Numerical simulation and infrared-thermographic ... - CiteSeerX

Numerical simulation and infrared-thermographic measurement of the cooling of wire rod A. Lindemann, J. Schmidt, H. Boye Otto-von-Guericke University, Institute of Fluid Dynamics and Thermodynamics, P.O. Box 4120, 39016 Magdeburg, Germany

Abstract In order to achieve a defined cooling of the wire rod, the wire blocks are followed by an intense cooling area and an air cooling area. The model to describe the heat transfer in the air-cooling area as well as the extensive measurements that were carried out are presented in this paper. In order to evaluate the quality of the cooling it is in particular necessary to have knowledge of the differences in the temperatures and cooling down speeds laterally to the transport direction. A two dimensional model of the heat transfer is developed for this purpose. This is based on quasi-continuous observation of the heat transfer in longitudinal and lateral direction on the basis of the real discrete position geometry. The results of the simulations and experiments are compared.

1 Introduction In modern rolling mills defined cooling of the wire rod is possible, since their modular structure offers a large range of variation in the cooling speed. This is necessary for the realization of the required mechanical properties for the rolling products (Lehnert et al., 1995). Over the last few years, numerical simulations have become increasingly important for the design and optimum operation of such cooling areas. Among other things, the number of costly and time-consuming preliminary tests can be minimized. This requires continuous description of the entire cooling process in the area of the water- and air-cooling line. With the previous works by (Kuehne et al., 2001), (Muehlenbruch et al., 2000) and (Kuehne et al., 1998) there is a powerful algorithm available for simulating the heat transfer in the intense cooling pipes. The model of the air-cooling line is presented in this article. After passing through a short intense cooling line in which the temperature is reduced down to laying temperature (approximately 800
C), the rolled wire is placed, by means of a loop conveyer, into loops on the conveyor of the air cooling area, Fig. 1. The conveyor consists of different sections in which direct heat treatment of the wire can take place. The placement of the wire in loops leads to material accumulation on the edge, whereas in the center of the conveyor the wire sections are situated free from one another. This leads to different temperatures and cooling speeds over the width of the conveyor, which has a negative effect regarding the desired uniform structural quality of the loop. One important aim is therefore homogeneous cooling of the wire over the width of the conveyor. This can be realized by the use of suitable airflow velocity profiles. A calculation model for the determination of the two-dimensional heat flux distribution was developed because of the high number of influencing parameters, e.g. wire speed, wire diameter, conveyor speed, air speed and the packing density as well as the large range of variation in the arrangement of the different sections. This model is based on the analysis of the three-dimensional structure of the wire loops on the conveyor, which is dependent on technological parameters, as well as on the well-tested empirical correlations for the description of the heat transfer with forced and natural convection taken from the relevant literature. In order to validate and fit the model parameters, calculations were made using the flow simulator program, Fluent, and the results from experimental investigations done under rolling mill conditions were used. The measurement of the two-dimensional temperature field for the entire conveyor area was carried out by means of infrared thermography. The model as well as the extensive measurements are presented in this paper and the results of the simulations and experiments are compared.

 2 Model The model should formulate in particular the heat transfer conditions in the air-cooling line. The heat transfer coefficient determined or the heat flux can be used as the boundary condition for the solution of the unsteady 2D heat conduction problem in wire in order to predict the structure quality arising. First, the necessary geometrical dimensions must be determined from the technological boundary conditions. Subsequently, in order to determine the total heat transfer coefficient, the individual coefficients for each respective type of heat transport must be determined. If the blowers are in operation, the calculation of forced convection is necessary, otherwise the calculation is done with natural convection (Fig. 2). Radiation is determined for all construction variants considering the respective environmental conditions. If the cover is closed, the heat is essentially transferred by radiation to the walls and cover. u w d w ϑw ε

Input:

uc

ϑa

dl

ua

geometry ∆ y l ∆ z l ϕ(x) ψ(x) y i+1 = yi + ∆ y l

close

cover open

conveyor

switch off

blower switch on forced convection αfc (x)

natural convection αnc(x)

wire loops

loop conveyer

radiation . q r (x)

.cover q t,co (yi )

heat transfer surface Aht

heat conduction

ϑ w(yi)

ϑ w (x,yi); ϑ w(yi)

blower coil forming chamber

Fig. 1. Air-cooling area; infrared image and schematic depiction.

heat transfer surface Aht (x)

Fig. 2. Program flow chart for the calculation of the wire cooling along the conveyor ( -direction).

2.1 Geometry of the wire loops The basis for the model is the description of the three-dimensional geometry of the wire loops on the conveyor. In Fig. 3 the deposited wire in the  -plane is shown at different rolling speeds. The material accumulation on the edge of the wire deposited by the loop conveyer as well as the representative conveyor section   , which constantly returning in the axial direction  , are clearly visible. The representative section   is the distance between two loops in axial direction in dependence on the rolling speed  , conveyor speed  and wire diameter   . The sum of all wire sections   in the representative section   corresponds to the length of a wire loop.  On the basis of the representative section   , the model establishes a quasi-continuous description of the wire ! mass distribution   #"$% and of the heat transfer surface &'("$ in the  - and  -direction. The mass flow is given by:

!



)

!    *,+./1-032 %4) %

; :  A *,+5/6-03 287 9 = ? %4)  < > @   % 

7*

B: C< >D+E/1-03 2GF8H 3IJ>KGL

with the distribution function of the wire on the conveyor F8H 3I :



F8H G  8 >MIN)

PO  ?   >K

)

!    :  > %


» Y[Z3\J¼ X ¼ »;½€ Y‚¾pX ¿ ¥À¾p» ¿ \Ur ¸ · Ž « » Y[Z3\#¥ ¸ · š k (6) u with emissivity ¼ and temperatures ¾ of the wire and environment as well as the radiation constant ½ € is used. The shape factors ¹PX>» for each particular wire section at the position Z are calculated separately using quasi-continuous functions. Thereby, the shielding effect of the other wire sections as well as the borders and covers are considered. Adaptation of the function ¹PX>»1Y[Z3\ modeled on the technological parameters is possible with the assistance of the temperature distribution measured. This is purposeful for natural convection at which the largest differences in temperature arise (Z -direction).

