Proceedings of the 15th International Heat Transfer Conference, IHTC-15 August 10-15, 2014, Kyoto, Japan

IHTC15-8596

*Corresponding Author: buchlin@vki.ac.be

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STUDY OF THERMAL CONDUCTANCE IN A STRIP-ROLL SYSTEM

J.-M. Buchlin1*, M. Delsipée1, Ph. Planquart1, M. Renard2

1 von Karman Institute for Fluid Dynamics-, Rhode-Saint-Genèse, Belgium

2 DREVER Int. SA, Angleur, Belgium

ABSTRACT The paper describes an experimental investigation carried out on a semi-industrial prototype of regenerative roll quench unit to determine the contact thermal conductance (CTC) between a roll and a moving strip. The quantitative infrared thermograpy allows the temperature mapping of the strip while the angular evolution of the roll temperature is obtained by mean of thermocouples connected to a telemetry acquisition system. A thermal model allows the determination of the CTC. Typical results emphasize the effect of some parameters such as the velocity, the temperature and the tensile strength of the strip. KEY WORDS: Measurement and instrumentation – contact thermal conductance

1. INTRODUCTION The knowledge of heat transfer between two solids is often required when designing thermal systems. A typical example is the continuous annealing of moving strip based on the roll quench process [1-2]. The von Karman Institute has undertaken in close collaboration with DREVER International S.A, a research programme aiming to develop a new concept of annealing furnace for the treatment of steel strips. Called the roll regenerative furnace (RRF), this innovative technique, few energy intensive, consists of benefiting from the thermal potential provided by the hot strip leaving the furnace to preheat the cold strip entering the furnace by means of a set of rolls as illustrated in Fig. 1 [patent No WO 2009/007362 by DREVER International].

Hot strip

Cold strip

Fig. 1 Principle of the roll regenerative furnace

An engineering model involving basic unsteady conduction equations for the strips and the rolls has been developed to estimate the performance of the RRF [3]. Predictions show that one of the main controlling factors is the contact thermal conductance between the strip and the roll. Fig. 2 shows a typical example of

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the thermal performance expected in function of the CTC-value; the difference of the strip temperature, ΔT, between the inlet and outlet of the regenerator is plotted versus the number of rolls used (N).

0 2 4 6 80

100

200

300

N5 7 10

ΔT [°C]

CTC [kW/m2.K]

Fig. 2 Performance of the roll regenerative furnace [3]

A state of the art has been carried out in the frame of this research program to evaluate the knowledge about the CTC. It has been noticed that such parameter depends on the nature of the materials in contact, surface roughness, temperature level and contact pressure, which is function of the strip tensile strength. However, in regard of the sparse data found in the literature [4-5] concerning this specific configuration, an experimental investigation has been undertaken with the support of the Walloon region (Convention n°6240). The objective is the setting up of a database incorporating the effect of the operating parameters on the CTC for such a counter flow regenerator. The main issues of the project are reported in this paper.

2. THE EXPERIMENTAL FACILITY 3.1 The test facility Roll Regenerative Furnace (RRF ) A dedicated facility, called RRF (Roll Regenerative Furnace), has been constructed, a schematic of which is shown in Fig. 3. It consists of a (Inox or Carbon) steel band of 0.3m wide with a thickness eS = 0.3mm or 0.5mm thick, entrained by a pair of driving rolls of 0.3m in diameter and passing through a radiant heating tube unit of 100kW to reach a maximum temperature of 650° C. Then the hot strip is put in contact with a cylindrical steel roll of 0.8m in diameter and 0.02m thick. This roll is cooled on its opposite side (part without strip in contact) by an array of air jets (plenum1composed of 10 slot nozzles of 5mm with pitch of 60mm) to control its initial temperature at the attack of the strip. Similarly the strip undergoes on its return additional cooling by means of air multi jets (Plenum 2 designed as Plenum 1 but with nozzle pitch of 200mm) to maintain steady state conditions. The two jet plenums are supplied by a fan with a total volumetric flow rate of 2.8m3/s under a relative pressure of 10 kPa. The facility allows line velocity, U, ranging from 0.25 to 0.75 m/s. Fig. 4 provides some views of the facility.

