Campbell 1991 Parte i

Microstructural Engineering Applied to the Controlled Cooling of Steel Wire Rod: Part I. Experimental Design and Heat Transfer

P.C. CAMPBELL, E.B. HAWBOLT, and J.K. BRIMACOMBE

The goal of this study was to develop a mathematical model which incorporates heat flow, phase transformation kinetics, and property-structure-composition relationships to predict the mechanical properties of steel rod being control cooled under industrial conditions. Thus, the principles of microstructural engineering have been brought to bear on this interdisciplinary problem by combining computer modeling with laboratory measurements of heat flow, austenite decomposition kinetics, microstructure and mechanical properties, and industrial trials to determine heat transfer and obtain rod samples under known conditions. Owing to the length and diversity of the study, it is reported in three parts, 118'191 the first of which is concerned with the heat flow measurements. A relatively simple and reliable technique, involving a preheated steel rod instrumented with a thermocouple secured at its centerline, has been devised to determine the cooling rate in different regions of the moving bed of rod loops on an operating Stelmor line. The measured thermal response of the rod has been analyzed by two transient conduction models (lumped and distributed parameter, respectively) to yield overall heat-transfer coefficients for radiation and convection. The adequacy of the technique has been checked by cooling instrumented rods under well-defined, air crossflow conditions in the laboratory and comparing measured heat-transfer coefficients to values predicted from well-established equations. The industrial thermal measurements have permitted the characterization of a coefficient to account for radiative interaction among adjacent rod loops near the edge and at the center of the bed.

I. INTRODUCTION

MICROSTRUCTURAL engineering is an interdisciplinary approach to the quantitative prediction of the thermal, microstructural, and mechanical property evolution of a metal subjected to a given thermomechanical process. Recent demands on the metals industry to improve product quality and performance, while at the same time reducing cost, have spurred the development of this methodology. The root of the microstructural engineering approach is imbedded in the mathematical model, which links the basic principles of heat and mass transfer and microstructural phenomena to the operating process. In addition, both laboratory experiments and industrial trials are necessary to obtain empirical and semi- empirical relationships characterizing transport phenomena by which the model can be tuned to operating variables.

In the present study, microstructural engineering has been applied to the Stelmor cooling of steel wire rod, Ill a process situated after the finishing stand of a rod mill which provides controlled cooling of the steel through the temperature range of austenite decomposition. The process was developed to replace lead patenting, which

P.C. CAMPBELL, formerly Graduate Student, The University of British Columbia, is with BHP Central Research Laboratories, Wallsend, New South Wales 2287, Australia. E.B. HAWBOLT, Professor, Department of Metals and Materials Engineering and The Centre for Metallurgical Process Engineering, and J.K. BRIMACOMBE, Stelco/NSERC Professor and Director, The Centre for Metallurgical Process Engineering, are with the University of British Columbia, Vancouver, BC V6T 1Z4, Canada.

Manuscript submitted February 14, 1990.

utilized a molten lead bath to impart controlled thermal changes and desired properties to wire rod. In the Stelmor line, forced air is the cooling medium, but more re- cently, other processes have exploited water and molten salt baths to develop desired cooling characteristics, t2,3,aJ Nonetheless, since its development nearly 25 years ago, the Stelmor process has become the most popular patenting technique in the world. In 1982, there were 69 mills with 153 Stelmor lines operating in 26 countries, tSJ Global capacity for the production of wire rod through this process has been estimated to be 21 million tonnes per year. [2]

II. PROCESS DESCRIPT ION

In the Stelmor process, rods exiting the last stand of the rod finishing mill travel through an intermediate zone of water cooling boxes prior to arriving at the laying head (Figure 1). The water boxes provide control over rod temperature prior to continuous cooling, thus affecting prior austenite grain size, while the high-velocity water jets remove surface scale. At the laying head, the rod is looped continuously into coils and placed on the line where the chain conveyor, seen in Figure 1, pulls them through the successive cooling zones. Air is forced up from below the loops by a series of fans in zones to effect control of the rate of rod cooling. For lower carbon grades, where a maximum fraction of proeutectoid ferrite is desired, slow cooling rates, and thus, high transformation temperatures, can be achieved. For higher carbon grades, where a fine pearlite microstructure is desired, maximum cooling rates are employed. Typically, steel arrives at the Stelmor laying head between 840 ~ and 940 ~ is cooled through the austenite-ferrite and austenite-pearlite

METALLURGICAL TRANSACTIONS A VOLUME 22A, NOVEMBER 1991--2769

B

C c (E ip

D

Fig. 1--Schematic diagram of the Stelmor line: (a) delivery pipe and water boxes, (b) laying head, (c) conveyor, (d) plenum chambers, and (e) coil forming chamber.

transformation temperatures (770 ~ to 600 ~ and exits the line at a temperature suitable for handling ( -500 ~

