Simulation of Liquid Steel Flow Inside the Mould- Effect of Submerged Entry Nozzle

8/13/2019 Simulation of Liquid Steel Flow Inside the Mould- Effect of Submerged Entry Nozzle

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Proceedings of the 22th

National and 11th

InternationalISHMT-ASME Heat and Mass Transfer Conference

December 28-31, 2013, IIT Kharagpur, India

HMTC13xxxxx

SIMULATION OF LIQUID STEEL FLOW INSIDE THE MOULD: EFFECT OF SUBMERGED ENTRYNOZZLE

Kiran Kumar KNIT Warangal

Warangal-506 004INDIA

[email protected]

Hari NaikNIT Warangal

Warangal-506 004INDIAEmail

Praveena Devi NS R Engg. CollegeWarangal-506004

[email protected]

B Ramesh BabuNIT Warangal

Warangal-506 004INDIA

[email protected]

ABSTRACTA mathematical and computational model is

developed to numerically simulate the liquid steel flow inside

the mould in a continuous casting (CC) unit. A three

dimensional model (3-D) is presented in this paper.

Standard k turbulent model is used along with SIMPLE

algorithm to solve system of equations. Discharge jet angle

plays a vital role in the casting process with reference to the

casting defects. Discharge angle should be set such that jetdelivered into the mouldshould not cause excessive erosion of

the solidified shell at the impingement zone at the narrow faceof the slab section and there should not be much turbulence at

meniscus. Jet discharge angle depends on the angle of

Submerged entry nozzle (SEN) outlet port. A shallow jet

discharge angle delivers liquid metal directly to the meniscus,resulting in an excess surface turbulence and promoting

entrapment of slag into liquid steel. Whereas, deeper jet

angles drives the liquid steel too deep into the pool, causing

less inclusion floatation in the mould.

NOMENCLATUREP Static pressure, N/m

2

Q Flow rate, m3

/min Molecular viscosity, N-s/m

2

Vc Casting Speed (m/min)

W mould width (mm)

SEN Submerged Entry Nozzle

F Maximum force of steel at incidence angle, (N)

Density of steel ( kg/m3)

D Diameter

g Acceleration due to gravity (m/s2)U Absolute velocity (m/s)

Under-relaxation factor

I Unit tensor

Stress tensor

ij Dissipation tensor

Ret Turbulent Reynolds number

General variable

vr

Velocity vector

ur

Angular velocity vector

Aur

Surface area vector

Diffusion coefficient for

Gradient of

S Source of per unit volume

facesN Number of faces enclosing cell

Value of convicted through face f( )

n Magnitude of normal to face f

Under-relaxation factor

kG Generation of turbulence KE due to mean velocity

gradients

bG Generation of turbulence kinetic energy due to

buoyancy

k and Inverse effective Prandtl numbers of k and

respectively

kS and S User-defined source terms for k and

,respectively

k and

Turbulent Prandtl numbers for k and

,respectively

S Surface

V Volume

1C

,

2C

,

3C

,

4C

Constants

Suffix:i x coordinate

j y coordinate

k z coordinate

t turbulentin inlet

out outletf face


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INTRODUCTIONContinuous casting of steel is a very complex process

involving turbulent flow physics. Figure 1 shows theschematic of the continuous casting process. In this process,

the molten steel flows from the tundish through a submerged

entry nozzle (SEN) into the copper mold.

Figure: 1 Schematic of continuous casting process [1].

Both the steady-state flow pattern and transient variations in

the mold cavity are important to steel quality in continuouscasting. Excessive meniscus velocities and surface turbulence

lead to inclusion defects due to slag entrainment and level

fluctuations in the mold. Insufficient surface flows lead tomeniscus freezing and other surface defects. The mold flow

pattern should be optimized to achieve a flat surface profile

with stable meniscus velocities of the desired magnitude andminimum turbulence.