Blower

Radiant Heater

StripRoll Shell

Plenum 2

DrivingRollers

Fig. 3 3D schematic of the RRF facility

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Fig. 4 Views of the RRF Facility 2.2 The instrumentation Fig. 5 provides a schematic of the roll instrumentation. The roll is instrumented with two identical combs of 5 thermocouples of 0.5mm size; one at the middle of the roll and the other off-centered close to the edge. For each comb the thermocouples are located at 0.2mm, 5mm, 10mm, 15mm and 19.8 mm from the external surface of the roll, respectively. Prior to be inserted in the roll, all the thermocouples are calibrated in a thermostatic bath with control temperature at 0.1°C. The thermal contact inside the roll is ensured by coating the thermocouples with high thermal conductivity glue. Regular checking of calibration is performed before each test. The thermocouples are connected to a data acquisition card, part of a WIFI telemetry unit mounted on the axis of the roll. The signal received on PC is treated by dedicated software developed on Labview and Signal Express platforms. The external face of the strip is black painted and scanned by an SC3000 IR camera. The thermograms are processed by an in-house DIP program to obtain the thermal mapping of the strip and the different angular evolutions of the strip temperature.

Two pyrometers scan the strip; the first is positioned at the exit of the heating chamber and the second downstream the roll. They allow the monitoring of the inlet and outlet strip temperature.

IR Ca mera

Moving strip

Roll shellThermocouples

Pyrometer

Pyrometer

Telemetry

IR Ca mera

Moving strip

Roll shellThermocouples

Pyrometer

Pyrometer

Telemetry

Fig. 5 Thermometric instrumentation of the RRF facility The entraining roll is equipped with tachymeter and strain gauges, all connected to the electrical power cabinet of command, to monitor in real-time the velocity and strength of the strip, respectively. This latter is adjusted by varying the force of a mechanical tensor by means of metal cast weights.

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2.3 The preliminary tuning tests Campaigns of preliminary test are conducted to perform tuning of the different modules and assess the good functioning of the instrumentation. These tests allow also the understanding of the system behaviour. As an example Fig. 6a shows the time evolution of the thermal field in the roll for a heating setting fixed at 300°C. The strip with a thickness of 0.5mm, runs at 0.25m/s and undergoes a strength, σ, of 2,3kg/mm2. The thermocouples situated near the roll surface reproduce clearly the transient during the contact with the strip (temperature up and down). The established thermal regime is characterized by a periodic behavior as observed in the dashed-line box displayed in Fig. 6a. The CTC determination is based on one cycle of the established regime. Fig. 6b shows dimensionless surface temperature of the roll during the part of this cycle when the strip is in contact; the time is now replaced by the angular position θ=ωt where ω is the rotation speed. It is worthwhile remarking that the roll surface temperature passes through a maximum between 35° and 45°; It means that all the heat transfer with the strip is achieved after this angle.

0 2 4 6 8200

220

240

260

r [mm]399.8398390385

TR [°C]

t [mn]

TSo=294°CU=0.25 m/seS=0.5mm

0 30 60 90 120 150 1800

0.4

0.8

1.2Test

12

(TR-TR,min)/(TR,max-TR,min)

θ [°]

es= 0.3mmU=0.25m/sσ = 2kg/mm2 r = 399.8mm

(a) (b)

Fig. 6 Time and angular evolution of roll temperature

The strip temperature is inferred from false-color thermograms obtained with the IR camera. These thermal mappings confirm that the central region of the strip exhibits a uniform transversal distribution. Fig. 7a displays a typical IR measurement conducted in the central web region while Fig. 7b plots typical angular distribution of the strip temperature, TS, along the central axis for two heating conditions; in theses experiments the strip thickness is eS=0.3mm and the strength is adjusted to 2 kg/mm2. In agreement with Fig. 6b, Fig. 7b shows that the strip reaches thermal equilibrium rather quickly at about 40°, indeed. The asymptotic trend noticed in Fig. 7b indicates the end of the heat exchange between the roll and the strip. 2.4 The analytical model The determination of the CTC-value results from an analytical treatment of the strip and roll measurements. The theoretical model on which relies the data processing expresses the enthalpy variation of the strip (the Biot number is here very small):

( ) ⋅ ⋅ = − −SS S S CTC envS

d TUC T e q qR d

ρθ

(1)

R is the external roll radius and qenv represents the heat loss to the environment, which is estimated from thermal convection [6-8] and radiation models [3]. Eq. 1 anticipates a variation of the strip temperature high enough to

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affect the value of the heat capacity. qCTC represents the heat exchange between the strip and the roll, from which the CTC-value is deduced.

