Effect of Air Temperature on the Thermal Behavior and Mechanical Properties of Wire Rod Steel during Stelmor Cooling

Abstract

The effect of air temperature (T_a) on the thermal behavior and mechanical properties of steel wire rods is investigated during the Stelmor air cooling process using a numerical model and an offline cooling simulator. During the Stelmor cooling process, the temperature of the wire rod measured in the summer (28°C) is higher than that in the winter (4°C). The average temperature difference of the wire rod between the seasons is approximately 5°C. In addition, the tensile strength (TS) in the summer is lower than that in the winter: the average TS difference between the seasons is approximately 19 MPa. The different cooling rates of the wire rod depending on T_a are associated with the simple temperature difference between seasons instead of variations in the thermophysical properties of air with temperature. The variation in the cooling rate of the wire rod with T_a is affected significantly by forced convection because the absolute value of the forced convection is approximately 10 times higher than that of natural convection, and the heat flux by thermal radiation is almost unchanged by T_a. The forced convective heat transfer coefficient decreases with T_a because the Reynolds number decreases owing to the decrease in density and increase in kinematic viscosity of air as T_a increases. The deviation in temperature of the wire rod between the summer and winter seasons increases in a wire rod with a small diameter that is fabricated using high forced air because the amount of forced convection increases as the wire diameter decreases and the applied air velocity increases. It is concluded that different working conditions are necessary depending on the T_a, particularly when the wire diameter is small, the blower power is high, and the laying head temperature is high during the Stelmor cooling process.

1. Introduction

In the manufacturing of wire rod steels measuring 5–25 mm in diameter in mass-scale operations, the Stelmor type cooling process is typically adopted owing to its wide cooling rate spectrum afforded by the use of simple cooling equipment.^1,2,3,4,5) For slow cooling, insulator covers are used because they reduce the thermal radiation from the wire rod to the surrounding. Air-blowing fans are used to cool wire rods rapidly because they increase the heat transfer mechanism of forced convection.⁶⁾ Consequently, most steel wire rod manufactures adopt the Stelmor type cooling process to achieve their price competitiveness in the wire rod steel industry.^7,8)

However, in spite of its competitiveness in term of production cost, the Stelmor type cooling process presents some disadvantages that must be solved to satisfy the higher quality demands of customers. One of the issues in Stelmor cooling is the deviation in the mechanical properties of the wire rod depending on season. In other words, the tensile strength (TS) of the wire rod differs between the summer and winter seasons. For example, the TS of the wire rod in the summer was lower than that in the winter. This TS deviation with season causes quality issues in the final product and operating problems in the downstream wire drawing process. In addition, this fluctuation of mechanical properties depending on season necessitated downstream annealing, normalizing, or patenting heat treatments.

In case of pearlitic steels, which are primarily fabricated using the Stelmor cooling process with forced air, many steel making companies have attempted to obtain a fine pearlite microstructure by controlling the cooling rate, since the strength of pearlitic steels increases with decreasing lamellar spacing.^2,9,10,11) Accordingly, the reduced cooling rate of the wire rod with increasing air temperature (T_a) decreases the TS of pearlitic steel.¹²⁾ In addition, the range of required specification in TS and microstructures of pearlitic steels becomes narrow as the strength of wire rod increases. In this harsh situation, the TS deviation of wire rod depending on T_a or season becomes a more significant issue in the wire rod manufacturing industry to meet the stringent customer’s demands.

Although several studies exist regarding TS deviation in the wire ring owing to the wire ring geometry during Stelmor cooling, few studies have been reported regarding the effect of T_a on the cooling behavior in Stelmor cooling. For example, the TS deviation of the wire ring reduced by using the different coolants such as molten salt bath,^13,14) hot water,^15,16) and mist.¹⁷⁾ In these processes, new coolants are introduced, which increases the cooling rate of the wire rod as well as the uniformity of the mechanical properties of the wire ring. However, the application of new coolants is costly and difficult to implement in industrial plants. Hence, a practical solution for controlling the cooling rate is to modify the process conditions of the Stelmor cooling process. Particularly, tailoring the air velocity with region of the wire ring might be a practical approach. For example, some researchers increased the TS uniformity of wire ring by modifying the distribution of air velocity during the Stelmor cooling process.^18,19,20)

However, all of them have not considered the variation in T_a based on season. To the best of our knowledge, only one study was reported regarding the thermal behavior of a wire ring depending on T_a. Xue et al.¹²⁾ reported the effect of T_a and humidity on the thermal behavior of wire rods in a Stelmor type air cooling process using SWRH82B pearlitic steel with 12.5 mm in diameter. They showed that the TS of the wire rod varied with the weather conditions, i.e., the TS of the wire rod decreased with T_a. Furthermore, they discovered that the cooling rate increased with decreasing T_a and increasing air humidity. However, the study primarily focused on the results of the cooling rate of the wire rod with T_a and the corresponding humidity. Accordingly, some ambiguities need to be clarified, i.e., the underlying cooling mechanism and the effects of process conditions on the cooling behavior of the wire rod depending on T_a.

Meanwhile, studies pertaining to the water temperature for plate and sheet cooling during hot steel slab rolling have been extensively reported because the thermal properties and cooling mechanism of water vary with water temperature.^21,22,23) These results reveal that the cooling rate of the steel plate or sheet increased with decreasing water temperature.