I l l . SCOPE AND OBJECTIVES

In the present study, a mathematical model has been developed to enable prediction of the thermal history, microstructural evolution, and mechanical properties of steel rod cooled by the Stelmor process. In addition, a series of experiments has been conducted in the laboratory at The University of British Columbia (UBC) as well as on an operating Stelmor line at the Stelco Hilton Works No. 2 Rod Mill in Hamilton, ON, Canada. The experiments were performed to obtain data on heat transfer from cooling rods, microstructural evolution, and on microstmcture-composition-property relationships in order to augment existing data in the literature. Part I of this three-part article includes experimental design and results pertaining directly to the heat-transfer aspects of the project. Investigation of the microstructure evolved in continuously cooled rod and correlations developed to link steel composition, microstructure, and mechanical properties are presented in Part II. uS] Formulation, val- idation, and predictions of the mathematical model are given in Part III. u91

Turning specifically to Part I, it was realized at the outset that within the timeframe of this project, heat transfer on a Stelmor line would be too complex to predict accurately from first principles. Both the forced convection of air through the array of rod loops and the radiative interchange among them could not be charac- terized easily from existing correlations. Thus, a reliable technique was sought to measure the cooling conditions in the relatively hostile environment of a Stelmor line. This was accomplished by instrumenting lengths of steel rod with thermocouples at the centerline and measuring the thermal response. The temperature-time results were then utilized to calculate heat-transfer coefficients as a function of process parameters. The method was checked first in the laboratory under well-defined air cross flow conditions. Correlations for describing the heat-transfer coefficients as a function of the process variables were subsequently incorporated into the mathematical model. It should be stressed that the instrumented rod tests in both the laboratory and plant also provided vital steel samples for microstructural examination and mechanical property evaluation.

IV. PREVIOUS WORK- -HEAT TRANSFER

Heat flow in the long rods processed on the Stelmor line is essentially one-dimensional, governed by the following transient heat conduction equation:

O(OT] kOT OT - - k +- - -+ qre = PCp [1] Or \ Or/ r Or -~t

where qrR is the heat released due to the austenite decomposition reactions. This equation can be solved utilizing numerical techniques, as outlined in Part III of this article. 09/An important aspect of the solution of Eq. [1] is the characterization of the boundary condition at the rod surface, which can be written as

OT r = ro -k - - = hov(T s - Ta) [2]

Or

where hov represents the overall heat-transfer coefficient. Although the Stelmor process employs forced air to cool the steel rods, radiation from the rod surface also contributes to the removal of heat. As a result, the overall heat-transfer coefficient must be linked to the combined effects of convection and radiation, or in equation form:

hov = hc + hR [3]

Radiation heat losses from a cooling rod can be quan- tified by the following equation:

he = irE \ Ts Ta / [4]

where F is a radiation factor which accounts for the emissivity and relative geometries of the cooling body and its surroundings while temperatures are absolute (K). Assuming that the rod is capable of radiating unhindered to a black body at ambient temperature, F simply re- duces to e, the emissivity of the steel (=0.8 for an ox- idized surfacet6]), which allows ready solution of Eq. [4]. In an actual system, such as the Stelmor process, the value for F will depend on the geometry of the overlapping rods, for which a simple solution is not available in the literature. As a result, experiments, or detailed radiative calculations, are required to determine the radiation factor as a function of bed position and steel temperature.

Clearly, the heat-transfer coefficient, due to convection, is the key thermal variable which must be controlled in the Stelmor process. Correlations for convective heat transfer from cylindrical bodies in crossflow are available in the literature for a range of cooling fluids.t7.8.9] All of the correlations are empirical and relate the Nusselt number (Nu) to the Reynolds number (Re) and Prandtl number (Pr). One of the equations, as given by Kreith and Black, E71 is

Nu = CReXpr y [5]

where C, x, and y are constants which depend on the magnitude of Re and on the cooling medium.

Correlations also have appeared in the literature, where the objectives were to study heat transfer from cooling steel rods and bars. Mehta and Geiger u~ conducted a set

2770--VOLUME 22A, NOVEMBER 1991 METALLURGICAL TRANSACTIONS A

of experiments in a bar mill to determine the effect of operating parameters on the cooling rates of steel bars. Although the cooling medium employed in the mill was water, the principles utilized for the investigation are ap- plicable to air cooling. The thermal response of the bars, measured in the mill, was utilized to back-calculate surface heat fluxes and heat-transfer coefficients via solution of the transient heat-conduction equation (Eq. [ 1]).

Stelmor cooling of rods was examined experimentally by Hanada et al. I~l~ The objective of the experiments was to quantify the differences among cooling conditions at various locations on the bed and for different Stelmor deck configurations. Although details of the experimental technique were not reported fully, rod samples 200 mm in length and 5.5 or 11 mm in diameter were instrumented with a CHROMEL-ALUMEL* thermo-

*CHROMEL-ALUMEL is a trademark of Hoskins Manufacturing Company, Hamburg, MI.

couple inserted through a radial hole drilled to the centerline. No detail was provided on the method utilized to anchor the thermocouple in place. In order to simulate the Stelmor process, the instrumented rod was either placed in bundles with other rods at various angles of contact or was cooled as a single rod. The bundles and single rods were preheated to a temperature typical of Stelmor cooling, then cooled in a crossflow of air. Results showed the effect of cooling air velocity, rod diameter, and geometry of the cooling bundle on the average cooling rate of the instrumented rods. Additional work on a pilot-scale Stelmor line showed the effect of bed position and damper angles on the average rod cooling rates.

