Analysis of Scarfed Shape Effect over Slab Heating Process

Hyun-Joon Kim / PDT-3 Seoul Office, CD-adapco Group

Jun-Seok Lim, Hyeong-Jin Kim Hyundai-Steel Co., Ltd.

2

• C-Hot Strip Mill Introduction

• Problem Description

• Governing Equations

– Energy Equation and Radiation Transfer Equation

– Finite Volume Stress Model Equation

• Geometry & Mesh Generation

• Physics & Boundary Conditions

• Result

Table of Contents

3

Slab Reheating Furnace

R2

Descaler

F1

Laminar flow

Down Coiler

Edger2

Heat Holding Cover

Finishing Mill

#3 #2

#1

#4

R1

Edger1

Run Out Table

F2 F3

F4 F5

F6 F7 Roughing Mill

Crop Shear

Descaler

Coil yard

Skin Pass Mill

Hot Final Line

#3

#2 #1

Edge Heater

Type : Walking beam type

Injection Pressure : 220 bar

Type : Stop and go type

Type : 4hi reversible

Type : Rotary Drum type

Cutting ability : API-X80, 60mm T x 2,000mm W

Type : 4hi Irreversible X 7 stands

Type : Oil hydraulic operation X 2ea

Type : 4hi irreversible

Type : 4hi irreversible

Injection Pressure : 220/(300) bar

Slab Size Press

C-HSM Facilities

4

◎ Slab Reheating Furnace

HSB

(Hydraulic Scale Breaker)

#2 RF #1 RF #3 RF Provision

RM2 RM1 SSP

◎ Roughing Mill

C-HSM Facilities

5

Laminar Flow

(DC)

Down Coiler

◎ Down Coiler

◎ Finishing Mill

FM FSB

(Finishing Scale Breaker)

Crop

Shear

Edge

Heater

Heat

Holding

Cover

C-HSM Facilities

6

(단위 : 명, 만톤)

인원 2,100

생산능력 430

인원 700

인원 4400

생산능력 1100

총인원 8,800

생산능력 1,850

인원 1,600

생산능력 330

인원 160

생산능력 7

열연 강판

- 자동차, 가전, 건자재용 열연강판

철근

- 건축 및 교량용 철근

형강

- H형강, ㄱ/ㄷ/CT/I 형강 등

기타

열연강판 실수요 자동차용 H 형강 교량용 건축용

철근 건축 및 교량

후판 롤 스테인리스

철도레일 잉곳 무한궤도

당진 공장

해외 (청도)

서울 사무소

포항 공장

인천 공장

▣ 현대제철 소개

현대제철 사업 분야

□ 1953. 06. 대한중공업 공사 설립 □ 1964. 09. 인천제철㈜ 설립

□ 1970. 04. 인천중공업㈜ 인수합병 □ 1978. 06. 현대그룹에 편입

□ 2004. 10. 한보철강 당진공장 자산인수 □ 2006. 03. 현대제철㈜ 상호 변경 □ 2006. 10. 일관제철소 기공식 □ 2010. 04. 일관제철소 준공식

창업기 (1953~1969) 발전기 (1970~1999)

도약기 (2000~ )

공장현황 주요생산품

현대제철 연역

7

▣ 열연기술개발팀 업무

설비 합리화 / 정상화

생산 피치 최적화

회수율 향상

치수 제어

표면 품질 개선

최적 설비 유지 핵심제품 생산기술

고품질 제조 기술

프로세스 고도화

생산성 향상/원가절감

자동차용 내/외판재

고강도강 / 합금강

일본向 수출재

Level 2 수식모델

Level 1 자동제어

품질 설비 개선

열연공정에서 고품질 제조기술 확립

품질 기술 표준 제정 및 개정

품질관련 주요 공정인자 선정

강종 개발 지원

품질 향상을 위한 설비 개선

설비 유지/보수 기준 설정

투자관련 조업 기술 지원

수식모델 운영 및 Logic 개선/개발

신 제어 기능 개발 및 적용

공정 개선 방안 개발

품질관리 설비 진단 열연기술일반

8

PROBLEM DESCRIPTION

Chapter 1

9

Scarfing Process

• To remove impurities of raw slab plate, scarfing process must be performed before rolling process

