Proceedings of the ASME ASME Flows in Manufacturing Processes July 14-16, 2002, Montréal, Québec , Canada

Put Paper Number Here EXPERIMENTAL AND NUMERICAL STUDY OF CONVECTIVE HEAT TRANSFER IN AN ARRAY OF SLOT JETS Jean-Marie Buchlin* Philipe Planquart*

Jean-Baptiste Gouriet* Jeroen Van Beeck*

Michel Renard‡

* von Karman Institute for Fluid Dynamics Chaussée de Waterloo 72, B-1640 Rhode-Saint-Genèse, Belgium ‡ Drever International S.A. Parc Scientifique du Sart-Tilman, 4030 Angleur, Belgium

ABSTRACT This last application is the concern of the present paper. The manufacturing of steel sheets for automobile bodies requires the use of continuous annealing or galvanizing lines. Actually, to achieve specified metallurgical and mechanical properties, a steel strip has to be annealed, after the cold rolling process, which has given the desired thickness to the sheet. This process involves heating the strip to a specified temperature between 600°C and 900°C, holding at this temperature and then cooling to a temperature below 500°C at a prescribed rate, depending on the quality required. The cooling rate could be 50°C/s, for a steel strip of 1 mm thick. The strip is cooled down by strong impingement of cold atmosphere gases on both faces through transversal slot nozzles. The weight reduction of automobiles is one of the key issues for the development of this industry. New steel grades, such as high-strength steels, Dual-Phase, TRIP-steels, etc., can be used to reach this objective, as proven in project ULSAB. But the production of these steel grades requires important improvements of both process and equipment. In particular, progress is required in cooling technology in order to obtain the desired mechanical properties.

The paper describes a study of convective heat transfer in a multiple-jet systems composed of straight and inclined slot nozzles. The application concerned is the fast cooling of moving strip. The experimental approach involves the application of infrared thermography associated with the steady-state heated foil technique. Three-dimensional numerical simulations performed with the code FLUENT compare agreeably with the IR data. The study aims to determine the effect on the average heat transfer coefficient of the slot Reynolds number up to the value of 100000, the nozzle spacing normalised by the slot hydraulic diameter in the range 6 ≤ W/S ≤ 18, the normalised nozzle emergence length, E/S, from 5 to 17 and the normalised nozzle to strip standoff distance Z/S from 3 to 10. The geometrical arrangements tested include perpendicular (90º) and tilted (60º) nozzles. A thermal entrainment phenomenon is found for cooling system of small width. A corrective factor is derived to account for this effect. The experimental findings are compared with existing correlation; deviations, which are observed at high values of the Reynolds number may reach 25%. The numerical simulation emphasises the benefit to use H2/N2 gas mixture to enhance significantly the cooling rate.

Therefore, the paper presents a study of design parameters allowing the optimisation of this gas cooling system. It aims to determine the local and mean convective heat transfer coefficient in an arrangement of gas slot nozzles. The optimisation of gas fast cooling systems requires identifying and modelling the design parameters that control convective heat transfer such as the Reynolds number, the spacing, the emergence and the tilting of nozzles as well as the standoff distance with respect to the strip.

INTRODUCTION Impinging fluid jets are widely used in industrial processes where high momentum, heat and/or mass transfer rates have to be reached [1]. Typical applications are the jet wiping, the drying of paper and textiles, the cooling of turbine blades [2], the anti-icing of aircraft [3] [4], the tempering of glass sheets and the cooling of moving metal strips [4[ [5].

The methodology adopted in the present study combines both experimental tests and numerical simulations. The objective is

1

Copyright © 2002 by ASME

twofold. In a first step dedicated laboratory experiments are conducted on small-scale model. The experimental data are used to work out an engineering correlation and provide support for code validation. Then, numerical simulations are performed to predict performance of real industrial systems and extend the applicability range of the design correlation.

photograph in figure 2 displays a general view. The model consists of a plenum (settling chamber) and a set of slot nozzles in the front side, both made in Plexiglas for visualisation purpose. The jets impact on a vertical uniformly heated flat plate. In actual cooling systems, the exhausting jet velocity often reaches 75m/s. At this Mach number (M=0.2), the compressibility effects are negligible. The scale-model fulfils this incompressibility condition in order to extend the laboratory correlation to industrial situation. The ventilator delivers a nominal flow rate of 5Nm3/s at a pressure of 10000Pa. The piping system is designed to avoid low frequency contents in the flow and fluidic phenomena that might affect the steadiness of the flow. A vane diffuser ensures the connection between the network and the plenum, which is implemented with a calibrated perforated plate. Several pressure taps have been mounted on settling chamber in order to control its efficiency. Finally, deviations lower than 1.5% appear in the pressure distribution through the plenum and the flow rate varies of only 1% between the slots.