Most of the steel plants all over the world are producing

the flat products by continuous casting technique. Therefore it

is very important to understand the role of liquid steel flow in

the mold for better quality of steel product. Extensive

mathematical and experimental work was carried out by

various researchers in the past. Brian G. Thomas [2]

investigated on the formation of several different types of

defects related to flow phenomena. The amount of gas

injection into the tundish nozzle to avoid air aspiration is

quantified by modeling. Chaudhary.R et al.[3] have comparedcomputational models and experiments with a one-third scale

water model to characterize flow in the nozzle and mold to

evaluate well-bottom and mountain-bottom nozzle

performance. Velocities predicted with the three-dimensional

k- turbulence model were well agreed with both particle-

image velocimetry and impeller measurements in the watermodel. Gupta and Lahiri [3] carried out 2-D studies on the

effect of submergence depth, port diameter, port angle, and

nozzle exit velocity on the flow pattern in the mould of

continuous casting. They concluded that the meniscus profile

keeps on fluctuating at any casting speed. Glitz K et al. [4]

worked on different experimental and numerical in order toevaluate the steel-slag interface dynamics. Simulations of

water flow in continuous casting molds are carried out

employing the software ANSYS CFX 11.0. The results are

compared to experimental and numerical results published in

the literature. ANSYS CFX results presented good

agreement with the experimental data. Rajat Kumar Das,

Sukanta Kumar Das [6] proposed that the free surface is wavyin nature. Three different submerged entry nozzle (SEN)

models were taken for numerical analysis. Contribution of

water velocity, different port to Bore ratio (P/B), size of upper

recirculation roll on free surface were investigated for

designing a submerged entry nozzle. It was observed that

Pent-Roof type nozzle is a better one as it shows lesser

fluctuation. Hence, in this paper effect of various port angle ofSEN is studied by developing numerical modeling in CFD

commercial software FLUENT.

MATHEMATICAL MODEL AND NUMERICALANALYSIS

CFD is a numerical technique to obtain an approximate

solution numerically. We have to use a discretization method,

which approximate the differential equation by a system of

algebraic equations, which can be then solved on computer.

The approximations are applied to small domains in space

and/or time so that the numerical solutions provide results at

discrete locations in space and/or time. Accuracy of numerical

solutions is development on the quality of discretizationmethod.

The Mass Conservation Equation :

The equation for conservation of mass, continuityequation, can be written as follows:

( ). mv St

+ =

r (1)

The eqn. 1 is the general form of the mass conservationequation and is valid for incompressible as well as

compressible flows. The source Sm is the mass added to the

continuous phase from the dispersed second phase (e.g. due to

vaporization of liquid droplets) and any user-defined sources.

For steady state incompressible fluid flow, the continuityequation is given by

( ).v F =r

(2)

Where,

$ $

i i i

i j kx x x

= +

$

(3)

$ $i j k

v u i u j u k = + +r

$ (4)

Momentum Conservation Equation

Conservation of momentum is an inertial (non-

accelerating) reference frame is formulated by

( ) ( ) ( ). .v v v p g F t + = + + +r r r ur ur (5)

Where, g =ur

gravitational body force,

F=external body forces (e.g. that arise from interaction with

the dispersed phase), F also contains other model-dependent

source terms such that porous media and user defined sources.

The stress tensor is given by

)2

.3

V V VI

= +

ur ur (6)

Where, the second term on the right hand side is taken for

consider the effect of volume dilation.For steady state incompressible fluid flow, the momentum

conservation equation is given by

( ) ( ). .v v p g F = + + +r r ur ur

(7)


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Turbulent Model :Standard k- model

The simplest complete models of turbulence are two-equation model in which the solution of two separate transport

equations allows the turbulent velocity and length sales to be

independently determined. The standard k- model in

FLUENT falls within this class of turbulence model and has

become the workhorse of the practical engineering flow

calculations in the time since it was proposed. Robustness,

economy, and reasonable accuracy for wide range of turbulentflows explain its popularity in industrial flow and heat transfer

simulations. It is a semi-empirical model, and the derivation of

the model equations relies on phenomenological

considerations and empiricism. The standard k- model is a

semi- empirical model based on model transport equation for k

is derived from the exact equation while the model transport

equation for as obtained using physical reasoning and bears

little resemblance to its mathematically exact counterpart. In

the derivation of the k- model, it was assumed that the flow is

fully turbulent, and defects of molecular viscosity are

negligible.

