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The temperature distribution and underlying cooling mechanism of steel wire rod in the Stelmor type cooling process
Applied Thermal Engineering 142 (2018) 311–320
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
The temperature distribution and underlying cooling mechanism of steel wire rod in the Stelmor type cooling process
T
Joong-Ki Hwang Department of Steel Industry, Suncheon Jeil College, Suncheon 57997, Republic of Korea
H I GH L IG H T S
temperature distribution within wire ring during Stelmor process is investigated. • The middle and inner edge regions have a higher cooling rate than the center region. • The cooling behavior of edge region is highly related to the ring pitch. • The ring pitch control is necessary to improve the uniformity within wire ring. • The • The proposed empirical equations well predict the cooling rate with areas.
A R T I C LE I N FO
A B S T R A C T
Keywords: Wire rod steel Stelmor Temperature distribution Uniform cooling
The temperature distribution within wire ring during the Stelmor type cooling process has been investigated to understand the underlying cooling mechanism of steel wire rod using the well-designed off-line simulator and numerical simulation. The temperature deviation within wire ring varied with increasing air velocity and the maximum temperature deviation occurred at the air velocity of 10 m/s. Interestingly, the middle and inner edge regions of wire ring had a higher cooling rate than the center region under the air blowing cooling conditions because the air velocity around middle and inner edge regions was higher than that around center region. The cooling behavior of edge region is highly related to the ring pitch: the cooling rate of edge region dramatically decreased with decreasing ring pitch due to the more complicated ring structure. The proposed empirical equations as a function of wire diameter and air velocity can predict the cooling rates of wire ring well at both center and edge regions, which is a great benefit in industrial applications.
1. Introduction The direct heat treatment process for controlling the mechanical properties of hot-rolled products is becoming crucial in the steel manufacturing industry to decrease the total production cost under the highly competitive steel market. In the field of wire rod, it has been already 54 years since controlled cooling processes, such as a Stelmor cooling system, were developed. The straight hot rolled wire rod is laid into circle loops, hereafter referred to as wire ring, by a heading head on the roller conveyor in an overlapping pattern after passing through the intensive water cooling boxes. The starting temperature of wire ring is approximately 850 °C and wire ring is cooled on the roller conveyor with forced air by a series of fans below to obtain the desired microstructure and corresponding mechanical properties as shown in Fig. 1a. In recent years, the Stelmor type cooling process has become the most popular controlled cooling process to produce the steel wire rod with the diameter range from 5 mm to 20 mm [1,2] since it possesses several
E-mail address: [email protected]. https://doi.org/10.1016/j.applthermaleng.2018.07.016 Received 22 May 2018; Received in revised form 1 July 2018; Accepted 3 July 2018 Available online 04 July 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
advantages. Firstly, it can eliminate or reduce the post heat treatment of downstream processes, such as patenting, annealing, and quenching/ tempering, which saves the energy and environment and enhances the price competitiveness of mills [2–4]. Secondly, it can produce a wide range of products with just single cooling line using roller conveyors, cooling fans below the conveyor, and insulation covers over the conveyor. Namely, this flexible controlled cooling process enables mills to produce a wide spectrum of plain carbon steels, alloy steels, stainless steels, and other specialty grades [5,6]. Certainly, the development of the Stelmor cooling process into the wire rod industries has increased the quality demand of customers as well as the productivity of mills. Therefore, it is necessary to understand the cooling mechanism of Stelmor cooling process in order to satisfy the strict customer's demand for the high quality wire rod. Stelmor cooling process controls the cooling rate and the phase transformation of wire ring with adjusting the opening ratio of fans and the distribution of air velocity within wire ring, and finally tailors the
Applied Thermal Engineering 142 (2018) 311–320
J.-K. Hwang
Fig. 1. (a) Schematic description of the Stelmor type cooling process and (b) the wire ring shape on the conveyor roller during the cooling process.
temperature except for Campbell et al. and Hanada et al.. Campbell et al. [11] measured the heat transfer coefficient during air cooling using the single rod with 1.6 mm in diameter K-type thermocouple. The thermocouples were mounted at the rod centerline to minimize the disturbance of thermal response. Hanada et al. [10] also measured the centerline temperature of test pieces using K-type thermocouples during the air cooling. In contrast to the thermocouple measurement, the use of infrared pyrometers has following errors in measuring the temperature of wire ring.
microstructure and mechanical properties of wire rod [7,8]. Even though this air cooling process looks simple, the cooling rate is very different in each region within wire ring due to the complex geometrical structure of wire ring as shown in Fig. 1b. Therefore, during the last four decades, there have been many research papers on the Stelmor type cooling process. Agarwal and Brimacombe [9] developed a mathematical model incorporating both heat transfer and the phase transformation of austenite to pearlite in eutectoid carbon steel rods based on the one-dimensional (1D) finite difference method (FDM). They investigated the effect of rod diameter, manganese contents, air velocity, and starting temperature for cooling on the temperature profile and austenite transformation. Hanada et al. [10] constructed a off-line simulator for the Stelmor cooling process in the ratio of actual Stelmor of 1/1 in width and 1/3 in length for improving the uniform cooling characteristic of wire ring. They found the optimum air velocity distribution with wire ring position and reduced the scatter of tensile strength of wire ring from 16 to 9 MPa. Morales et al. [2] developed a mathematical 1D model to predict the temperature profile and the austenite-pearlite transformation kinetics of eutectoid steel wire rods in a Stelmor cooling process. They studied the effect of conveyor speed and fan failures during the cooling process. Campbell et al. [11] proposed a 1D model and validated it in a laboratory equipment and a real plant. They considered both center and edge regions of wire ring and measured the temperature of wire rod using thermocouples. Lindemann and Schmidt [12] developed a mathematical model considering the geometry of wire ring to predict the thermal behavior of wire ring. Yu et al. [13] implemented an online controlled cooling system for the Stelmor cooling process and took into account the phase transformation during the cooling process. Nobari and Serajzadeh [14] developed a 2D mathematical model based on finite element method (FEM) to predict temperature distribution in steel wire rods. Phase transformation was also considered and numerical results were validated by experimental measurement using a pyrometer in the real plant. Xue et al. [1] developed an integrated 1D model to investigate the effect of ambient temperature and humidity on the Stelmor cooling process. They reported that the convective heat transfer coefficients and heat flux increase as humidity increases and temperature decreases. Recently, Hong et al. [15] proposed a 3D mathematical model to predict the temperature distribution and austenite-pearlite transformation kinetics in a Stelmor cooling process. They calculated the temperature distributions and cooling curves of wire ring by considering the convective and radiative heat transfer as well as the latent heat during phase transformation. As mentioned above, considerable efforts to understand the cooling behaviors of wire rod have been focused on the mathematical modeling and numerical simulation since it is very difficult to measure the temperature of wire ring. In addition, to the best of the author's knowledge, most of the experimental studies were performed using the infrared pyrometers to measure the
(i) The results of measurement in radiation energy by pyrometers are inaccurate because the wire rod has a round shape not a plate. (ii) Radiation loss can occur when the diameter of wire rod is smaller than the measuring spot size of pyrometer. (iii) The measured temperature of center region can be underestimated and edge region can be overestimated due to the low packing density of center region and the high packing density of edge region as shown in Fig. 1b. (iv) The radiation energy is very sensitive to the surface conditions of wire ring. The wire rods have a variety of scale thickness and properties according to the cooling conditions and chemical compositions. (v) Optical pyrometers only measure the surface temperature of specimens and the upper layered wire rings due to the measurement positions. Accordingly, we are faced with difficulties in measuring the accurate temperature of wire ring to control the mechanical properties. In addition, most researchers only considered the center region, and a few ones [8,10,11,14,16–18] focused on the center and edge regions of wire ring. Based on the author's experiences, it is insufficient to consider the center or center/edge regions to understand the cooling mechanism of wire ring and to remove the post heat treatments by producing wire rods with uniform mechanical properties. This is mainly due to the complex geometrical structure of wire ring during the cooling process as shown in Fig. 1 [12]. Therefore, in this study, the temperature of wire ring was measured at the several points during the cooling process using thermocouples to understand the underlying cooling mechanism of wire rod in the Stelmor cooling process. The simulator for Stelmor cooling process was designed and installed to provide well-defined cooling conditions. And then the measured temperature of each region in wire ring with thermocouples was analyzed with the aid of numerical simulation. 2. Experimental procedure A simulator for Stelmor cooling process was structured to explore 312
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Fig. 2. (a) Schematic description of the simulator for Stelmor cooling process and (b) picture of conveyor roller and air nozzle in the simulator. Table 1 Process parameters of Stelmor cooling test using the simulator in this experiment. Specimen
SUS304
SWRH82A
Experimental conditions
Comments
Diameter of wire rod (mm)
Heating temperature (°C)
Conveyor speed (m/s)
Air velocity at nozzle (m/s)
Ring pitch (mm)
5.5 8 13 10
910
0.3
0, 5, 10, 20
17 34 25, 40, 63 20, 50, 100
1050
27
Thermocouple test
Tensile test
600 and ungrounded. The standard limit of error in this K-type thermocouple is 0.75% of measured temperature in the range of 293–1250 °C. Thermocouples were embedded through a 1 mm-diameter hole drilled to the core of wire rod to minimize the disturbance of thermal response on the wire rod surface [10,11]. Temperature data were stored by a multi-channel date recorder apparatus and sampling interval is 200 ms. Uniaxial tensile tests were carried out at an initial strain rate of 10−3 s−1 using an Instron machine at room temperature. After performing the cooling tests as a function of the ring pitch, 4 rings were selected at random and each wire ring was divided into 8 sections as shown in Fig. 3b, and then tensile tests were carried out to measure the standard deviation of tensile strength within wire ring. High carbon steel, SWRH82A, with the chemical composition given in Table 2 was used and the specific cooling conditions are summarized in Table 1.
