A Simplified Practical Model for a Walking Beam Type Reheat Furnace with Specific Heat Transfer Characteristics

Transcription

1 Journl of Modeling nd Optimiztion 8:2 (2016) A Simplified Prcticl Model for Wlking Bem Type Rehet Furnce with Specific Het Trnsfer Chrcteristics Lingyn Hu College of Informtion Engineering, Dlin University, Dlin , Chin E-mil: hulingyn@dlu.edu.cn Abstrct: A simplified technique is introduced to develop mthemticl model ccording to the specific het trnsfer chrcteristics in wlking bem type rehet furnce. The model cn predict the het flux on billet surfce nd temperture distribution inside billet by the therml rdition in furnce chmber. Considering the boundry conditions, the hot gs blckness coefficient is corrected during rditive het flux clcultion which improves model ccurcy. The model is simulted with Mtlb softwre. Simulting results verify the effectiveness nd fesibility of the proposed modeling method. Keywords: rehet furnce; rditive het trnsfer; therml model; trnsient het conduction eqution 1. Introduction In the metllurgicl industry, wlking bem type rehet furnces re one of widely used equipment for slb or billet het tretment. It s the typicl longitudinl, lrge furnce which continuously rehets semi-finished billets to certin temperture which is pproprite for processing in the next rolling mill [1]. The nlysis of trnsient heting chrcteristics for the billets in this type of furnce hs ttrcted considerble ttention during the pst severl decdes since the het tretment process should reduce energy consumption, pollutnt emissions nd operting cost. Furthermore, t the furnce exit, requirement of the uniform temperture distribution inside the billet gretly increses the importnce of fst nd ccurte prediction of het tretment process becuse this determines the product qulity nd productivity. Thus models nd methodology for investigting the furnce combustion behvior nd het trnsfer process hve very importnt prcticl significnce to metllurgicl engineering systems in steel plnts [2]. Up to now, number of vluble results hve been reported nd successfully pplied in different types of rehet furnces. The min techniques include the following pproches. The first one solves the full Nviere- Stokes nd energy conservtion equtions governing the hot gs flow nd combustion process with therml rditive trnsport phenomen in furnce. A few studies hve been crried out with CFD simultions [3, 4, 5] where both convection nd rdition with fluid flow clcultions re considered. Although the sophisticted CFD simultions cn be employed to predict the therml chrcteristics in furnce, in prctice it firly costs much due to the lrge computtionl time required in order to mnge the complexity of the lrge-scle furnce. The other pproch, which is simplified but cn resonbly simulte the therml behvior of billet, focuses on the nlysis of rditive het trnsfer in the furnce nd trnsient het conduction inside the billet [1-2,6-15]. In the simplified het trnsfer models, only rdition het trnsfer in the furnce is considered. The rdition clcultions re done using different rdition het trnsfer model, for exmple in literture [1, 6, 7], the temperture distribution inside the slbs is expressed s 1-dimensionl model. Other furnce models like [2, 8-10] clculte the temperture distribution in the billets with 2-dimensionl model. In [11-13], the full 3- dimensionl temperture model is discussed. However, complex three dimensionl trnsient model mkes the problem difficult to nlyze ccurtely nd economiclly in prcticl ppliction. It cn be seen from the bove literture points of view tht there re mny vrious models vilble in the heting process, however every furnce hs its own configurtion nd het trnsfer mechnism. There is no uniform model pplicble to ll kinds of rehet furnces. Thus, it should be considered to build specific model iming t different het chrcteristics for different engineering systems. This pper refers to the het tretment process for copper-lloy billet products in the wlking bem furnce. Different from other works, the flt-flme burners re ll locted on the top of the furnce. The gs flow is smll. And this mens ll het resource comes from the upside of the billets. And convection flow is not involved in the het exchnge. In terms of the therml chrcteristics, we ttempt to build model esily to implement in prcticl engineering systems. Tking boundry conditions into ccount, the hot gs blckness coefficient correction is ddressed during the modeling 19