Instrumented steel rods were employed to tune a math-

ematical model for prediction of phase evolution during rod cooling by Iyer et al. tl2j The technique employed for temperature measurement during the tests involved threading a steel plug, instrumented with a thermocouple, into a hole to the rod centerline. An air source supplied a constant velocity for cooling of the 10-mm- diameter rods employed in the tests. A range of cooling rates was studied, and the thermal responses of the rods were found to compare favorably with mathematical model predictions.

Although these earlier studies provided encouraging results on heat transfer under Stelmor conditions, it was decided to confirm the findings in this work. But more importantly, a technique for measuring cooling rates was sought which performed equally well under laboratory and plant conditions.

V. APPARATUS AND SAMPLE PREPARATION

In order to cool steel rod under well-defined conditions in a crossflow of forced air and thereby simulate the Stelmor process, the apparatus shown in Figure 2 was constructed. The equipment made use of a "constant velocity duct" (CVD) at the discharge end to provide a uniform air velocity at the rod surface, over a length of 200 mm. A 10-hp Rootes-type compressor with a rated capacity approaching 100 1/s supplied air to the CVD, resulting in a peak air velocity of 22 m/s. The velocity was controlled by bleeding air from a parallel line orig- inating at the compressor. Five vanes were mounted in- side the upper zone of the CVD to facilitate uniform air flow through the discharge end. To increase back pressure in the system and enhance the uniformity of the velocity distribution at the bottom of the CVD, a 60-mesh

Fig. 2 - - Diagram showing test rod m position under constant velocity duct for typical laboratory rod cooling test.


screen was inserted 50-mm upstream of the air discharge. A pitot tube was employed to evaluate the distribution of air velocities at the discharge end of the duct. An orifice plate situated upstream from the CVD was calibrated against the average air velocity exiting the apparatus and was utilized to measure the air velocity for each test. Owing to heatup of the compressor during its operation, the air temperature was measured with a ther- mometer, and a mean temperature was recorded for each cooling test.

The composition of all steel grades utilized in the laboratory and plant tests is presented in Table I. The steels employed in the experiments were obtained from Stelco Inc. in Hamilton, ON, Canada and are typical of plain- carbon material rolled in a rod mill. The steel grades can be divided into three categories: (1) eutectoid or near- eutectoid grades (steels A, B, and F in Table I), (2) medium-carbon grades (steels C, D, G, and H), and (3) lower carbon grades (steels E, I, and J). Steel grades A through E were employed for the laboratory experiments, while grades C and E through J were under study in the plant trials. Table II summarizes the conditions investigated during the laboratory tests for which four different rod diameters, between 8 and 15 mm, were adopted and air velocities from the CVD ranged from 6 to 22 m/s. A summary of conditions in the plant trials is presented in Table III; three rod diameters (7.5, 9.1, and 15 mm) were examined in the tests, and two locations on the Stelmor deck were investigated, as indicated in the table. In total, 68 tests were performed in the plant. During the campaign, the conveyor speed ranged from 0.43 to 0.71 m/s, but for the majority (90 pct) of the trials, it was 0.46 to 0.56 m/s.

For the laboratory tests, 350-mm lengths were cut from the rod loops supplied by Stelco and straightened, with some of the samples being machined down to smaller diameters. As indicated in Figure 2, the centerline temperature in the rod samples was monitored by a thermocouple which was connected to a chart recorder (Kipp and Zonen model BD 41) and data logger (John Fluke Manufacturing Inc. model 2280). The method employed for attaching the thermocouple to the rod is depicted in Figure 3. As can be seen, two holes were drilled into the centerline of the rod, one through which a 0.25-mm- diameter mullite-sheathed, CHROMEL-ALUMEL thermocouple was introduced and the other through which

Table II. Summary of Steel Grades, Rod Diameters, and Air Velocities Studied in the Laboratory

Rod Steel Diameter Air Grade (mm) Velocity (m/s)

A (1080) 10 20, 18, 16, 14, 21, 20, 9, 11, 19,22

B (1070) 15 22, 16, 11, 9 B 11 22, 10, 6 B 8 22, 15, 6 C (1038) 11 22, 15, 10, 6 C 8 22, 13,6 D (1037) 11 22, 16, 12 E (1020) 11 22, 15, 13, 6 E 8 22, 12, 6

Table III. Summary of Steel Grades, Rod Diameters, and Number of Tests Completed during Plant Trials

Rod Number of Number of Steel Diameter Center Edge Grade (mm) Bed Tests Bed Tests

C 15 7 4 E 15 7 1 F 9.1 4 3 F 7.5 5 4 G 9.1 4 3 H 7.5 6 2 I 9.1 6 2 J 7.5 5 5

a steel set screw was threaded to anchor the thermocouple junction. This arrangement provided an effective means for ensuring good contact between the therrno- couple and the rod while minimizing disturbance of the thermal response being measured.