the cooling mechanism of wire rods under the well-defined conditions as shown in Fig. 2. The simulator consists of conveyor roller, air blower, air nozzle, reheating furnace, and wire ring. Prior to the experiment, the reheating furnace was heated to the desired temperature and then wire ring was placed in the reheating furnace by conveyor roller. Nitrogen gas was used to minimize the oxide scale formation on the wire rod and the wire ring traveled back and forth in the reheating furnace using rollers for the uniform heating. Once the wire ring was heated to the desired temperature, it was held for an additional 10 min for soaking. The temperature deviation within the wire ring in the reheating furnace was about 9 °C. The wire ring was then withdrawn quickly from the reheating furnace by conveyor roller and placed in the ambient or forced air cooling conditions. During the cooling process, the wire ring traveled back and forth by conveyor rollers at the speed of 0.3 m/s and it was cooled by the forced air derived by fans under the conveyor roller. The air velocity at the nozzle was controlled by blower RPM, and the tests were performed at the specific air velocity as shown in Table 1. The air velocity at the nozzle was measured by a pitot static tube type velocity meter and the forced air temperature as well as ambient temperature was about 24 °C. In order to understand the underlying cooling mechanism of wire rod, the effect of wire diameter, ring pitch, and air velocity on the cooling rate was investigated as summarized in Table 1. Wire diameters of 5.5, 8, and 13 mm were selected for this study because these diameters are the main size typically processed by Stelmor type cooling processes. The effect of ring pitch, characteristic spacing between two consecutive wire ring at the center region as shown in Fig. 2 [19], on the cooling behavior was also analyzed by changing the ring pitch from 25 mm to 63 mm. The size of wire ring is 650 mm due to the limited simulator scale and austenitic SUS304 stainless steel was chosen as the main test material due to the no latent heat by no phase transformation during the cooling process. Nine points were measured within wire ring using 1 mm-diameter K-type thermocouples as shown in Fig. 3a, which is sheathed in inconel
3. Results 3.1. Temperature distribution within wire ring To evaluate the performance of the simulator for the Stelmor cooling process, the air velocity at nozzle with the blower RPM was measured using the pitot static tube type velocity meter. The measured velocity profiles along the transverse direction of conveyor are shown in Fig. 4a. The maximum deviation of air velocity on the conveyor was about 10% and this result confirmed the uniformity of air velocity along the transverse direction. In addition, Fig. 4b represents that average air velocity was proportional to the blower frequency, indicating that this air blowing system was well designed for the experiment. Fig. 5 shows the influence of air velocity over the range of 0–20 m/s of 13 mm-diameter wire rod. The ring pitch was set as 40 mm, which is a general cooling condition in the industrial fields. As expected, the center region cooled fast compared to the edge and middle regions at 313
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Fig. 3. Schematic description of (a) measurement points of temperature in wire ring using thermocouples and (b) specimen preparation for tensile test of wire ring.
air velocity in more detail, temperature deviation within wire ring was compared as a function of air velocity as shown in Fig. 7a. The deviation of temperature within wire ring increased with cooling process and had a maximum, and then decreased with decreasing temperature: the maximum temperature deviation occurred at the center temperature of approximately 350 °C. Fig. 7b shows the maximum temperature deviation of wire ring with air velocity. The deviation of temperature increased, and then decreased with increasing air velocity: the maximum deviation of temperature was approximately 140 °C and occurred at the air velocity of 10 m/s. Fig. 8 shows the influence of air velocity over the range of 0–20 m/s of 8 mm-diameter wire rod. The size of 8 mm wire rod also had a similar trend to the 13 mm wire rod: middle regions cooled fast compared to the center region with increasing air velocity and the temperature deviation within wire ring decreased with increasing air velocity. Similarly, 5.5 mm-diameter wire rod had a similar trend. It is necessary to note that some temperature data measured by thermocouples exhibited erratic behaviors because of the poor contact with test material or damage of thermocouple. This is mainly due to the vibration and movement of wire ring on the roller conveyor of simulator. These data were discarded in this study: no temperature data of inner edge in Fig. 8.
Table 2 Chemical composition in weight percent of the steels used in the present study. Grade
C
Mn
Si
Cr
Ni
Fe
SUS304 SWRH82A
0.08 Max. 0.82
2.0 Max. 0.42
1.0 Max 0.2
18–20 –
8.0–10.5 –
Bal. Bal.
the velocity of 0 m/s. However, the middle regions had higher cooling rates than the center region under the air blowing conditions, and this trend became stronger with increasing the air velocity, which is not consistent with the general knowledge. It is well known that the center region of wire ring has the fastest cooling rate regardless of cooling conditions [11]. It will be dealt with in the discussion section because it is not easy to understand this unexpected cooling behavior of wire ring. The temperature deviations between center and edge region became smaller with increasing air velocity, which is also inconsistent with the general knowledge. In this study, edge regions were divided into two regions: inner edge (Edge_C) and outer edge (Edge_E) as shown in Figs. 3a and 6. Unexpectedly, edge regions had different cooling behaviors with the cooling conditions. The outer edge region cooled slowly irrespectively of cooling conditions; whereas, the inner edge region cooled slowly under the low air velocity and cooled fast under the high air velocity. For instance, inner edge region had a higher cooling rate than the center region at the air velocity of 20 m/s (Fig. 5d). In order to analyze the temperature deviation within wire ring with
3.2. Effect of wire diameter and air velocity It is known that wire rod diameter, air velocity at nozzle, starting temperature for cooling, and latent heat during phase transformation
Fig. 4. (a) Velocity profiles at nozzle along the transverse direction of conveyor and (b) average air velocity with blower frequency of the simulator. 314
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Fig. 5. Comparison of temperature profiles with regions of 13 mm-diameter wire rod at the air velocity of (a) 0 m/s, (b) 5 m/s, (c) 10 m/s, and (d) 20 m/s.
