Heat Transfer &. Solidification Model CON1D

Transcription

1 Heat Transfer &. Solidification Model CON1D Ya Meng Department of Materials Science &. Engineering University of Illinois at Urbana-Champaign March, 2001

2 Improvements to CON1D6.2 Microsegregation model Spray zone model Oil casting heat flux model New format of input file New output files (18 total) Updated manual, source codes & input, output example files can be downloaded from website

3 Microsegregation Model First developed by Y.M. Won 14 elements has been taken into account Has been incorporated into CON1D (optional) User inputs cooling rate, interested position CON1D calculates liquidus and solidus temperature (.ext), which are used for whole simulation CON1D output 5 information-only files: -.seg: solidification time, CR, SDAS, Tsol from shell surface to inside -.liq: liquid concentration at shell surface -.lqi: liquid concentration at at some distance under shell surface -.sol: solid concentration at shell surface -.sli: solid concentration at some distance under shell surface

4 Equilibrium partition coefficients, diffusion coefficients and liquidus line slopes of the 14 solute elements Element k δ/l k γ/l D δ (cm 2 /sec) D γ (cm 2 /sec) m ( o C/%) n ( o C/%) C exp(-19450/RT) exp(-32160/RT) Si exp(-59500/RT) 0.3exp(-60100/RT) Mn exp(-53640/RT) 0.055exp(-59600/RT) P exp(-55000/RT) 0.01exp(-43700/RT) S exp(-51300/RT) 2.4exp(-53400/RT) Cr exp(-57310/RT) exp(-52340/RT) Ni exp(-57360/RT) 0.34exp(-67490/RT) Cu exp(-57360/RT) 0.7exp(-68350/RT) Mo exp(-57690/RT) 0.068exp(-59000/RT) Ti exp(-59200/RT) 0.15exp(-59980/RT) V exp(-57360/RT) 0.284exp(-61900/RT) Nb exp(-60220/RT) 0.83exp(-63690/RT) W exp(-58200/RT 0.13exp(-57300/RT) N exp(-18900/RT) 0.91exp(-40270/RT) Notes : R is gas constant of cal/mol-k and T is temperature in K

5 Spray zone model Enhanced user-control spray zone parameters for parametric study - natural convection heat transfer coefficient - user-input spray coefficient, convection coefficient, ambient temperature for different spray zones - can simulate air mist spray cooling zones Validated by China steel measured data - input conditions and measured data from LIN, Kuan-Ju

6 Schematic of Spray Zones Region radiation, hrad natural/forced convection, hconv Spray nozzle spray impinging, hspray Roll Slab z heat transfer roller contact, hroll

7 rad steeel Spray zone model ( ) ( ) 2 2 T + T T s T h = σ ε + h conv = user h h spray roll = input s n w amb = Coeff A Q 1 ( b T ) amb amb ( h + h + h ) L + ( h + h ) ( Pitch L L ) rad conv spray spray L rad roll contact ( 1 q) spray roll contact q = fraction of heat flow per zone going to roll (-) conv Where, σ = Stefan Boltzman constant (5.67e-8W/m 2 K 4 ) ε steel = steel emissivity (-) Τs, Τamb = steel surface temperature, ambient temperature (K) Qw = water flux (l/m 2 sec) Coeff, A, n, b = coefficients for spray heat transfer (-) Lspray, Lroll contact = spray length, roll contact length (m) q

8 Model Validation:China Steel Casting Conditions Water Spray only Casting Speed: (m/min) 0.55 Air Mist 0.56 Pour Temperature: ( o C) Slab Geometry: (mm*mm) Nozzle Submergence Depth: (mm) Working Mold Length: (mm) Carbon Content: (%) Mold Oscillation Frequency: (cpm) Oscillation Stroke: (mm) Mold Thickness (with Water Channel): (mm) Initial Mold Cooling Water Temperature: ( o C) Water Channel Geometry (depth*width*distance): (mm 3 ) * *5* * *6*28 Cooling Water Flow rate: (m/s)

9 Ambient temperature below spray zones: 35 o C Spray zone coefficients: A=1.57, n=0.55, b= Minium convection heat transfer coefficient (natural): 8.7(W/m^2K) No. zone rol. water spray contct frac.of spray conv. amb. starts # rad. flowrate width length angle q thr rol coeff coeff. temp. (mm) (m) (l/min/row) (m) (m) (Deg) (W/m^2K) (DegC) Water Spray only End of last spray zone (mm) Air Mist Model Validation:China Steel Spray Zones Variables End of last spray zone (mm)