The experimental technique followed for the laboratory tests, involving pitot tube and rod temperature response measurements, was repeated in the plant, at the Stelco Hilton Works No. 2 Rod Mill, with minor changes. For temperature response determination, thermocouples were mounted at the rod centerline utilizing the same technique, but longer rod lengths ( -450 ram) were cut. Heating of the samples was once again accomplished in

Table I. Chemical Analysis of Rod Samples Employed in Laboratory and Plant Experiments (in Weight Percent)

Grade Code C Mn P S Si Cu Ni Cr Mo V Cb

A 0.789 0.74 0.021 0.033 0.237 0.005 0.002 0.052

Fig. 3 - -Schemat ic diagram of method employed to mount thermocouples at centerline position in rods for Stelmor simulation tests.

a tube furnace, situated directly adjacent to the Stelmor line. The temperature in the rod samples was monitored by a strip chart recorder (Kipp and Zonen model BD41) during heating. However, during cooling, a hand-held data logger (Metrosonics Company Model DL-702), which could be carried easily along the length of the bed, was employed.

In order to supply rods with a uniform temperature over a sufficient length, the tube furnace was specially constructed, with particular attention being paid to minimizing the longitudinal thermal gradient. A 63-mm OD quartz tube was wound with 2.4-mm-wide CHROMEL strip and insulated with two layers of 6.4-ram-thick FIBERFRAX* sheet. This assembly was contained in a

*FIBERFRAX is a trademark of Standard Oil Engineered Materials Company, Niagara Falls, NY.

shell of thermobestos insulation and encased in an alu- minum tube. The furnace was 690 mm in length and designed for a peak temperature of 900 ~ operating with a 220 V power supply. To minimize scale formation on the test rods, a flow of nitrogen of approximately 3 to 6 1/min was maintained through the furnace. Measure- ment of the axial temperature profile down the furnace showed that the 200-mm center section was isothermal to within ---5 ~

ing, the centerline temperature was monitored by the data logger, with a sampling frequency of 1 Hz. Upon com- pletion of cooling, individual rods were removed from the CVD and saved for mechanical testing and microstructural examination. Rods also were sectioned through the thermocouple area to verify the exact location of the hot junction. In all cases, the hot junction proved to be at or near the centerline of the rod.

To obtain a range of cooling rates typical of Stelmor cooling, a variety of rod diameters from 8 to 15 mm was studied in conjunction with cooling air velocities ranging from 5 to 22 m/s. The measured thermal response from the tests provided data for determination of heat-transfer coefficients at the rod surface as a function of rod temperature, diameter, and air velocity (Table II).

B. Plant Trials

For the plant trials, a slightly different method was followed. Sample heating was monitored by the strip chart recorder only. After reaching the desired test temperature, samples were also soaked for approximately 5 minutes. However, it was difficult to maintain this soak period in all cases, because test times were dictated by the rolling mill schedule. In each test, an attempt was made to match the grades and diameters of the instrumented rod with those being processed on the line. At the appropriate time, the thermocouple leads were dis- connected from the chart recorder and connected to the hand-held data logger. Each instrumented rod was quickly withdrawn from the furnace and placed on the Stelmor line during normal operation. Care was taken to ensure the instrumented rod was woven into the rod loops, thus preventing unwanted movement as it traveled the length of the line. The instrumented rods were placed at two locations, one at the center of the bed, where the coils are loosely packed, and one at the edge of the bed, where the packing density is much higher. A schematic diagram of the two positions is shown in Figure 4. The sampling frequency of the hand-held data logger was 1 Hz. Temperatures were recorded until the instrumented rod reached the end of the Stelmor deck, where- upon it was removed from the coils and saved for

VI. PROCEDURE

A. Laboratory Tests

Prior to each laboratory test, the tube furnace was heated to, and held at, the desired austenitizing temperature while being flushed with nitrogen at a flow rate of 3 1/min. For the medium- and high-carbon grades, an austenitizing temperature of 850 ~ was chosen, whereas for the low-carbon grades, a temperature of 875 ~ was adopted. Rod samples were placed in the tube furnace, and the centerline temperature was monitored with the strip chart recorder. Once the desired temperature had been achieved, the samples were held for an additional 5 minutes soak- ing time. For the laboratory tests, the rods were then withdrawn quickly from the furnace and placed in the cross flow of air, as indicated in Figure 2. During cool-

Fig. 4 - -Schemat ic diagram of relative packing density of coils at the edge and center of the Stelmor line.