Fig. 9 shows the influence of wire rod diameter on cooling rate at center and outer edge regions. The effect of wire diameter on the cooling rate is significant and the cooling rate decreased exponentially with increasing diameter of wire rod: about twofold increase in cooling rate was seen with decreasing the wire diameter from 13 mm to 5.5 mm. The cooling rate of both center and outer edge regions increased parabolic way with increasing air velocity as shown in Fig. 10. The hot rolled wire ring on the Stelmor cooling conveyor dissipates heat through radiative and convective heat transfer [19]. The convective heat transfer is divided into natural one and forced one. Fig. 10 mainly shows the effect of forced convective heat transfer in wire rods: heat transfer by forced air. The forced convective heat transfer coefficient from circular cylinder in cross-flow is known as a function of wire rod diameter and air velocity, and calculated from an empirical correlation as follows [21]:
Fig. 6. The ring structure of edge region and definition of inner edge and outer edge of wire ring.
have a strong influence on the cooling rate of wire rod. Many researchers [2,9,11,14,19,20] reported that wire rod diameter and air velocity are the main factors to govern the cooling history of wire rod.
Fig. 7. (a) Comparison of variations in temperature deviation within wire ring with center temperature and (b) the maximum temperature deviation of wire ring with air velocity of 13 mm-diameter wire rods. 315
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Fig. 8. Comparison of temperature profiles with regions of 8 mm-diameter wire rod at the air velocity of (a) 0 m/s, (b) 5 m/s, (c) 10 m/s, and (d) 20 m/s.
Fig. 9. Comparison of cooling rate at center and outer edge regions with wire rod diameter.
k ρVd ⎞ hforced = 0.683 ⎜⎛ ⎟ d⎝ μ ⎠
0.466
⎛ Cp μ ⎞ ⎝ k ⎠
⎜
Fig. 10. Comparison of cooling rate at center and outer edge regions with air velocity.
0.33
results of experiment and Eq. (1) as a function of wire diameter and air velocity. In other words, the cooling rates in Fig. 10 were fitted with the variables of wire diameter and air velocity at nozzle using the Origin software. The equations can be described as follows:
⎟
(1)
where k, d, ρ, μ, V, and Cp refer to thermal conductivity, wire diameter, density, kinematic viscosity, air velocity, and specific heat, respectively. Although this correlation is strictly valid only at the center region due to the structure similarity between circular cylinder in cross-flow and the shape of wire ring at the center region, its use in the middle and edge regions can be also permissible provided that the ring pitch is sufficiently large. In case of the wire rods for fast cooling with the forced air, the ring pitch is relatively large enough to apply Eq. (1) to the middle and edge regions with a modification of constants in Eq. (1). The cooling rate of wire rod by forced convection may have this kind of formulation. Meanwhile, radiative and natural convective heat transfer are highly related to the cooling condition at the air velocity of 0 m/s. The cooling rates (CR) of wire rod were derived based on the
CR center = (11.6−0.63d) + 0.65V1.12 − 0.037d
(2)
CR edge = (7.8−0.45d) + (1.81−0.128d)V 0.44 + 0.038d
(3)
where the first term represents the contribution of radiative and natural convective heat transfer and the second term represents the contribution of forced convective heat transfer. When the air blower is off for the slow cooling, the roller conveyor also moves the wire ring at a specific velocity. In this case, the air velocity can be set as the conveyor moving speed because the forced convective heat transfer also works in this condition. Fig. 11 shows the comparison between the measured and calculated 316
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Fig. 11. Comparison of the measured and calculated cooling rates of (a) center region and (b) edge region.
wire ring. For instance, the cooling rate of wire ring with 63 mm pitch increased approximately 70% in comparison with the wire ring with 25 mm pitch at the edge region. This result indicates that the ring pitch is one of the most important parameters for the uniform cooling of wire ring in the Stelmor type cooling process. In order to analyze the effect of wire ring pitch in more detail, tensile strength was measured after air cooling tests as summarized in Table 1 and Fig. 3b. Fig. 13 shows the standard deviation of tensile strength with the ring pitch. The deviation of tensile strength increased with decreasing ring pitch, which is consistent with the results of cooling rate as a function of ring pitch as shown in Fig. 12. The standard deviation of tensile strength was reduced to about 10 MPa at the ring pitch of 100 mm. It is obvious that the ring pitch needs to be maximized to decrease the deviation of mechanical properties within wire ring.
cooling rates at the temperature of 750 °C based on the Eqs. (2) and (3). All the calculated values were found to be in good agreement with the corresponding measured values at the center region: the relative differences were less than 7%. Meanwhile, two values were somewhat different at the edge region due to the complex geometry of wire ring at the edge region as shown in Fig. 6. Overall, the proposed equations are capable of predicting the cooling rate of wire ring at the center and edge regions under the different cooling conditions. 3.3. Effect of wire ring pitch The ring pitch is a important parameter in Stelmor type cooling process because ring pitch controls the packing density of wire ring [18], which means ring pitch is highly related to the cooling rate of wire ring. The ring pitch is calculated using Eq. (4).
P=
4. Discussion
πDVconveyor Vrolling
(4)
The most interesting characteristic of the present study is the higher cooling rate of middle region in wire ring compared to the center region under the air blowing cooling conditions, which is inconsistent with the general knowledge. Moreover, the inner edge region cooled fast at the air velocity of 20 m/s compared to the center region. Obviously, the ring density at the middle and edge regions is higher than that of the center region [17]; therefore, the cooling rate of wire ring at the middle and edge regions can be lower than that of the center region regardless of the cooling conditions. However, the inverse results were derived at the air blowing cooling conditions in this study. Accordingly, it is essential to quantitatively evaluate the ring density. A constant ring pitch was assumed at the specific cooling condition to calculate the ring
where P, D, Vconveyor, and Vrolling refer to ring pitch, wire ring diameter, conveyor speed, and finial rolling speed, respectively. Eq. (4) indicates that the cooling rate can be tailored by these process parameters as well as air velocity and wire diameter. Fig. 12 shows the measured cooling rate of the 13 mm-diameter wire rod as a function of ring pitch and air velocity. Interestingly, the center regions had a similar cooling rate regardless of the ring pitch, which means the cooling history at the center region is independent of the ring pitch in the general cooling conditions. On the other hand, the edge regions had a big difference with the ring pitch: the cooling rate dramatically decreased with decreasing ring pitch, resulting in a high deviation of cooling rate within
Fig. 12. (a) Schematic explanation of ring pitch and (b) comparison of cooling rate of 13 mm diameter wire rod at center and edge regions with air velocity and ring pitch. 317
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easy to understand the unprecedented phenomenon of cooling rate difference between center and middle/inner edge using the calculated ring density. Therefore, a computer simulation was applied to analyze the velocity distribution around wire ring. Fluent commercial software, ANSYS version 17, was used in simulating wire rod cooling process with the 2D module. Steady state and realizable k-ε turbulence model were applied [22]. To shorten the calculation time, the half of full geometry was simulated stemming from the symmetrical constraints of wire ring in nature. The wire diameter is 13 mm and the wire ring size is 650 mm. The air velocity at nozzle was set as a constant velocity of 20 m/s and other process parameters were kept same as the actual experimental conditions. The total number of grids in the computational domain was chosen approximately 1.41 × 105 cells based on the grid convergence test. The solution of discretization equations and numerical skill were reported in detail by Patankar [23], and will not be handled here. Fig. 16a shows the contour of velocity vector at the plane perpendicular to the moving direction of wire ring. As expected, the velocity of forced air around outer edge region was much lower than that around center region, which is confirmed by the velocity profile along the transverse direction of moving wire ring as shown in Fig. 16b. Interestingly, the air around middle and inner edge regions of wire ring had a higher velocity compared to the air around center region because of the small distance between wire rods at the middle and inner edge regions. In other words, the velocity increased at the small inter-distance between wire rods since the forced air has to pass through the narrow gap as shown in Fig. 17, which increased the forced convective heat transfer, finally increased the cooling rate at the middle and inner edge regions of wire ring during the air blowing cooling conditions. This result is crucial from an industrial point of view. The dichotomous thinking of center and outer edge regions [8,11,14,16–18] cannot eliminate the post heat treatments of wire ring because middle and inner edge regions of wire ring had a higher tensile strength than center or outer edge regions. Therefore, the middle and inner edge regions as well as center and outer edge region are always considered to get a homogeneous microstructure and mechanical properties within wire ring in the Stelmor type cooling process. Ring pitch is a very important parameter in the Stelmor type cooling process because ring pitch controls the packing density of wire ring [18,24], and finally controls the cooling rate and microstructure of the wire ring as shown in Figs. 12 and 13. The ring pitch is highly related to the edge region of wire ring since center and middle regions sustain a single cylinder shape with changing the ring pitch in the general cooling conditions, but the edge region has a more complicated
Fig. 13. Standard deviation of tensile strength of SWRH82A pearlitic steel with ring pitch.
