Numerical analysis of heating characteristics of a slab in a bench scale reheating furnace

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1 International Journal of Heat and Ma Tranfer 5 (27) Technical Note Numerical analyi of heating characteritic of a lab in a bench cale reheating furnace Sang Heon Han a, *, Seung Wook Baek a, Sang Hun Kang b, Chang Young Kim c a Diviion of Aeropace Engineering, Department of Mechanical Engineering, Korea Advanced Intitute of Science and Technology, Kuung-dong, Yuung-ku Daejeon, Republic of Korea b Korea Aeropace Reearch Intitute, 45 Eoeun-dong, Yuung-ku Daejeon, Republic of Korea c Reearch Intitute of Indutrial Science and Technology, 32 Hyoja-dong, Nam-ku Pohang, Republic of Korea Received 29 September 26 Available online 1 February Introduction The heat tranfer to a lab in a reheating furnace depend on variou factor uch a the hape of furnace, type of burner, arrangement of burner, burner operating condition, type of fuel, location of the lab, and the lab thermal property. The furnace geometry a well a intallation of burner ha deciive role in determining the flow and temperature field which have direct influence on the heat tranfer. A lab i heated by conduction, convection and radiation. Conduction and convection are incurred by combution ga, while radiation heat come from furnace wall a well a product gae. However, conduction and convection exert only a little contribution, a a lab i motly heated by the radiation. Radiation heat tranfer i largely affected by the compoition of combution ga and flame temperature which are determined by the characteritic of turbulent combution. A few numerical reearche have been conducted to imulate a reheating furnace and heating lab. Li et al. calculated radiative heating of lab in a furnace chamber uing zone method [1]. Chapman et al. performed numerical modeling and parametric tudie for a direct fired continuou reheating furnace [2]. Zhang et al. tried to predict the thermal performance of a regenerative reheating furnace by uing FLUENT [3]. They ued P1 method for radiation model and PDF model for turbulent combution. The prediction of tranient lab temperature wa carried out in a walking-beam type reheating furnace by Kim and Huh [4]. They calculated teady tate heat tranfer to lab uing * Correponding author. Tel.: ; fax: addre: freezia@kait.ac.kr (S.H. Han). FLUENT and performed eparate calculation of the temperature ditribution in lab with finite difference method. Chen et al. analyzed energy conumption and performance of reheating furnace in a hot trip mill by mean of both numerical and experimental method [5]. The preent work i to imulate the tranient heating characteritic of a lab inide bench cale reheating furnace intalled in POSCO Corporation. The bench cale reheating furnace i a tet facility for invetigating the lab heating characteritic. It operation make it poible to overcome many limitation exiting in the experiment with full cale reheating furnace. ally, a lab i inerted into the furnace and it temperature variation i meaured in both the ga field and the lab with thermocouple. The numerical analyi i performed here by developing it own code. A detailed numerical calculation of heating characteritic of lab i carried out with the developed code and it reult are validated in comparion with experiment. 2. Theoretical model The developed code adopt the SIMPLE algorithm [6 8], the tructured curvilinear grid, the tandard k e model for turbulence [9], the eddy diipation model for combution [1,11], and FVM method for radiation [12 14]. The weight um of gray ga model i applied to the radiation olving procedure for better accurate olution [15,16]. Fuel i aumed to be a mixture of CO, H 2,CH 4,C 2 H 6. Fuel i injected into the furnace through a burner in a premixed tate. Chemical reaction of fuel are governed by imple two tep reaction. While CH 4 and C 2 H 6 are initially oxidized to the mixture of CO and H 2 O, H 2 i directly oxidized to H 2 O by one tep reaction /$ - ee front matter Ó 26 Publihed by Elevier Ltd. doi:1.116/j.ijheatmatranfer