METALLURGICAL TRANSACTIONS A VOLUME 22A, NOVEMBER 1991 2773

subsequent mechanical testing and microstructural evaluation.

The set point on the Stelmor blowers at the Hilton Works is not continuously variable but is either "full on" or "off." In an attempt to determine the air velocity distribution with the blowers set at full on, a series of pitot tube measurements was made on the line during a down period in the plant. With air to the Stelmor decks turned on but in the absence of rod loops, the pitot tube was moved to various locations on the bed in each of the four cooling zones. For each measurement, the pitot tube was held at the same height as the rod loops when the Stelmor line is in operation. In total, 16 separate regions on two Stelmor lines were investigated, yielding nearly 450 individual air velocities to map out the velocity distribution across the bed as well as along its length.

VII. RESULTS

A. Laboratory Tests

The results of the pitot tube measurements of the velocity profile over the length of the CVD for three orifice plate pressure drops are shown in Figure 5. The results confirm the essentially uniform (-+ l0 pct) air velocity over the length of the CVD.

Two typical thermal responses measured at the centerline of a high-carbon (steel B 1070) and a low-carbon (steel E 1020) steel rod cooled during the laboratory tests are shown in Figure 6. Recalescence due to both the austenite-ferrite and austenite-pearlite transformations is evident for the 1020 grade, while recalescence due only to the austenite-pearlite transformation is apparent for the 1070 steel. Owing to the differences in rod diameter, as well as cooling air velocity, a significant difference between average rod cooling rates exists in the two samples. Similar results were obtained from the remainder of the laboratory tests, and a complete report can be found elsewhere. [~31

The cooling curves were employed to determine heat- transfer coefficients as a function of rod diameter and air

30

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28

26

24

22

20

18

16 U-Tubeah=8.8 rnrn Hg

14

12

10

8

6

4 , , , , 3 5

U-TubeAh=2.7 rnm Hg

i i i i i b i i i , i i i

7 9 11 13 15 17 19

Blower Outlet Position (cm)

Fig, 5 - Velocity profiles for three orifice plate pressure drops. Note the constant velocity across the width of the duct.

0 e,....

Z}

r'~ E (l) I---

900

850 , , ~

8OO

750

7O0

650 ",,/'-",,

600

550

500

.. . . . . Steel B 1070 8-ram Dia. 22 m/s Vel. Steel E 1020 1 l-ram Dia. 6 m/s Vel.

20 40 60 80 100

Time (s) Fig. 6--Typical laboratory thermal responses measured in 8-mm- diameter (steel B 1070) and 1 l-ram-diameter (steel E 1020) rods cooled with air velocities of 22 and 6 m/s, respectively.

velocity. Two techniques were adopted: one assumed negligible temperature gradients (lumped parameter), and the other was based on a finite-difference technique to back-calculate an effective heat-transfer coefficient from the measured centerline temperature. The first method assumes negligible internal resistance to heat flow, which can be assessed by the magnitude of the Biot modulus, Bi:

hD Bi = - - [6]

k

where h is the heat-transfer coefficient, D is the rod diameter, and k is the thermal conductivity of the material. In general, if Bi < 0.1, there will be a small error in assuming negligible internal gradients for calculation of the heat-transfer coefficients. [~4] For this condition, the heat-transfer coefficient is given by

hov - -proC~ In [7] 2t LT---~- TA J

where Ta is the ambient air temperature, To is the initial temperature (for a given time interval), T is the temperature at time t, and ro is the rod radius. The specific heat of the steel, Cp, was calculated at each temperature based on the composition and phases present, with values taken from the literature.i~s,16jT]

The second method involved the use of an iterative scheme whereby the heat-transfer coefficient was ini- tially guessed; then finite-difference equations were utilized to solve for the rod centerline temperature (the model will be described in detail in Part IIIil9]), and the predicted temperature was compared with the measured value. A difference of 0.01 ~ was taken as a limiting value for each series of iterations. This process was repeated for successive time steps throughout the thermal excur- sion of each rod sample. The advantage of this technique is that the radial temperature gradient through the cooling rod is not ignored, particularly for large diameter rods and high cooling rates, thus providing a more re- alistic estimation of the overall heat-transfer coefficient, hov.


A plot of calculated heat-transfer coefficient as a function of rod centerline temperature, employing both techniques for a cooling test on steel C (1037), is presented in Figure 7. It may be noted that in the temperature range from 620 ~ to 700 ~ where the austenite decomposition reactions occur, the latent heat released by the transformations makes calculated h values meaningless. However, it can be seen that for temperatures before and after the transformation, little difference exists between the heat-transfer coefficients calculated by the two meth- ods. It is also evident that the change in the magnitude of the overall heat-transfer coefficient as the sample cools, ~190 W/m 2 ~ at 800 ~ reducing to ~120 W/m 2 ~ at 500 ~ is due primarily to the decrease in radiative heat transfer. Plots similar to that shown in Figure 7 were utilized to determine the variation in overall heat-transfer coefficient as a function of temperature for all laboratory tests.