To access to a refined description of the thermal exchange between gas jets and strip, the experimental approach involves infrared thermography. The code FLUENT is used to carry out the numerical analysis.

NOMENCLATURE A = Cross section of the lateral entrance e = Thickness of the heated flate plate E = Emergence of the nozzle Fe = Corrective factor for thermal entrainment h = Convective heat transfer coefficient k = Thermal Conductivity l = Length of the slot Nu = Nusselt number q = Heat flux Re = Slot Reynolds number S = Hydraulic diameter of the slot T = Temperature W = Nozzle-to-nozzle spacing x = Distance along the plate y = Distance in the spanwise direction Z = Nozzle-to-strip standoff distance β = Tilt angle of the nozzle Subscript a = Air amb = Ambiant cv = Convection f = Jet at the nozzle exit J = Joule l = Heat losses rad = Thermal radiation tot = Total w = Wall Operator ∇ = Gradient ∇ . = Divergence = Average

[m2] [m] [m] [-] [W/m2.K] [W/m.K] [m] [-] [W/m2] [-] [m] [K] [m] [m] [m] [m] [º]

Figure 1: Schematic of the multiple slot jet setup

EXPERIMENTAL APPARATUS AND PROCEDURES Experimental facility A model of a fast cooling system has been designed at scale 2/3. Figure 1 shows a schematic of the tests set-up while the

Figure 2: General view of the facility

2

Copyright © 2002 by ASME

The facility allows the investigation on the cooling rate of the jet Reynolds number Re, based on the hydraulic slot-diameter S, up to 100000.

e and k are the thickness and the thermal conductivity of the plate, respectively. The total heat transfer coefficient, htot, models natural convection and thermal radiation effects together. The heat transfer coefficient by radiation can be inferred from the radiosity concept [6]. The relations (1) and (2) show that hcv can be determined readily once the foil properties and the temperature field Tw are known.

The slots arrangement can be adjusted to investigate the effect of parameters such as the nozzle spacing W (6 ≤ W/S ≤ 18), the length of the nozzle E (5 ≤ E/S ≤ 17) and the impinging angle β (β=60° and 90°corresponding to perpendicular jet ). More than 25 slot nozzles have been designed to cover the whole range of each parameter. The translation of the multijets system allows to change the stand-off distance, Z, between the nozzle and the flat plate in the range of 3 ≤ Z/S ≤ 10.

TYPICAL EXPERIMENTAL RESULTS Figure 3 shows a restored thermogramme corresponding to a typical slots arrangement. It is a faithful representation of the impinging flow. The lowest temperatures are measured at the impingement of 90° jet. The cooling rate decreases as the jet angle decreases. The low spanwise distortion of the isotherm contours denotes the two-dimensional character of the impinging flow for this specific configuration.

The vertical flat plate is a constant heat-flux surface of 1.7m long and 0.27m wide. It consists of three adjacent electrical-circuit boards. Each circuit is made of copper foil of 27 µm thick, coating an epoxy sheet of 1 mm thick. The copper layer of the plates is machined to produce a Π-shape continuous electrical resistance. The design of the heated flat plate is optimised to provide uniform heat flux, qJ. The Joule heating is monitored by a potentiometer and measured with ammeters and voltmeters. The copper face is exposed to the impinging flow while an infrared camera scans the other side, which is painted black. The IR scanner is an AGEMA Thermovision 900 system with a HgCdTe detector sensitive in the 8-12 µm wavelength range and cooled by liquid nitrogen. The standard optical set-up is 20° vertical x 10° horizontal giving an instantaneous field of view (IFOV) of 1.5mrad. The IR-camera is located at about 0.75 m. from the fat plate yielding a typical resolution on the skin of less than 1mm. The camera is mounted on a displacement carriage to scan the flat plate along the vertical direction. More than 17 images are necessary to reconstruct a complete thermogramme. The thermogrammes are calibrated by measuring the surface temperature at dedicated points with T-type thermocouples flush-mounted on the heated element. The convective heat transfer coefficient is inferred from the plate surface temperature Tw (x,y) by application of the Newton relation:

h( x, y ) =

q cv ( x, y ) Tw ( x, y ) − T f

(1)

In the above expression, Tf is the temperature of the jet at the nozzle exit.