2 8:2 (2016) Journl of Modeling nd Optimiztion to mke the computtion result more precise. At lst, the temperture distribution inside billet is simulted with Mtlb softwre. 2. Configurtion of the furnce Figure1 illustrtes the bsic structure of the wlking bem rehet furnce considered in the present work. The bsic function of rehet furnce is to het copper billets up to required temperture while mintining uniform temperture in the billet with temperture grdient not greter thn 5 t the exit of the furnce. The requirement of the uniform temperture distribution is to ensure the qulity of billets. The present rehet furnce is divided into three prts: preheting, heting nd soking zones. The totl dimensions of the furnce re 6352mm 1600mm 21800mm (Width Height Length). There re number of flt-flme burners locted on the top of the furnce. The billets re successively moved into the furnce where fuel-fired burners serve s het sources. In order to mintin the temperture uniformity in the furnce, the heting zone is divided into two sub-zones nd there re eight burners equipped on the top of ech zone. Accordingly the soking zone is divided into eight sub-zones with two or three burners in ech zone. The lst two sub-zones next to the outlet re regrded s the dditionl heting zones. There is no burner in the preheting zone. Exhust gs is re-circulted to prehet billets in this re. Thus billets re mostly heted in the heting nd soking zones. The min role of soking zone is to reduce the temperture grdient inside billet. Burners Inlet Outlet 1600 Preheting zone Heting Heting zone I zone II Soking zone Figure 1. Configurtion of the bem rehet furnce (mm) The billet is moved forwrd by the periodic bem motion. The copper billets minly hve the following two specifictions. One type is mde of beryllium bronze nd the size is 0.33m 0.15m 5.0m (Width Height Length). The other type is mde of iron bronze nd the size is 0.43m 0.21m 5.0m. The billets re ssumed to be isotherml of mbient temperture 25 when moving into the furnce t the inlet. Billet residence time from chrging into the furnce to exit is typiclly 300min to obtin the men billet temperture of 850. The fuel is nturl gs with het vlue 34.91MJ/ Nm Mthemticl formultion 3.1 Het chrcteristics nd ssumptions Intrinsiclly, the combustion process nd hot gs flow within furnce chmber influence the het trnsfer process through conduction, convection nd therml rdition simultneously. However, in present work, the burners re flt flme nd ll the burners re locted on the top of the rehet furnce. The pulse combustion control technology is pplied. Air flow is smll inside the furnce. Therefore, it is mostly the upper rditive het trnsfer with over 95% proportion of ll energy exchnge in the furnce. Rdition emitted by hot gs on the upper side of the billet is bsorbed. The bsorbed rdition is converted into het energy nd it further penetrtes inside the billets by mens of conduction. By the bove nlysis of het chrcteristics, the following technologicl specifictions nd ssumptions re given: (1) Therml rdition is the only considered mode of het exchnge in the inner heting environment. Other types of het trnsfer like convection re negligible. When systems come into stble stte, the het exchnge between billets nd bems is negligible, s well s the furnce inner wlls. 20