Comparisons between theoretically predicted and em- pirically calculated values for h have been made for the laboratory data at several temperatures. Utilizing Eq. [5] with the properties of air evaluated at the mean film temperature, as given by Kreith and Black, ~71 the convective heat-transfer coefficient was calculated from the fol lowing equation:

\ 0.466 ~ ~ 1/3

hc = 0 .683- [8] D\ lx ] \ k II

as a function of rod diameter and cooling air velocity. Figure 8 shows a comparison of measured and predicted heat-transfer coefficients for a rod temperature of 525 ~ The heat-transfer coefficients are plotted as a function of v~176 , wh ich according to Eq. [8], should provide a linear relationship, owing to the fact that over a small range of temperature (---5 ~ the radiative heat-transfer coefficient is constant and indepen- dent of rod diameter or air velocity. The predicted line shown in Figure 8 is based on the sum of Eqs. [4] and [8]. The agreement between the measured and predicted

210

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03 c"

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200

190

180

170

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150

140

130

120

110

100

90

80

70

1 525 ~ [] I

I

[] Measured h o

- - Predicted h t~

[]

i i , 1 i

0.6 0.'8 1 1.2 1.4 V 0,466 D o.534

Fig. 8 - -Measured heat-transfer coefficient at 525 ~ for the laboratory tests plotted against (air velocity)~ diameter) ~ The solid line is based on the combined effects of radiation and convection (Eqs. [4] and [8]).

values is seen to be quite good, as would be expected, and provides confirmation of the use of the instrumented rod to characterize cooling under Stelmor conditions. Similar results have been obtained at other temperatures for the laboratory results.

Additional support for predicting the heat-transfer coefficients, based on the combined effect of radiation and convection according to Eqs. [4] and [8], can be found in the literature. Average cooling rates for two rod diameters at various air velocities reported by Hanada et al. (lu have been converted into heat-transfer coefficients, employing the techniques outlined previously. The results, shown in Figure 9, once again exhibit good agreement between predicted and measured hedt-transfer coefficients.

200

190

~" 180 E 170

160

'~ 150 (1) o 140

130 o 0 120

110 03 t-- 100

t-- 90 ~ 8o o 7- 70

60

Test C7

o Finite-Difference Method

Lumped-Parameter Method

0 0

0 mO@Om 0+ +

[ ] 0

t~

t~ t~

Phase Transformation Range

500 540 580 620 660 700 740 780

Temperature (~

Fig. 7--Heat-transfer coefficients calculated from measured rod centerline temperature, utilizing both a lumped-parameter and a finite- difference technique. The results are for a steel C (1037) 8-mm-diameter rod cooled with an air velocity of 6 m/s .

300 B._~. Measured h-5.5 mm Dia.

280 o o Measured h-ll mm Dia. o

260 Predicted h o E o ~ 240

~ 220

9 -~ 200 O o [] [] O 13 []

O O [ ]

0 160

140

120 []

I-- 100 ~o o

t 60

40 ~ 0.2 0.4 0.6 0.8 1 1.2 1.4 1,6 1.8 2

V 0.466 D 0.534

Fig. 9 - - Measured heat-transfer coefficient from Hanada et a l . [HI plotted against (air velocity)~ 466/(rod diameter) ~ The solid line is based on the combined effects of radiation and convection (Eqs. [4] and [8]).


B. Plant Trials

The transverse profiles of the air velocities, measured at several locations on two Stelmor lines, are presented in Figure 10. As can be seen, in an attempt to provide uniform cooling across the loops, a higher air velocity of nearly 30 m/s is applied to the edge of the bed, where the packing density of the rods is highest, as compared to about 18 m/s at the center, where the rod packing is minimum.

Typical thermal responses measured at the centerline of instrumented rods during the plant trials are shown in Figure 11. As can be seen, they have a similar appear- ance to those obtained in the laboratory tests (Figure 6). It is important to note, however, that some of the temperature responses measured in the plant exhibited er- ratic behavior and, therefore, were discarded. This behavior was thought to arise from vibration and move-

Fig. 10- -Average air velocities measured on Stelmor lines 2 and 3. The shaded area indicates --- 1 standard deviation for the measurements.

s

D_ E t-

850

800

750

700

650

600

550

500

, . . . . . . Steel F 1080 7.5-rnm Dia. ', ~ Edge FFFF ',, ~ - - Steel E 1020 ',,,, \\, / _ ~ 15-mmDia.

2(3 40 6() ' 80

Time (s)

Fig. 11 --Typical plant thermal responses measured in 7.5-mm-diameter (steel F 1080) and 15-mm-diameter (steel E 1020) rods, cooled at the edge and center of the Stelmor bed, respectively. The "FFFF" in the figure legend indicates that cooling air was "on" in all four cooling zones for the tests.

ment of the test rods on the Stelmor line, which resulted in poor thermocouple contact or from damaged thermocouple wires. The valid thermal responses from the plant tests were employed to calculate the heat-transfer coefficients as a function of process variables. As was indicated earlier, the Stelmor process variables include a difference in air velocity between the center and the edge of the bed and the option of operating the line with or without forced air flow. In this latter condition, radiative cooling dominates, with the combination of forced (due to motion of the line) and natural convection contribut- ing in a minor way to the overall heat transfer.