density mathematically, which means the rolling speed, conveyor roller speed, and wire ring size are constant during the specific cooling process. The volume of wire rod was, also, assumed to be equivalent to the 2D projected area to simplify the calculation. The ring density on the roller conveyor can be expressed as follows:
ρi =
D θd 2 i
×2
δP
=
D θd× 2 i D P 2n
2
=
2nθi d P
(5)
where ρi, θi, δ, and n refer to ring density, angle, length of unit grid, and the number of grid, respectively, which is shown in Fig. 14. The δ and n has a following relationship:
δ=
D 2n
(6)
The θi is geometrically calculated by following equation using Fig. 14: n−1
θi = 90−
2δi ⎞ ⎝ D ⎠
∑ θi−cos−1 ⎛ k=0
(7)
where θ0 is a zero and Eq. (7) was calculated with the aid of numerical tool: C language. Fig. 15 shows the calculated results based on Eq. (5). The ring density of the middle and edge region is higher than that of the center region: the center region has the minimum ring density and middle region has approximately 1.3 times higher and inner edge region has 2.2 times higher ring density than the center region. It is not
Fig. 14. Schematic representations to analytically derive the ring density along the transverse direction of wire ring. 318
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Fig. 15. Profile of relative ring density along the transverse direction of wire ring of (a) the total region from outer edge to outer edge and (b) the partial region from inner edge to inner edge.
Fig. 16. (a) Contour of velocity vector and (b) velocity profile along the transverse direction of moving wire ring.
rod cooling process to produce wire rods with desired mechanical properties, especially uniform mechanical properties within wire ring. The ring pitch depends on several process parameters as shown in Eq. (4) and it can be tailored with the combination of these parameters. Meanwhile, most of the wire rod mills use uniform cooling apparatus to minimize the variation of mechanical properties of wire rod by adjusting the air flow distribution in center and edge regions of wire ring [11,15,16]. This study shows that the key factor in determining the amount of air flow rate with regions is the ring pitch, not the diameter of wire rod [24], conveyor speed, air velocity, and temperature of wire rod. Most of the results in this study can be applied to the industrial scale since the off-line simulator was structured after analyzing the real Stelmor cooling equipment. However, the size of wire ring is 650 mm and the maximum air velocity at nozzle is 33 m/s due to the limited simulator scale. In case of real plant, the wire ring size and maximum air velocity are about 1100 mm and 45 m/s, respectively. Therefore, the predicted cooling rate from Eqs. (2) and (3) can be strictly applied to the limited cooling conditions, air velocity between 0 and 33 m/s. In addition, the difference in thermal properties between stainless steel and plane carbon steel was considered to apply the results of this study to the industrial fields. Based on the author's experiences, small modifications are necessary to use Eqs. (2) and (3) according to the steel grade, ambient temperature, and the specific cooling conditions.
Fig. 17. Schematic explanation of air velocity distribution along the transverse direction of moving wire ring.
geometry with decreasing the ring pitch as shown in Fig. 6. The cooling rate of edge region sharply decreased with decreasing ring pitch due to a higher ring density and more complicated ring structure. This phenomenon also explains the good agreement between the measured and calculated cooling rate at the center region and some deviations between two values at the edge region as shown in Fig. 11. In the center region, it can obey the empirical formula with changing the wire rod diameter, air velocity, and ring pitch due to the same cooling mechanism: the cross flow over circular cylinders [11]. Meanwhile, the ring geometry of edge region can be somewhat changed with wire rod diameter and ring pitch as shown in Fig. 6; therefore, it is not easy to predict the cooling rate of the edge region with the one estimated regression equation. Furthermore, around edge region, the contour of velocity is complex and it will be varied with changing the ring pitch as shown in Fig. 16a. From a practical point of view in wire rod industries, the ring pitch control is considered as a great starting point in the wire
5. Conclusions Based on the systematic study on the Stelmor type cooling process using the well-designed off-line simulator and numerical simulation, the following conclusions can be drawn. 319
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1. As the wire ring cooled on the Stelmor cooling conveyor, the maximum temperature deviation occurred when the center temperature reached approximately 350 °C. The temperature deviation within wire ring increased, and then decreased with increasing air velocity: the maximum temperature deviation was approximately 140 °C and occurred at the air velocity of 10 m/s. 2. The middle and inner edge regions of wire ring had a higher cooling rate than the center region during the air blowing cooling conditions because the air around middle and inner edge regions had a higher velocity compared to the air around center region. This is due to the smaller distance between wire rods at the middle and inner edge regions. 3. The ring pitch controls the density of wire ring, and finally controls the cooling rate, microstructure, and mechanical properties. The ring pitch is strongly related to the cooling rate of the edge region since the cooling rate of edge region dramatically decreased with decreasing ring pitch stemming from the higher ring density and more complicated ring structure. 4. The cooling rates of wire ring at the center and edge regions were predicted using the empirical equations as a function of wire diameter and air velocity. These equations are helpful in designing the cooling condition to produce high quality wire rod steels.
24 (2003) 415–421. [4] W.P. Krejdovsky, D.M. Jones, B.V. Kiefer, Improved wire rod properties resulting from controlled cooling in modern water box and Stelmor conveyor cooling system, Wire J. Int. (February) (2007) 56–61. [5] Y. Lee, Rod and Bar Rolling: Theory and Applications, first ed., CRC Press, 2004, pp. 23–24. [6] A. Tendler, Controlled cooling of rods, Wire J. (February) (1981) 84–91. [7] P.C. Campbell, E.B. Hawbolt, J.K. Brimacombe, Microstructure engineering applied to the controlled cooling of steel wire rod: Part2. Microstructural evolution and mechanical properties correlations, Metall. Mater. Trans. A 22A (1991) 2779–2790. [8] P.C. Campbell, E.B. Hawbolt, J.K. Brimacombe, Microstructural engineering applied to the controlled cooling of steel wire rod: Part3. Mathematical model-formulation and predictions, Metall. Mater. Trans. A 22A (1991) 2791–2805. [9] P.K. Agarwal, J.K. Brimacombe, Mathematical model of heat flow and austenitepearlite transformation in eutectoid carbon steel rods for wire, Metall. Mater. Trans. B 12B (1981) 121–133. [10] Y. Hanada, K. Ueno, A. Noda, H. Kondoh, T. Sakamoto, K. Mine, New type Stelmor equipment of wire rod and bar mill, Kawasaki Steel Tech. Rep. 15 (1986) 50–57. [11] P.C. Campbell, E.B. Hawbolt, J.K. Brimacombe, Microstructure engineering applied to the controlled cooling of steel wire rod: Part I. Experimental design and heat transfer, Metall. Mater. Trans. A 22A (1991) 2769–2778. [12] A. Lindemann, J. Schmidt, ACMOD-2D-A heat transfer model for the simulation of the cooling of wire rod, JMPT 169 (2005) 466–475. [13] 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) 2949–2953. [14] A.H. Nobari, S. Serajzadeh, Modeling of heat transfer during controlled cooling in hot rod rolling of carbon steels, Appl. Therm. Eng. 31 (2011) 487–492. [15] L. Hong, B. Wang, S. Feng, Z. Yang, Y. Yu, W. Peng, J. Zhang, A three-dimensional mathematical model to predict air-cooling flow and temperature distribution of wire loops in the Stelmor air-cooling system, Appl. Therm. Eng. 116 (2017) 766–776. [16] S. Lenka, S. Kundu, S. Chandra, S.B. Singh, Effect of recalescence on microstructure and phase transformation in high carbon steel, Mater. Sci. Technol. 29 (2013) 715–725. [17] I. Jain, S. Lenka, S.K. Ajmani, S. Kundu, An approach to heat transfer analysis of wire loops over the Stelmor conveyor to predict the microstructural and mechanical attributes of steel rods, J. Thermal Sci. Eng. Appl. 8 (2016) 021019. [18] A. Zufia, J.M. Llanos, Mathematical simulation and controlled cooling in an EDC conveyor of a wire rod rolling mill, ISIJ Int. 41 (2001) 1282–1288. [19] E. Anelli, Application of mathematical modeling to hot rolling and controlled cooling of wire rods and bars, ISIJ Int. 32 (1992) 440–449. [20] A. Lindemann, J. Schmidt, H. Boye, Numerical simulation and infrared-thermographic measurement of the cooling of wire rod, Heat Transf. 4 (2002) 735–740. [21] F.P. Incropera, D.P. Dewitt, T.L. Bergman, A.S. Lavine, Fundamentals of Heat and Mass Transfer, seventh ed., John Wiley and Sons Ltd, Chichester, 2012. [22] S. Pramuditya, M. Takahashi, H. Ninokata, Computational fluid dynamics study on cross flow pressure drop for triangular array rod assemblies with wire, Ann. Nucl. Energy 87 (2016) 803–816. [23] S.V. Patankar, Numerical heat transfer and fluid flow, first ed., Tayor & Francis, Boca Raton, FL, 1980. [24] S.K. Cho, Effect of wire rod size and its packing density on the tensile strength deviation of high carbon steel wire rod in the Stelmor process, Wire J. Int. (February) (1998) 114–120.