3 Journl of Modeling nd Optimiztion 8:2 (2016) (2) For ny billet, the temperture of prticipting surfce is homogeneously distributed inside billet. (3) The furnce chmber temperture is continuously piecewise liner function long furnce length. The totl het exchnge fctor is consistent in the sme furnce zone. 3.2 Conductive het trnsfer Conductive het trnsfer inside the billet cn be normlly clculted from the trnsient three dimensionl het conduction eqution s follows: dt T T T ρcp = [ λ ] + [ λ ] + [ λ ] (1) d tx x y y z z where ρ, c p, λ re density, specific het nd conductivity of billet. T denotes the billet current temperture. xyz,, respectively represent billet width, length nd height directions. As mentioned in the bove sections, there is no burner on the bottom nd wll in the furnce. All the flt burners re equipped on the furnce top. Thus the het energy bsorbed by the billets is verticlly rdition. Menwhile bsing on the ssumptions given in 3.1, the trnsient model cn be simplified into the following one-dimensionl het conduction eqution: dt T ( z) ρcp = λ dt z z (2) Hence 2 2 dt λ T T = = σ (3) 2 2 dt ρcp z z The simplifiction process nd conductive het trnsfer flow cn be illustrted with Figure 2. C i-1 x,y,z-1 Billet j Billet j C i-1 x-1,y,z C i x,y,z C i-1 x,y-1,z τ Simplify C i-1 x,y,z-1 C i x,y,z h Energy trnsport Figure 2. Simplifiction of het conduction in billet i where Billet j denotes the jth billet in the furnce, Cxyz,, represents the ith micro-cell cube inside the billet. τ is the specific time period for the micro cube to bsorb het energy. Hence, the het trnsfer only occurs long billet z-xis, nmely through thickness or height direction from top to bottom. By the bove het exchnge nlysis, it cn be found lthough the model is simplified, its het trnsfer much more conforms to the prcticl het chrcteristics. And the temperture trnsient model is composed by two prts: trnsient het conduction eqution nd boundry conditions. 3.3 Boundry conditions In this section, the boundry conditions will be nlyzed. It s the essentil initil stte in order to get the temperture distribution inside the billet. Let q (), t q () t,( comm is deleted here) be used for the upper nd b 21

4 8:2 (2016) Journl of Modeling nd Optimiztion bottom rditive het flux on the billet surfce in the eqution (2). Then the system initil function nd boundry conditions re given by T( zt, ) = ϕ( z), 0 < z< H,0 < t t0 T( z) λ z= 0 = q() t (4) z T( z) λ z= H= qb() t z where H represents the billet thickness, ϕ( z) is the initil temperture function long z-xis. There is no burner on the flnk nd bottom, ll the het energy comes from the upper side, so qb () t will be negligible. As the therml rdition minly comes from the hot gs in furnce, then the therml rdition eqution is given by Tg 4 T 4 m QRg = C0 εg ϕ gm ( ) ( ) Sm (5) where Q is the rditive het flux, T, T Rg g m represent the gs nd billet surfce tempertures, Sm, ε g nd C0 re 2 4 the billet surfce heted re, gs blckness nd rdition coefficient with C0 = 5.675[ W / ( m K )] respectively. ϕ gm is the rdition ngle coefficient. In the het nd soking zones, the rdition gs is minly composed by CO2, H 2O. Becuse the rdition hs strong selectivity, the gs blckness coefficient need correct to get the precise computtion. Tking the het zone I for exmple, the corrected gs blckness coefficient is given by ε = ε + ε ε (6) g CO2 H2O where εco, εh O, ε denote the CO2, H 2O blckness coefficient nd corrected vlue of gs blckness. The 2 2 following procedure is given to clculte ε g in eqution (6): Step1: First clculte the verge effective ry distnce L het of heting zone I According to the furnce configurtion, we hve S = W L (7) Het _ top Inner Het S = 2 H L + 2 W L + S (8) Het _ Inner Het Het Inner Het Het _ top where L Het, H Het nd W Inner represent chmber length, height nd inner width of het zone I. S Het _ Inner, S Het _ top re the furnce inner re nd furnce top re of het zone I. The chmber volume V Het with hot gs is: VHet = WInner LHet HHet (9) Then the verge effective ry