B

A

B

A

150 200 250 300

0

10

20

30

40TS [°C]

θ [°]

es= 0.3mmU=0.25m/sσ = 2kg/mm2

350 450 550 650

0

10

20

30

40TS [°C]

θ [°]

es= 0.3mmU=0.25m/sσ = 2kg/mm2

(a) (b)

Fig. 7 Thermal behavior of the strip

Eq. 1 shows that the knowledge of the local dTS/dθ -value calculated from accurate curve fitting of the TS(θ) experimental profile (see Fig. 7b) allows the determination of the local CTC-value:

( )

( )

( )

− ⋅ ⋅ −= =

− −

SS S S envS

CTC

S RM S RM

d TUC T e qq R dCTC

T T T T

ρθ (2)

To be consistent with the engineering developed in [3] and as pointed out in Eq. 2, the adopted definition of the CTC is based on the mean temperature of the roll:

= ⋅ ⋅ ⋅ ⋅ ⋅∫ ∫i

R R

RM R R R R RR R

T C u T dr C u drρ ρ (3)

Follows a definition of the mean contact thermal conductance, CTCm, in agreement with [3]:

( ) ( ) ( )( )

=⋅ −∫

S c

So

TS Sm c STc RM

e U d TCTC C TR T T

θρθ

θ (4)

Where θc is the angular coverage of the strip on the roll.

3. THE CTC RESULTS Experiments are carried out to identify the effect of different parameters such as the strip strength σ (1 to 2 kg/mm2), the strip velocity U (0.25 to 0.75 m/s), the initial strip temperature TSo (150 to 650 °C) and the initial

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strip-roll temperature difference ΔTSRo (50 to 225°C). Moreover, Inox and Carbon steel strips are successively tested. Fig. 8 emphasizes the effect of the strip tensile force on the angular variation of the contact thermal conductance. The CTC deteriorates clearly when σ decreases. One notices 50% drop of CTCmax. To seek for the best performance all the other results are presented for the highest σ tested.

0 10 20 30 40 500

1

2

3

4

12

CTC [kW/m2.K]

θ [°]

es=0.3 mm; U=0.25 m/s

200 °C< TS< 330°C

σ [kg/mm2]

Fig. 8 Effect of the strip strength on the CTC

Fig. 9 highlights interesting angular evolutions of the CTC, which constitute recurring results obtained throughout several tests performed at different operating conditions. One observes a rather low value at the beginning of the strip-roll contact up to an angle of about 10°, indeed. Such a finding reveals a very weak mechanical contact probably due to a poor flatness of the strip that does not fit perfectly the roll curvature. Obviously when happening, this undesirable event will yield poor performance of the roll regenerator furnace. Fig. 9 emphasizes also the effect of the web motion on the CTC evolution. The increase of the strip velocity shifts the thermal equilibrium towards the larger θ-values; that affects slightly the global value of the contact thermal conductance.

0 10 20 30 400

2

4

6

150 45350 105

CTC [kW/m2.K]

e=0.3mmσ = 2 kg/mm2

U=0.25 m/s

θ [°]

TSo Δ TSRo [°C]

0 10 20 30 400

2

4

6

150 45350 105

CTC [kW/m2.K] eS=0.3mmσ = 2 kg/mm2

U=0.37m/s

θ [°]

U=0.50 m/s

TSo Δ TSRo [°C]

Fig. 9 Effect of weak mechanical contact on the CTC

To synthesize the effect of the different operating parameters on the strip-roll heat exchange, the results are resented in terms of CTCm. In the industrial RRF design the foreseen angular coverage, θc, will be ranging between 25° and 45°, therefore these two values are considered in the presentation of the following results. Fig. 10 shows the effect U on the mean contact thermal conductance. The CTCm-values plotted in Fig. 10 result from an average of the data obtained at each strip velocity but for different thermal conditions tested. The results fall in the range of 2kW/m2.K to 4.5kW/m2.K in agreement with the sparse literature [4,5]. Even though the

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effect is small for Inox steel data, those of the Carbon steel tests indicate an increase of the CTCm as the strip speed augments.

