static model of the meniscus for continuous casting

Transcription

1 Elimination or minization of oscillation marks A path to improved cast surface quality static model of the meniscus for continuous casting A. Moinet & A.W. Cramb 9th AISI / DOE TRP Industry briefing session 1

2 Outline Introduction Continuous casting The meniscus area Oscillation marks Model Numerics Description of the problem Simplifications: Limits Turbulence Shell removal Results Determination of key parameters for this simulation Effect of heat input and/or insulating panel on oscillation marks 2

3 Introduction: continuous casting Liquid steel is injected through the nozzles, and cools down along the mold To prevent sticking, molten slag and mold oscillations (negative strip time) Various defects are thought to be created at the meniscus 3

4 Description of the meniscus area Heat input: hot metal Conduction through liquid metal: convection, diffusion, turbulence Conduction through solid metal: diffusion Mushy zone: latent heat release Liquid and solid slag : conduction, radiation Free surface movements, surface tension Solidified slag: glassy/crystalline structure 4

5 Perpendicular to the withdrawal direction Typically, one mark per oscillation of the mold Up to a few millimeters deep Source of other defects (inclusions, cracks), necessity of hot rolling Observations: formation happen at the meniscus level, heat release No certain explaination Oscillation marks Withdrawal direction 5

6 Theory for oscillation mark formation: meniscus overflow 6

7 Goal of the project The partial solidification of the meniscus is likely to be responsible for oscillation marks We need to better understand what s going on near the meniscus Eventually, the meniscus area will be modelled, including all the phenomena aforementionned (heat, flow, free surface, thermal radiative transfer) Simplifications must be done, limit boundaries must be formulated A preliminary static thermal model for the meniscus was designed 7

8 Numerical methods Heat transport: Governed by Fourier s law: Continuous second order differential equations can be solved by finite element methods Solidification modeling ρ C dt dt Latent heat release in regions where: T solidus < T < T liquidus Use of effective heat capacity p T t 2 = ρ C p + V. T = k T + Q Q = ρ H L f t = ρ H L f T T t = C p latent heat T t C latent heat = ρ H L f T ρ C p eff dt dt T t 2 = ρ C peff + V. T = k T + Q 8

9 Numerical methods: Issues with solidification modeling The effective heat capacity is not continuous and it can be much larger than the actual heat capacity Ex: δ-ferrite: C p = 800 J/K/kg, C peff = 9000 J/K/kg The area where to use C peff instead of C p moves: the mesh cannot be easily adapted Various methods: 9

10 Description of the model 50 mm 10 mm 100 mm 50 mm 10

11 Description of the model In an actual (transcient) conditions, the solidified steel is withdrawn. If not, solid steel accumulates and the calculated thickness of the shell will not be realistic. A flow that simulates steel withdrawal was calculated and applied to all calculations 11

12 Temperature at boundaries: issues Steel is injected in the mold at a temperature slightly superior to the liquidus temperature From the exit of the nozzle to the surface of the mold, there exists a temperature gradient that is a function of the flow field and the conductivity of the metal Both the flow field and the steel conductivity are not trivial 12

13 Boundary conditions: Inlet (mass controlled) Outlet (free flow) Temperature at boundaries: dependance on flow field k-ε for tubulence Fluid flow (m/s) [Fluent simulation] k-ε model: Effective thermal conductivity (K/m/s) [Fluent simulation] 13

14 Boundary conditions: T = T superheat Temperature at boundaries: dependance on flow field No solidification but T = T liquidus Border 2 Temperature drop is not linear or uniform within the mold It is stronger around the meniscus Horizontal gradient is smaller on border 1 Temperature has to be set on border 2 Border 1 14

15 Effective thermal conductivity in the meniscus area k-ε model: Effective thermal conductivity (K/m/s) around the meniscus [Fluent simulation] Effective thermal conductivity decreases linearly with the distance to the surface of the mold Rather than calculating the turbulences at each step, effective thermal conductivity will be approximated by a linear function of the distance to the mold 15

16 To summarize The mold is 100 mm thick, the slag layer is 1-2 mm thick and the 50 mm around the meniscus are investigated The heat input: fixed temperature before the meniscus The heat release: water cooling, forced convection, function of h (convection coefficient) Heat conduction in the liquid metal: proportional to the distance to the border We want to see how various parameters affect the meniscus 16

17 To summarize slag Steel Solidus 1492 C Liquidus 1530 C Thermal conductivity in solid 40 W/m/K Effective thermal conductivity in liquid 5,000 W/m/K Latent heat of fusion 250,000 J/kg Density 7000 kg/m3 Heat capacity 800 J/K/kg Slag Thermal conductivity in solid 1 W/m/K Radiative heat transfer no Density 1000 kg/m3 casting parameters Withdrawal velocity 0.02 m/s Superheat 27 C water cooling convection coefficient 20,000 W/K/m 2 Copper mold Steel (liquid) Steel (solid) 17

18 Effects of superheat Superheat = 18 C Superheat = 27 C Superheat = 36 C 18

19 Effects of water cooling convection coefficient h = 20,000 W/K/m 2 h = 40,000 W/K/m2 h = 10,000 W/K/m 2 19

20 Effects of effective conductivity in the liquid steel K eff max = 5,000 W/m/K K eff max = 6,000 W/m/K K eff max = 4,000 W/m/K No effective conductivity 20

21 Effects of radiative heat transfer in theslaglayer No radiative heat transfer Absorption coefficient = 5000 m -1 Absorption coefficient = 2000 m

22 Effects of the slag layer conductivity k = 0.5 W/M/K k = 1 W/m/K k = 2 W/m/K 22

23 Heat input Heat input could reduce heat transfer, in order to prevent freezing of the meniscus The effect of heat input at the meniscus level (a quantity similar to the heat flux, 1 MW/m 2 ) was monitored slag mold steel Heated area 23

24 Heat input (1 MW/m 2 ) 24

25 Heat input (1 MW/m 2 ) 25

26 Heat input (100 MW/m 2 ) 26

27 Heat input (100 MW/m 2 ) 27

28 Insulating panel An insulating material is inserted between the slag layer and the mold, at the meniscus level The effect of heat input at the meniscus level (a quantity similar to the heat flux, 1 MW/m 2 ) was monitored slag mold steel insulated area 28

29 Insulating panel 29

30 Insulating panel + heat input slag mold insulated area Heated area steel 30

31 Insulating panel + heat input: 10 MW/m 2 31

32 Conclusions A model for studying the meniscus at steady state was designed When focusing on the meniscus area, some parameters can be neglected or simplified: turbulent heat transport, mold water cooling Superheat is a sensitive parameter but can be evaluated The slag properties are very sensitive Inputting heat transfer in the mold can hinder solidification of the steel shell. However, energy input rates are very high to have any effect Inserting an insulating board can be effective The heat needs to be brought directly on the steel 32

33 Thank you for your attention 33