Similar to the laboratory results, the calculated surface heat-transfer coefficients for 800 ~ have been plotted against V0"466//O 0"534 in Figure 12 for center and edge positions and three rod diameters employed in the experiments. The line in Figure 12 represents the predicted heat-transfer coefficient based on convection only. Owing to the difficulty in predicting the radiative component of the heat-transfer coefficient in rods bundled on the Stelmor line, no attempt has been made to predict an overall heat- transfer coefficient from first principles, although this is an important next step. Instead, plots such as those shown in Figure 12, have been employed to determine the relative magnitude of hR, assuming the difference between the average measured heat-transfer coefficient and the predicted value based on convection is due to radiation.

A series of plots similar to Figure 12 has been pro- duced at different temperatures from the plant thermal data. The difference between the measured heat-transfer coefficient and that predicted from the correlation for convection only (Eq. [8]) has been calculated to determine the radiative component of the heat-transfer coefficient as a function of rod temperature. Figure 13 shows the calculated radiative heat-transfer coefficient for the center and edge of the bed as a function of temperature. As can be seen, with decreasing temperature there is a dramatic decrease in the magnitude of the radiative component, as would be expected. The radiative coefficient at the center of the bed is consistently larger than that at the edge, where greater radiative interchange occurs

280

260

~E 240

~, 220 C

200 E: 180 o 0 160

~ 140

I-- 120 t~

100 "1- 80

60

O Center Full (800~ + Edge Full (800~

- - Pred. h Convective

D

0 +

O

0

o ; B ~ O o :~

J

0.7 0 9 1.1 1 V 0.466 D 0.534

Fig. 12- -Measured heat-transfer coefficient at 800 ~ for the plant 0 466 tests plotted against (air veloc i ty) /(rod diameter) ~ The pre-

dicted line is based on convection only (Eq. [8]).


80

~. 7O

6o

o 50

~ 4o t-

F- -- 30

T ~ 20 ._.

"~ 10 rr

0

c~ Center of Bed Tests , , m

/ + Edge of Bed Tests

i i i i i i i

400 500 600 700 800

Temperature (~

Fig. 13--Calculated values for radiative heat-transfer coefficient from the plant trials plotted against temperature. Also included is the predicted value from Eq. [4].

among the more densely packed loops (Figure 4). Also included in Figure 13 is the predicted radiative heat- transfer coefficient based on Eq. [4]. A comparison of the predicted and measured values for the radiative heat-transfer coefficient can be utilized to construct an effective "radiation correction factor," R, for the two locations on the Stelmor bed. This correction factor can be utilized in the following equation to calculate hR:

\ Ts TA/' [9]

Results from the plant trials have been employed to obtain the value of R for the center (Rc) and edge (RE) position of the bed. Each is plotted in Figure 14 as a function of rod temperature. The equations are

Rc = 2.02x-~ -~176176176 [10]

RE = 8.94x-~176176176 [1 1]

1.1 o Center of Bed Tests

1 + Edge of Bed Tests / /~

- Predicted 0.9 - -

0.8 u_ ~ 0.7

~ 0.6

0 0.5

g ~ 0.4

~ O.3 rr

0.2

0.1 - - ' r ~ - ' ~ r ~ - - - ~ r - - ~ r 400 500 600 700 800

Temperature (~

Fig. 14--Radiation correction factor for center and edge of bed plotted against temperature. Lines are calculated from the regression equations for both parameters (Eqs. [10] and [11]).

where x represents 875-T in degrees centigrade. Equations [10] and [11] are employed in the mathematical model to predict the radiative heat-transfer coefficient for cooling conditions obtained on the Stelmor line but, it should be noted, apply to conditions where the rod surface temperature is less than 875 ~

VIII. SUMMARY AND CONCLUSIONS

In this first part of a three-part paper on microstructural engineering applied to the controlled cooling of steel rod, the question of heat transfer in the process is addressed experimentally and theoretically. A series of experiments, conducted in the laboratory as well as on an operating Stelmor line, has been performed to measure the thermal response of an instrumented steel rod under controlled cooling conditions. Results from the experiments were utilized to back-calculate the overall heat-transfer coefficient, and a comparison of the measured values was made with empirical correlations. The following conclusions can be drawn from the work:

1. The experimental technique employed for the laboratory and plant tests provided a reproducible means for measuring the thermal response at the centerline of a cooling rod.

2. Comparison between predicted and measured heat- transfer coefficients for the laboratory tests showed that reasonable estimates of hR and hc could be made utilizing standard equations for laboratory conditions.