Therefore, this study investigated the effect of T_a depending on season on the cooling rate of wire rods to understand how it affects the mechanical properties of the wire ring. In addition, the effects of air velocity, wire diameter, and laying head (LH) temperature on the cooling behavior of the wire rod with T_a were evaluated to propose the optimal design options for process designers during Stelmor type cooling. The results were primarily derived via both numerical simulations using a thermal model and experiments using an offline Stelmor cooling simulator.

2. Experimental Procedures

2.1. Stelmor Cooling Test Using Offline Simulator

A schematic diagram and an image of an offline Stelmor cooling simulator used in the present study are shown in Fig. 1. The offline simulator primarily comprises a conveyor roller, an electric reheating furnace, a centrifugal air blower, a duct, an air nozzle, and a wire ring. The duct has mesh wire screens to make the uniform flow from the blower to the air nozzle. The wire rod was heated to 880°C for the temperature measurement test and 1050°C for the mechanical test under N₂ gas to reduce the formation of oxide scale on the wire surface. After 600 s-soaking at the target heating temperature, the wire rod was drawn to a conveyor roller with forced air. The wire rod was cooled in the forced air on the conveyor roller while it was shifted back and forth owing to the limited length of the conveyor roller of the offline simulator as shown in Fig. 1. The diameter of the wire ring was 650 mm and its ring pitch was 45 mm because the width of the cooling simulator used in this study was 850 mm. SWRH82A high carbon steel with a 10 mm-diameters was used (Table 1) because it is generally produced under forced air cooling conditions via Stelmor cooling. The cooling experiments were conducted at an air velocity of 30 m/s. The air velocity at the nozzle was measured using a velocity meter with pitot static tube. The process conditions are presented in Table 2. The test was conducted in the summer and winter seasons using the same process conditions and operators. In other words, same wire ring was used for temperature measurements. Meanwhile, for the measurement of TS, different two wire rings with the same ring conditions such as ring diameter, ring pitch, and ring contact point were used because each wire ring was divided into several pieces after the cooling test to evaluate the TS.

Fig. 1.

Schematic illustration and photograph of offline Stelmor cooling simulator used in this study. (Online version in color.)

Table 1. Chemical compositions of the SWRH82A wire rod steel used in the present study.

Element	C	Mn	Si	P	S	Fe
Weight percent	0.82	0.42	0.2	< 0.01	< 0.01	Balance

Table 2. Working conditions of cooling test using offline Stelmor cooling simulator.

	Parameter	Value
Specimens	Test wire rod steel	SWRH82A
	Wire rod diameter	10 mm
	Ring diameter	650 mm
	Ring pitch	45 mm
Process conditions	Temperature in furnace	880°C for temperature measurement 1050°C for TS measurement
	Soaking time in furnace	600 s
	Air velocity at air nozzle	30 m/s
	Conveyor speed	0.3 m/s
	Average ambient temperature	4.3°C in winter and 27.7°C in summer

2.2. Measurements of Temperature and Mechanical Properties

The temperatures at the center and edge regions of the wire ring were measured using K-type thermocouples with 1.0 mm-diameter, which were embedded in the wire ring before the experiment. Figure 2(a) presents a schematic illustration of the measurement points of temperature in the wire ring using thermocouples and the embedded position of the thermocouple. The hole was drilled to a depth of 5.0 mm in the wire rod, and then the thermocouple was embedded in a hole to reduce the thermal disturbance on the surface of wire rod²⁴⁾ and to avoid the undesired breakage of thermocouples as it travels the conveyor roller. Temperature data were gathered using a multi-channel date recorder at a sampling interval of 0.2 s. The inset in Fig. 2(a) shows that the measured ambient temperature in the winter and summer seasons was approximately 4°C and 28°C, respectively.

Fig. 2.

Schematic illustration of (a) temperature measurement using thermocouple and (b) obtained tensile specimen within wire ring. Inset in (a) shows measured air temperature in winter and summer seasons. (Online version in color.)

The uncertainty of the thermal behavior of the wire rod depending on T_a was primarily achieved based on temperature measurements using thermocouples. The error in this thermocouple was approximately 0.75% of the measured value in the temperature range from 20 to 1250°C. The error of the data recorder was approximately ±0.05%. In addition, the depth accuracy of the thermocouple in the wire rod was to ±0.5 mm. The total error of the measured temperature performed with the thermocouple was determined to within ±3.0%.

Tensile tests were performed at a strain rate of 10⁻³ s⁻¹ using an Instron machine at room temperature. After the cooling experiments in the winter and summer seasons, six wire rings were chosen, subsequently each wire ring was segmented into eight sections as illustrated in Fig. 2(b): 2 in the center region (③⑦), 4 in the middle region (②④⑥⑧), and 2 in the edge region (①⑤). Subsequently, tensile tests were carried out to evaluate the TS and standard deviation of the TS within the wire ring using the same Instron machine. The yield strength and elongation were not measured because no standard tensile specimens were used in this mechanical test. In other words, tensile tests were performed in the state of the wire rod.