Transport equations for the standard k- model

The turbulence kinetic energy k, and its rate of dissipation , isobtained from the following transport equations:

( ) ( ) ii k b m k i i k j

kk ku G G Y S

t x x x

+ = + + + +

(8)

And2

1 3 2( ) ( ) ( )i

i k b

i i j

u C G C G C S t x x x k k

+ = + + + + (9)

The turbulent (or eddy) viscosity, t, is computed bycombining k and follows:

2

t

kC

= (10)

The values of constants used are

C1=1.44, C2=1.92, C=0.09, k =1.0, =1.3

Discretization

A control-volume based technique is used to convert the

governing equations to algebraic equations that can be solvednumerically. This control volume technique consists of

integrating the governing equations about each control

volume, yielding discrete equations that conserve on each

control volume basis. Discretization of the governing

equations can be illustrated most easily by considering the

steadystate conservation equation for transport of a scalar

quality over control volume V as follows:

. .v

v d A d A S dV = + r ur ur

(11)

$ $

i j k

i j kX X X

= + +

$ (12)

Equation (11) is applied to each control volume, or cell, in the

computational domain.

. ( ) .faces facesN N

f fff f n

f f

v A A S V

= + r ur ur

Where,$ $

f i j kA A i A j A k= = + +

ur$

. fffV A =ur ur

Mass flux through the face f

The equations solved by FLUENT take the same general

form as the given above and apply readily to multi-

dimensional, unstructured meshes composed of arbitrary

polyhedral. FLUENT stores discrete values of the scalar at

the cell centers, however, face values f are required for the

convective terms in equation and must be interpolated fromthe cell center values. This is accomplished using an upwind

scheme. Upwinding means the face center values are derived

from quantities in the cell upstream, or upwind, relative to

the direction of the normal velocity vn in equation 13.

FLUENT allow us to choose from several upwind schemes:

first-order, second-order upwind, power law and quick. The

diffusion terms in equation are central-differential and arealways second-order accurate.

Under relaxation

Because of the nonlinearity of the equation set being

solved by FLUENT, it is necessary to control the change of .

This is typically achieved by under-relaxation, which reduces

the change of produced during each iteration. In a simple

form, the new value of the variable within a cell depends

upon the old value, old, the computed change in , , and

the under-relaxation factor, , as follows:

old = + (14)

Descretization of the continuity equation

0facesN

f f

f

j A = (15)

Where, Jf = the mass of flux through face f,

The face value of the velocity is momentum-weightedaveraging, using weighing factors

0 1

( )ff f c cJ J d P P= + (16)

Where, pc0 and pc1 = the pressures within the two cells on

either side of the face, and Jf contains the influence of the

velocities in these cells. The term df is a function of ap, the

averaging of the momentum equation ap coefficients for the

cells on either side of the f.

Discretization of the momentum equationThe discretized x-momentum equation is:

.p nb nb f

nb

a u a u P A i S = + + $ (17)

The pressure field and face mass fluxes are not known a prior

and must be obtained as a part of the solution.FLUENT uses a co-located scheme, whereby pressure and

velocity are both stored at cell centers. However, equation (17)

requires the value of the pressure at the face between cells.

Pressure at the face is interpolated using momentum equation

coefficient.

2.1 Convergence criteriaScaled residual has been selected as the convergence criteria.

The conservation equation for general variable at cell p is

p p nb nb

nb

a a b = + (18)Here ap is the center coefficient, anb are the influence

coefficients for the neighboring cells and b is the contribution

of the constant part of the source term sc in S=Sc+Spand of

the boundary conditions.

p nb p

nb

a a S= (19)

Unscaled residual R is defined as:

nb nb p p

cellsP nb

R a b a

= + (20)

Scaled residual is defined as:


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nb nb p p

cellsP nb

p p

cellP

a b a

Ra

+

=

(21)

The unscaled residual for continuity is defined as:c

cellsP

R RateofmasscreationincellP= (22)

Scaled redual; for continuity equation is defined as:

5

c

iterationN

c

iteration

RR

R

= (23)

The denominator is the largest absolute value of the

continuity residual in the first five iterations. As a

convergence criterion, these scaled residuals have been

continuously monitored and the iteration continues till the

values is 1 10-6

. It has been observed that with these default

convergence criteria, simulated solution is reasonably

accurate. However in case where the geometry is complicated,

these default criteria have been further reduced to get a bettersolution.

COMPUTATIONAL MODEL

Figure 2: Actual Continuous casting (CC) unit

Actual schematic of CC unit is shown in figure 2. A

3-D computational model with meshing is shown in Figure 3.With the aid of computational fluid dynamics, the complex

internal flows inside the mould can be predicted. Thus it isuseful to get the desired casting with less defects. This article

describes the three-dimensional simulation of internal flow

inside the mould. A commercial three-dimensional Navier-

Strokes code called FLUENT with a turbulent model is used

for simulation of present problem. In calculation finite-volume

method is used for discretization of governing equations forthis problem.

