“current results of the solidification modelling in

Simulation & Modellierung metallurgischer Prozesse,

Department Metallurgie, Montanuniversität Leoben 1

PFAU 9.0 | Johannes Kepler Universität Linz | 03 Nov 2014

“Current results of the solidification modelling

in continuous casting”

Dr. Alexander Vakhrushev

Simulation & Modellierung metallurgischer Prozesse,

Department Metallurgie, Montanuniversität Leoben 2

OUTLINE

Introduction

Modelling of casting process

Inclusions modelling

Liquid slag model verification

Heat transfer through the refractory

Conclusions & outlook

#3

Ladle

Tundish

Mold

Strand

Support

rolls

Stopper

Processes to simulate: continuous casting

[Wikipedia]

#4

OUTLINE

Introduction






#5

Results of the thin slab casting simulation

#6

METALLURGICAL AND MATERIALS TRANSACTIONS B

We got 10 pages of comments & questions

Constructive

Didn’t require a content change

Some interesting results were added

Enforced some important improvements:

Direct usage of T-dependent properties (IDS)

Reconsider heat fluxes (narrow face)

#7

Direct usage of the IDS data

Solid fraction Specific heat Thermal conductivity

# idsToOPENCAST.py IDS_data_file_name_prefix

#9

Flow / solid shell interaction

Stream lines Shell thickness

#10

Shell thickness verification: 30% of solid

Cut I

#11

Tipp: strong back flow for some designs

Pressure inlet

Velocity outlet

(fixed normal + slip)

#12

Boundary conditions to suppress backflow

Pressure inlet:

turbulentIntensityKyneticEnergyInlet, I=4%

turbulentMixingLengthDissipationRateInlet, d=0.07*D

Velocity outlet:

fixedNormalSlip with casting velocity

No back flow at all

#13

OUTLINE

Introduction






#14

DNS flow simulation in a tundish

#15

DNS vs. RANS flow simulation in a tundish

DNS

K-epsilon

#17

Particle flow in a tundish (DNS simulation)

#18

OUTLINE

Introduction






#19

Motivation: focus on the SEN region

(a) mechanisms of slag entrapment

(b) SEN refractory erosion kinetics

(c) free surface oscillation/waves

(d) patterns of turbulent jet flow

(e) sensitivity of all phenomena to SEN design

(e)

(c) (b)

(d)

(a)

#20

Governing equations of the numerical model

𝜌mixture = 𝛼melt ⋅ 𝜌melt + 𝛼slag ⋅ 𝜌slag + 𝛼air ⋅ 𝜌air

𝜇mixture = 𝛼melt ⋅ 𝜌melt ⋅ 𝜂melt + 𝛼slag ⋅ 𝜌slag ⋅ 𝜂slag + 𝛼air ⋅ 𝜌air ⋅ 𝜂air

𝜂mixture = 𝜇mixture 𝜌mixture

∇ ∙ 𝑢 = 0

𝜕𝛼𝑖𝜕𝑡

+ ∇ ∙ 𝑢 𝛼𝑖 = 0

Mixture properties:

Incompressible turbulent flow:

𝑆 surf = 𝜎𝑖𝑗 𝜅𝑖𝑗 α𝑗∇α𝑖 − α𝑖∇α𝑗

𝑖 ,𝑗

𝜅𝑖𝑗 = −∇ ∙ α𝑗∇α𝑖 − α𝑖∇α𝑗

α𝑗∇α𝑖 − α𝑖∇α𝑗 where

Scalar transport of volume fraction:

𝜕𝜌𝑘

𝜕𝑡+ ∇ ∙ 𝜌𝑢 𝑘 = ∇ ⋅ 𝜇 +

𝜇t

𝑃𝑟t,k∇𝑘 + 𝐺 − 𝜌𝜖

𝜕𝜌𝜖

𝜕𝑡+ ∇ ∙ 𝜌𝑢 𝜖 = ∇ ⋅ 𝜇 +

𝜇t

𝑃𝑟t,ϵ∇𝜖 + 𝜌𝐶1𝜖𝜖 − 𝐶2𝜖𝜌

𝜖2

𝑆𝑘

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

𝜕𝜌𝑢

𝜕𝑡+ 1 − 𝛼air ∇ ∙ 𝜌𝑢 ⊗ 𝑢 = −∇𝑝 + ∇ ∙ 2𝜇eff𝐃 + 𝜌𝑔 + 𝑆 surf

𝛼melt + 𝛼slag + 𝛼air = 1

a) b)

𝑘 (𝑚2𝑠−1)

Standard model Modified

a) b)

𝑘 (𝑚2𝑠−1)

Standard model Modified

#21

Experimental setup and simulation domain

melt slag airmelt slag air

a)

b)

c)

Simulationdomain

Outflow

Outf

low

Meniscus

a)

b)

c)a)

b)

c)

Simulationdomain

Outflow

Outf

low

Meniscus

#22

Water modelling results

1.5 m/min

#23

Simulation results / comparison with experiment

𝑢 , m s

a) b)

Flow simulation:

Comparison with the water modelling results:

Slag position / velocity vectors Velocity magnitude Stream-lines

Experiment Simulation

Time-averaged int. position

#24

OUTLINE

Introduction






#25

Heat transfer through refractory: motivation

Estimate heat losses through the SEN

Can it lead to the solidification at the flow stagnation zones?

when ~ 1 K of superheat

is predicted !!!

#26

Model development: ÖGI solidification benchmark

Al

Cu

symmetry

symmetry

symmetry

insulated

insulated

insulated HTC specified

solidifying shell

liquid core

#27

Model development: ÖGI solidification benchmark

finalAlp

Alfinal

Cup

Cu

Alinit

Alp

AlCuinit

Cup

Cu

TCmTCm

LTCmTCm

curve red

curve blue

Al

Cu

#28

2D solidification with the heat transfer in SEN

Mold: wall heat flux

Mel / slag interface:

HTC specified SEN / melt wall: HTC

SEN / air wall:

HTC + radiation

Simulated

Not simulated

#29

2D solidification with the heat transfer in SEN

#30

OUTLINE

Introduction






#31

Shell formation (DNS)

#33

Shell thickness: comparison DNS vs. RANS

RANS DNS

#34

Future work: DNS simulation of a free surface

#35

Particle simulation with 2 phase VOF

#36

THANK YOU FOR YOUR ATTENTION!

“current results of the solidification modelling in

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