3. Numerical Model

3.1. Physical Problem and Assumptions

Figure 3 shows a schematic illustration of the numerical modeling under consideration. Heat transfer along the longitudinal direction of the wire rod was disregarded because the wire rod was infinitely long and the temperature difference along the longitudinal direction was much smaller than that along the radial direction of the wire rod. Therefore, the conductive heat transfer along the longitudinal direction of the wire during the cooling process is negligible. However, the heat transfer along the radial direction of the wire rod is not negligible because of the mass effect of the wire. Additionally, the cooling of the wire ring by conductive heat transfer associated with the contact between the wire ring and conveyor roller was disregarded in this study. In this case, the wire was assumed to be axisymmetric, indicating that one-dimensional (1D) analysis is sufficient for analyzing the temperature field of the wire rod during Stelmor cooling.

Fig. 3.

(a) Physical domain, (b) associated heat transfer mechanisms, and (c) typical microstructure of SWRH82A wire rod steel during Stelmor cooling process under forced air. (Online version in color.)

The total heat flux on the wire surface was used as the thermal boundary condition. During the Stelmor cooling process, forced convective heat transfer needs to be considered because the wire rod is cooled by the forced air driven by the fan under the conveyor roller.²⁵⁾ In addition, both the radiative and natural convective heat transfers must be considered because of the high temperature difference between the wire rod and ambient air.^26,27)

Phase transformation occurs during the cooling processes of plain carbon steels. Austenitic phase is transformed into pearlitic, ferritic, and/or martensitic phases. During the phase transformation of steels, latent heat is released^28,29,30) because each phase has different specific heats. Accordingly, the latent heat caused by the phase transformation in plain carbon steels needs to be considered during the cooling process because the phase transformation affects the thermal behavior of steels. Based on the microstructural evolution of the SWRH82A wire rod steel after the cooling process under forced air (Fig. 3), austenite was fully transformed into pearlite in this steel. In other words, no pro-eutectoid ferrite, pro-eutectoid cementite, martensite, and bainite were generated during the cooling process under forced air.

The thermophysical properties of both the wire rod steel and air were only described as function of temperature herein.

3.2. Thermophysical Properties of Air Depending on Temperature

The thermal properties of air depend on temperature, and the variation in the thermal properties of air changed the heat transfer coefficient during the cooling process of the wire rod. Figure 4 shows the density (ρ_a), specific heat (c_p,a), kinematic viscosity (υ), thermal diffusivity (α), thermal conductivity (k_a), and volumetric thermal expansion coefficient (β) of air as a function of temperature.³¹⁾ It is observed that c_p,a, υ, α, and k_a increase with T_a, whereas ρ_a and β decrease with T_a.

Fig. 4.

Thermophysical properties of air as a function of temperature: (a) density and specific heat, (b) kinematic viscosity and thermal diffusivity, (c) thermal conductivity, and (d) volumetric thermal expansion coefficient. (Online version in color.)

3.3. Thermal Properties of Eutectoid Plain Carbon Steel

The density, thermal conductivity, and specific heat of steel are dependent on temperature. Figure 5 presents the thermal conductivity and specific heat of the eutectoid steel as a function of temperature based on Ref. 32). In pearlitic steels, the thermal conductivity (k_p) tends to decrease with increasing temperature, whereas the thermal conductivity of austenitic steels (k_γ) increased gradually with temperature. The specific heat of both microstructures increased with temperature. During cooling, the k and c_p of the wire rod were obtained using the calculation of each phase fraction (X_i) as follows:   

$$k\left(T\right)={\sum }_{i=\gamma ,p}{k}_i\left(T\right)X_i$$(1)

  

$$c_p\left(T\right)={\sum }_{i=\gamma ,p}{c}_{p,i}\left(T\right)X_i$$(2)

Fig. 5.

Variations in (a) thermal conductivity and (b) specific heat of eutectoid plain carbon steel used in this study as a function of temperature. (Online version in color.)

Meanwhile, the density of the wire rod was calculated using the following equation, regardless of the phase.^32,33)   

$$\rho \left(T\right)=7\mathrm{\hspace{0.17em} }840-0.367T\left(°\mathrm{C}\right)$$(3)

3.4. Governing Equation and Boundary Conditions

Since the temperature gradients along the axial and angular directions of the wire rod were disregarded, the temperature distribution of the wire rod was governed by the following 1D transient conduction equation in cylindrical coordinates:   

$$\rho c_p\frac{\partial T}{\partial t}=\frac{\partial }{\partial r}\left(k\frac{\partial T}{\partial r}\right)+\frac{1}{r}\left(k\frac{\partial T}{\partial r}\right)+q_L$$(4)

where t denotes the time, and r is the radial coordinate of the domain. q_L is the heat source generated by the latent heat released by the phase transformation of the wire rod during the cooling process. The amount of heat released from the phase transformation is typically calculated using the enthalpy difference (ΔH) and volume fraction change (ΔX) of each phase in a specified time step (Δt).^34,35) In this study, eutectoid steel was cooled under forced air cooling conditions; therefore, the austenite was fully transformed into pearlite (Fig. 3). In this case, the heat generated by the phase transformation can be calculated as follows:   

$$q_L=\rho \mathrm{\Delta }{H}_p\frac{\mathrm{\Delta }{X}_p}{\mathrm{\Delta }t}$$(5)

The Avrami-type equation is typically used to calculate X during the cooling process.³⁶⁾ In this study, ΔH was used based on the results of Kramer et al.³⁷⁾ as shown in Fig. 6, because the chemical composition of the present steel was similar to that of Kramer et al.’s and several researchers have well predicted the thermal behavior of plain carbon steels using this result.^25,34,38)

Fig. 6.