Acknowledgements The author deeply appreciates Mr. M.S. Choi in POSCO for the experiments, and POSCO (Grant no. 2013N007) for financial support. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at https://doi.org/10.1016/j.applthermaleng.2018.07. 016. References [1] J. Xue, M. Liu, Y. Deng, Effects of ambient temperature and humidity on the controlled cooling of hot-rolled wire rod of steel, Appl. Therm. Eng. 62 (2014) 148–155. [2] R.D. Morales, A. Lopez, I.M. Olivares, Mathematical simulation of Stelmor process, Ironmak. Steelmak. 18 (1991) 128–138. [3] M. Kazeminezhad, A.K. Taheri, The effect of controlled cooling after hot rolling on the mechanical properties of a commercial high carbon steel wire rod, Mater. Des.
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Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Research Paper
The temperature distribution and underlying cooling mechanism of steel wire rod in the Stelmor type cooling process
T
Joong-Ki Hwang Department of Steel Industry, Suncheon Jeil College, Suncheon 57997, Republic of Korea
H I GH L IG H T S
temperature distribution within wire ring during Stelmor process is investigated. • The middle and inner edge regions have a higher cooling rate than the center region. • The cooling behavior of edge region is highly related to the ring pitch. • The ring pitch control is necessary to improve the uniformity within wire ring. • The • The proposed empirical equations well predict the cooling rate with areas.
A R T I C LE I N FO
A B S T R A C T
Keywords: Wire rod steel Stelmor Temperature distribution Uniform cooling
The temperature distribution within wire ring during the Stelmor type cooling process has been investigated to understand the underlying cooling mechanism of steel wire rod using the well-designed off-line simulator and numerical simulation. The temperature deviation within wire ring varied with increasing air velocity and the maximum temperature deviation occurred at the air velocity of 10 m/s. Interestingly, the middle and inner edge regions of wire ring had a higher cooling rate than the center region under the air blowing cooling conditions because the air velocity around middle and inner edge regions was higher than that around center region. The cooling behavior of edge region is highly related to the ring pitch: the cooling rate of edge region dramatically decreased with decreasing ring pitch due to the more complicated ring structure. The proposed empirical equations as a function of wire diameter and air velocity can predict the cooling rates of wire ring well at both center and edge regions, which is a great benefit in industrial applications.
1. Introduction The direct heat treatment process for controlling the mechanical properties of hot-rolled products is becoming crucial in the steel manufacturing industry to decrease the total production cost under the highly competitive steel market. In the field of wire rod, it has been already 54 years since controlled cooling processes, such as a Stelmor cooling system, were developed. The straight hot rolled wire rod is laid into circle loops, hereafter referred to as wire ring, by a heading head on the roller conveyor in an overlapping pattern after passing through the intensive water cooling boxes. The starting temperature of wire ring is approximately 850 °C and wire ring is cooled on the roller conveyor with forced air by a series of fans below to obtain the desired microstructure and corresponding mechanical properties as shown in Fig. 1a. In recent years, the Stelmor type cooling process has become the most popular controlled cooling process to produce the steel wire rod with the diameter range from 5 mm to 20 mm [1,2] since it possesses several
E-mail address: [email protected]. https://doi.org/10.1016/j.applthermaleng.2018.07.016 Received 22 May 2018; Received in revised form 1 July 2018; Accepted 3 July 2018 Available online 04 July 2018 1359-4311/ © 2018 Elsevier Ltd. All rights reserved.
advantages. Firstly, it can eliminate or reduce the post heat treatment of downstream processes, such as patenting, annealing, and quenching/ tempering, which saves the energy and environment and enhances the price competitiveness of mills [2–4]. Secondly, it can produce a wide range of products with just single cooling line using roller conveyors, cooling fans below the conveyor, and insulation covers over the conveyor. Namely, this flexible controlled cooling process enables mills to produce a wide spectrum of plain carbon steels, alloy steels, stainless steels, and other specialty grades [5,6]. Certainly, the development of the Stelmor cooling process into the wire rod industries has increased the quality demand of customers as well as the productivity of mills. Therefore, it is necessary to understand the cooling mechanism of Stelmor cooling process in order to satisfy the strict customer's demand for the high quality wire rod. Stelmor cooling process controls the cooling rate and the phase transformation of wire ring with adjusting the opening ratio of fans and the distribution of air velocity within wire ring, and finally tailors the
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Fig. 1. (a) Schematic description of the Stelmor type cooling process and (b) the wire ring shape on the conveyor roller during the cooling process.
temperature except for Campbell et al. and Hanada et al.. Campbell et al. [11] measured the heat transfer coefficient during air cooling using the single rod with 1.6 mm in diameter K-type thermocouple. The thermocouples were mounted at the rod centerline to minimize the disturbance of thermal response. Hanada et al. [10] also measured the centerline temperature of test pieces using K-type thermocouples during the air cooling. In contrast to the thermocouple measurement, the use of infrared pyrometers has following errors in measuring the temperature of wire ring.