10 Model Validation: China Steel Shell Temperature for Water Spray Only Case Shell temperature (DegC) Distance from meniscus (mm) Distance below shell surface (mm) exp-10 exp-12.5 exp-100 cal-0 cal-10 cal-12.5 cal-100

11 Model Validation: China Steel Shell Temperature for Air Mist Case Shell temperature (DegC) Distance below meniscus (mm) Distance below shell surface (mm) exp-10 exp-35 exp-95 cal-0 cal-10 cal-35 cal-95

12 Heat Transfer Model for Billet Casting User chosen heat transfer model - oil casting - mold powder casting - user input heat flux Validated by trial at POSCO - input conditions and measured data from PARK, J.K.

13 q h int rad = = ( h + h )( T T ) σ rad conv s Model Description mold 2 2 ( T + T )( T + T ) s ε 1 steel mold + ε 1 s mold 1 mold T mold r contact d air k air T s h conv 1 = r + contact d k air air r radiation Where, qint = heat flux transferred across gap (W/m 2 ) hrad =effective radiation heat transfer coefficient (W/m 2 K) hconv = effective convection heat transfer coefficient (W/m 2 K) Ts = surface temperature of the steel shell ( C) Tmold = surface temperature of the mold (outermost coating layer) ( C) rcontact = strand/mold contact resistance(m 2 K/W) dair = thickness of the air gap (mm) kair = conductivity of the air gap (W/mK) σ = Stefan Boltzman constant (5.67e-8W/m 2 K 4 ) εsteel, εmold = steel, mold surface emissivity (-)

14 Model Validation:Trial at POSCO Simulation Parameters Casting Speed: 2.2 m/min Pour Temperature: 1540 o C Slab Geometry: 120 mm*120 mm Meniscus Level: 100 mm Working Mold Length: 700 mm Carbon Content: Mold Thickness (with Water Channel): Mold Taper: Mold Conductivity: Initial Mold Cooling Water Temperature: Cooling Water Flow rate: Cooling Water Velocity: Air Conductivity: Contact Resistance: 0.1 wt% 6 mm 0.75 %/m 360 W/mK 30 o C 1100 l/m 6.6 m/s 0.1 W/mK 5.6e-4 m 2 K/W

15 Model Validation: Heat Flux Time (s) Heat Flux (MW/m 2 ) CON1D predicted Measured instantaneous Measured average Distance below meniscus (mm)

16 Model Validation: Mold Temperature 160 Mold temperature ( o C) Predicted Measured Hot face Cold face Distance below top of mold (mm)

17 Model Validation: Shell Thickness (Center) 10 Shell Thickness (mm) Liquidus 10% Solid 20% Solid 30% Solid 40% Solid 50% Solid 60% Solid 70% Solid Solidus Measured Distance below meniscus (mm)

18 Air Gap Calculation Distortion or shrinkage, x (mm) Strand side Mold side Shell shrinkage (maximum) Mold wall during operation Mold taper Air gap Mold distortion Distance below meniscus, z (mm) Mold distortion/air gap, x (mm) Strand side Mold distortion Air gap (maximum) Center air gap used in CON1D Corner air gap used in CON1D Distance below meniscus, z (mm) Mold side

19 Air Gap Comparison Air gap size (mm) Measured Measured Measured Measured Used in CON1D Distance from corner of strand (mm)

20 Model Validation: Shell Thickness (Corner) Shell thickness (mm) Liquidus 50% solid 60% solid 70% solid Solidus Measured Distance below meniscus (mm)

21 Shell Temperature Comparison Shell surface temperature ( o C) Center Corner Distance below meniscus (mm)

22 Conclusion Microsegregation model - incorporated 14 elements effects on solidus and liquidus Spray zone model - calibrated by measured shell temperature at China Steel - can simulate both spray water only and air mist cases Oil casting heat flux model - calibrated by measured data at POSCO: mold cooling water temperature mold thermocouple temperature shell thickness - solid fraction for tracer test is 0.6

23 Future Work Improve interface model of CON1D - validate mold friction model - oil casting heat transfer model Mold flux crystallization & viscosity Mold temperature fluctuation model 2D simulation Parametric study