• Usually processed by experts person or machine

10

Problem Description

• Scarfed slab has problem with its uniformity of temperature distribution which leads to defective product

• Depth of scarfed shape is 2mm, 4.4mm, 6.8mm

Linear shape

Sine Wave Shape

11

GOVERNING EQUATION

Chapter 2

12

Solid Energy Equation

• The governing equation for energy transport in a solid is

additionally, we will consider (ir)radiative heat flux from the slab surfaces. Thus the source term will be radiation heat flux term

p p s

V A A V

dC T dV C T d d s dV

dt v a q a

:

:

:

:

p

s

C specific heat

T temperature

heat flux vector

solid convectivevelocity

q

v

13

Radiation Transfer Equation

• The radiation transfer equation(RTE) is

Since full computation of RTE is compute intensive, so we will use Surface-to-Surface(S2S) radiation model

4

0

42

,4

,,

dsITn

asIas

sI ss

Change in I along

path segment ds in

an elementary solid

angle dω

Decrease in I due to

absorption and out-scattering

Increase in I

due to surface

emission

Increase in I

due to in-scattering

2

-8 2

, Radiation intensity; flux per unit area normal to ray per unit solid angle, W/(m Sr)

, Stefan-Boltzmann constant, 5.672 10 W/(m K)

Scattering phase function; probability that a ray from on

s

I s

a

e direction

will be scattered into the same direction as another ray

Refractive index ( 1 most of the time)n

14

S2S Radiation Model

• The total amount of radiation power emitted by and received by is

• The surface emissive power for a given spectrum or band is the product of the emissivity and the blackbody emissive power for that spectrum or band

1dS

2dS

2 2

1 2 1 1 1

2

coscos

dSP i dS

L

4

, , 1 2 ,i i i iE T T

1 2

1 2

, fraction of totalblackbodyemission for thespectrumor band

, lower and upper wavelength boundsof thespectrumor band

iT

15

Finite Volume Stress Model

• The differential form of the solid momentum equation is

For all cells in the domain , the discrete form of the momentum equation becomes

u b

displacement field

stress tensor field

bodyforce

u

b

i i i j j i i

i f i

V V i

u s b

normalsurfacevector of facej js

i V

16

GEOMETRY & MESH GENERATION

Chapter 3

17

Importing 3D-Curve from File

• Lower surface is sine wave shape, thus

• Using spreadsheet program, we can export the position data

sinpos

pos

xy h

18

Using 3D-CAD Tool in STAR-CCM+

• STAR-CCM+ supports direct CAD geometry creation

Upper

Lower

Symmetry Side

19

Meshing Setup

• Using Trimmed Hexahedral Meshing Model

• By employing volumetric controls, anisotropic mesh generation is allowed

20

Generating Grids

• Takes about 30 sec ~ 1 min.

– Approx. 13K ~ 14K Cells are created

21

PHYSICS & BOUNDARY CONDITIONS

Chapter 4

22

Creating Physics Continua

• Physics models are selected as follows

– Implicit Unsteady

– Solid

– Segregated Solid Energy

– Constant Density

– Radiation

– S2S Radiation

– Gray Thermal Radiation

23

Defining Material Properties

• STAR-CCM+ supports polynomial in T, table, user code, field functions for material properties

– Polynomial in T : Density, Specific Heat

– Table Data or field function : Thermal Conductivity

• When using tables, user can select interpolation method

– LINEAR, SPLINE, STEP

24

Settings Material Properties

• Thermal conductivity, specific heat are function of temperature

• By adopting numerical methods, extract piecewise polynomial functions are defined