microstructure and mechanical properties of wire rod [7,8]. Even though this air cooling process looks simple, the cooling rate is very different in each region within wire ring due to the complex geometrical structure of wire ring as shown in Fig. 1b. Therefore, during the last four decades, there have been many research papers on the Stelmor type cooling process. Agarwal and Brimacombe [9] developed a mathematical model incorporating both heat transfer and the phase transformation of austenite to pearlite in eutectoid carbon steel rods based on the one-dimensional (1D) finite difference method (FDM). They investigated the effect of rod diameter, manganese contents, air velocity, and starting temperature for cooling on the temperature profile and austenite transformation. Hanada et al. [10] constructed a off-line simulator for the Stelmor cooling process in the ratio of actual Stelmor of 1/1 in width and 1/3 in length for improving the uniform cooling characteristic of wire ring. They found the optimum air velocity distribution with wire ring position and reduced the scatter of tensile strength of wire ring from 16 to 9 MPa. Morales et al. [2] developed a mathematical 1D model to predict the temperature profile and the austenite-pearlite transformation kinetics of eutectoid steel wire rods in a Stelmor cooling process. They studied the effect of conveyor speed and fan failures during the cooling process. Campbell et al. [11] proposed a 1D model and validated it in a laboratory equipment and a real plant. They considered both center and edge regions of wire ring and measured the temperature of wire rod using thermocouples. Lindemann and Schmidt [12] developed a mathematical model considering the geometry of wire ring to predict the thermal behavior of wire ring. Yu et al. [13] implemented an online controlled cooling system for the Stelmor cooling process and took into account the phase transformation during the cooling process. Nobari and Serajzadeh [14] developed a 2D mathematical model based on finite element method (FEM) to predict temperature distribution in steel wire rods. Phase transformation was also considered and numerical results were validated by experimental measurement using a pyrometer in the real plant. Xue et al. [1] developed an integrated 1D model to investigate the effect of ambient temperature and humidity on the Stelmor cooling process. They reported that the convective heat transfer coefficients and heat flux increase as humidity increases and temperature decreases. Recently, Hong et al. [15] proposed a 3D mathematical model to predict the temperature distribution and austenite-pearlite transformation kinetics in a Stelmor cooling process. They calculated the temperature distributions and cooling curves of wire ring by considering the convective and radiative heat transfer as well as the latent heat during phase transformation. As mentioned above, considerable efforts to understand the cooling behaviors of wire rod have been focused on the mathematical modeling and numerical simulation since it is very difficult to measure the temperature of wire ring. In addition, to the best of the author's knowledge, most of the experimental studies were performed using the infrared pyrometers to measure the
(i) The results of measurement in radiation energy by pyrometers are inaccurate because the wire rod has a round shape not a plate. (ii) Radiation loss can occur when the diameter of wire rod is smaller than the measuring spot size of pyrometer. (iii) The measured temperature of center region can be underestimated and edge region can be overestimated due to the low packing density of center region and the high packing density of edge region as shown in Fig. 1b. (iv) The radiation energy is very sensitive to the surface conditions of wire ring. The wire rods have a variety of scale thickness and properties according to the cooling conditions and chemical compositions. (v) Optical pyrometers only measure the surface temperature of specimens and the upper layered wire rings due to the measurement positions. Accordingly, we are faced with difficulties in measuring the accurate temperature of wire ring to control the mechanical properties. In addition, most researchers only considered the center region, and a few ones [8,10,11,14,16–18] focused on the center and edge regions of wire ring. Based on the author's experiences, it is insufficient to consider the center or center/edge regions to understand the cooling mechanism of wire ring and to remove the post heat treatments by producing wire rods with uniform mechanical properties. This is mainly due to the complex geometrical structure of wire ring during the cooling process as shown in Fig. 1 [12]. Therefore, in this study, the temperature of wire ring was measured at the several points during the cooling process using thermocouples to understand the underlying cooling mechanism of wire rod in the Stelmor cooling process. The simulator for Stelmor cooling process was designed and installed to provide well-defined cooling conditions. And then the measured temperature of each region in wire ring with thermocouples was analyzed with the aid of numerical simulation. 2. Experimental procedure A simulator for Stelmor cooling process was structured to explore 312
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Fig. 2. (a) Schematic description of the simulator for Stelmor cooling process and (b) picture of conveyor roller and air nozzle in the simulator. Table 1 Process parameters of Stelmor cooling test using the simulator in this experiment. Specimen
SUS304
SWRH82A
Experimental conditions
Comments
Diameter of wire rod (mm)
Heating temperature (°C)
Conveyor speed (m/s)
Air velocity at nozzle (m/s)
Ring pitch (mm)
5.5 8 13 10
910
0.3
0, 5, 10, 20
17 34 25, 40, 63 20, 50, 100
1050
27
Thermocouple test
Tensile test
600 and ungrounded. The standard limit of error in this K-type thermocouple is 0.75% of measured temperature in the range of 293–1250 °C. Thermocouples were embedded through a 1 mm-diameter hole drilled to the core of wire rod to minimize the disturbance of thermal response on the wire rod surface [10,11]. Temperature data were stored by a multi-channel date recorder apparatus and sampling interval is 200 ms. Uniaxial tensile tests were carried out at an initial strain rate of 10−3 s−1 using an Instron machine at room temperature. After performing the cooling tests as a function of the ring pitch, 4 rings were selected at random and each wire ring was divided into 8 sections as shown in Fig. 3b, and then tensile tests were carried out to measure the standard deviation of tensile strength within wire ring. High carbon steel, SWRH82A, with the chemical composition given in Table 2 was used and the specific cooling conditions are summarized in Table 1.
the cooling mechanism of wire rods under the well-defined conditions as shown in Fig. 2. The simulator consists of conveyor roller, air blower, air nozzle, reheating furnace, and wire ring. Prior to the experiment, the reheating furnace was heated to the desired temperature and then wire ring was placed in the reheating furnace by conveyor roller. Nitrogen gas was used to minimize the oxide scale formation on the wire rod and the wire ring traveled back and forth in the reheating furnace using rollers for the uniform heating. Once the wire ring was heated to the desired temperature, it was held for an additional 10 min for soaking. The temperature deviation within the wire ring in the reheating furnace was about 9 °C. The wire ring was then withdrawn quickly from the reheating furnace by conveyor roller and placed in the ambient or forced air cooling conditions. During the cooling process, the wire ring traveled back and forth by conveyor rollers at the speed of 0.3 m/s and it was cooled by the forced air derived by fans under the conveyor roller. The air velocity at the nozzle was controlled by blower RPM, and the tests were performed at the specific air velocity as shown in Table 1. The air velocity at the nozzle was measured by a pitot static tube type velocity meter and the forced air temperature as well as ambient temperature was about 24 °C. In order to understand the underlying cooling mechanism of wire rod, the effect of wire diameter, ring pitch, and air velocity on the cooling rate was investigated as summarized in Table 1. Wire diameters of 5.5, 8, and 13 mm were selected for this study because these diameters are the main size typically processed by Stelmor type cooling processes. The effect of ring pitch, characteristic spacing between two consecutive wire ring at the center region as shown in Fig. 2 [19], on the cooling behavior was also analyzed by changing the ring pitch from 25 mm to 63 mm. The size of wire ring is 650 mm due to the limited simulator scale and austenitic SUS304 stainless steel was chosen as the main test material due to the no latent heat by no phase transformation during the cooling process. Nine points were measured within wire ring using 1 mm-diameter K-type thermocouples as shown in Fig. 3a, which is sheathed in inconel
3. Results 3.1. Temperature distribution within wire ring To evaluate the performance of the simulator for the Stelmor cooling process, the air velocity at nozzle with the blower RPM was measured using the pitot static tube type velocity meter. The measured velocity profiles along the transverse direction of conveyor are shown in Fig. 4a. The maximum deviation of air velocity on the conveyor was about 10% and this result confirmed the uniformity of air velocity along the transverse direction. In addition, Fig. 4b represents that average air velocity was proportional to the blower frequency, indicating that this air blowing system was well designed for the experiment. Fig. 5 shows the influence of air velocity over the range of 0–20 m/s of 13 mm-diameter wire rod. The ring pitch was set as 40 mm, which is a general cooling condition in the industrial fields. As expected, the center region cooled fast compared to the edge and middle regions at 313
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Fig. 3. Schematic description of (a) measurement points of temperature in wire ring using thermocouples and (b) specimen preparation for tensile test of wire ring.
air velocity in more detail, temperature deviation within wire ring was compared as a function of air velocity as shown in Fig. 7a. The deviation of temperature within wire ring increased with cooling process and had a maximum, and then decreased with decreasing temperature: the maximum temperature deviation occurred at the center temperature of approximately 350 °C. Fig. 7b shows the maximum temperature deviation of wire ring with air velocity. The deviation of temperature increased, and then decreased with increasing air velocity: the maximum deviation of temperature was approximately 140 °C and occurred at the air velocity of 10 m/s. Fig. 8 shows the influence of air velocity over the range of 0–20 m/s of 8 mm-diameter wire rod. The size of 8 mm wire rod also had a similar trend to the 13 mm wire rod: middle regions cooled fast compared to the center region with increasing air velocity and the temperature deviation within wire ring decreased with increasing air velocity. Similarly, 5.5 mm-diameter wire rod had a similar trend. It is necessary to note that some temperature data measured by thermocouples exhibited erratic behaviors because of the poor contact with test material or damage of thermocouple. This is mainly due to the vibration and movement of wire ring on the roller conveyor of simulator. These data were discarded in this study: no temperature data of inner edge in Fig. 8.
