 C/s on cooling rate and 10 C on transformation temperature, which is mainly because of the temperature difference between the ambient temperature and steel surface temperature. When the ambient temperature is 55 C, the maximum difference due to variation in humidity is about of 0.45 C/s on cooling rate and 6 C on transformation temperature, which is mainly because of the thermophysical properties variance of moist air. Within the range of studied weather conditions, low ambient temperature and high humidity increase the cooling performance of wire steel. 5.3. Effect on quality results of wire rods Different cooling performance determines different microstructures of product, and then determines different mechanical properties. Fig. 8 shows the ultimate tensile strength (UTS) under different weather conditions, which is evaluated from the average
Fig. 5. Calculated results of heat flux as changing with the surface temperature.
Fig. 6. Calculated average cooling rate at the center of wire rod during incubation period.
temperature during phase transformation period, according to the empirical relationship between the isothermal transformation temperature and experimental result [2]. It indicates that the UTS vary from 1139 MPa to 1206 MPa among the range of studied weather conditions. The industrial inspection results of UTS with the corresponding temperature and humidity (measured by local weather station) are also shown in Fig. 8. The ambient temperatures are binned into 5 levels to compare with the calculated UTS. As can be seen, although the measured data is endowed with various types of uncertainties, it is clear enough to distinguish the difference due to different ambient conditions, and the agreement between measurement and prediction under similar ambient conditions. With the same ambient conditions as industrial results, corresponding UTS were calculated and compared with the measured results. As shown in Fig. 9, although there is not a perfect accuracy due to complex industrial process, the predicted results also can explain 20% variance of the measured results. It means, when the ambient conditions are involved, the precision can be increased by
Fig. 7. Calculated average temperature at the center of wire rod during phase transformation period.
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Fig. 8. Calculated results of ultimate tensile strength compared with the industrial results.
20%, which is significant for product quality improving in industrial practice. 5.4. Effect on control of wind speed In the industrial process, what we need is not only to predict product quality from processing conditions, but also to control the operating conditions that can stabilize and improve the product quality. Using the inverse solution of the model, we can obtain the corresponding wind speeds, with which the products can maintain equal cooling process at different ambient temperatures and humidity. In order to simplify the solution of inverse heat-transfer, the wire rod is assumed to behave as a lumped capacity as discussed in sensitive analysis, then we can obtain from Eq. (1)
i dT g ks h 4 hðT TN Þ þ 3 s s0 T 4 Tsur ¼ dt rs Cps Rrs Cps
(14)
Set right-hand sides of the equation equal to constant (6.5 C/ s), it means that the average temperature of wire rod decreases at a constant cooling rate except phase transformation period. Then, assuming that the wind speed can be regulated continuous everywhere, we can achieve the wind speed at every time step by using the inverse method step by step.
Fig. 9. Comparison between the industrial UTS and the predicted UTS.
Fig. 10. Calculated wind speedetime curves for the same cooling process at different weather conditions.
Fig. 10 shows the calculated wind speedetime curves under three different typical weather conditions. It is evident from the figure that the wind speed varies within a wider range to acquire the same cooling effect at different conditions. Even though at the same weather conditions, the speed also varies with the surface temperature of steel, it is mainly because of the reduction of thermal radiation. Fig. 11 shows the average wind speed from incubation begins to transformation ends at different conditions. The variation range of the results is between 20 m/s to 25 m/s. Actually, the cooling conveyor is divided into several segments along the longitudinal direction, every of which has a blower with the same wind speed, so further optimization is required to determine the steady-state set-points of every blower. Considering that the blower power increases cubically as a function of wind speed, the influence of weather on energy consumptions is also significant. So integrated optimization is also required for production scheduling, such as arrange production at winter or at night as much as possible. 6. Conclusion An integrate model was developed to investigate the effect of ambient temperature and humidity on the production of hot rolled wire rod after controlled cooling process.
Fig. 11. Calculated average wind speed from the incubation begins to the transformation ends.
J. Xue et al. / Applied Thermal Engineering 62 (2014) 148e155
A quantitative analysis of heat transfer, cooling performance and mechanical property in the production of hot rolled wire rod has been demonstrated with different ambient temperature and humidity. The integrate model can be effectively applied to predict products quality, stabilize operating conditions and optimize production schedule. Acknowledgements This work was supported by the National Key Basic Research and Development Program of China (2009CB320602), the National Natural Science Foundation of China (61025018, 61021063, 60834004) and the National Science and Technology Major Project of China (2011ZX02504-008). The authors are grateful to Xingtai Iron & Steel Corp., LTD, China for providing technical supports and test samples. References [1] A.H. Nobari, S. Serajzadeh, Modeling of heat transfer during controlled cooling in hot rod rolling of carbon steels, Appl. Therm. Eng. 31 (2011) 487e492. [2] S. Phadke, P. Pauskar, R. Shivpuri, Computational modeling of phase transformations and mechanical properties during the cooling of hot rolled rod, J. Mater. Process. Technol. 150 (2004) 107e115. [3] W.-H. Yu, S.-H. Chen, Y.-H. Kuang, K.-C. Cao, Development and application of online Stelmor controlled cooling system, Appl. Therm. Eng. 29 (2009) 2949e 2953. [4] K. Czaputa, G. Brenn, The convective drying of liquid films on slender wires, Int. J. Heat Mass. Transfer 55 (2012) 19e31.
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