Variation in enthalpy of transformation in plain carbon steel during phase transformation with temperature. (Online version in color.)

Boundary and initial conditions must be specified to solve Eq. (4). At the center of the wire rod, it was assumed that the temperature distribution was symmetrical, and heat was dissipated at the surface of the wire rod as follows:   

$$\frac{\partial T}{\partial r}=0\hspace{1em}\mathrm{a}\mathrm{t}\mathrm{\hspace{0.17em} }\hspace{0.17em}r=0$$(6)

  

$$-k\left(T\right)\frac{\partial T}{\partial r}=h_t\left(T_s-T_{\infty }\right)\hspace{1em}at\mathrm{\hspace{0.17em} } r=R$$(7)

where R is the radius of the wire rod. h_t is the total heat transfer coefficient, which mainly comprises three heat transfer coefficients, as follows:   

$$h_t=h_f+h_n+h_r$$(8)

where h_f, h_n, and h_r indicate the forced convective, natural convective, and radiative heat transfer coefficients, respectively.

It is assumed that the wire rod has a constant temperature of 880°C prior to cooling.

3.5. Heat Transfer Coefficients

After hot rolling, wire ring on the conveyer roller in Stelmor cooling process primarily dissipates heat through forced convective, radiative, and natural convective heat transfer as illustrated in Fig. 3. The wire rod on the conveyer roller is assumed to be a circular cylinder. In this case, the wire rod can be cooled by a cross-flow. It is noteworthy that the assumption mentioned above is only valid in the central region of the wire ring owing to the geometric similarity.³⁹⁾ Under the assumption, the heat transfer coefficient can be calculated using well-established simple empirical equations.

Firstly, the heat of the wire rod was dissipated by forced air under the conveyor roller, that is, forced convection. It has been widely reported^{5,26,34,40,41,42)} that the diameter (D) of the wire rod and the air velocity (V) are the main parameters governing the cooling behavior of the wire rod. Accordingly, the forced convective heat transfer coefficient of the circular cylinder under cross-flow is empirically represented as follows:³¹⁾   

$$h_f=C\frac{k}{D}R{e}_D{}^{n}P{r}^{0.33}$$(9)

where C and n are constants that are empirically determined by the Reynolds (Re) number as listed in Table 3. In such a case, Re is defined as follows:   

$$R{e}_D=\frac{VD}{v}$$(10)

The Prantl (Pr) number is defined as the ratio of the kinematic viscosity to the thermal diffusivity of air as follows:   

$$Pr=\frac{v}{\alpha }$$(11)

Table 3. C and n values with Re number for forced convection.

ReD	C	n
4–40	0.911	0.385
40–4000	0.683	0.466
4000–40000	0.193	0.618
400000–400000	0.027	0.805

Secondly, the heat of wire rod was dissipated through an air flow driven by the density difference, that is, natural convection. Although natural convection does not dominant the heat dissipation of the wire rod, it cannot be disregarded, and the coefficient of natural convection was calculated using the following empirical equation:³¹⁾   

$$h_n=C\frac{k}{D}R{a}_D{}^n$$(12)

here both C and n are empirically determined constants using the Rayleigh (Ra) number as listed in Table 4. In this cooling system, Ra is represented as follows:   

$$R{a}_D=\frac{g\beta \left(T_s-T_{\infty }\right)D^3}{v\alpha }$$(13)

where g is the gravitational acceleration.

Table 4. C and n values with Ra number for natural convection.

RaD	C	n
10−10–10−2	0.675	0.058
10−2–102	1.020	0.148
102–104	0.850	0.188
104–107	0.480	0.250

Thirdly, the heat of the wire ring was dissipated into the ambient via radiation. Although geometric factors including the ring pitch, the ring shape, and the distance from the ring to surrounding mechanical components affect the radiation,⁴³⁾ the radiative heat transfer coefficient is generally calculated as follows:   

$$h_r=\frac{{\epsilon }_s\sigma \left(T_s^4-T_{\infty }^4\right)}{\left(T_s-T_{\infty }\right)}$$(14)

where ε_s is the total emissivity including the shape factor, and ε_s was calculated based on the results of experimental tests performed in this study. Here, σ is the Stefan-Boltzmann constant, T_s the surface temperature of the wire rods, and T_∞ the surrounding or ambient temperature. The dimensionless numbers and thermal properties of air were obtained based on the film temperature (T_f), which was calculated as follows:   

$$T_f=\frac{T_s+T_{\infty }}{2}$$(15)

3.6. Phase Transformation Model

It is known that the isothermal kinetics of the austenite decomposition can be described based on the Avrami-type equation³⁶⁾ as follows:   

$$X=X^e\left[1-exp\left(-b{t}^n\right)\right]$$(16)

here X^e indicates the thermodynamic equilibrium fraction, which is determined based on the equilibrium phase diagram at a specific pressure, chemical composition, and temperature. The b and n values are important constants to be determined experimentally for the prediction of the phase transformation of metals.⁴⁴⁾ The n value is assumed to be constant regardless of temperature when the mechanism of phase transformation is fixed, whereas the b value is dependent on the temperature and phase transformation mechanism.

