Transactions on Modelling and Simulation vol 10, 1995 WIT Press, ISSN X

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1 High temperature heat transfer in glass during cooling - an experimental and computational approach K. Storck, M. Karlsson, B. Augustsson,* D. Loyd Applied Thermodynamics and Fluid Mechanics, Department of Mechanical Engineering, Linkoping University, Linkoping, Sweden * Glass Technical Department, PLM Limmared AB, Limmared, Sweden Abstract The influence of internal radiation on the thermal transport is an essential question in heat transfer calculations in glass at high temperatures. The internal radiation in semi-transparent materials may contribute to the energy transport in a way that may be mixed-up with thermal conductivity. During certain conditions this effect is large and causes an apparently higher value of the thermal conductivity, which can be much larger than the true thermal conductivity. During other circumstances, the literature indicates that this contribution may be neglected. In this study hot glass is put into a mould and the temperature of the glass surface as well as the temperature of the mould is measured. The experimental procedure is simulated with a finite element package and the measurements and the calculations are compared. The initial temperature of the glass is 1400 C and the mould is preheated to 400 C. The temperature of the glass surface is measured with a radiation pyrometer measuring in a wavelength interval where the glass is opaque. The mould temperature is measured at different locations with thermocouples. The study shows that the contribution of internal radiation to the heat transfer within the glass may be neglected for certain practical cases and for relatively thin plates of glass during unsteady state conditions. The radiative heat transfer out from the glass may still be significant. 1 Introduction In this study we discuss the cooling of glass. Hot glass is put into a mould and the temperature of the glass surface as well as the temperature of the mould are measured. The experimental procedure is simulated with a finite element package and the results from the calculations are compared to the measured data. This is done in order to investigate the influence of the internal radiative heat transfer of the glass on the time dependent temperature distribution. Radiative heat transfer within semi-transparent materials may sometimes be mixed-up with conduction. This is due to the radiative redistribution of heat within the domain, resulting in a flattening of the temperature gradient, implying a larger thermal conductivity than the true value. This phenomena gets more evident for a larger domain and when the conductive heat transfer is small compared to the radiation. For optically thin plates the radiation emitted from one

2 136 Computational Methods and Experimental Measurements point will not be absorbed within the semi-transparent domain. Furthermore, for unsteady state conditions, the conduction may be the dominant heat transfer mechanism and the internal radiation will not make a major contribution to the heat transfer. The project is carried out in a collaboration between the Department of Mechanical Engineering, Linkoping University, Linkoping, Sweden, and the Glass Technical Department at PLM Limmared AB, Limmared, Sweden. The aim is to obtain a better knowledge of the heat transfer mechanisms in glass bottle manufacturing. 2 Measurement Equipment In order to simplify the calculations and the evaluation of the measurements, the mould, shown in figure 1, is symmetric. The mould is made of cast iron and the mould boundary surface (the part of the mould surface which comes into contact with the glass) is highly polished. The mould is placed on a stand with three sharpened legs in order to minimise the thermal conduction out from the underside. The mould and stand are preheated in an oven and transported with a fork fitting in two holes in the base of the stand. The temperature of the mould is measured at six points, three on the underside of the mould and three 1.0 mm below the boundary surface. The points are positioned at the same distance from the axis of symmetry and equally spaced 120 apart. The temperature at the centre of the glass surface is measured with a radiation pyrometer measuring in a wavelength spectrum of /xm, where the glass is opaque. Comparing the output from the three thermocouples at the boundary surface respectively at the underside, it can be examined if the heat is equally distributed in the mould during the preheating and the cooling period. Glass boundary surface Mould 120mm Sharpend legs Stand ' Holes for transport fork Figure 1: The mould is placed on three sharpened legs and the equipment is transported with a fork fitting in two holes in the base of the stand. The placement and attachment of the thermocouples are shown in figures 2 and 3. The thermocouples are of K-type (chromel/alumel). On the underside of the mould they are tightly screwed. On the upper side the attachment is different. The thermocouple threads are led to the boundary surface of the mould through two thin holes emerging from a larger hole drilled from the underside. In the larger hole the threads are led through a ceramic cylinder. The threads are welded to the mould boundary surface and the surface is carefully polished. This method will cause the threads to melt and the actual measuring point will be located at a distance approximately 1.0 mm below the boundary surface.

