Model Prediction of Heat Losses from Sirosmelt Pilot Plant

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1 00 mm 855 mm 855 mm Model Predition of Heat Losses from Sirosmelt Pilot Plant Yuua Pan 1 and Miael A Somerville 1 1 CSIRO Mineral Resoures Flagsip, Private Bag 10, Clayton Sout, VIC 169, Australia Keywords: Sirosmelt, eat los eat transfer, modelling 1. Introdution Te Sirosmelt pilot plant is a type of vertile Top-Submerged-Lane (TSL) smelting furnae loated at te Clayton laboratories of CSIRO. Tis reator is used to elp assess te tenial feasibility of a variety of pyrometallurgial proesses at a feed rate of about 50 kg/. Tese feasibility studies also rely on eat and mass balane models to assess material flows and energy requirements. A restrition in te ability to ondut aurate eat and mass balane studies as been te lak of knowledge of te amount of eat losses troug te walls and base (bottom) of te Sirosmelt furnae. Tis paper presents a model of eat transfer in wall and bottom of te Sirosmelt furnae so as to predit te amount of eat lost during steady state smelting operations.. Sirosmelt Furnae Constrution Te Sirosmelt reator is a ylindrial ped vessel made from speially ut refratory briks formed into an annular pe. Te briks are eld in plae by a mild steel sell. Layers of mineral wool and astable refratory elp to insulate te reator and take up te gap between te briks and steel sell. As sematially sown in Figure 1, te vessel is onstruted in four main parts wi onsist of a base (bottom) and tree setions of wall, i.e., lower (Setion 1), middle (Setion ) and upper (Setion ). Te top of te furnae is overed wit a lid (not sown in Figure 1). In normal operation te slag bat is ontained in te lower setion wile te middle and upper setions are used to disentrain te gas pase from slag splas. Layer No. Layer No. Wall materials Bottom materials 1 4 Tikness (mm) 1 Mild steel sell 4 Kaowool insulation 10 Castable refratory Mag-rome brik 110 Temperature measurement position Furnae/Wall Setion Furnae/Wall Setion Furnae/Wall Setion 1 Tikness (mm) 668 mm 1 Mild steel sell 10 Kaowool insulation 10 Castable refratory 65 4 Mag-rome brik 110 Q bottom 1 4 T bottom Figure 1: Semati illustration of pilot-le Sirosmelt furnae. T top 05 mm T bulk T bulk T bulk1 = T bat T side T side T side1 Q side Q side Q side1 1

2 . Heat Transfer Model Model Assumptions Te following assumptions were made in te formulation of te eat transfer model: Steady-state eat transfer. Te furnae is divided into tree setion namely lower, middle and upper setions as sown in Figure 1, wit ea of wi being assumed to be a perfetly mixed reator, i.e., uniform temperatures are assumed in melt bat (Furnae Setion 1) and in te gas pase in Furnae Setions and. Te average temperatures in gas pase in Furnae Setions and were linearly interpolated between te bat temperature (T bat ) and te top temperature (T top ) estimated from measured off-gas temperature. Heat loss troug sealed furnae top (wit a lid) negleted. One-dimensional eat ondution normal to and aross lining material layers and air gaps between neigbouring material layers (i.e., transverl eat transfer in all lining material layers negleted). Natural and fored onvetion and radiation at furnae wall and bottom sell outer surfaes. Radiation between two neigbouring material layers in an air gap. Te tikness of all air gaps assumed to be 0.1 mm. Overall Heat Transfer Equation Te eat loss rate troug multi-layered wall or bottom of te Sirosmelt furnae an be desribed by te overall eat transfer equation: Tbulk Ta Q (1) R j i i were, Q is te eat transfer rate troug furnae wall or bottom in Watts (W), T bulk te average temperature of a bulk material (e.g., melt bat in Furnae Setion 1 and gas pase in Furnae Setions and ) in Kelvin (K), T a te ambient temperature (K); i denotes a material layer in furnae wall and bottom; j denotes te eat transfer loation (su as furnae bottom or a setion of wall); and R i te termal resistane of te i t material layer or te interfae between tis material layer and air, e.g., furnae sell outer surfae and air gap (K/W). Modelling Priniple Te modelling priniple is to determine eat transfer resistanes (R i ) of various material layers omprising te furnae wall and bottom so tat te temperature distributions aross te wall and bottom and te resultant eat transfer rates (eat loss rates) an be alulated using Eq. (1). Details of te eat transfer resistane alulations and te modelling proedure an be found in Appendix A. Material Termopysial Properties Te termopysial properties of various materials involved in te model are listed in Table 1. Tey are onsidered as temperature dependent (exept for steel sell). Appendix B provides te detailed forms of te equations used for alulating te termopysial propertie i.e., Eqs. (B.1) to (B.8) in Table 1.

