CCC Annual Report UIUC, June 12, 2007

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1 CCC Annual Report UIUC, June 12, 27 Modeling heat transfer & depression formation in Al- strip casting Aravind Sundararajan, Graduate Student & Brian G. Thomas, Wilkins Professor Department of Mechanical & Industrial Engineering Universit of Illinois at Urbana-Champaign 1 Planar Flow Melt-Spinning (PFMS Process r Zone III (Θ 3 φ 24" z Crucible Nozzle Contact zone Copper-Berllium Wheel Metal Entr Upstream Meniscus Strip Zone I (Θ 1 G Zone II ( Θ 2 Contact zone (close-up view T s Zone I Nozzle Downstream Meniscus Shell 2 B P D L Zone II Plate T V c 5mm 34 mm 12.7mm

2 r r z Casting direction 5 mm Wheel side 3 Metals Processing Simulation Lab Liquid side (LS Wheel side (WS B Aravind Sundararajan Wav transverse surface depressions A Qualit Issue: Strip surface defect B Liquid side A λ = ~ 5 mm Strip hot face Liquid strip Strip cold face Wheel hot outer face Aluminum strip Wheel cold inner face Solid strip Cu-Be wheel 4 Governing Equation 2 T 2T k T k T =k Q r r t r t r Model Assumptions Metals Processing Simulation Lab Aravind Sundararajan Thus circumferential conduction in the wheel and conduction in strip along casting direction neglected. Large Pe number obtained for wheel & strip for length scale of.2 mm. Strip thickness doesn t change after exiting Zone I No slipping between strip & wheel Negligible heat loss along strip width. ρc p Mathematical Model Description Tliq + delta n n 1 z qs qw rw 1 qamb Tamb Universit of Illinois at Urbana-Champaign GAP/ Wheel-strip interface (hgap z rs qsup Universit of Illinois at Urbana-Champaign Sample No.: ETFa1-4 (Al 7% Si allo Periodic wav surface depressions observed on both sides of the strip Deeper depression on liquid side (visual inspection Depressions separated b a pitch (λ = ~ 5 mm 53 mm

3 Process Conditions (# ODSU6_43, ccle number3 G = domain height: (mm L = Puddle length (mm D = Nozzle opening width (mm B = Nozzle Breadth: Vc = Wheel speed (linear (m/s: Ts = Superheat: (K t = contact time (ms: T = Strip thickness (mm Strip width (W Angles (θ 1, θ 2, θ 3 in deg T (ambient Aluminum Grade Wheel Grade T initial (wheel mm (3.13,15, o C Al-7% Si Cu-Be 31.7 o C 5 Process Parameters & Material Properties Wheel Outer radius (m Wheel Inner radius (m H.T coefficient (wheel-ambient W/ m 2 K (inside & outside H.T coefficient (wheel-ambient W/ m 2 K (wheel sides H.T coefficient (wheel-strip W/m 2 K puddle region h o t o m F(t cast 225 G.1 sec.33 Thermo-phsical Properties Conductivit (W/m K Specific Heat (J/kg K Densit (kg/m 3 Latent Heat of Fusion (KJ/ Kg Solidus ( o C Liquidus ( o C Wheel Strip

4 Parameters Simulation Conditions Domain height (G in mm Mesh size (dr in mm STRIP1D (with superheat flux.25.1 Mesh size (dz in mm Time increment (dt in sec No of nodes in wheel Zones No of nodes in strip θ (deg Variation of conditions throughout the cast Distance (mm Time (sec Cumulative time (sec h (W/m 2 K hgap =f(t tcast hgap =f(t tcast Temperature criterion for determining Shell Thickness: 614 o C (% solid Model Development Test problem with: constant properties no wheel Simple conduction through liquid moving with strip 8

5 Domain and BCs G 714 o C Eulerian Fluid-Flow model (FLUENT q = Fluid in motion L Stationar strip 614 o C r z 7.2 m/s T The model domain comprises of liquid region (T > 614 o C The fluid moving with the strip along z direction at a speed of 7.2 m/s is equivalent to the transient ABAQUS and STRIP1D models formulated in a Lagrangian Frame with simple conduction through the superheated liquid. Using fixed temp lower BC, outputs the heat flux (super heat at the solidification front which enters the solid strip. This heat flux is input as a superheat flux curve into the STRIP1D Model heat lfux (W/m Heat flux Vs. distance Superheat flux from Fluent Superheat flux to Strip STRIP1D distance (mm Area under the graph gives the total Superheat flux of 1.72 MW/m entering the domain. 9 Comparison of shell growth Vs. time between ABAQUS and Strip 1D (2 versions Strip Thickness (mm Strip 1D VS. Abaqus 2D Model, delta= 3 STRIP1D ABAQUS const props STRIP1D using superheat flux from FLUENT, domain =1.5mm STRIP1D using superheat flux method, Domain=.25mm Liquidus Solidus Time (sec All 3 methods match! STRIP1D run with simple conduction in liquid (constant K=135 W/m K and c p = 119 J/Kg K ABAQUS run with constant properties STRIP1D run with superheat flux input from Fluent 1