2 22 S.H. Han et al. / International Journal of Heat and Ma Tranfer 5 (27) Nomenclature k turbulent kinetic energy, m 2 2 T temperature, K W k molecular weight, kg/mol ma fraction of pecie k Y k Greek ymbol e turbulent diipation emiivity of a lab e q denity of mixture, kg/m 3 k thermal conductivity, W/m/K Subcript fu fuel g, ga field and lab pr product C xk H yk þ x k 2 þ y k O 2! x k CO þ y k 4 2 H 2O; k ¼ H 2 ; CH 4 ; C 2 H 6 CO þ 1 2 O 2! CO 2 Eddy diipation model, propoed by Magnuen and Hjertager [1], i ued to imulate turbulent combution in the code. It i an extended model of eddy-break-up [EBU] model to be applied to both premixed and non-premixed flame, wherea EBU wa intended only for premixed flame. According to thi model, the reaction rate R fu i defined a R fu ¼ q e k min ay fu; a Y O 2 ; b Y p 1 1 þ 1 where 1 ¼ :5 W O 2 ð3þ W fu Here e=k i the reciprocal of turbulent mixing time t and 1 i the toichiometric ma ratio of oxygen to fuel. Empirical contant a and b, ued in the above equation, are 4 and 2, repectively. On the urface of the lab, the incoming heat flux from ga field i balanced with conductive heat flux into the lab. The incoming heat flux to the lab conit of conductive and radiative heat fluxe. ot k g on e rt 4 þ e q R in ¼ k ot ð4þ g on ; ð1þ ð2þ 3. Reult and dicuion Fig. 1 how an overall feature of the bench cale reheating furnace which ha the dimenion of 6. m m m. There exit a ingle burner at the center of left end of the furnace and it port i implified to be a imple circle with diameter of.182 m. Exhaut ga exit the furnace through the right-hand ide wall. One lab of.7 m.4 m.85 m i located at the height of.21 m from the furnace bottom and the lab i teted at two different axial location of.5 and 4. m from the burner wall. Temperature i meaured at three location in the ga field. The location of the thermocouple, which meaure ga temperature, are plotted in Fig. 2a. The figure i the top view located at z ¼ 1:3 m. Their location vary along x-coordinate, wherea their y and z coordinate are fixed to.5 m and 1.3 m. Three temperature meaurement poition inide the lab are hown in Fig. 2b. It i a central cro ection of a lab which i perpendicular to x-direction. The thermocouple are located along the z-directional center line of the cro ection. Fig. 3 and 4 how a variation of experimental and computational lab temperature at three location S 1, S 2 and S 3 inide the lab a hown in Fig. 2. The computational reult in Fig. 3 for axial lab location of.5 m how more deviation from the experimental one than thoe for 4. m in Fig. 4. Thi i due to the fact that the lab heating i more intene and the thermo-fluid mechanical characteritic where the ubcript g,, and n denote ga, olid, and normal direction, repectively. q R in i the incoming radiative heat flux and e T 4 i the radiative emiion from the lab urface to ga field. The lab urface temperature T i calculated by tranformation of Eq. (4). T i obtained through a linearization to get more table convergence. T ¼ k g T D g þ e q r in þ 3e rt 4 T þ k D ð5þ g þ 4e rt 3 k D þ k D (unit:m) Z X Y Aterik denote previou iteration tep and D mean the pacing between two neighboring node. T i updated at the end of each iteration and it i ued for boundary condition in later iteration tep. 6. Fig. 1. Geometrical model of the bench cale furnace.