3 Material Table 1: Material termopysial properties used in te model Termal ondutivity (W/mK) Heat apaity (J/kgK) Kinemati visosity (m /s) Density (kg/m ) Termal expansivity (1/K) Emissivity Sell (mild steel).889 a d Insulation (kaowool) Eq. (B.1) b e Castable (alumina-silia) Eq. (B.) d Brik (magnesia-rome) Eq. (B.) d Air Eq. (B.4) a Eq. (B.5) a Eq. (B.6) a Eq. (B.7) a Eq. (B.8) a a Ref. [1], b Ref. [], Ref. [], d Ref. [4], e Ref. [5]. 4. Results and Disussion Experimental Measurement Hig temperature smelting experiments were performed on te pilot-le Sirosmelt furnae in order to alibrate and validate te eat transfer model. Te furnae wall and bottom sell outer surfae temperatures were measured using an infra-red pyrometer during a period of steady state operation were te proess variables were kept onstant and te bat temperatures stabilised to witin 5 C. Te measurement positions are indiated in Figure 1 and te measured average surfae temperatures in tree experiments are given in Table. Tese measurements were used to alibrate and validate te model. Table : Measured bat temperature and average sell outer surfae temperature* Loation Bat Bottom Wall Setion 1 Wall Setion Wall Setion Experiment No. T bat ( C) T bottom ( C) T side1 ( C) T side ( C) T side ( C) EXP EXP EXP *Te average was taken over te temperatures measured at four loations in ea wall setion wile te bottom surfae temperature (T bottom ) was measured at only one loation (i.e., rougly te entre of te furnae bottom),.f., Figure 1. Model Calibration Tere exist some parameters in te model tat are pratially unertain and ave to be affirmed by means of alibrating te model against te experimental measurements. Among tem, te ambient air flow veloity, i.e., u in Eq. (A.15), for fored onvetion eat transfer at te furnae bottom and wall outer surfaes. Tis veloity depends on loal wind onditions around te furnae. In tis work a onstant air flow veloity (u) was osen as a solely adjustable parameter for model alibrations. In te present work, te model alibration was performed in su a way tat, troug adjusting u, te alulated furnae sell outer surfae temperatures approximately mated measured ones in one experiment (EXP 1), and it was found tat te magnitude of te ambient air veloity was around 0.8 m/s. Ten, by setting u = 0.8 m/s in te model, furter model simulations were arried out for two oter experimental ases (EXP and EXP ). Figure sows a omparison of te predited wall and bottom sell surfae temperatures wit te measured ones in te tree experiments. As seen from tis figure, one alibrated wit measured data from only one experiment (i.e., EXP 1), te model ould give rater promising preditions of te sell surfae temperatures for oter two experiments (EXP and EXP ) witin about 15%.

4 Temperature, o C Temperature, o C Calulated temperature, C % % Tbottom Measured temperature, C Figure : Comparison between predited and measured wall and bottom sell outer surfae temperatures. (Solid symbols denote data from EXP 1 for model alibration.) Predited Temperature Distributions aross Furnae Wall and Bottom After te model alibration proedure, te model ould be used to predit te temperature distributions aross te linings of te furnae wall and bottom and to investigate sensitivities of furnae eat loss to a range of proess parameters. Figure sows te predited temperature profiles in te furnae wall and bottom for te experimental ase EXP 1. Tside1 Tside Tside Sell Air gaps Castable refratory Insulation EXP 1 Brik Sell Air gaps Castable refratory Insulation EXP 1 Brik Tside1 ( C) 00 Tside ( C) Tside ( C) Distane from wall sell outer surfae, mm (a) Temperature profiles in wall (b) Temperature profile in bottom Figure : Predited temperature profiles aross furnae bottom and different wall setions. Effet of Bat Temperature on Heat Loss Rate Figure 4 sows te effet of bat temperature on eat loss rates from furnae bottom and different wall setions. It an be seen from Figure 4(a) tat te absolute eat losses from different loations of te furnae all inrease wit inreasing bat temperature. Witin te bat temperature range ( C) investigated, te predited total absolute eat loss from te furnae ranges from kw, and for a bat temperature of 100 C, for instane, te model predits te total eat loss to be lose to 11.5 kw. Te magnitudes of te eat losses from te upper setions (Wall Setions and ) inrease faster tan tose from te bottom and te lower wall setion (Wall Setion 1). Tis leads to te relative eat loss from te wall (as perentage of total eat loss) inreasing wit te bat temperature wereas tat from te bottom dereases wit inreasing te bat temperature, as sown in Figure 4(b). Furtermore, it an be seen from Figure 4(b) tat major eat loss ours from te furnae Heigt from bottom sell outer surfae, mm 4