To describe the non-isothermal kinetics of metals during the continuous cooling process, Eq. (16) is extended based on the theory of the additivity rule proposed by Scheil.^45,46) Diffusional phase transformations occur after the incubation period during the cooling process. According to the additivity rule, a continuous cooling process or non-isothermal kinetics are regarded as the summation of the infinitesimal segments of the isothermal step. In this case, the incubation time is assumed to be complete and phase transformation begins when the following equation is satisfied:   

$${\sum }_{t=0}^t\frac{\mathrm{\Delta }t}{\tau \left(T_i\right)}=1$$(17)

where τ is the time required for the transformation start under isothermal condition at the current isotherm T_i or the incubation time of time-temperature-transformation diagram. The phase fraction transformed during the i th step (X_i) is determined as following equation:^47,48)   

$$X_i=X_i^e\left[1-exp\left(-b{(t^{\prime }+\mathrm{\Delta }t)}^n\right)\right]$$(18)

  

$$t^{\prime }={\left[-\frac{1}{b}ln\left(1-\frac{X_{i-1}}{X_i^e}\right)\right]}^{\frac{1}{n}}$$(19)

here t′ is the transformation time required to achieve X_i−1 in the i th step. The latent heat by phase transformation in Eq. (5) was calculated using the following incremental fraction transformed in the i th time step:   

$$\mathrm{\Delta }{X}_i=X_i-X_{i-1}$$(20)

The b and n values need to be determined by performing the isothermal cooling experiments. In this study, no experiment was conducted to determine the b and n values because the b and n values for pearlitic reaction have been reported previously. For example, Campebell et al.²⁵⁾ successfully predicted the temperature history of plain carbon steels during a Stelmor type air cooling process. Therefore, the b and n values adopted by Campebell et al.⁴⁹⁾ were used in the present study. For 0.82 wt.% carbon steel, the n value was set to 2.15 regardless of temperature, and the b value was described as a function of temperature as shown in Fig. 7. For the calculation of n, b, and incubation time, the effects of plastic deformation prior to the cooling process and austenite grain size on the transformation kinetics were not considered in this study.

Fig. 7.

Variation in ln b in pearlitic steel with temperature during the cooling process. (Online version in color.)

3.7. Numerical Methods and Grid Independency

The heat transfer equation in Eq. (4) is impossible to be solved owing to the temperature dependency of the thermal properties and latent heat by phase transformation; therefore, it was discretized in space and time using a central difference scheme to simulate the heat conduction phenomenon of the wire rod, as described by Patnakar.⁵⁰⁾ The discretized equations were solved iteratively using the tridiagonal matrix algorithm until the temperature contour within the wire rod satisfied the convergence criterion as follows:   

$$max\left(\frac{\left|T_i-T_i^{old}\right|}{T_i}\right)\le {10}^{-6}$$(21)

where T_i and $T_{\text{i}}^{\text{old}}$ are the present and previous iteration values in the time step, respectively.

A grid convergence test was performed using the three mesh systems for a time step of 0.5 s: the first one had 21 elements; the second 31 elements; and the third 41 elements. Based on the results of the temperature profiles, the three mesh systems showed similar results; therefore, the first grid system was adopted.

4. Results

4.1. Experimental Results

Figure 8(a) shows the measured temperature histories of the wire ring at the central and edge regions with T_a. In both regions, the temperatures measured during the summer season were higher than those in the winter season. For a better understanding of the temperature deviation between the two seasons, the temperature difference (ΔT) of the wire rod was defined as following equation, and the results are shown in Fig. 8(b).   

$$\mathrm{\Delta }T=T_{summer}-T_{winter}$$(22)

Fig. 8.

Comparison of measured temperature (a) profiles and (b) differences in wire ring between summer and winter seasons with the region. (Online version in color.)

The average temperature difference of the wire rod with the season was approximately 5°C, and the temperature difference at the edge region of the wire rod between the two seasons was somewhat higher than that at the center region. Furthermore, Fig. 8(b) shows that the temperature difference between the two seasons did not increase monotonically with the cooling time owing to the latent heat released by the phase transformation of the pearlitic steel during the cooling process.

Figure 9(a) compares the measured TS of the wire ring manufactured during the summer and winter seasons. The TS of the wire rod fabricated during the summer season was lower than that in the winter season. The average TS difference between the seasons was approximately 19 MPa. The edge region exhibited a higher TS deviation despite a lower number of tensile specimens compared with the center and middle regions. In addition, the standard deviation of the TS decreased in the winter season compared with the summer season as shown in Fig. 9(b), which is unexpected and difficult to explain in this study.

Fig. 9.

Comparison of (a) tensile strength with ring position and (b) standard deviation of tensile strength with season. Number in (a) indicates the wire ring number in Fig. 2(b). (Online version in color.)

4.2. Numerical Results

4.2.1. Model Validation

Figure 10(a) compares the temperature profiles at the central region between the experimental test and numerical simulation with the cooling time. In this study, ε_s was assumed to be 0.65 based on the temperature comparison between the experiment and simulation. The predicted temperatures of the center region exhibited a reasonable agreement with the measured values although the results of the model were over-predicted during the phase transformation of the steel. This indicates that the phase transformation model used in this study needs to be modified. Especially, the ΔH by phase transformation used in this study should be reduced based on the present results.

Fig. 10.

Comparison of the measured temperature profiles using offline simulator and predicted temperature profiles using model at (a) center and (b) edge regions. (Online version in color.)