3 S.H. Han et al. / International Journal of Heat and Ma Tranfer 5 (27) lab G1 G2 G (unit: m).7 (unit: m) S1 S2 S3 furnace. The lope in a temperature profile i largely affected by radiative heat tranfer becaue it i more dominant than convection. The ma average temperature of a lab i raied to 925 C at the time of 36 for the.5 m location while it i 69 C for the 4. m location. Fig. 5 repreent a tranient variation of ga temperature at three location. At the uptream location, G 1 the ga temperature i the lowet due to the effect of intake of freh air during the inertion of a lab. At the mid-location, G 2 the ga temperature reache the highet temperature and then it decreae going downtream at the location, G 3. Thi trend i alo well oberved by computation, which i imilar regardle of the lab location. But the ga temperature for lab location of 4. m i oberved to be lower than that for.5 m, ince the fuel flow rate i lower a lited in Table 1. ally, the meaurement how an unteady behavior owing to it inherent burner characteritic. On the other hand, the computational prediction ga filed 12 Fig. 2. Location of the thermocouple. are more complex for axial lab location of.5 m. Therefore, the lab at.5 m i heated up fater than that at 4. m location. For the cae of 4. m location, a very good agreement between computational and experimental one i oberved. The lope in temperature variation i important becaue it i correlated to the rate of heating of a lab. The heating rate can be ued for deigning reheating Ga Temperature( o C) G 1 Probe 8 G 1 Probe 9 (Open) G 2 Probe (Solid) 75 (Open) G 2 Probe 85 (Solid) G 3 Probe G 3 Probe m location 4.m location Fig. 5. Tranient temperature plot for the ga field. Ga Temperature( o C) S 1 Temperature ( o C) S 2 Temperature ( o C) S 3 Temperature ( o C) S 1 S 2 S 3 Fig. 3. Variation of temperature for three location inide lab for the lab location of.5 m S 1 Temperature( o C) S 2 Temperature( o C) S 3 Temperature( o C) S 1 S 2 S 3 Fig. 4. Variation of temperature for three location inide lab for the lab location of 4. m.

4 222 S.H. Han et al. / International Journal of Heat and Ma Tranfer 5 (27) Table 1 Burner inlet condition Location (m) Fuel flow rate (m 3 /h) Air flow rate (m 3 /h) exhibit an almot teady behavior in ga temperature variation. al ga temperature i een to lowly rie becaue a heat lo from hot ga to a lab decreae with time on account of increae in the lab temperature. When a lab i heated up, it corner are heated fater than any other region. A corner ha larger thermal reitivity than the other region, becaue heat penetrate into the lab from three adjoining urface. The temperature of a corner i raied up to 241 C in only 1, while inner region inide the lab remain at 41 C. In cae of edge, the number of heat penetration direction i two. So the lab alo experience larger temperature build-up on edge than on flat plain urface. Fig. 6 illutrate variation of the temperature difference between inner lab point and three other point corner, edge and flat urface on the upper urface of the lab. Corner temperature i taken from the corner point of x ¼ :5 and y ¼ :375, while the edge temperature i from the middle point of y ¼ :375 line. Plain urface temperature i taken from the center point of the upper urface. Maximum temperature difference between corner and inner lab i 419 C at 21 for.5 m lab location and 264 C at 55 for 4. m lab location. Maximum temperature difference between edge and inner lab i 255 C at 32 for.5 m lab location and 155 C at 7 for 4. m lab location o that the maximum temperature difference occur earlier for the corner than for the edge. Thi i due to quicker heating of the corner than the edge. The flat urface reache the maximum temperature difference earlier than any other region. It i becaue the heat tranfer from the center point of flat urface to inner lab travel the hortet ditance among other. Fig. 7 repreent a tranient variation of variou heat fluxe from hot ga to the lab. It i een that over 9% of heat flux come from the radiation. Heat flux continue to decreae with time becaue of the rie in the lab temperature. It i alo oberved that heat fluxe for two different location are revered at certain time. Thi i becaue the Temperature( o C) Corner Edge Flat urface Solid(.5m) Open(4.m) 2 3 Fig. 6. Variation of temperature difference between repective point and inner lab. Heat flux (kw/m 2 ) lab temperature for lab location of.5 m i raied more quickly than that for the 4. m location on account of larger heat tranfer rate in the early tage. 4. Concluion Total flux Radiative flux Conductive flux Radiation percentage Solid(.5m) Open(4.m) 2 3 Fig. 7. Tranient variation of variou heat fluxe. A numerical program ha been developed and applied to invetigate the heating characteritic of the lab in a bench cale reheating furnace. It numerical reult were validated by comparion with the experimental data obtained in the tet facility intalled in POSCO company. 