3 Experiment Verification of the model carried out by experiments in a rolling mill during commissioning. Infrared thermographic measurements of the cooled wire on the conveyor under different technological parameters, e.g. rolling speed, conveyor speed, wire diameter, power of blowers YÂÁ \ , cover position and laying temperature WDX8Y[f…rª~B\ (cp. su input param. in Fig. 2) serve this purpose (Fig. 1 and 7). The measurements with a 5
and a 20
lens make different

Ã

2

heat transfer coeff. /W/(m K)

recording positions and various geometric resolutions possible. In order to carry out the comparison calculations, the cooling air speed (blower section) as well as the emissivity ¼;Y‚¾Ä\ of the steels in the wavelength range used must be known. The mean emissivity values were determined in the range of 0.69 to 0.78 in consideration of scaling rates. The air speed distribution was measured pointwise for different blower powers over a blower section with the point distances of 60 mm x 75 mm in Z(¥ and f3¥ direction.

L2

L1

L0

L0 40 30

L2

20 10 center 0 0

Fig. 7. Infrared image of the wire loops on the conveyor in the range of blower sections; evaluation lines L0 - L2 (see Fig. 8).

total (measurement) natural conv. (calc.) radiation (difference) L1

50

edge 0,15

0,3 0,45 conveyor width /m

0,6

Fig. 8. Experimentally determined total heat transfer coefficient and calculated heat transfer coefficient for convection and radiation as a result.

4 Comparison of simulation and experiment In the following the results of experimental investigations and of simulation calculations are presented and compared using examples. Fig. 8 presents the measured heat transfer coefficient ÅPÆUÇ飃 , the calculated heat transfer coefficient ÅGÊ1 and the heat transfer coefficient for radiation Å as a result for an example case. Figure 9 and Fig. 10 show the

-

1000 transformation start temperature

800

700

c p (T) for low alloy steels

600

wire temperature /°C

900

800

experiment (different coils) c p = 700 J/(kg K) = const.

wire temperature /°C

700 600 500 95% 400 90% 80% 70% 60%

300 200 100 0

1−3 0

4 5 6 7 20

natural convection forced convection

50 % 80 % 100 %

500 400

blower no. 4 and 5

300 200

blower power

100

experiment simulation

blower no.

40 conveyor length /m

60

80

Fig. 9. Comparison of the experimental and simulated cooling curves with use of different input values for the specific heat capacities.

0

0

10

20 30 conveyor length /m

40

50

Fig. 10. Comparison of the experimental and simulated cooling curves for natural and forced convection with use of different blower powers.

measured and the simulated cooling curves for chosen blower powers, for different steel qualities, for different values of rolling speed and diameter of wire rod as well as for natural and forced convection. In these figures can be seen the good conformity between experiment and simulation as well as the importance of the input values, especially the specific heat capacity ËÍÌ . The influence of the phase transition from austenite to pearlite is clearly visible. In (Shukla et al., 1994) the effect of the cooling velocity on the transformation start temperature of a 6 mm

Î wire rod are presented in the air velocity range of 0 to 40 m/s. The model considers the decrease in the transformation start temperature with increasing cooling air speed using the measured Ḯ|Y‚¾Ä\ -function (Lindemann et al., 1998).

5 Summary The developed calculation model is based on the analysis of the three-dimensional structure of the wire loops on the conveyor, which is dependent on technological parameters. Using the model, it has been possible to determine the two-dimensional heat flux distribution and the resulting wire temperatures over the conveyor. The parameters of model equations can be adapted to the particularities of a given cooling line as has been done in the in the present case. References S. Kuehne, G. H. D. Muehlenbruch and J. Schmidt, Heat Transfer in Intensive Cooling Tubes with Turbulence Bushes in G. de Vahl Davis and E. Leonardi (ed.), CHT’01: Advances in Computional Heat Transfer II, vol. 1, page 599, Begell House Inc., New York, Wallingford, 2001. S. Kuehne, H. Boye, G. H. D. Muehlenbruch and J. Schmidt, The influence of Turbulence Promoters on Subcooled Flow Boiling in J. S. Lee (ed.), Heat Transfer 1998, vol. 2, page 309, Taylor and Francis, Levittown, 1998. W. Lehnert, N. D. Cuong and H. Wehage, Simulation of Austenitic Microstructure in Rod and Wire Rolling of Quenched and Tempered Steel Grades, Steel Research, vol. 66, pp. 470-475, 1995. A. Lindemann, J. Al-Karawi and J. Schmidt, Thermal Analytical Study of Steels at High Temperature Including the Range of Melting, Thermochimica Acta 310, pp. 133-140, 1998. G. P. Merker, Konvektive Waermeuebertragung, Springer-Verlag, Berlin, Heidelberg, 1997. G. H. D. Muehlenbruch, H. Boye, J. Schmidt, Modelling of Heat Transfer in the Region of Convection Controlled Film Boiling, Heat and Mass Transfer, vol. 36, pp. 265-271, 2000. K. P. Shukla, S. Chandra and K. Mandal, Mathematical Simulation of Stelmor Cooling of Wire Rods, Tata Search, pp. 84-88, 1994. Verein Deutscher Ingenieure, VDI-Waermeatlas, VDI-Verlag, Duesseldorf, 1994.