5 Heat loss rate, kw Relative eat loss rate from sidewall, % Relative eat loss rate from bottom, % wall representing 9 9% of total eat loss wile only limited amount of eat is lost troug te furnae bottom (7 8%). Tis is beause te wall as a tinner lining layer and a mu larger eat transfer area tan te bottom Q total, fit = T bat (a) Absolute eat loss rates (b) Relative eat loss rates Figure 4: Predited influene of bat temperature on eat loss rates from furnae bottom and different wall setions. 5. Summary Bat temperature, C Wall setion 1 Wall setion Wall setion Bottom Total Total, fitted A eat transfer model as been developed for prediting eat losses from a pilot-le Sirosmelt furnae. Te model is also apable of prediting temperature distributions aross te furnae wall and bottom. Te model as been alibrated against te measured furnae sell outer surfae temperatures. Te modelling results indiate tat 9 9% of eat is lost from te furnae wall and 7 8% from te bottom. Te proportion of total eat loss from te sidewall inreases wit te inreasing bat temperature wereas tat from te bottom dereases. For a bat temperature of 100 C, total eat losses were found to be lose to 11.5 kw. In future planned work tese eat loss alulations will form part of a eat and mass balane of te Sirosmelt furnae. Referenes 1. Hayne WM, CRC Handbook of Cemistry and Pysi 95t Edition, Material Data Seet from Isolite Insulating Produts Co. Ltd.. Material Data Seet from Sinagawa Refratories Australasia Pty Ltd. 4. Mikron Instrument Company, In., Table of Emissivity of Various Surfaes, ttp://www-eng.lbl.gov/~dw/projets/dw49_lhc_detetor_analysis/alulations/ emissivity.pdf. 5. Material Data Seet from Morgan Termal Cerami Kaowool 160 Cerami Felt, ttp:// ramifeltenglis.pdf. 6. Geiger, GH and Poirier, DR, Transport Penomena in Metallurgy, Addison-Wesley Publising Company, Witaker S, Fored Convetion Heat Transfer Correlations for Flow in Pipe Past Flat Plate Single Cylinder Single Spere and for Flow in Paked Beds and Tube Bundles, Amerian Institute of Cemial Engineer 18(), 197, ttp:// Bat temperature, C Sidewall Bottom

6 Appendix A Termal Resistane Calulation and Modelling Proedure Calulation of Termal Resistanes Te termal resistane, R i, involved in Eq. (1) an be alulated as i) for a flat material layer in bottom, Li Ri (A.1) ki Ai were, L is te material layer tiknes m; k te material termal ondutivity, W/mK; A te eat transfer area, m ; and i te material layer identity; ii) for a ylindrial material layer in wall, 1 r i, R i ln (A.) k ihi ri, were, H is te eigt of a furnae wall setion, m; and r i, and r i, te ot fae and old fae radii of te it material layer, respetively, m; iii) at furnae wall and bottom sell outer surfae A T T T T A 1 R (A.) n f a Convetion Radiation were, is te onvetive eat transfer oeffiient, W/m K; te emissivity of steel sell; te Stefan-Boltzmann onstant (= W/m K 4 ); and subsripts, n, and f stand for, sell/ambient surfae, natural onvetion and fored onvetion, respetively; a iv) in a flat air gap in bottom (assuming te ot and old faes are in parallel), ka A Ri i T T T T A 1 (A.4) Condution Radiation were, is te tikness of air gap, m; A te average area between ot and old faes in air gap, m ; and subsripts a, and stand for, air, lining surfae, ot fae and old fae, respetively; iv) in a ylindrial air gap in wall (assuming te ot and old faes are in parallel), k ah k Ri r ln r T T T T 1 A A 1 1 A 1 (A.5) Condution Radiation were k stands for a furnae wall setion identity. 6