Figure 3: Typical IR thermogramme

The convective flux qcv is obtained by subtracting the heat losses ql to the Joule heating qJ. The heat losses include the contribution of the radiation qrad , the foil conduction qcd along the two dimensions , Ox-Oy, and the possible natural convection on the face not exposed to the flow. Making use of the two-dimensional fin theory, the following expression is applied:

q l = −e∇.(k∇Tw ) + htot (Tw − Tamb )

The axial distribution of the Nusselt number, Nu, based on the hydraulic slot diameter and corresponding to the jet arrangement and temperature field shown in figure 3, is plotted in figure 4. Peak of Nusselt number of 400 and more can be reached at the impingement of the peripheral perpendicular jets. However, the two 60°-tilted jets, designed to create additional moving strip stabilisation yield a lower cooling.

(2)

3

Copyright © 2002 by ASME

entrainment effect will be more important for a cooling unit with a small width l.

500

Nu

1

400

Fe 0.9

300

0.8

200 Z/S = 4.55 ; W/S = 18.2 ; E/S = 11.35 Re = 100000

100 0 -60

-40

-20

0

20

40

0.7

Re = 100000 ; Z/S = 4.55 ; E/S = 17.5

X/S

0.6

60

0.5

Figure 4: Axial distribution of Nu number

1 (n − 1).W

cv .dx − ( n −1).W 2

(3)

Flow visualisations and numerical simulations (seen next section) prove the existence of an entrainment of air from the lateral environment surrounding the jet system into the cooling device. Such a situation has already been reported and analysed in literature [7] [8] [9] [10] [11] [12]. When the ambient temperature differs from that of the jet, this lateral air entrainment will affect the cooling efficiency. Since such airflow is not necessary at the jet temperature, it may affect the heat transfer between the impinging jets and the plate. This effect depends on the enthalpy of the entering air flux compared to the enthalpy of the jets. Based on this fact, a corrective model has been developed. It leads to a correction factor Fe by which the experimental average Nusselt number has to be multiplied to disregard this thermal entrainment effect:

Fe = 1 −

T plate − T jet

 A f 2 l 

15

20

Figure 6 plots the corrected average Nusselt number versus the jet Reynolds number based on the mean velocity, Uj, at the exit of the nozzle. Although the Martin’s correlation [1]

where n represents the number of slots.

T jet − Tamb

10

Figure 5 displays the variation of the correction factor, Fe , versus the normalised nozzle spacing for the types of slot arrangement tested. In the present case, the thermal entertainment enhances the heat transfer since the initial temperature of the jets turns to be higher than the temperature of the surrounding environment. As seen, the correction magnitude depends on the nozzle spacing. It is limited to 10% for array of perpendicular slot nozzles but may reach 30% when nozzle spacing is increased, as it is the case for tilted nozzles.

( n −1).W 2

∫h

5

Figure 5; Correction factor due to thermal entrainment

For engineering purpose like the design of industrial heat exchanger, it is more convenient to calculate an average convective heat transfer coefficient, from the local distribution. The actual cooling system runs with several consecutive plenums. The scale-model considers only one of them. Therefore, in order to transpose the correlation’s laws to industrial cases, it is convenient to compute a peak-to-peak integration:

hcv =

W/S

W/S=10 E/S=11.35 W/S=10 E/S=17.35 W/S=10 Martin W/S=6.25 E/S=17.35 W/S=6.25 Martin

250

150

10-3Re 50 20

40

60

80

100

Figure 6: Effect of Reynolds number on the mean Nusselt Number: comparison with the Martin’s correlation (4) does not account for the effect of the nozzle emergence length, E/S, a comparison with the IR data is proposed in figure 6. To be coherent with the applicability condition of the Martin’s correlation, only perpendicular-slot arrangements are considered.

In Eq. (4) f is an increasing function of the ratio A/l2 where A is the lateral entrance cross-section area and length of the slot. From the correction factor one can discern that the thermal

4

Copyright © 2002 by ASME

Figure 6 shows that the increase of the nozzle emergence is not really benefit to the heat transfer coefficient (line with bullet symbols). However, the E/S-effect lessens as the normalised nozzle spacing, W/S, decreases (bullet and square symbols). It is worth noting that the Martin’s correlation (dashed line) tends to underestimate the IR data. The absolute deviation grows as the Reynolds number augments. However, above the range of the validity of Martin’s relation (Re ≤ 40000) the relative deviation (NuIR-NuMartin)/NuIR is around 25% for the conditions relative to figure 6. At constant Reynolds number, the discrepancy enlarges as W/S increases.

the velocity of the moving strip.

Figure 8 - Surface grid of the computational domain. A standard k-ε turbulence model with wall functions is used for the computation. Second order upwind discretisation scheme is used for all the equations solved in steady state. The standard Simple algorithm is adopted for the pressure-velocity coupling. The boundary conditions are imposed based on the experimental conditions (temperature and velocity of the impinging jets, temperature of the ambient air, heat flux imposed on the heated plate).