1. The corner of the lab are heated fater than any other region becaue they have larger thermal reitivity than the other region edge and flat plain urface. The temperature difference between a corner point conidered and inner lab point increae until a certain intant, but after then it continuouly decreae by action of inward conduction. Maximum temperature difference between the corner point and inner lab i 419 C at 21 for.5 m lab location and 264 C at 55 for 4. m lab location. 2. It wa found that over 9% of the total heat tranfer from the ga to the lab occurred by radiation. Therefore, a very accurate method would be neceary in olving the radiative tranfer equation. Numerical method for radiation ha to be able to treat ga emiion a well a wall emiion with appropriate accuracy. In thi repect, the finite volume method for radiation wa turned out to be very uitable for the imulation of a reheating furnace through the comparion of prediction with experimental reult. 3. The premixed aumption combined with eddy diipation model made ome difference in predicting ga phae temperature, but it worked out a pretty favorable prediction of lab temperature. Thi i becaue a lab i motly heated by radiation of which quantity i not critically dependent on the location of flame but on the ize and temperature of the flame. So, premixed combution model i thought to be the appropriate aumption for the imulation of lab-heating characteritic of a real Percentage (%)

5 S.H. Han et al. / International Journal of Heat and Ma Tranfer 5 (27) cale reheating furnace. The burner can be more implified with the premixed aumption than with the non-premixed aumption and it can make full cale calculation, which require huge computing power, more probable. Acknowledgement The financial aitance by the Combution Engineering Reearch Center at KAIST i gratefully acknowledged. The experimental data adopted in thi paper work i upplied from Reearch Intitute of Indutrial Science & Technology (RIST) at the city of Po-Hang. Reference [1] Zongyu Li, P.V. Barr, J.K. Brimacombe, Computer Simulation of the lab reheating furnace, Can. Metall. Quart. 27 (1988) [2] K.S. Chapman, S. Ramadhyani, R. Vikanta, Two-dimenional modeling and parametric tudie of heat tranfer in a direct-fired furnace with impinging jet, Combut. Sci. Technol. 97 (1994) [3] C. Zhang, T. Ihii, S. Sugiyama, Numerical modeling of the thermal performance of regenerative lab reheat furnace, Numer. Heat Tranfer Part A 32 (1997) [4] Jong Gyu Kim, Kang Y. Huh, Prediction of tranient lab temperature ditribution in the re-heating furnace of a walking-beam type for rolling of teel lab, ISIJ Int. 4 (2) [5] W.H. Chen, Y.C. Chung, J.L. Liu, Analyi on energy conumption and performance of reheating furnace in a hot trip mill, Int. Commun. Heat Ma Tranfer 32 (25) [6] S.V. Patankar, Numerical heat tranfer and fluid flow, Hemiphere, 198. [7] M. Peric, A finite volume method for the prediction of three dimenional fluid flow in complex duct, Ph.D diertation, Imperial College, [8] Joel H. Ferziger, M. Peric, al Method for Fluid Dynamic, third ed., Springer, 22. [9] B.E. Launder, D.B. Spalding, The numerical computation of turbulent flow, Comput. Meth. Appl. Mech. Eng. 3 (1974) [1] B.F. Magnuen, B.H. Hjertager, On mathematical modeling of turbulent combution with pecial emphai on oot formation and combution, in: 16th ympoium on Combution, 1977, pp [11] Deni Veynante, Luc Vervich, Turbulent combution modeling, Progre Energy Combut. Sci. 28 (22) [12] B.G. Carlon, K.D. Lathrop, Tranport Theory-the Method of Dicrete Ordinated in Computing Method in Reactor Phyic, Gordon & Breach Science Publiher (1968) [13] E.H. Chui, P.M.J. Hughe, G.D. Raithby, Implementation of finite volume method for calculating radiative tranfer in a pulverized fuel flame, Combut. Sci. Technol. 92 (1993) [14] S.W. Baek, M.Y. Kim, J.S. Kim, Nonorthogonal finite-volume olution of radiative heat tranfer in a three-dimenional encloure, Numer. Heat Tranfer Part B 34 (1998) [15] M.F. Modet, The weighted-um-of-gray-gae model for arbitrary olution method in radiative tranfer, ASME J Heat Tranfer 113 (1991) [16] T.K. Kim, J.A. Menart, H.S. Lee, Nongray radiative ga analye uing the S N dicrete ordinate method, ASME J. Heat Tranfer 113 (1991)