6 Temperature along the domain height at various time intervals for ABAQUS vs. STRIP1D Temperature ( o C t =.14 s t =.37s Temperature along domain t = s Pour temperature Solidus t = s Liquidus + delta STRIP1D without superheat flux input STRIP1D with superheat flux input ABAQUS 2D Model Distance ( along the domain (mm STRIP1D run with K=135 W/m K and c p = 119 J/Kg K for L=23.3 mm ABAQUS run with constant properties STRIP1D run with superheat flux input from Fluent 11 Model Application to a realistic case I STRIP1D model of transient heat conduction in wheel, gap, and strip for series of ccles for sample # ODSU6_43 Salient Features of the Model Modeling Interface/gap heat transfer coefficient as a function individual ccle time of cast, i.e. h gap = f (t cast Superheat Flux deliver into the pool taken into account from separate 2D Eulerian model of fluid flow / heat transfer in liquid pool Gap effect on heat transfer coefficient Modeling of thermocouple effect in wheel 12

7 Velocit & temperature in the liquid pool and Superheat flux profile from Fluid-flow Model Courtes: Rajneesh Chaudhar Heat flux (MW/m Superheat Heat Flux Profile t=.215mm - FLUENT t=.168mm - FLUENT t=.168mm using superheat ratio method distance (mm Area under the curve: (Total superheat flux into the domain.215mm strip : 427 kw/ m (1 K superheat.168 mm strip : 353 kw/ m ( 78.3K superheat Strip thickness observed to decrease with domain height (G heat flux (t=.168mm = heat flux (t=.215mm *superheat (t=.168mm/superheat(t=.215mm 13 Heat Balance (puddle exit Gap (mm Strip Thickness (mm Superheat (kw/m Total Heat Fluent, (insulated (kw/m Superheat temperature ( T deg Total heat - Fluent (const temp (kw/m (.237** t =. 168mm m = ρtν = 24*. 168* 7. 2 = kg t =. 215mm m = ρtν = 24*. 215* 7. 2 = kg Converting the effect of / sm q1 = m cp T = 2. 83* * 1 = 329kW / m / sm q2 = m cp T = 3. 62* * 1 = 421kW / m shell thickness (from STRIP1D, to an equivalent effect of superheat temperature Superheat temperature for a flux of 353 kw/ m q2 * T1 * t1 353* 1* 215 o T2 = = = 75 q1 * t2 427* 237 Superheat should match total heat computed b Fluent (insulated. It comes close (within 3.5% error ** thickness value obtained from STRIP1D for a superheat flux of 353 kw/m 14

8 Gap height Vs. time : Experimental data for sample ODSU6_ Gap Vs Time = -.879x Gap, G (mm.6.4 = -.833x Highs.2 Lows Time, t (sec 15 Effect of Gap (mm on h (kw/ m 2 22 h vs. G, gap 2 h (kw/ m 2 K G, gap (mm Empirical relation between h and Gap (G : h = 225 G 16

9 Gap Heat transfer coefficient (h gap as a function of time Heat transfer coefficient hgap (KW/m2K kw/ m 2 K h g a p Heat transfer coefficient Vs. time 4 Zone I 2 Zone II Zone III ( h amb = 25 W/m 2 K time (sec h, < t < t m = t h, t t < t t 17 I Loss of Contact between strip & wheel m =.33, t o =.1 sec h = 17 kw/ m 2 K (=225 G, t I =ccle time Heat Flux in gap as compared to Experimental measurements for 1K superheat 1 Heat Flux into the wheel Vs. time STRIP1D prediction Outer Heat Flux (MW/m Zone I Measurements b Birat et al. Measurements b Blejde and Mahapatra at Castrip LLC Zone II Texture A Texture B Time (sec Strip 1D heat flux in Zones I & II the gap matches the extrapolated value of the line of best fit to Birat et al (2. data. Reference : (1 Guowei Li and B.G.Thomas : Transient Thermal Model of the Continuous Single-Wheel Thin- Strip Casting Process, Metall. Trans. B, 1996, vol. 27B, pp Reference: (2 J.Birat, M.Larrecq, J.Lamant, and J.Petegnief: Mold Operation for Qualit and Productivit, ISS, Warrendale, PA, 1988, pp