3. For an operating Stelmor line, heat-transfer coefficients reflected the radiative interaction among adjacent loops on the bed. By assuming the portion of the overall heat-transfer coefficient due to convection can be predicted reasonably by a published equation, correlations for hR as a function of rod temperature and position on the bed have been determined.

Bi C

G D F h hc

hov hR

k Nu Pr qrR

F ro R Rc

RE

NOMENCLATURE

Biot number empirical constant used in Eq. [5] specific heat, J kg -1 ~ rod diameter, m radiation factor in Eq. [4] heat-transfer coefficient, W m -2 ~ t heat-transfer coefficient due to convection, W m -2 ~

overall heat-transfer coefficient, W m 2 ~ heat-transfer coefficient due to radiation, W m -2 ~ thermal conductivity, W m -~ ~ Nusselt number Prandtl number rate of heat release during phase transformation, W radial position, m rod radius, m radiation correction factor radiation correction factor for center of the Stelmor line radiation correction factor for edge of the Stelmor line


Re t

T TA To T~ x

Y P o

8 /z v

Reynolds number time, s temperature, K or ~ ambient temperature, K or ~ initial temperature, K or ~ surface temperature, K or ~ empirical constant used in Eq. [5] and symbol denoting undercooling, ~ in Eqs. [10] and [11] empirical constant used in Eq. [5] density, kg m -3 Stefan-Boltzman constant, 5.6710 -8 W m -2 K -4 emissivity kinematic viscosity, m 2 s -1 air velocity, m s -1

ACKNOWLEDGMENTS

The authors wish to acknowledge the Natural Sciences and Engineering Research Council of Canada for support of research expenses. The University of British Columbia awarded a University Fellowship, while the Cy and Emerald Keyes Foundation provided a scholarship to P.C. Campbell. The cooperation of Steltech and Stelco Steel in organizing the plant trials is deeply appreciated.

REFERENCES

1. J.K. Brimacombe, E.B. Hawbolt, I.V. Samarasekera, P.C. Campbell, and C. Devadas: in Proc. Thermec "88, I. Tamura, ed., Iron and Steel Institute of Japan, Tokyo, pp. 783-90.

2. A. Tendler: Wire J., 19-81, vol. 14, pp. 84-91. 3. J. Tominaga, K. Matsuoka, and S. Inoue: Wire J. Int., 1985,

vol. 18, pp. 62-72. 4. P. Bercy, U.G. Boel, N. Lambert, and M. Economopoulos: Metall.

Plant Technol., 1984, vol. 4, pp. 46-51. 5. A.A. Jalil: Iron Steel Eng., 1982, vol. 59, pp. 46-48. 6. G.H. Geiger and D.R. Poirier: Transport Phenomena in

Metallurgy, Addison-Wesley, Reading, MA, 1973, pp. 367-69. 7. F. Kreith and W.Z. Black: Basic Heat Transfer, Harper and Row,

New York, NY, 1980, pp. 249-51. 8. C.O. Bennett and J.E. Myers: Momentum, Heat andMass Transfer,

McGraw-Hill, New York, NY, 1974, pp. 381-83. 9. Chemical Engineer's Handbook, J.H. Perry, ed., McGraw-Hill,

New York, NY, 1969, pp. 10.13-10.15. 10. A.J. Mehta and G.H. Geiger: Mechanical Working and Steel

Processing Conf. XV, ISS-AIME, Pittsburgh, PA, 1977, pp. 458-82.

11. Y. Hanada, K. Ueno, A. Noda, H. Kondoh, T. Sakamoto, and K. Mine: Kawasaki Steel Technical Report, 1986, vol. 15, pp. 50-57.

12. J. Iyer, J.K. Brimacombe, and E.B. Hawbolt: Mechanical Working and Steel Processing Conf. XXII, ISS, Pittsburgh, PA, 1984, pp. 47-58.

13. P.C. Campbell: Ph.D. Thesis, The University of British Columbia, Vancouver, 1989.

14. F. Kreith: Principles of Heat Transfer, 3rd ed., Intext Educational Publishers, New York, NY, 1973, p. 140.

15. British Iron and Steel Research Association: Physical Constants of Some Commercial Steels at Elevated Temperatures, Butterworth's Scientific Publications, Guildford, Surrey, United Kingdom, 1953, pp. 3-14.

16. I. Barin, O. Knacke, and O. Kubaschewski: Thermochemical Properties of Inorganic Substances; Supplement, Springer-Verlag, New York, NY, 1977, pp. 245-46.

17. JANAF Thermochemical Tables, The Thermal Research Laboratory, Dow Chemical Company, Midland, MI, 1960.

18. P.C. Campbell, E.B. Hawbolt, and J.K. Brimacombe: Metall. Trans. A, 1991, vol. 22A, pp. 2779-90.

19. P.C. Campbell, E.B. Hawbolt, and J.K. Brimacombe: Metall. Trans. A, 1991, vol. 22A, pp. 2791-2805.


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