NUMERICAL SIMULATIONS Three-dimensional numerical simulations are performed with the general-purpose commercial code FLUENT (Version 5.5). The mesh is generated using Gambit and consists only of hexahedral elements. The Pave algorithm is used for the creation of the surface mesh in all the surfaces located in the x-z plane.

A typical comparison between IR measurements and numerical simulation is shown in figure 9. The Nusselt number distribution along the centre line of the plate is plotted versus the reduced axial distance. Good agreement is observed assessing the correct modelling of the complex flow topology. Maximum values for the Nusselt number are within 10 % of the experimental values. The mean heat transfer coefficient is also within 10% of the experimental values. However, the minimum values between the jets are smaller than the experimental values measured with the IR camera. This region of low heat transfer coefficient corresponds to an unstable region. By doing a steady state simulation, we do not allow the separation point to move with respect to time and therefore the curve of heat transfer coefficient is less smooth numerically than experimentally.

A typical mesh for a configuration with two vertical jets and one inclined jet is shown in figure 7. The mesh is refined close to the heated plate to capture better the gradients of velocity, temperature and turbulence quantities. Afterwards, the grid structure is translated with a constant step in the y direction using the cooper algorithm of Gambit. This method creates a regular grid in the y-direction and allows controlling easily the position of the first grid cells. Special care has been taken for the position of the first grid cell near the heated wall. This position has been optimised to allow a good validation with the experimental results obtained with the IR camera.

400

IR data FLUENT

Nu

Re = 60000 Z/S = 4.55 W/S = 14.5

300 Figure 7 - Surface grid in the x-z plane

200

The complete surface mesh of the computational domain is shown in figure 8. Two planes of symmetry are shown in this figure. They were used in order to keep the number of cells relatively small. The computational domain is wider than the width of the slits in order to capture also the flow structure on the side of the jets.

100

X/S 0 -30

Typically 300000 cells are used for the discretisation of the entire computational domain. This number doubles when the effect of the moving strip of the flow field is investigated. In this latter case, one symmetry plane is removed to take into account

-20

-10

0

10

Figure 9: Experimental -numerical comparison. Figure 10 displays a typical numerical simulation of the airflow

5

Copyright © 2002 by ASME

The numerical simulation is also an appropriate means to appreciate the enhancement of the heat transfer produced by using H2/ N2 gas mixture instead of air. Such an investigation would be difficult in the pilot facility for safety consideration but can easily be approached with CFD.

in the experimental tests section. Path lines represented as function of time in seconds provides the flow visualisation. The numerical simulation reproduces correctly the entrainment of ambient air between the different jets as observed during the experimental tests. The ambient air entering in the computational domain is represented by blue path lines. It is sucked between the impinging jet and escapes back in the upper part of the domain.

500 Re = 100000 Z/S = 4.55 E/S = 11.35

Nu 400

symmetry axis

300 200 100

X/S 0

0

20

40

60

Figure 12: Nu-distribution in an industrial cooling unit. Figure 13 shows the axial distribution of the Nusselt number obtained for 5% and 60% H2, respectively, as normalised by the Nusselt number for air only. The increase of hydrogen content has a strong effect on the heat transfer rate, particularly in the impingement region. The numerical simulations indicate that the average heat transfer coefficient increases almost linearly with the H2 content. At constant Reynolds number, using 30%H2 may readily double the cooling efficiency. Moreover, performance equivalent to that of air may be reached with H2 jets working at lower Reynolds number and thus at lower power consumption.

Figure 10 : Lateral air entrainment in the test set-up. Numerical simulations have been also performed to test industrial situations. As predicted by Eq. (4), the numerical simulations shows that the increase of the cooling width leads to the disappearance of the lateral air entrainment as shown by the path lines plotted in figure 11.

5 % Hydrogen 5 60

Nu / Nua 4 3

Re = 60000 Z/S = 4.55

2 1

X/S 0 -20

Figure 11 : Flow pattern in an industrial cooling unit. Typical Nusselt number distribution in cooling unit of industrial size is plotted in figure 12. Since the design is symmetric only the left part is represented. It is clear that jet-to-jet interaction and end effects (X/S=0) introduce distortion in the heat transfer profile.

-15

-10

-5

0

5

10

15

20

Figure 13 : Effect of H2 content on heat transfer coefficient.

6

Copyright © 2002 by ASME

GM, eds), pp. 133-138, Eds. Européennes Thermique et Industrie, 1994.