200 400 600 800 1000 1200 1400 1600

400

500

600

700

800

900

1000

1100

1200

Specific Heat (J/Kg-K)

Temperature (C)

Specific Heat

Interpolated

200 400 600 800 1000 1200 1400 1600

20

30

40

50

60

70

Conductivity (W/m-K)

Temperature (K)

Conductivity

Interpolated

25

Polynomial Material Properties

• For Non-linear material properties

• WYSWYG Material Property Definition Wizard

0 200 400 600 800

60

80

100

120

140

160

180

Thermal Conductivity (W/m-K)

Temperature (C)

200 400 600 800 1000 1200

6600

6800

7000

7200

7400

7600

7800

Density (Kg/m^3)

Temperature (K)

200 400 600 800 1000 1200

650

700

750

800

850

900

950

1000

Specific Heat (J/kg-K)

Temperature (K)

26

Ambient Temperature of Furnace

• When the slab came into furnace, radiant heat transfer to the slab is dominant and needs to be applied

• Needs to be interpolation technique to applying arbitrary time

• For the best fitting, “Monotone Hermite Spline Interpolate” is used with JAVA script

0 2000 4000 6000 8000 10000 12000 14000

200

400

600

800

1000

1200

1400

1600

Temperature (K)

Time (s)

27

Initial Conditions

• Initial Temperature of Slab : 4 ℃

• Emissivity of Slab

– Temperature dependent

– Use field function

200 400 600 800 1000 1200 1400 1600

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

Emissivity

Temperature (K)

Emissivity

Curve Fit

28

Position of Data Points

• Extract temperature and other thermal data for the critical position

29

RESULT

Chapter 5

30

Temperature of Slab

• The correspondence of solution with experimental data is quite good

0 2000 4000 6000 8000 10000 12000

0

200

400

600

800

1000

1200

Temperature (C)

Time (s)

Exp (10)

Exp (11)

Predicted (10)

Predicted (11)

31

Boundary Irradiation Heat Flux

• Shows scarfed depth is important factor of heating uniformity

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

260770

260780

260790

260800

260810

260820

Boundary Irradiation (W/m^2)

Position [m]

Upper-2mm

Upper-4.4mm

Upper-6.8mm

-0.1 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

260806

260808

260810

260812

260814

260816

260818

260820

Boundary Irradiation (W/m^2)

Position [m]

Lower-2mm

Lower-4.4mm

Lower-6.8mm

32

Effect of Scarfing Shape

• Difference of scarfed shape is almost negligible

0 2000 4000 6000 8000 10000 12000

-2

0

2

4

6

8

10

12

14

Temp. Difference (C)

Time (sec)

(1)-(2) (6.8mm)

(1)-(2) (4.4mm)

(1)-(2) (2.0mm)

0 2000 4000 6000 8000 10000 12000

-2

0

2

4

6

8

10

12

14

16

18

Temp. Difference (C)

Time (sec)

(5)-(6) (6.8mm)

(5)-(6) (4.4mm)

(5)-(6) (2.0mm)

Linear shape

Sine Wave Shape

33

Temperature Difference between Points

• Temperature difference between (5) and (6) point

• As scarfing depth increased, temper- ature difference increased

• After full heating process is ended, final temperatures are approaching gradually

0 2000 4000 6000 8000 10000 12000

-2

0

2

4

6

8

10

12

14

16

18

Temp. Difference (C)

Time (sec)

(5)-(6) (6.8mm)

(5)-(6) (4.4mm)

(5)-(6) (2.0mm)

34

Conclusion

• To reduce depth of scarfing is very important

– To maintain products quality, scarfing effect during slab heating process must be analyzed

– Type of scarfing shape is important

• STAR-CCM+ predicts transient temperature of slab well

– Temperature Error from experimental data < 0.5%

– As scarfing depth increased Temperature difference between lower and upper envelope is increasing

– Scarfed shape effect negligible. The most important factor is depth of scarfed shape