User-friendly model of heat transfer in. preheating, cool down and casting

Transcription

1 ANNUAL REPORT 2010 UIUC, August 12, 2010 Use-fendly model of heat tansfe n submeged enty nozzles dung peheatng, cool down and castng Vaun Kuma Sngh, B.G. Thomas Depatment of Mechancal Scence and Engneeng Unvesty of Illnos at Ubana-Champagn Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Lance C. Hbbele 1 Objectves Develop a use fendly speadsheet based tool to calculate l the heat tansfe coeffcents and flame tempeatue dung peheatng of the nozzle. Develop a use f fendly speadsheet based tool to model the heat tansfe n submeged enty nozzles dung the thee stages: peheat, cool down and castng. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 2

2 Model & computatonal doman Model of Nozzle exposed to ambent Slde Gate (Flow Contol) Flux Molten Steel Jet Molten Steel Lqud Steel Pool Soldfyng Steel Shell Tundsh 1. Peheat 2. Cool down Gas Bune Ambent Nozzle Layes Nozzle Layes Insulaton Insulaton Ambent Ambent 3. Castng Molten Ambent Tundsh Nozzle Steel Lqud Sold Nozzle Insulaton Steel Layes Clog Steel Clog Submeged Enty Nozzle Plane of Symmety Insulaton Laye Gas 1. Peheat Ambent Bune Submeged Depth Nozzle Insulaton Layes Coppe Mold Model of Nozzle submeged n steel 2. Cool down Ambent Ambent 3. Castng Molten Steel Lqud Steel Nozzle Layes Nozzle Layes Insulaton Insulaton Molten Steel Contnuous Wthdawl Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 3 Models Developed Flame Tempeatue Calculaton Model Heat Tansfe Coeffcents Calculaton Model Model fo heat tansfe n the efactoy dung the thee stages: peheat, cool down castng Ambent slce Submeged slce. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 4

3 Flame Tempeatue Calculaton Model Input Page Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 5 Calculaton of Flame tempeatue and heat tansfe coeffcents Use can select fom the followng gases as fuel: Methane, hydogen, popane, natual gas, blast funace gas and acetylene. The speces consdeed ae: CO 2, O 2,O,CO,H 2 O, N 2,NO,OH,H,H 2 Fo natual gas and blast funace gas, use can specfy the pecentage of vaous consttuents (natual gas: mathane 94%, ethane 3%, popane 1%, butane 0%, CO 2 1%,O 2 0%,N 2 1%) Reactants tempeatue and pessue need to be enteed. The eacton s a constant pessue pocess. The use can choose between excess a and oxygen enchment. The amount of excess a o a enchment needs to be specfed. The flame tempeatue calculated fo the above composton of natual gas wth 50% excess a was found to be 1510 C. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 6

4 Heat Tansfe Coeffcents Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 7 Heat Tansfe Coeffcents Fee Convecton to ambent: The Chuchll and Chu [1] equaton fo flow ove a vetcal flat plate s used Nu avg = Ra P Foced Convecton fom flame: The Petukhov, Kllov, and Popov [1] s used [( f /8)Re P] 1/6 9/16 D Nu = 1/2 2/ ( f /8) (P 1) The foced heat tansfe coeffcent was calculated l to be 72.5 W/m 2 K. The fee heat tansfe coeffcent was calculated to be 7.6 W/m 2 K Sleche and Rouse equaton was used to calculate the foced convecton heat tansfe coeffcent fom molten steel flowng on the nsde of the nozzle. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 8 8/27 2

5 Popetes of mxtue of gases n combuston poducts Themal conductvty of the mxtue of gases s calculated usng Saxena and n Mason [3]: y λ λ m n = 1 y A = j = 1 j j Whee λ m = the themal conductvty of the gas mxtue = the themal conductvty of pue λ y, y j = mole factons of component and j A j = 1 + ( η / η ) ( M / M ) 1 / 2 [8 (1 + M / M )] 1 / 2 1 / 4 j j j 2 Whee, η A j = η η j M M η ae the vscostes of pue and j espectvely j j A j And Μ, Μ j ae the molecula weghts of pue and j Themal dffusvty, knematc vscosty, densty and specfc heat ae calculated usng the patcle mxtue ule. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 9 Heat Tansfe Model fo the efactoy Man Page Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 10