distnce L cn be clculted by het L het 4 V Het = η (10) S Het _ Inner where η is the gs rdition coefficient, generlly tking η =0.85~0.9. Step2: Clculte the synthetic pressure in furnce The prtil pressure P, P in het zone I cn be obtined through Combustion technicl mnul [14], then we hve where P per formul, the corrected CO2 H2O P per = P P HO 2 + P H2O CO2 syn H2O CO2 het (11) P = ( P + P ) L (12), P syn re the prtil pressure proportion nd synthetic pressure of heting zone I, bsing on the bove ε cn be inquired, then corrected gs blckness coefficient cn be obtined with (6). The rdition ngle coefficient between hot gs nd copper billet cn be clculted by SHet _ top ϕ gm = (13) S According to (1)-(7), the het flux density cn be given by m 22

5 Journl of Modeling nd Optimiztion 8:2 (2016) Q T T q t C (14) Rg g 4 m 4 ( ) = = εg 0 ϕgm ( ) ( ) Sm If defining het trnsfer coefficient C( gm) = εg C0 ϕgm, then Tg T 4 m 4 q ( t) = C( gm) ( ) ( ) Using the het flux boundry conditions nd het conduction eqution, temperture distribution inside billet cn be obtined. The discretiztion process is done using norml finite volume method which will not be detiled here. In the next section, the simultion for billet temperture distribution will be discussed. (15) 4. Results nd nlysis Simultion nlysis of billet in furnce zone will be discussed with the help of Mtlb softwre. Tking the heting zone I for exmple, the following prmeters nd dt re collected in the engineering project of Ningxi Bem Rehet Furnce in Chin: Tble 1. System prmeters ( Heting Zone I) Number Furnce prmeters Discription 1 Flt burner power 230kw 2 Flt burner number 8 3 Billet mteril C Bem step velocity m / min 5 temperture setpoint Billet regultion 330(mm) 150(mm) 5000(mm) According to the Copper Fbriction Mnul [15], the totl heting nd holding time for billet inside furnce needs t lest 300 minutes. The current chmber temperture is 850 which cn be mesured by the thermocouples locted in the furnce top. The billet surfce tempertures cn be mesured by the contct temperture sensors. And the technicl prmeters of ε, ε cn be obtined by consulting the ε m CO2 H2O Combustion Technology Mnul. Then furnce gs blckness correction cn be clculted s well s ϕ gm nd C gkm. The initil temperture inside billet conforms to the prbolic eqution. Use the bove therml model nd boundry conditions nd progrm it into M file in Mtlb softwre. Let t 0 represent the time tht billet styed in heting zone I. After simultion, we cn obtin the following billet temperture distribution pictures: () Verticl view of billet temperture distribution (b) Side view of billet temperture distribution Figure 3. Billet temperture distribution t t 0 =30min in heting zone I 23

6 8:2 (2016) Journl of Modeling nd Optimiztion The simultion clcultion begins from the point t 0 =30min when billet is chrged into the heting zone I. And the simultion time 30 minutes is tken. From the simultion results on figure 3(), it cn be found tht the upper side temperture is gretly higher thn the bottom side s the het trnsfer rdites from the furnce top. The mximum temperture different is bout 170 from top to bottom surfce. From the picture on figure 3(b), the temperture difference is lrger in the middle of billet thn the two end sides. The mximum rising temperture vlue long billet height is 45 during the heting period time. In order to compre the heting effects when billet is in different time nd positions, the time t0=50min is the next point to clculte the temperture distribution. The simultion time still keeps 30 minutes. The results re shown in Figure 4. () Verticl view of billet temperture distribution (b) Side view of billet temperture distribution Figure 4. Temperture distribution t t 0 =50min in heting zone I From the pictures, it cn be found tht the temperture difference gets smller inside billet 20 minutes lter in heting zone I. And the temperture rise velocity gets more slowly with billet stying longer in furnce. The mximum temperture different is bout 140 from top to bottom. The rising temperture vlues long billet height is 15 during the heting period. For the bove simultion process, ny point temperture point cn be clculted if the billet thickness vlue nd certin time re offered. 