Table 2 Chemical composition in weight percent of the steels used in the present study. Grade
C
Mn
Si
Cr
Ni
Fe
SUS304 SWRH82A
0.08 Max. 0.82
2.0 Max. 0.42
1.0 Max 0.2
18–20 –
8.0–10.5 –
Bal. Bal.
the velocity of 0 m/s. However, the middle regions had higher cooling rates than the center region under the air blowing conditions, and this trend became stronger with increasing the air velocity, which is not consistent with the general knowledge. It is well known that the center region of wire ring has the fastest cooling rate regardless of cooling conditions [11]. It will be dealt with in the discussion section because it is not easy to understand this unexpected cooling behavior of wire ring. The temperature deviations between center and edge region became smaller with increasing air velocity, which is also inconsistent with the general knowledge. In this study, edge regions were divided into two regions: inner edge (Edge_C) and outer edge (Edge_E) as shown in Figs. 3a and 6. Unexpectedly, edge regions had different cooling behaviors with the cooling conditions. The outer edge region cooled slowly irrespectively of cooling conditions; whereas, the inner edge region cooled slowly under the low air velocity and cooled fast under the high air velocity. For instance, inner edge region had a higher cooling rate than the center region at the air velocity of 20 m/s (Fig. 5d). In order to analyze the temperature deviation within wire ring with
3.2. Effect of wire diameter and air velocity It is known that wire rod diameter, air velocity at nozzle, starting temperature for cooling, and latent heat during phase transformation
Fig. 4. (a) Velocity profiles at nozzle along the transverse direction of conveyor and (b) average air velocity with blower frequency of the simulator. 314
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Fig. 5. Comparison of temperature profiles with regions of 13 mm-diameter wire rod at the air velocity of (a) 0 m/s, (b) 5 m/s, (c) 10 m/s, and (d) 20 m/s.
Fig. 9 shows the influence of wire rod diameter on cooling rate at center and outer edge regions. The effect of wire diameter on the cooling rate is significant and the cooling rate decreased exponentially with increasing diameter of wire rod: about twofold increase in cooling rate was seen with decreasing the wire diameter from 13 mm to 5.5 mm. The cooling rate of both center and outer edge regions increased parabolic way with increasing air velocity as shown in Fig. 10. The hot rolled wire ring on the Stelmor cooling conveyor dissipates heat through radiative and convective heat transfer [19]. The convective heat transfer is divided into natural one and forced one. Fig. 10 mainly shows the effect of forced convective heat transfer in wire rods: heat transfer by forced air. The forced convective heat transfer coefficient from circular cylinder in cross-flow is known as a function of wire rod diameter and air velocity, and calculated from an empirical correlation as follows [21]:
Fig. 6. The ring structure of edge region and definition of inner edge and outer edge of wire ring.
have a strong influence on the cooling rate of wire rod. Many researchers [2,9,11,14,19,20] reported that wire rod diameter and air velocity are the main factors to govern the cooling history of wire rod.
Fig. 7. (a) Comparison of variations in temperature deviation within wire ring with center temperature and (b) the maximum temperature deviation of wire ring with air velocity of 13 mm-diameter wire rods. 315
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Fig. 8. Comparison of temperature profiles with regions of 8 mm-diameter wire rod at the air velocity of (a) 0 m/s, (b) 5 m/s, (c) 10 m/s, and (d) 20 m/s.
Fig. 9. Comparison of cooling rate at center and outer edge regions with wire rod diameter.
k ρVd ⎞ hforced = 0.683 ⎜⎛ ⎟ d⎝ μ ⎠
0.466
⎛ Cp μ ⎞ ⎝ k ⎠
⎜
Fig. 10. Comparison of cooling rate at center and outer edge regions with air velocity.
0.33
results of experiment and Eq. (1) as a function of wire diameter and air velocity. In other words, the cooling rates in Fig. 10 were fitted with the variables of wire diameter and air velocity at nozzle using the Origin software. The equations can be described as follows:
⎟
(1)
where k, d, ρ, μ, V, and Cp refer to thermal conductivity, wire diameter, density, kinematic viscosity, air velocity, and specific heat, respectively. Although this correlation is strictly valid only at the center region due to the structure similarity between circular cylinder in cross-flow and the shape of wire ring at the center region, its use in the middle and edge regions can be also permissible provided that the ring pitch is sufficiently large. In case of the wire rods for fast cooling with the forced air, the ring pitch is relatively large enough to apply Eq. (1) to the middle and edge regions with a modification of constants in Eq. (1). The cooling rate of wire rod by forced convection may have this kind of formulation. Meanwhile, radiative and natural convective heat transfer are highly related to the cooling condition at the air velocity of 0 m/s. The cooling rates (CR) of wire rod were derived based on the
CR center = (11.6−0.63d) + 0.65V1.12 − 0.037d
(2)
CR edge = (7.8−0.45d) + (1.81−0.128d)V 0.44 + 0.038d
(3)
where the first term represents the contribution of radiative and natural convective heat transfer and the second term represents the contribution of forced convective heat transfer. When the air blower is off for the slow cooling, the roller conveyor also moves the wire ring at a specific velocity. In this case, the air velocity can be set as the conveyor moving speed because the forced convective heat transfer also works in this condition. Fig. 11 shows the comparison between the measured and calculated 316
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Fig. 11. Comparison of the measured and calculated cooling rates of (a) center region and (b) edge region.
wire ring. For instance, the cooling rate of wire ring with 63 mm pitch increased approximately 70% in comparison with the wire ring with 25 mm pitch at the edge region. This result indicates that the ring pitch is one of the most important parameters for the uniform cooling of wire ring in the Stelmor type cooling process. In order to analyze the effect of wire ring pitch in more detail, tensile strength was measured after air cooling tests as summarized in Table 1 and Fig. 3b. Fig. 13 shows the standard deviation of tensile strength with the ring pitch. The deviation of tensile strength increased with decreasing ring pitch, which is consistent with the results of cooling rate as a function of ring pitch as shown in Fig. 12. The standard deviation of tensile strength was reduced to about 10 MPa at the ring pitch of 100 mm. It is obvious that the ring pitch needs to be maximized to decrease the deviation of mechanical properties within wire ring.
cooling rates at the temperature of 750 °C based on the Eqs. (2) and (3). All the calculated values were found to be in good agreement with the corresponding measured values at the center region: the relative differences were less than 7%. Meanwhile, two values were somewhat different at the edge region due to the complex geometry of wire ring at the edge region as shown in Fig. 6. Overall, the proposed equations are capable of predicting the cooling rate of wire ring at the center and edge regions under the different cooling conditions. 3.3. Effect of wire ring pitch The ring pitch is a important parameter in Stelmor type cooling process because ring pitch controls the packing density of wire ring [18], which means ring pitch is highly related to the cooling rate of wire ring. The ring pitch is calculated using Eq. (4).