The edge temperature of the wire ring is difficult to predict owing to the geometric complexity of the wire ring. In this study, the correction factor (ϕ) was used to predict the temperature in the edge region based on the h_t in the center region as follows:   

$$h_{t,e}=\phi \mathrm{\hspace{0.17em} }{h}_{t,c}$$(23)

In other words, the value of ϕ was determined by comparing the predicted temperatures with the measured temperatures of the edge regions as a function of the cooling time. The obtained ϕ value was approximately 0.72 as shown in Fig. 10(b). The model also over-predicted the temperature in the edge region during the phase transformation.

Overall, the predicted temperature of the wire rod was in good agreement before the phase transformation using the correction factor; however, the temperature by the present model was overpredicted compared with measured temperature during the phase transformation. These results showed that the phase transformation model or each coefficient for prediction used in this study should be modified to obtain the more accurate result. However, this study was conducted based on the assumption that the mechanical properties of the wire ring depend on the cooling rate of wire rod until just before the phase transformation of the material. Accordingly, additional modifications of phase transformation model were not conducted in this study.

4.2.2. Influence of Air Temperature

To evaluate the effect of T_a on the thermal behavior of the wire ring during Stelmor cooling, the proposed model was executed with different T_a values. Figure 11(a) compares the temperature histories of the wire ring at the center region for different T_a using the model. Figure 11(b) shows a comparison of the cooling rate and transformation starting temperature based on Fig. 11(a). The cooling rate was calculated based on the wire surface temperature at 700°C, and the transformation starting temperature was defined as the minimum temperature in the initial stage of the phase transformation of the steel. The transformation starting temperature increased and the cooling rate decreased as T_a increased. Based on the present results in center region of the wire ring, the relation between cooling rate (CR) and TS of this wire rod can be derived as follows:   

$$\mathrm{T}\mathrm{S}\left(\mathrm{M}\mathrm{P}\mathrm{a}\right)=523.8+51.4\cdot \mathrm{C}\mathrm{R}\left(°\mathrm{C}/\mathrm{s}\right)$$(24)

This result showed that TS increased with increasing cooling rate, which is highly related to the grain refinement effect by the small lamellar spacing of pearlitic steel with increasing cooling rate because it has been reported that the lamellar spacing of pearlitic steel decreases as the cooling rate increases or the transformation starting temperature decreases.⁵¹⁾

Fig. 11.

(a) Comparison of temperature profiles of wire rod and (b) variations in the cooling rate and transformation starting temperature at center region with air temperature.

4.2.3. Influence of Air Velocity

Figure 12(a) compares the temperature histories of the wire ring at the central region with the air velocity using the model. Apparently, the cooling rate increased with the air velocity. The temperature difference in the wire rod between the seasons increased with increasing the air velocity as shown in Fig. 12(b), indicating that the deviation in the mechanical properties of the wire rod manufactured by forced air increased between the seasons as compared with the wire rod manufactured without blowing. In particular, the wire rods fabricated using the insulator cover was not significantly affected by the T_a or season.

Fig. 12.

Comparison of (a) center temperature profiles and (b) temperature differences of wire ring between summer and winter seasons for the different air velocities.

4.2.4. Influence of Wire Rod Diameter

To understand the influence of the wire rod diameter on the thermal behavior of the steel with T_a during the Stelmor cooling process, the thermal behavior was evaluated using the model. Figure 13(a) compares the temperature profiles of the wire rod at the central region with D and T_a. As expected, the cooling rate increased significantly as D decreased.⁵²⁾ In addition, the temperature difference of the wire rod with T_a increased with decreasing D as shown in Fig. 13(b). The results indicate that the mechanical properties of the wire rods with a small diameter were sensitive to the T_a or season. Therefore, much attention is necessary for the wire rod with a small diameter with season or T_a.

Fig. 13.

Comparison of (a) center temperature profiles and (b) temperature differences of wire rod between summer and winter seasons for different wire diameters.

4.2.5. Influence of LH Temperature

The LH temperature is an important process parameter in Stelmor cooling because it is the starting temperature for the cooling of the wire rod.²⁶⁾ To evaluate the effect of the LH temperature on the thermal behavior of the wire rod with T_a or season, the temperature profile was predicted using the model. Figure 14(a) compares the temperature profiles of the wire rod at the central region for different LH temperatures. Additionally, the temperature difference of the wire rod with the LH temperature was compared as shown in Fig. 14(b). The influence of the LH temperature on the thermal behavior of the wire rod with T_a was insignificant. However, as the LH temperature decreased, the temperature deviation of the wire rod before the phase transformation decreased, resulting in a low deviation of the mechanical properties with T_a. Accordingly, the author believes that the deviation in the mechanical properties of the wire rod decreases with T_a or season by reducing the LH temperature.

Fig. 14.

Comparison of (a) center temperature profiles and (b) temperature differences in wire rod between summer and winter seasons for different laying head temperatures. (Online version in color.)