6 Heat Tansfe Model fo the efactoy Featues Use can ente the numbe of s he wants n the model. Each can have dffeent thckness and dffeent numbe of nodes. The use can choose at what tmes the esults have to be plotted. Use can select the nodes whee the esults ae to plotted. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 11 Heat tansfe model assgn efactoy popetes The table gets populated based on the numbe of s enteed by the model. Use can select whch mateal should be assgned to each by choosng fom the dop down menu (whch get automatcally populated to show all the mateals n the excel fle) Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 12

7 Govenng Equaton and fnte dffeence equaton fo nteo nodes Gas Bune Ambent Inne suface efactoy Bulk efactoy Oute suface efactoy Insulaton Heat conducton equaton n cylndcal co odnates [1] T 1 T ρ Cp = k t Usng Taylo sees [1] expanson, the equaton s dscetzed as: 2 2 T k T T T 1 T T ρ C p = + 2 t =α + 2 t n+ 1 n n n n n n T T 1 T+ 1 T 1 T+ 1 2T + T 1 =α + 2 Δt 2Δ Δ n+ 1 n n 1 1 n T T = T + αδ tt T 1 Δ 2Δ Δ 2Δ Δ Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 13 n Fnte Dffeence Equatons (Sde nodes wth convecton) 1 2 Sde Half Cell Gas Bune Inne suface efactoy Bulk efactoy Heat balance on sde half cell gves: T T ρ CpV = ka2 2+ ha1δt 1 t Oute suface efactoy Insulaton Ambent n+ 1 n n n Δ T T ΔT T + 1 ρ Cp = k+ + h T T 2 Δt 2 Δ n ( ambent ) 2αΔt Δ T T 2Δth T T T T n n n+ 1 n + 1 n = ambent Δ 2 Δ ρcpδ ( ) Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 14

8 Fnte Dffeence Equatons (Inteface Nodes) Gas Bune Ambent nteface Inne suface efactoy Bulk efactoy Oute suface efactoy Insulaton T 1 T ρ C p = k t n+ 1 n T T 1 T T C ρ p = k k Δt Δ + 1/ /2 1/2 1 1/2 n + 1 T n 1 n n n n T Δ T+ 1 T Δ T T 1 ρ Cp = + k2 k1 Δt Δ 2 Δ 2 Δ n+ 1 n Δt Δ n n Δ n n T = T + α 2 ( 1 ) α 1 ( 1 ) 2 + T+ T T T 2 2 Δ Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 15 Steel Shell Soldfcaton Model Enthalpy fomulaton of the tansent 1-D heat conducton equaton s solved: H 1 T ρ = k t Top ow tempeatues: T = Tpou Top ow enthalpes [2]: T pou H = Cp * Tpou + Lf *nt Tsoldus whee L f s the latent heat of fuson. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 16

9 Steel Shell Soldfcaton Model Enthalpy of nteo nodes: kδt H = H + T T T ρ + + Δ 2Δ Δ 2Δ Δ n+ 1 n n n n Enthalpy of sde nodes wth convecton: n n n+ 1 n 2hΔt n 2kΔt ΔT T + 1 H H + T T = steel + + ρδ ρδ 2 Δ Afte the enthalpy has been calculated the tempeatues ae then calculated usng [2] : H H L f T = mn, max, Tsol Cp Cp Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 17 Valdaton of Steady State Aspect of the Model Compaed the esults of the smulaton when t eaches steady state wth analytcal Soluton. Govenng equaton fo Analytcal soluton [1]: 1 T k = 0 T flame Heat flux though the nozzle s calculated usng: h flame, T 1 z q = Tflame Tambent 1 ln( o / ) h k h flame ambent o Fnally, the tempeatues n the nozzle ae : T T = T h 1 flame = T + q q flame q T = T1 ln k Refactoy, k h ambent, T 2 o T, = t 2 ambent hambento Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 18 o T ambent

10 Smulaton condtons fo valdaton of steady state aspect of the model Label Symbol Value Unts Oute Radus of Refactoy o 67.5 mm Bulk Refactoy Wall Thckness t 29.5 mm Intal Nozzle Tempeatue T nttal 27* C Ambent Tempeatue T ambent 27 CC Flame Tempeatue T flame 1460 C Intenal Convecton heat tansfe Coeffcent (Foced) h flame 50 W/(m 2 K) Extenal Convecton heat tansfe Coeffcent (Fee) Themal Conductvty h ambent 7.3 W/(m 2 K) K W/m-K Specfc Heat C p 804* J/kg-K Densty ρ 2347 kg/m 3 Stefan Boltzman's Constant σ 5.67E-8 Emmssvty ε 0.96 * Paametes equed by tansent smulaton method Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 19 Valdaton Steady state aspect of the model The esults of the smulaton ae n good ageement wth that of the analytcal soluton Sngle Laye, No adaton Sngle Laye, wth adaton Fou Layes, No adaton Fou Layes, wth adaton Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 20