P=
4. Discussion
πDVconveyor Vrolling
(4)
The most interesting characteristic of the present study is the higher cooling rate of middle region in wire ring compared to the center region under the air blowing cooling conditions, which is inconsistent with the general knowledge. Moreover, the inner edge region cooled fast at the air velocity of 20 m/s compared to the center region. Obviously, the ring density at the middle and edge regions is higher than that of the center region [17]; therefore, the cooling rate of wire ring at the middle and edge regions can be lower than that of the center region regardless of the cooling conditions. However, the inverse results were derived at the air blowing cooling conditions in this study. Accordingly, it is essential to quantitatively evaluate the ring density. A constant ring pitch was assumed at the specific cooling condition to calculate the ring
where P, D, Vconveyor, and Vrolling refer to ring pitch, wire ring diameter, conveyor speed, and finial rolling speed, respectively. Eq. (4) indicates that the cooling rate can be tailored by these process parameters as well as air velocity and wire diameter. Fig. 12 shows the measured cooling rate of the 13 mm-diameter wire rod as a function of ring pitch and air velocity. Interestingly, the center regions had a similar cooling rate regardless of the ring pitch, which means the cooling history at the center region is independent of the ring pitch in the general cooling conditions. On the other hand, the edge regions had a big difference with the ring pitch: the cooling rate dramatically decreased with decreasing ring pitch, resulting in a high deviation of cooling rate within
Fig. 12. (a) Schematic explanation of ring pitch and (b) comparison of cooling rate of 13 mm diameter wire rod at center and edge regions with air velocity and ring pitch. 317
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easy to understand the unprecedented phenomenon of cooling rate difference between center and middle/inner edge using the calculated ring density. Therefore, a computer simulation was applied to analyze the velocity distribution around wire ring. Fluent commercial software, ANSYS version 17, was used in simulating wire rod cooling process with the 2D module. Steady state and realizable k-ε turbulence model were applied [22]. To shorten the calculation time, the half of full geometry was simulated stemming from the symmetrical constraints of wire ring in nature. The wire diameter is 13 mm and the wire ring size is 650 mm. The air velocity at nozzle was set as a constant velocity of 20 m/s and other process parameters were kept same as the actual experimental conditions. The total number of grids in the computational domain was chosen approximately 1.41 × 105 cells based on the grid convergence test. The solution of discretization equations and numerical skill were reported in detail by Patankar [23], and will not be handled here. Fig. 16a shows the contour of velocity vector at the plane perpendicular to the moving direction of wire ring. As expected, the velocity of forced air around outer edge region was much lower than that around center region, which is confirmed by the velocity profile along the transverse direction of moving wire ring as shown in Fig. 16b. Interestingly, the air around middle and inner edge regions of wire ring had a higher velocity compared to the air around center region because of the small distance between wire rods at the middle and inner edge regions. In other words, the velocity increased at the small inter-distance between wire rods since the forced air has to pass through the narrow gap as shown in Fig. 17, which increased the forced convective heat transfer, finally increased the cooling rate at the middle and inner edge regions of wire ring during the air blowing cooling conditions. This result is crucial from an industrial point of view. The dichotomous thinking of center and outer edge regions [8,11,14,16–18] cannot eliminate the post heat treatments of wire ring because middle and inner edge regions of wire ring had a higher tensile strength than center or outer edge regions. Therefore, the middle and inner edge regions as well as center and outer edge region are always considered to get a homogeneous microstructure and mechanical properties within wire ring in the Stelmor type cooling process. Ring pitch is a very important parameter in the Stelmor type cooling process because ring pitch controls the packing density of wire ring [18,24], and finally controls the cooling rate and microstructure of the wire ring as shown in Figs. 12 and 13. The ring pitch is highly related to the edge region of wire ring since center and middle regions sustain a single cylinder shape with changing the ring pitch in the general cooling conditions, but the edge region has a more complicated
Fig. 13. Standard deviation of tensile strength of SWRH82A pearlitic steel with ring pitch.
density mathematically, which means the rolling speed, conveyor roller speed, and wire ring size are constant during the specific cooling process. The volume of wire rod was, also, assumed to be equivalent to the 2D projected area to simplify the calculation. The ring density on the roller conveyor can be expressed as follows:
ρi =
D θd 2 i
×2
δP
=
D θd× 2 i D P 2n
2
=
2nθi d P
(5)
where ρi, θi, δ, and n refer to ring density, angle, length of unit grid, and the number of grid, respectively, which is shown in Fig. 14. The δ and n has a following relationship:
δ=
D 2n
(6)
The θi is geometrically calculated by following equation using Fig. 14: n−1
θi = 90−
2δi ⎞ ⎝ D ⎠
∑ θi−cos−1 ⎛ k=0
(7)
where θ0 is a zero and Eq. (7) was calculated with the aid of numerical tool: C language. Fig. 15 shows the calculated results based on Eq. (5). The ring density of the middle and edge region is higher than that of the center region: the center region has the minimum ring density and middle region has approximately 1.3 times higher and inner edge region has 2.2 times higher ring density than the center region. It is not
Fig. 14. Schematic representations to analytically derive the ring density along the transverse direction of wire ring. 318
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Fig. 15. Profile of relative ring density along the transverse direction of wire ring of (a) the total region from outer edge to outer edge and (b) the partial region from inner edge to inner edge.
Fig. 16. (a) Contour of velocity vector and (b) velocity profile along the transverse direction of moving wire ring.
rod cooling process to produce wire rods with desired mechanical properties, especially uniform mechanical properties within wire ring. The ring pitch depends on several process parameters as shown in Eq. (4) and it can be tailored with the combination of these parameters. Meanwhile, most of the wire rod mills use uniform cooling apparatus to minimize the variation of mechanical properties of wire rod by adjusting the air flow distribution in center and edge regions of wire ring [11,15,16]. This study shows that the key factor in determining the amount of air flow rate with regions is the ring pitch, not the diameter of wire rod [24], conveyor speed, air velocity, and temperature of wire rod. Most of the results in this study can be applied to the industrial scale since the off-line simulator was structured after analyzing the real Stelmor cooling equipment. However, the size of wire ring is 650 mm and the maximum air velocity at nozzle is 33 m/s due to the limited simulator scale. In case of real plant, the wire ring size and maximum air velocity are about 1100 mm and 45 m/s, respectively. Therefore, the predicted cooling rate from Eqs. (2) and (3) can be strictly applied to the limited cooling conditions, air velocity between 0 and 33 m/s. In addition, the difference in thermal properties between stainless steel and plane carbon steel was considered to apply the results of this study to the industrial fields. Based on the author's experiences, small modifications are necessary to use Eqs. (2) and (3) according to the steel grade, ambient temperature, and the specific cooling conditions.
Fig. 17. Schematic explanation of air velocity distribution along the transverse direction of moving wire ring.
geometry with decreasing the ring pitch as shown in Fig. 6. The cooling rate of edge region sharply decreased with decreasing ring pitch due to a higher ring density and more complicated ring structure. This phenomenon also explains the good agreement between the measured and calculated cooling rate at the center region and some deviations between two values at the edge region as shown in Fig. 11. In the center region, it can obey the empirical formula with changing the wire rod diameter, air velocity, and ring pitch due to the same cooling mechanism: the cross flow over circular cylinders [11]. Meanwhile, the ring geometry of edge region can be somewhat changed with wire rod diameter and ring pitch as shown in Fig. 6; therefore, it is not easy to predict the cooling rate of the edge region with the one estimated regression equation. Furthermore, around edge region, the contour of velocity is complex and it will be varied with changing the ring pitch as shown in Fig. 16a. From a practical point of view in wire rod industries, the ring pitch control is considered as a great starting point in the wire
5. Conclusions Based on the systematic study on the Stelmor type cooling process using the well-designed off-line simulator and numerical simulation, the following conclusions can be drawn. 319
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1. As the wire ring cooled on the Stelmor cooling conveyor, the maximum temperature deviation occurred when the center temperature reached approximately 350 °C. The temperature deviation within wire ring increased, and then decreased with increasing air velocity: the maximum temperature deviation was approximately 140 °C and occurred at the air velocity of 10 m/s. 2. The middle and inner edge regions of wire ring had a higher cooling rate than the center region during the air blowing cooling conditions because the air around middle and inner edge regions had a higher velocity compared to the air around center region. This is due to the smaller distance between wire rods at the middle and inner edge regions. 3. The ring pitch controls the density of wire ring, and finally controls the cooling rate, microstructure, and mechanical properties. The ring pitch is strongly related to the cooling rate of the edge region since the cooling rate of edge region dramatically decreased with decreasing ring pitch stemming from the higher ring density and more complicated ring structure. 4. The cooling rates of wire ring at the center and edge regions were predicted using the empirical equations as a function of wire diameter and air velocity. These equations are helpful in designing the cooling condition to produce high quality wire rod steels.
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