7 Calulation of Heat Transfer Coeffiients Te onvetive eat transfer oeffiient () involved in Eqs. (A.) to (A.5), was evaluated from te Nusselt number, i.e., ka Nu (A.6) L were, is te eat transfer oeffiient (W/m K); k a te termal ondutivity of air (W/mK); L te arateristi lengt of an interfae (m); and Nu te Nusselt number. Nu was alulated using te following publised empirial dimensionless orrelations: i) At bottom sell outer surfae, For natural onvetion eat transfer (at a orizontal flat surfae) [6], Nu 0.7Gr Pr 1 4 n (A.7) were Gr is te Grasof number and Pr te Prandtl number. For fored onvetion eat transfer (at a orizontal flat surfae) [7], Nu 0.664Re Pr, for laminar flow witre 10 (A.8) Nu f f 4 5 1, for turbulent flow witre Re Pr a (A.9) were Re is te Reynolds number, wi is defined as ul Re (A.10) were, u is te air veloity (m/s); te air density (kg/m ); te air dynami visosity (Pas); and L te arateristi lengt for te furnae bottom sell outer surfae (m). and are evaluated at te average temperature of air film at te sell surfae, i.e., T 0. 5 T T (A.11) film a and L is evaluated as te edge lengt of a square wit te me area as te furnae bottom sell outer surfae. ii) At sidewall sell outer surfae, For natural onvetion eat transfer (at a vertial ylindrial surfae) [8], Nu n 0.5 Gr Pr, for laminar flow wit 110 Gr 110 (A.1) Gr Pr, for turbulent flow wit 110 Gr 1 10 Nu n 0.1 (A.1) For fored onvetion eat transfer (at a vertial ylindrial surfae) [7], Nu.4Re Re Pr (A.14) f 4 0 a were Re is defined for ylindrial wall sell surfae as ud Re (A.15) were D is te furnae outer diameter (m). Air properties used for alulating te parameters in Eqs. (A.1) to (A.14) are evaluated at te average temperature of air film at sell surfae using Eq. (A.11). Modelling Proedure An iterative metod was adopted to use Eq. (1) to alulate eat transfer rate (Q) troug furnae bottom and wall, respetively. Te modelling proedure is: 7

8 1) Estimate a series of te ot fae and old fae temperatures of ea material layer (T and T ) in bottom or wall and te temperature at te sell outer surfae of bottom or wall (T ); ) Use Eqs. (A.1) to (A.5) to alulate termal resistanes (R i ) of various material layers (inluding air gaps and air film at te sell outer surfae), wi omprise te furnae bottom or wall; ) Use Eq. (1) to alulate eat transfer rate (Q), from wi T and T of ea material layer as well as T are predited; 4) Compare te predited values of T, T and T wit tose estimated values in step 1) orrespondingly until te absolute temperature differenes all fall below 1 C. Oterwise, repeat steps 1) troug 4) until te fore-mentioned riterion is met. In te present work, te model simulations were performed by means of Mirosoft Exel spreadseet alulations on a personal omputer. Appendix B Equations for Calulating Termopysial Properties Te following equations are used for alulating material termopysial properties as funtions of temperature (T in K): 1) Termal ondutivity of insulation layer (kaowool) []: k T T, (W/mK) (B.1) ) Termal ondutivity of astable refratory layer (alumina-silia) []: 4 k T, (W/mK) (B.) ) Termal ondutivity of brik layer (magnesia-rome) []: k T T T, (W/mK) (B.) 4) Termal ondutivity of air [1]: k T.010 T T, (W/mK) (B.4) 5) Heat apaity of air [1]: Cp T T T, (J/kgK) (B.5) 6) Kinemati visosity of air [1]: ( ) Density of air: T T T ) 10 6, (m /s) (B.6) 5.91 T, (kg/m ) (B.7) 8) Termal expansivity of air: 1 T, (1/K) (B.8) 8

Natural Convection Experiment Measurements from a Vertical Surface

Natural Convection Experiment Measurements from a Vertical Surface OBJECTIVE Natural Convetion Experiment Measurements from a Vertial Surfae 1. To demonstrate te basi priniples of natural onvetion eat transfer inluding determination of te onvetive eat transfer oeffiient.