11 Valdaton of tansent aspect of the model Compae the esults of the smulaton wth that of the lumped themal heat capacty model. System undegong a tansent themal esponse to a heat tansfe pocess has a nealy unfom tempeatue and small dffeences of tempeatue wthn the system can be gnoed. The model s vald only f the Bot numbe (hl/k) < 0.1 The govenng equaton s [1] ρ dt VC = ha( T T ) p dt To solve ths equaton, one ntal condton s equed: t=0: T=T o. Solvng the equaton, the tempeatue at any tme,t can be calculated fom: T Te T T o e = e ( ha/ ρvc ) t p whee T o s the ntal suface tempeatue, T e s the ambent tempeatue. e Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 21 Smulaton Paametes Valdaton of tansent aspect of the model Label Symbol Value Unts Oute Radus of Refactoy o 67.5 mm Bulk Refactoy Wall Thckness t 29.5 mm Intal Nozzle Tempeatue T nttal 1100 C Ambent Tempeatue T ambent 27 C Extenal Convecton heat tansfe Coeffcent (Fee) Themal Conductvty h ambent 7.3 W/(m 2 K) ambent K 1000 W/m-K Specfc Heat C p 804 J/kg-K Densty ρ 2347 kg/m 3 Stefan Boltzman's Constant σ 5.67E-8 Emmssvty ε 0.96 Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 22

12 Compason of Results of lumped model and tansent smulaton The esults of the smulaton ae n good ageement wth that of the lumped themal heat capacty model Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 23 Output page of the tool Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 24

13 Compason wth measuements (nsde heat tansfe coeffcent = 72 W/m 2 -K) Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 25 Compason wth measuements (nsde heat tansfe coeffcent = 18 W/m 2 -K, emssvty = 0.5) Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 26

14 Paametc Study Paametes Hghest Tempeatue Dffeence n temp. between nne and oute suface Foced Convecton = 72 W/m 2 -K, emssvty = C 90 C Foced Convecton = C 30 C W/m 2 -K, emssvty = 0.5 Themal Conductvty s 954 C 150 C halved Emssvty nceased to C 100 C Specfc Heat s doubled 954 C 100 C Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 27 Conclusons The tempeatue n the nne suface of the nozzle eached 900 C afte a peheat tme of 2 hous. If the nsde heat tansfe coeffcent s educed to 18 W/m 2 -K the tempeatue n the nne suface of the nozzle s 585 C. Results fom numecal smulaton match those of expements fo ths case. The tool can be used to pedct the tempeatues n the nozzle dung dffeent stages of peheat, cool down and castng. The tool can be used to calculate the flame tempeatue and heat tansfe coeffcents fo dffeent fuels and vayng composton. A entanment should be deceased, because excess a educes the flame tempeatue. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 28

15 Refeences 1. Incopea, F.P., and Dewtt, P.D., 2002, Fundamentals of Heat and Mass Tansfe, John Wley and Sons, New Yok. 2. Thomas, B.G. and B. Ho, "Spead Sheet Model of Contnuous Castng," Jounal of Engneeng fo Industy, ASME, New Yok, NY, Vol. 118, No. 1, 1996, pp Polng, B.E., O Connell J.M., and Pausntz, J.M., 2001, The Popetes of Gases and Lquds, McGaw-Hll, New Yok. 4. Moan, J.M., and Shapo, H.N., 2004, Fundamentals of Engneeng Themodynamcs, John Wley and Sons, New Yok. 5. Repot on Modelng of Tundsh Nozzle Peheatng by J. Maeno and B.G. Thomas. Unvesty of Illnos at Ubana-Champagn Metals Pocessng Smulaton Lab Vaun Kuma Sngh 29 Acknowledgements Contnuous Castng Consotum Membes (ABB, Acelo-Mttal, l Baosteel, Cous, LWB Refactoes, Nuco Steel, Nppon Steel, Postech, Posco, ANSYS-Fluent) Rob Nunnngton, LWB Refactoes Unvesty of Illnos at Ubana-Champagn Mechancal Scence & Engneeng Metals Pocessng Smulaton Lab Lance C. Hbbele 30