5. Conclusions We hve investigted prcticl model with specific het trnsfer chrcteristics in bem rehet furnce. As ll the flt flme burners re instlled on furnce top, the therml rdition is the dominnt het exchnge mode in furnce. This lso determines the het conduction direction from top to bottom inside copper billet. Bsing on these therml chrcteristic, the trnsient conductive eqution is simplified into one-dimensionl mode. To improve the model ccurcy, the hot gs blckness coefficient nd rdition ngle coefficient re clculted respectively during the clcultion of het flux boundry conditions. The simulton results verify the effectiveness of the proposed pproch. The model cn predict the rditive het flux on billet surfce nd the temperture distribution in billet during heting process. In the prcticl engineering systems, only if we know the prcticl technicl prmeters of the furnce, the billet temperture distribution nd het flux prediction cn be clculted quickly by progrmmed functions. The modeling methodology cn be extended nd pplied to the similr type of rehet furnce in metllurgy domin. 6. Acknowledgments This work ws supported by the Ntionl Science of Chin (grnt no ), nd funding of Lioning Science Technology Reserch Progrm of Chin (grnt no. L ). 24

7 Journl of Modeling nd Optimiztion 8:2 (2016) 7. References [1] A. Steinboeck, D. Wild, T. Kiefer. A Mthemticl Model of Slb Reheting Furnce with Rditive Het Trnsfer nd Non-prticipting Gseous Medi. Interntionl Journl of Het nd Mss Trnsfer, 2010(53): [2] M. Y. Kim. A Het Trnsfer for the Anlysis of Trnsient Heting of the Slb in Direct-fired Wlking Bem Type Reheting Furnce. Interntionl Journl of Het nd Mss Trnsfer, 2007(50): [3] Y. Tng, J. Line, T. Fbritius, J. Hrkki. The Modeling of the Gs Flow nd Its Influence on the Scle Accumultion in the Steel Slb Pusher-type Reheting Furnce. ISIJ Interntionl, 2003(43): [4] J. G. Kim, K. Y. Huh, I. T. Kim. Three-dimensionl Anlysis of the Wlking Bem Type Reheting Furnce in Hot Strip Mills. Numericl Het Trnsfer, Prt A, 2000(38): [5] C. T. Hsieh, M. J. Hung, S. T. Lee. Numericl Modeling of Wlking-bem-type Slb Reheting Furnce. Numericl Het Trnsfer, Prt A, 2008(53): [6] C. Mio, Y. Ki, Y. F. LIU. Inverse Estimtion of Trnsient Het Flux to Slb Surfce. Journl of iron steel reserch, 2012, 19(11): [7] M. Y. Gu, G. Chen, X. H. Liu. Numericl Simultion of Slb Heting Process in Regenertive Wlking Ben Reheting Furnce. Interntionl Journl of Het nd Mss Trnsfer, 2014(76): [8] V. K. Singh, P. Tlukdr. Comprisons of Different Het Trnsfer Models of Wlking Bem Type Rehet Furnce. Interntionl Communictions in Het nd Mss Trnsfer, 2013(47): [9] N. Depree, J. Sneyd, S. Tylor. Development nd Vlidtion of Models for Anneling Furnce Control from Het Trnsfer Fundmentls. Computer nd Chemicl Engineering, 2010(34): [10] M. Suzuki, K. Ktsuki, J. I. Imur. Simultneous Optimiztion of Slb Permuttion Scheduling nd Het Controlling for Reheting Furnce. Journl of Process Control, 2014(24): [11] J. Y. Jng, J. B. Hung. Optimiztion of Slb Heting Pttern for Minimum Energy Consumption in Wlking-bem Type Reheting Furnce. Applied Therml Engineering, 2015(85): [12] J. M. Csl, J. Porteiro, J. L. Miguez. New Methodology for CFD Three-dimensionl Simultion of Wlking-bem Type Reheting Furnce in Stedy Stte. Applied Therml Engineering, 2015(86): [13] A. Emdi, A. Sboonchi, M. Theri. Heting Chrcteristics of Billet in Wlking Herth Type Reheting Furnce. Applied Therml Engineering, 2014(63): [14] X. Ch. Xu, L. X. Zhou. Combustion Technology Mnul (Chinese). Beijing: Chemicl Industry Press [15] W. J. Zhong. Copper Fbriction Mnul (Chinese). Beijing: Metllurgicl Industry Press