0.2 0.4 0.6 0.80

2

4

6

InoxCarbon U [m/s]

CTCm [kW/m2.K]

θc=25°

0.2 0.4 0.6 0.80

2

4

6

InoxCarbon U [m/s]θc=45°

CTCm [kW/m2.K]

Fig. 10 Effect of the strip velocity on the CTCm

Fig. 11a shows that the heat exchange improves as the initial strip temperature, TSo, increases. However the benefit becomes negligible above 400°C. Similarly, an improvement of the CTCm (about 20%) is depicted in Fig. 11b when the initial temperature difference between the strip and the roll exceeds 150°C.

100 200 300 4002

4

6

25 45CTCm [kW/m2.K]

U=0.75 m/s TSo [°C]

θc [°]

0 50 100 150 200 2500

2

4

6CTCm [kW/m2.K]

ΔTBRo [°C]θc = 45 °

(a) Initial strip temperature (b) Initial strip-roll temperature difference

Fig. 11 Effect of the initial thermal conditions on CTCm

Finally it appears relevant to plot the data in function of the thermal efficiency factor Ω defined as the ratio of the effective exchanged heat over the coverage, θc, to the maximum heat that could be transferred from the strip to the roll. The expression of Ω is:

( )0

0 0

−Ω =

−S S c

S R

T TT T

θ (5)

It is worth noting that Ω does not depend on the strip velocity. Fig. 12 displays the results for both types of steel. Notice that as the angular coverage increases, TS tends TR and Ω approaches the unity. However, the contact thermal conductance keeps a more or less constant mean value (with ± 17% of standard deviation) in the range 0.4≤Ω ≤1.

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0.4 0.5 0.6 0.7 0.8 0.9 10

2

4

6

8

45 25

Ω

CTCm [kW/m2.K] θc [°]

Fig. 12 CTCm versus the thermal efficiency,

6. CONCLUSIONS

A study of the contact thermal conductance, CTC, between a moving strip and a roll is presented. The study is motivated by the modeling of the performance of a roll regenerative furnace that is a new concept of annealing furnace for the treatment of steel strips. A dedicated semi-industrial facility with only one roll and allowing strip temperature up to 650°C is used. Its main instrumentation involves quantitative infrared thermography and telemetric thermometry. To support data processing and physical interpretation simple analytical model is developed. It allows the determination of the angular evolution of the contact thermal conductance, which is based on the mean temperature of the roll. The results show that the heat transfer is achieved over an angular coverage not exceeding 45°. In most of the trials, low CTC-values are found for θ≤10°, revealing the importance to ensure a good mechanical adhesion and a high-quality flatness of the strip. Such a remark is corroborated by the low performance obtained at small strip tensile strength. The value of the contact thermal conductance averaged over the angular coverage, CTCm, is ranged between 2kW/m2K et 4.5kW/m2K in good agreement with the few data reported in the literature. No marked effect of the increase of the line velocity is found for the Inox steel strip while a benefit influence is observed for the Carbon strip. Higher is the initial strip temperature and the roll-strip temperature difference better is the CTCm. Plotted in function of the thermal efficiency Ω, the mean contact thermal conductance does not exhibit significant variation.

ACKNOWLEDGMENT

The authors would like to thank the Walloon region for its continuous support along this research programme.

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NOMENCLATURE C specific heat ( J/kg.K ) e thickness (m) CTC conductance ( W/m2.K ) q heat flux ( W/m2 ) R radius ( m ) T temperature ( °C )

θ angle ( ° ) ρ density ( kg/m- ) σ tensile strength ( kg/mm2 ) Ω thermal efficiency ( - ) ω rotation speed ( rd/s )

U,u velocity (m/s) subscript c coverage m mean CTC contact thermal conductance o initial env environment R roll M mean S strip

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