10 Accounting for convective heat transfer from the wheel sides Treating the Convective heat transfer on wheel sides as a heat source Taking into account 4 surfaces on the wheel sides 2 2 Area on wheel sides(a = 4Π( Volume of wheel(v = 5Π( mm Total heat taken out from sides = ha T W 2 ha T 4Π( 34 Heat (per unit volumeremoved from wheel sides = = h T 2 2 V 5Π( i.e. Heat Q sides source( Q = h( T T i sides air = h T W / mm 3 3 W / mm mm mm W / mm Plate 3 5mm 12.7mm Wheel 2 plates one on each side of the wheel with 2 surfaces each contribute to a total of 4 surfaces 19 Shell Growth as a function of time Shell Thickness (mm Zone I Liquidus Shell Growth Profile Cold Face Solid shell (T=555 o C occurs at Zone 2. Zone II f :.3 f :.5 f :.8 Hot Face Time (sec Cooling rate= (T liq -T sol /t sol, where t sol solidification time f :Solid fraction Solidus Cooling rates Cold face : 58 K/sec; Hot face : 6 K/sec 2

11 Metallograph & SDAS (measured b Cormac Brne et.al 4 SDAS Vs. Solidification time Experimental measurements SDAS (micrometers STRIP1D predicted SDAS Solidification time (sec Free side of the strip exposed to atmosphere STRIP1D model used to obtain solidification time (t sol Used Spinelli et.al model to predict the SDAS of the strip accordingl λ = 5 ( t sol Shell Growth as a function of time Shell Thickness (mm Shell Growth Profile Zone I.82m/s Liquidus Zone II Solidification rate =.82 m/s Time (sec (Within range of.5m/s and.1 m/s as reported b Brne et al., 25 22

12 Accounting for heat loss due to the thermocouple (TC embedded in the wheel Fast-response K-tpe MedTherm termocouple Screw threads x z 1.3 cm Sensor The TC embedded 2mm below the substrate surface Not in perfect contact with the substrate thereb causing an air gap This resists the heat flow to the thermocouple thereb lowering the value of the actual substrate temperature. Thus TC has been treated as a set of resistors and a relation between the measured and predicted temperature has been obtained. 23 Schematic of TC embedded in the wheel Cu-Wheel Air gap 2 mm thick T 12.7 mm Wire ( (amb T amb T 1 Parameters Airgap( part 1 part 2 part 3 part 4 wire-amb(5 L(m 3.E E-3 1.3E-2 1.3E E-2 Infinitel long L air L 12 L 23 L 34 L 45 L 56 d(m 8.E-4 8.E-4 2.E-3 7.2E-3 2.E E-3 k(w/mk 1.E-2 1.1E+1 1.1E+1 1.1E+1 1.1E+1 1.1E+1 A(m2 5.3E-7 5.3E E-6 4.7E E-6 2.7E-6 l/ka (K/W 5.97E+2 (R 1 4.1E+2 (R E+2 (R E+1 (R E+2 (R E+2 (R 56 R 6 (K/W (total resistance 2.34E+3 24

13 Wheel temperature (2mm deep Vs. time between STRIP1D and Experimental data (1 K superheat 12 1 Wheel temp Vs. time Wheel temp ( o C Experimental measurement 2mm below wheel surface adjusted according to resistance method 2 mm below surface Time (sec STRIP1D run wheel temperature values match the trend suggested b the experimental runs Faster cooling observed in real, owing to the behavior of the wheel as a lumped sstem during ambient cooling. 25 Wheel temperature (2mm deep Vs. time between STRIP1D and Experimental data (1 K superheat 12 Wheel temp Vs. time 1 Wheel temp ( o C Experimental measurement 2mm below wheel surface adjusted according to resistance method 2 mm below surface Time (sec ZOOM IN for Ccle no: 5 26

14 Shell thickness Vs. time between STRIP1D and Experimental results for (1 K superheat.3 Strip thickness Vs. time Strip thickness (mm start and end points are red Experimental Data Lows - STRIP1D Highs - STRIP1D time (sec Decreasing gap during cast considerabl alters the heat transfer coefficient which results in reduced strip thickness as observed. 27 Model Application to realistic case II (ODSU6_42 Temperature vs. time 1 8 Parameter ODSU6_43 (I ODSU6_42 (II Temp. ( o C 6 4 Shell Thickness (mm Experiemental data : TC temperature STRIP1D predictiontc temperature Velocit (m/s Strip thickness (mm Time (s Strip thickness Vs. time time (sec Experimental Data Lows Highs Cooling rate ( o /sec Superheat (kw/m Puddle length (mm Time in Zone I (ms Angle in zone II ( o Time in Zone II (ms Good agreement observed between model predictions and experimental observations