3 Computational Methods and Experimental Measurements 137 couple 4.0mm *"" 5.5mm Screw Figure 2: The placement and attachment of the thermocouples. The output from the six thermocouples arid the radiation pyrometer are collected with a data-logger, at a sampling frequency of 1 Hz, and later transferred to a computer. 3 Measurements Gullet is placed in a platinum cup and heated in an electric oven to a temperature of approximately 1400 C. At this temperature the glass has a viscous behaviour somewhat like glycerin and it must be cut with a pair of scissors from the cup when poured into the mould at the beginning of the measurement. The mould, placed on the stand, is preheated to approximately 400 C in an electric oven. The thermocouples are connected to the mould and to the datalogger when it is placed in the oven and the radiation pyrometer is on place when the mould is taken out. The mould, on its stand, is placed on a ceramic foundation and the data collection starts. The whole procedure of placing the mould on the foundation and pouring the glass takes approximately 1 minute. The actual pouring of the glass requires only about 10 seconds. The measuring time is 200 seconds and the thickness of the glass has been varied between 8 and 19 mm. 4 Governing Equations and Modelling The temperature field of the considered domain as a function of space and time can be obtained by solving the heat conduction equation, see e.g. Carslaw and Jaeger [1]. The equation in three-dimensional Cartesian space coordinates and time (x, y, z, t) is shown in equation (1). The temperature depends on space coordinates and time, i.e. T = T (x, y, z, t). The density, p, the specific heat capacity, c, and the thermal conductivity in direction i, &,, depend on coordinates and temperature. a / <%r\, a / #r\ a / #r\ ^ a;rw + %; (W + &; r'w = ^ w The boundary conditions for equation (1) are prescribed heat flux and convective heat transfer. The prescribed heatflux,gg, can vary along the boundary and with time. For an insulated boundary, the prescribed heat flux is zero. This boundary

4 138 Computational Methods and Experimental Measurements condition can be written as follows, where /^, ly and /% are the direction cosines. dt dt dt. _ The boundary condition for convective heat transfer is given below. The convective heat transfer coefficient, /&#, and the surrounding temperature, Tgum can vary along the boundary and with time. The radiation can be included in this boundary condition, see Holman [2]. ox oy = 0 (3) The finite element package THAFEM (Thermal and Heat Analysis by Finite Element Method) has been used, see Loyd et al [3]. The program is intended for twodimensional plane and axi-symmetric problems, stationary as well as time dependent. A standard finite element formulation is used, see e g Zienkiewicz [4]. 5 The Finite Element Model The model describing the mould and the glass consists of 2553 nodes and 4880 elements and is axi-symmetric. It is built up by four property areas, two of them contact areas. Four convective and one insulated boundaries are used. The size of the mould, the location of the boundary conditions and the four property areas are shown in figure 3. symmetry axis v 45 mm jr«* CJJ5 10 mm' ' K glass J j mould; symmetry v axis Conv. Bound. 3 c ^> Conv. Bound. \u I ' j glass / mould i "^ ; contact \ area ; 40mm ins. 20mm "'\ j * measuring points; Bound. 1 : contact ; vj_ i, j area r*- L 60mm ' Conv. Bound. 4 Figure 3: Axi-symmetric model describing the mould and the glass. \ >. Conv. Bound. 2 The glass is a separate property area as well as the mould. The two remaining ares are found in the zone between the glass and the mould, named "contact area" in the figure, one at the underside of the glass and one at the side inclined 15. These areas are used to model the thermal contact resistance between the glass and the mould. The contact is a function of the smoothness of the surface, the pressure the glass exerts on the surface and the state of the glass, i.e. whether the glass is liquid or has solidified. In this study we will keep the contact resistance independent of time. The convective part of the structure is divided into four regions because of the difference in natural convection and radiative heat flux. The natural convection is a function not only of the surface temperature and the surrounding fluid but also of the geometry of the surface. The radiative heat loss is a function of the

5 Computational Methods and Experimental Measurements 139 properties and temperature of the surface and its surroundings. For all convective boundaries the radiative heat transfer is linearised and added to the convective heat transfer coefficient. For convective boundary condition number one, i.e. the glass surface, the influence from the radiative heat flux is complicated by the fact that the radiation from the glass is not purely a surface effect. The radiant heat loss from the glass mainly origins from the inside of the domain. This means that the heat transfered from the domain is radiated as well as conducted to the surface. 6 Results from Measurements An example of the result from the measurements are shown infigures4 and 5. In figure 4 the glass thickness is 10 mm and in figure 5 it is 19 mm. Only one of the three thermocouples at the underside respectively the boundary surface of the mould is shown here. The thickness was measured after the completion of the measurement glass surface - mould boundary surface -* mould underside time [s] Figure 4: Measured temperature as a function of time. The glass thickness is 10 mm ^1000 glass surface mould boundary surface mould underside Z. 800 Q. * time [sj Figure 5: Measured temperature as a function of time. The glass thickness is 19 mm. In figure 6 the output from all six thermocouples connected to the mould is shown. The output shows that the temperature distribution is even in the mould during the measurement, except for one thermocouple on the the underside of the mould which gives a slightly higher output. This was not changed when