5. Discussion

5.1. Comparison of Heat Flux by Air Properties and Temperature Difference with Season

Based on the experimental and numerical results, the cooling rate and TS of the wire rod decreased with increasing T_a, which can cause consumer’s dissatisfaction in terms of the quality. Figure 15 compares the heat flux by forced convection, natural convection, and radiation with T_a. In this calculation, T_s and air velocity were assumed to be 700°C and 30 m/s, respectively. Approximately 70%, 20%, and 10% of the total heat were dissipated by forced convection, radiation, and natural convection, respectively, as shown in Fig. 15(b). The natural convection was relatively insignificant in the air blowing cooling conditions, however it cannot be disregarded in the no blowing cooling conditions. Meanwhile, radiative heat transfer was dominant during the cooling process of hot-rolled steels because the temperature of the specimen is high, in particular no blowing process conditions. That is, radiation and natural convection were strongly associated with the process conditions at an air velocity of 0 m/s. The heat flux by radiation was almost unaffected by the T_a (Fig. 15(d)) because it is proportional to the fourth power of each absolute temperature as shown in Eq. (14), indicating that the thermal behavior of the wire is insensitive to T_a in the range of conventional T_a. In contrast, the heat flux by forced convection and natural convection decreased with increasing T_a (Figs. 15(c) and 15(d)). Accordingly, the total heat flux decreased with increasing T_a.

Fig. 15.

Comparison of (a) absolute values and (b) percentage of heat flux in each heat transfer mechanism. (c) and (d) show heat flux values with rescale of (a). (Online version in color.)

The reduced total heat flux with increasing T_a is attributable to two factors: the variation in the thermophysical properties of air and the driving force of heat transfer by the temperature difference between the wire surface and ambient temperatures. Based on Eq. (7), the thermophysical properties of air affect the heat transfer coefficient, i.e., h_t, and the driving force of heat transfer by the temperature difference affects the temperature gradient, i.e., T_s − T_∞.

Figure 16(a) shows the comparison of heat flux with constant thermophysical properties of air. The air properties were fixed to the properties at 0°C. The variations in the each heat flux were similar to the variations in that at Fig. 15. In contrast, the heat flux was not relatively varied with T_a when the temperature difference was set as 700°C, that is, the temperature of air was fixed at 0°C and only the air properties varied with T_a. Figure 16(c) compares the total heat flux of the two conditions with T_a in more detail. The contributions of total heat flux variation with T_a by temperature difference and air properties were approximately 84% and 16%, respectively (Fig. 16(d)), indicating that the variation of cooling rate with season was highly dependent on the temperature difference of T_a with season rather than the difference in thermophysical properties of air with season.

Fig. 16.

Comparison of heat flux variations as a function of air temperature based on (a) constant thermophysical properties of air and (b) constant driving force of temperature difference. Comparison of (c) variations in total heat flux between (a) and (b), and (d) contribution of total heat flux variation with air temperature. (Online version in color.)

Meanwhile, it is noteworthy that the influences of humidity of ambient and emissivity of wire rod with season on the thermal behavior of the wire rod need to be considered to reveal the seasonal effects on the mechanical properties of the wire rod during Stelmor cooling. For example, the standard deviation of TS increased with T_a as shown in Fig. 9(b). In particular, the TS of the edge region in the wire ring showed a small deviation in winter season compared with the summer. What can be obtained from this unexpected result is that the lack of cooling ability with increasing T_a has a great effect on the edge region of the wire ring compared with the center region. However, this phenomenon is difficult to explain only with the approach of T_a with season. The author believes that this phenomenon is associated with the humidity of ambient and the emissivity of the wire rod with season; relevant additional research is currently in progress.

5.2. Working Conditions for Wire Rod during Stelmor Cooling with Season

The deviation in the mechanical properties of the wire rod between the summer and winter seasons needs to be reduced to produce high quality wire rod products; therefore, the optimal cooling conditions should be determined with season. In particular, the wire rod steel manufactured by the forced air in Stelmor cooling exhibited a high difference of cooling rate with season.

To understand the thermal behavior and reduce the deviation of mechanical properties of the wire rod with season, each heat transfer coefficient, i.e., h_f, h_n, and h_r, during the Stelmor cooling process should be evaluated with T_a. The thermophysical properties of air and cooling conditions simultaneously affect the heat transfer coefficients with T_a. Although the influence of the variations in the thermophysical properties of air with T_a on the cooling behavior of the wire rod was not prominent during Stelmor cooling compared with the simple temperature difference between the seasons (section in 5.1), the underlying cooling mechanism of the wire rod with air properties needs to be revealed for the better understand the cooling behavior of the wire rod with season. Figure 17 presents the variations in Re, Pr, and Ra with T_f. The Pr was almost constant with T_f. Meanwhile, Re decreased with T_f because ρ_a decreased (Fig. 4(a)) and υ increased (Fig. 4(b)) with T_f, leading to a decrease in h_f based on Eq. (9). Ra also decreased with T_f because β increased, and α and υ decreased with T_f, leading to a decrease in h_n based on the Eq. (12). The results are well described in Fig. 17(d). Note that the increased k_a with T_f (Fig. 4(c)) has a positive effect on the increase of the h_f and h_n.

Fig. 17.

Variations in (a) Re, (b) Pr, (c) Ra, and (d) h_f and h_n with film temperature of air. (Online version in color.)