CONCLUSIONS Local convective heat transfer coefficient in a multiple-jet systems composed of straight and inclined slot nozzles is experimentally and numerically determined. The concerned application is the fast cooling of moving steel strips.

[4] BUCHLIN (J-M). – Convective heat transfer in impinging-gas jet systems. In: “ Aero-Thermal Performance of Internal Cooling Systems in Turbomachines”, Lecture -Series 2000-03 edited by T. ARTS, von Karman Institute for Fluid Dynamics, Rhode Saint Genèse, Belgium, February 28 – March 3, 2000.

The experimental method involved the thermo-foil technique and the infrared thermography. The three-dimensional numerical simulations are performed with FLUENT (version 5.5).

[5] BUCHLIN (J-M) and DUBOIS (M). - Heat transfer of impinging multijet system. An application of the quantitative thermography. In : Quantitative Infrared Thermography QIRT 92 (Balageas D, Busse G, Carlomagno GM, eds), pp. 117-120, Eds. Européennes Thermique et Industrie, 1992.

On the whole, the numerical prediction agrees satisfactorily with the IR data. Both predict the thermal entrainment phenomenon, which is more pronounced for small slot widths. A correction factor which accounts for this lateral gas flow entrainment is proposed.

[6] SIEGEL ® and HOWELL (J.R). – Thermal Radiation Heat Transfer. HPC, Bristol, 1992

The nozzle tilting introduced to reduce strip flutter is accompanied by a decrease of the local heat transfer. The effects on the average heat transfer coefficient of the slot Reynolds number, the nozzle spacing, the nozzle emergence length and the nozzle-to-strip distance are appreciated. In this respect, deviations between the infrared data and the Martin’s correlation have been observed for high Reynolds numbers.

[7] KERCHER (D.M) and TABAKOFF (W).- Heat transfer by a square array of round air jets impinging perpendicular to a flat surface including the effect of spent air. Journal of Engineering for Power, Transaction of ASME, Vol. 92, No. 1, pp 73-82, January 1970.

After validation, the numerical simulation is extended to cooling unit of industrial size. The jet-to-jet interaction and end effects yield distortion in the heat transfer distribution. Moreover, the use of H2/N2 gas mixture instead of air may bring a significant increase of the cooling performance. Therefore, in producing H2-jets at lower velocity will give sufficient cooling performance at less aerodynamic excitation to strip fluttering.

[8] STRIEGEL (S.A) and DILLER (T.E). – The effect of entrainment temperature on jet impingement heat transfer. ASME Journal of Heat Transfer, Vol. 106, pp 27-33, Journal of February 1984-a [9] STRIEGEL (S.A) and DILLER (T.E). – An analysis of the effect of entrainment temperature on jet impingement heat transfer. ASME Journal of Heat Transfer, Vol. 106, No. 4, pp. 804-810, November 1984-b.

ACKNOWLEDGMENTS [10] HOLLWORTH (B.R.) and WILSON (S.I). – Entrainment effects on impingement heat transfer: Part I - Measurements of heated jet velocity and temperature distributions and recovery temperatures on target surface. ASME Journal of Heat Transfer, Vol.106, No. 4, pp. 797-803, November 1984.

This work was supported by the Walloon Region under Grant n°4125.

REFERENCES [1] MARTIN (H). - Heat and mass transfer between impinging gas jets and solid surfaces. Adv. Heat Transfer, Vol. 13, p. 1-60, 1977.

[11] HOLLWORTH (B.R.) and GERO ( L.R). – Entrainment effects on impingement heat transfer: Part II- Local heat transfer measurements. ASME Journal of Heat Transfer, Vol.107, pp. 910-915, November 1985.

[2] GOLDSTEIN (H.B). – Impingement cooling. In: “ Aero-Thermal Performance of Internal Cooling Systems in Turbomachines”, Lecture -Series 2000-03 edited by T. ARTS, von Karman Institute for Fluid Dynamics, Rhode Saint Genèse, Belgium, February 28 – March 3, 2000.

[12] GOLDSTEIN (R.J), SOBOLIK (K.A) and SEOL (W.S). – Effect of entrainment on the heat transfer to a heated circular air jet impinging on a flat surface. ASME journal of Heat Transfer, Vol. 112, pp. 608-611, August 1990.

[3] BUCHLIN (J-M); PRETREL (H); PLANQUART (P); LANGER ( H) and THIRY (F).- Infrared thermography study of a thermal anti-icing system. In : Quantitative Infrared Thermography QIRT 94 (Balageas D, Busse G, Carlomagno

7

Copyright © 2002 by ASME