6 140 Computational Methods and Experimental Measurements the mould was placed in a different position in the oven during the preheating. The reason for the changing was the suspicion that the placement of the electric heating element would affect the temperature distribution in the mould during preheating. It is highly probable that this thermocouple is malfunctioning ct y Q_ ~ 450 mould boundary surface mould underside time [s] Figure 6: The output from the six thermocouples show that the temperature distribution is even in the mould during the measurement. The slightly diverging thermocouple on the underside is probably due to malfunctioning. 7 Results from Finite Element Calculations The result from a finite element calculation for the case with 10 mm glass is shown in figure 7. In this case the contact resistance between glass and mould is 10 OOOW/nfK and the thermal conductivity of the glass 0.8 W/m K. In figure 8 the thermal conductivity of the glass is 2.0 W/m K glass surface mould boundary surface mould underside Q time [s] Figure 7: Result from thefiniteelement calculation. The glass plate is 10 mm and the thermal conductivity of the glass is 0.8 W/mK. 8 Discussion The rate of heat transfer in the studied problem is neither rapid nor slow. Compared to the cooling rate of glass at a glass bottle production site, the cooling

7 Computational Methods and Experimental Measurements glass surface mould boundary surface mould underside Z. 800 Q time [s] Figure 8: Result from the finite element calculation. The glass plate is 10 mm thermal conductivity of the glass is 2.0 W/mK. and the in this study is rather slow, see e.g. Storck et al [5], Pchelyakov and Guloyan [6] or McGraw [7]. On the other hand, the temperature change here is rapid in comparison to the melting procedure at a glass production site. The measurements in figure 4 and the finite element calculations in figure 7 have a good overall agreement, except on two occasions. Firstly at the early temperature peak at the boundary surface of the mould, marked "A" in figure 7, and secondly at the fall of the glass surface temperature at large time values, marked "B" The first divergence is caused by the radiative heat transfer to the mould from the hot glass. The radiation will cause a heat pulse in the beginning of the measurement, when the temperature difference between the glass and the mould is large. This is not completely taken into account in the calculations presented here. The second deviation is probably caused by a combination of a time varying contact resistance between the mould and the glass, and the modelling of the radiative heat transfer of the glass. When the glass is chilled beyond the solidification temperature, the contact between the glass and the mould will be less efficient to transfer heat. If the temperature distribution on the glass surface facing the mould is irregular, the glass becomes arched and the contact will decrease. Furthermore, the radiation from the glass is transfered to the surface by conduction in the model. The result is a steeper temperature gradient than in a model where the radiation can emanate from the whole glass structure. The early temperature peak at "A" can be increased in the calculations, e.g. by increasing the heat transfer coefficient of the contact between glass and mould, or by increasing the thermal conductivity of the glass. The latter gives the largest effect, see figure 8. However, both these methods lead to a steeper fall of the glass surface temperature at "B". This indicates that the resistance to heat transfer in the contact zones is smallest in the beginning of the cooling period, when the glass is fluid. It also indicates that the radiation does not contribute to the heat transfer within the glass in a "conductive" way in this temperature range and during unsteady state conditions. A combination of the methods mentioned above and thermal properties varying with time is a third method. The largest difficulty is to predict the contact resistance. The use of a time independent contact resistance clearly gives a divergence between the measurements and the calculations.

8 142 Computational Methods and Experimental Measurements 9 Conclusions The cooling of hot glass coming into contact with a cold mould surface has been studied. Temperature measurements at the glass surface and in the mould have been compared to finite element calculations. The radiative redistribution of heat within thin plates of glass, in the order of 10 mm or less, is generally small compared to the conduction during unsteady state conditions. The radiation emanating from the semi-transparent domain, on the other hand, is not negligible. The radiation from the glass reaching the mould is significant in the initial stage, when the temperature difference between the glass and the mould is large. The time and temperature variation of the contact resistance between the glass and the mould is vital to a careful calculation of the transient behaviour of the glass as well as the mould. Cooling of glass is a complex industrial problem. The measurements and calculations presented here are an introductory study which will be followed by a more comprehensive analysis. 10 Acknowledgement The authors would like to thank Mr Gunnar Andersson, Lic.Eng., Department of Mechanical Engineering, for valuable discussions and help with the computer program. We are also grateful to Mr Hakan Winther, M.Sc., and Mr Lennart Palmquist, both at PLM Limmared, for valuable discussions and for carrying out the measurements. References [1] Carslaw H.S. & Jaeger J.C. Conduction of heat in solids, 2 edn, Oxford University Press, [2] Holman J.P. Heat transfer, McGraw-Hill, London, [3] Loyd D., Andersson G. & Froier M. THAFEM - a Finite Element Program for Heat Transfer Analysis, Finite Element Systems - a Handbook, Ed. C.A. Brebbia, 3 edn, pp , Springer-Verlag, Berlin, [4] Zienkiewicz O.C. The Finite Element Method, McGraw-Hill, London, [5] Storck K., Karlsson M. & Loyd D. Analysis of the blank mould - a transient heat transfer problem in glass forming, Proc. of the Third Conference on Advanced Computational Methods in Heat Transfer, pp , Southampton, UK, 22nd- 24th August [6] Pchelyakov S.K. & Guloyan Yu.A. Heat transfer at the glass-mould interface, Glass and Ceramics, 1985, vol. 42, pp [7] McGraw D.A. Transfer of Heat in Glass During Forming, Journ. Am. Cer. Soc., 44, no. 7, 1961, pp