Meanwhile, the reduced cooling rate of the wire rod with T_a was strongly dependent on forced convection because the absolute value of h_f was approximately 10 times higher than that of h_n (Fig. 17(d)). In other words, the difference in the cooling rate of the wire rod with T_a increased with increasing the amount of forced convection because the thermal radiation was almost unaffected by the T_a, and the natural convection played a small contribution to the total cooling rate of the wire rod. It should be noted that the influence of the variation in T_a on the cooling rate of the wire rod was small during the slow cooling condition or no air blowing condition because thermal radiation was dominant compared with the natural convection in this cooling condition. That is the main reason why the TS of the wire rod manufactured under slow cooling conditions was almost constant with T_a or season. Accordingly, we need to concentrate on the thermal behavior of the wire rod by the forced convection to understand the effects of T_a on the cooling rate and mechanical properties of the wire rod. Figure 18(a) compares the h_f with the air velocity and temperature. As expected, h_f increased with the air velocity. In addition, the difference in h_f with T_a increased with the air velocity, leading to a higher temperature difference between the summer and winter seasons with increasing air velocity as shown in Fig. 12. Figure 18(b) shows a comparison of the h_f with D and T_a. As shown, h_f increased with decreasing wire diameter, and the difference in h_f with T_a increased with decreasing D, leading to a higher temperature difference between the summer and winter seasons with decreasing D as shown in Fig. 13.

Fig. 18.

Comparison of variations in forced heat transfer coefficient for different (a) air velocities and (b) wire diameters. (Online version in color.)

Overall, the deviations in the cooling rate and corresponding mechanical properties were closely related to the amount of forced convection. Therefore, the deviation in the mechanical properties of the wire rod between the summer and winter seasons increased in the wire rod with a small diameter that was fabricated using high forced air. For example, the pearlitic steel with a 5.5 mm-diameter exhibited a significant deviation in the mechanical properties between the summer and winter seasons because the wire diameter was relatively small, and pearlitic steel is typically manufactured under a strong forced air during the Stelmor cooling process. By contrast, ferritic steel with a 13 mm-diameter indicated an insignificant deviation in the mechanical properties between the summer and winter seasons because the wire diameter was relatively large, and ferritic steel is generally manufactured under the no blow condition in the Stelmor cooling process. Based on the present results, the operating conditions of the wire rod need to be changed depending on T_a to obtain constant material properties regardless of the season or T_a. In particular, it is strongly recommended that the different working conditions are necessary with season as the wire diameter is small, the blower power is high, and LH temperature is high during Stelmor cooling. For example, from the point of view of the mechanical cooling system, it is necessary for the blower to automatically control the amount of forced air as a function of wire rod diameter, LH temperature, and designed blower power by sensing T_a to reduce seasonal variations in mechanical properties of wire rod. In addition, the speed of conveyor roller should be increased with T_a because the deviation in cooling rate within wire ring increased with T_a.

6. Conclusions

Based on a study of the effect T_a on the thermal behavior of wire rod steel during the Stelmor type cooling process using a numerical model and an offline simulator, the following conclusions were obtained:

(1) The temperatures of the wire rod measured in the summer season (28°C) were higher than that in the winter season (4°C) during Stelmor cooling. The average temperature difference of the wire rod between the seasons was approximately 5°C. In addition, the TS of the wire ring fabricated during the summer season was lower than that in the winter season. The average TS difference between the seasons was approximately 19 MPa.

(2) The different cooling rates of the wire rod steel at different T_a were closely associated with simple temperature difference between the seasons rather than the variations in the thermophysical properties of air with temperature during Stelmor cooling.

(3) The reduced cooling rate of the wire rod with T_a was strongly dependent on the forced convection because the absolute value of h_f was approximately 10 times higher than that of h_n, and h_r was almost unaffected by T_a. The h_f decreased with T_a because Re decreased as T_a increased owing to the decrease in ρ_a and increase in υ with T_a.

(4) The deviation in the mechanical properties of the wire rod between the summer and winter seasons increased in the wire rod with a small diameter that was fabricated using high forced air because the amount of forced convection increased with decreasing wire diameter and increasing applied air velocity.

(5) The operating conditions for the wire rod steel needs to be changed with T_a to obtain constant material properties regardless of the season or T_a. In particular, it is strongly recommended that the different operating conditions are necessary as the wire diameter is small, the blower power is high, and LH temperature is high during the Stelmor cooling process.

Conflicts of Interest

The author declares no conflicts of interest.

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT, South Korea) (No. 2021R1A2C1011700).

Nomenclature

c_p: specific heat (J/kgK)

D: wire diameter (mm)

g: acceleration due to gravity (m/s²)

h_f: force convection heat transfer coefficient (W/m²K)

h_n: natural convection heat transfer coefficient (W/m²K)

h_r: radiative heat transfer coefficient (W/m²K)

h_t: total heat transfer coefficient (W/m²K)

ΔH: latent heat by phase transformation (kJ/kg)

k: thermal conductivity (W/mK)

q: heat flux (W/m²)

r: radial coordinate (m)

R: radius of wire rod (m)

Ra_D: Rayleigh number based on wire diameter

Re_D: Reynolds number based on wire diameter

Pr: Prantl number

T: temperature (K)

t: time (s)

V: average air velocity (m/s)

X: transformed phase fraction

Greek symbols

α: thermal diffusivity (m²/s)

β: volumetric thermal expansion coefficient (K⁻¹)

ε_s: total emissivity including shape factor

ν: kinematic viscosity (m²/s)

ρ: density (kg/m³)

σ: Stefan-Boltzmann constant (5.56×10⁻⁸ (W/m²K⁴))

τ: time required for the transformation start under isothermal condition (s)

ϕ: correction factor for heat transfer coefficient at edge region of the wire ring

Subscript

a: air

f: film condition

L: latent heat

p: pearlite

γ: austenite

s: surface

∞: ambient condition

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