15 Shell Growth as a function of time for Case II.3.25 Zone I Shell Growth Profile Cold Face Zone II f :Solid fraction Shell Thickness (mm Liquidus f :.3 f :.5 f :.8 Hot Face Solidus Solid shell (T=555 o C occurs at Zone 2. Time (sec Cooling rates Cold face : 56 K/sec; Hot face : 58 K/sec Criterion for Zone II exit is when shell is completel formed. 29 Computational Domain & 2D FE Mesh # ETFA1-11 Crucible Liquid puddle Crucible G =.7874 mm Vc = 6.23 m/s w =.2 mm l = 2.5 mm WHEEL Domain (l x w t = s L = mm t c = L/Vc =.365 s Domain size:.2 (thickness x 2.5 (length mm WS depression modeled as a clindrical trench running through strip width (B Note: w =.2 mm > T =.172 mm: ~14% liquid inside domain after end of analsis (t = t c B λ = 5 mm Liquid side x T Wheel side w x l r =.3 mm 3

16 2D FE Mesh & Thermal Boundar condition 4 noded linear quads (DC2D4 in ABAQUS Mesh size: ~ 4.75 x 4.75 microns near WS depression Wheel not included in thermal analsis Cauch-tpe BC applied on surface, S 1 Wheel side Liquid side r =.3 mm l = 2.5 mm.2 mm S 1 x Aluminum h wheel Air r = 3 µ m 31 Development of a 3D analsis 2D analsis: WS depression is a clindrical trench x B λ = 5 mm 3D analsis: WS depression comprises of rows of equall spaced (λ = 12 µm hemispherical craters (r = 3 µm T w =.2 mm l = 2.5 mm R.3 mm Liquid side r =.3 mm z Wheel side x w =.2 mm l = 2.5 mm b =.6 mm λ = 5 mm.12 mm 32

17 .6 mm 3D FE Mesh & Thermal boundar conditions Structured mesh with 8 noded linear bricks (DC3D8 in ABAQUS Mesh size: ~ 3.75 x 3.75 x 3.75 microns near WS depression Cauch-tpe BC applied on surface, S 1 : h wheel = 1.7 x 1 5 W/m 2 K Simulation conditions identical to 2D analsis 2.5 mm.2 mm z x O (,, r =.3 mm O (,, h wheel Crater with r = 3 µm (WS depression S1 Crater cavit filled with air.3 mm 33 Temperature contour & LS depression caused b a single crater Temperature ( o C Liquid side shell profile along -direction Far-field shell edge.172 mm LS depression d = µm SHELL z x WS crater r = 3 µm 34

18 Measured Comparison between measured & predicted LS depression shapes Liquid side depression 56 µm Predicted SHELL 172 µm Predicted profile Wheel side crater 16 µm Good match confirms the validit of modeling methodolog Formation of LS depression is a heat transfer-driven phenomena in the presence of a row of craters on the opposite (wheel side of the strip 35 Conclusions The superheat flux model used is a realistic treatment of the effect of the 2-D fluid flow on heat transfer in the liquid and associated effect on the strip solidification and cooling STRIP1D predictions matches simultaneousl with time-dependent experimental measurements of wheel temperature and strip thickness (given measured puddle length, gap thickness, strip speed, and other casting conditions. The particular choice of constant thermo-phsical properties used in STRIP1D reasonabl match both realistic temperature-dependent properties and constant in an ABAQUS simulation. Gap variations seem to decrease heat transfer coefficient in the contact region which explains the variation in shell thickness. Heat transfer near TC is affected b heat loss through sides and & TC wire, which has been taken into account. The shell growth profile also shows that the strip is mush even after it enters Zone II and shell rapidl forms onl at the end of Zone II. Zone II ends when the shell solidifies completel and is strong enough to shrink and leave the wheel. Computational models have been developed to simulate fundamental phenomena during initial solidification. Models can also include effect of surface tension, strain-rate, and phase-dependent mechanical behavior, stress, and shrinkage Practical insights can been gained into Steel Strip casting 36

19 Acknowledgements Continuous Casting Consortium Members (Nucor, Postech, LWB Refractories, Algoma, Corus, Labein, Mittal Riverdale, Baosteel, Steel Dnamics National Science Foundation DMI (Strip Professor Paul H. Steen and other graduate students from Cornell Universit for experimental data National Center for Supercomputing Applications (NCSA at UIUC ABAQUS TM, Fluent, Inc., CFX, UIFLOW (P. Vanka Other Graduate students, especiall J. Sengupta 37