Assumptions

The simulation of flow inside the copper mould is

done on following assumptions.

1. Steady state condition.2. Incompressible flow.3. Constant fluid properties.4. There is no leakage of fluid.

Mould walls are smooth.

Solution technique

Following technique is used for simulation of this

problem.

1. Copper mould is modeled using boundary layermesh.2. Standard k - turbulent model is used for turbulent

fluid flow.

3. The most appropriate numerical scheme for the flowequations is segregated implicit solver used for thismodel. The residuals decrease very fast and other

monitored solution parameter reach convergence.

4. The 0.0001 residual is used for convergence ofvelocity and turbulence parameters.

5. The first order upwind scheme is used for momentumequation.

6. The second order scheme is used for the pressure

correction.7. The under relaxation factor applied for 0.3 forpressure, 0.7 for momentum equation, 0.8 for

turbulent kinetic energy and 0.8 for dissipation rateare used for fast convergence of solution.

8. Liquid-solid is used as fluid.

a. Simulation conditions:

Parameters

Steel caster

(full scale)

Nozzle port angle

Nozzle port area

Nozzle bore diameter

Nozzle outer diameter

SEN depthAverage port

velocity

Fluid flow rate

Casting speed

Mold width

Mold thickness

Domain width

Domain thickness

Domain length

fluid fluid

slag

Liquids temperatureSolidus temperature

Inlet temperature

+25oto -25

o

69.9 mm (W) X80.1 mm (H)

75 mm

129 mm

180 mm0.886 m/s

595.4 LPM

1.76 m/min

1500 mm

225 mm

750 mm

112.5 mm (at the top)

3600 mm

7020 kg/m3(steel)

0.006 kg/ms (steel)

3000 kg/m3

1750K1760K

1800K

Table 1 Simulation Conditions.


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Figure 4: Computed velocity field in the slab caster mould for

parallel port SEN(0o)

Simulations were carried out by varying outlet port angles(+30o, +15

o, 0

o, -15

o, -30

o) of SEN. It is observed from the

results that the flow of the liquid steel inside the mould splits

into two recirculating zones as shown in figure 4. Irrespectiveof the port angle similar trends were observed for all the cases

considered. Upper recirculation helps in flotation of non-

metallic inclusions present in liquid steel to the free surface

where there are absorbed by the molten flux layer. Lower

recirculation is important for the dissipation of superheat of

liquid steel. Figure 5 presents the stream function contours of

the parallel port case (central axisymmetric of total mould is

presented). From the Fig 5 it can be observed that the steam

lines are strong in the lower part.

Increase in turbulent kinetic energy (k) appears to besteppes the jet angle. These turbulent parameters also have an

important influence on the temperature field. It is observed

that the turbulent kinetic energy is maximum at nozzle port

due to the strong shear layer around each incoming jet.

Maximum also appears where jet impinges at the narrow face

wall. At this point, the local generation of turbulence is greater

than the transport of turbulent from vicinity. Low the turbulent

kinetic energy leads to corresponding diminish in the flowfield. Values of maximum and minimum turbulent kinetic

energy is presented in Table 2.

Figure 5: Stream function contours of parallel port

Almost similar results were observed with different port

angles. Maximum varesults were observed for most upward

and downward port angles have much influence oncorresponding flow field. Higher the turbulent kinetic energy

results in higher heat flux leads to lower the temperature.

From the Table 2 it can evident that at higher angles, whether

it may upward or downward, turbulent kinetic energy is high

which causes higher heat flux thus lower is the temperature.

Nozzle port

angle

Minimum Maximum

00

2.252 x10-3

0.7089

+15 2.3531 x10-

0.7103

-15 1.212 x10-

0.7423

+30 2.54 x10-3

0.7448

-30 7.8 x10-3

0.80507

Table 2: TURBULENT KINETIC ENERGY

Variation of wall shear stress along the narrow face wall

mould for different port angles is presented in the Fig 6. Shear

stress is zero at the meniscus and at the center of jet

impingement area at the wall. Away from this point shear

stress again increases till it attains maximum value. Wall shearstress is of special significance from the view point of erosion

of solidifying shell which in the mould. Erosion causes

thinning of solid shell, which may lead to breakout of the

casting.

Heat flux found to be maximum at point of impingement

point, which is expected. Heat flux along the narrow face wall

is taken, because it is the area from which maximum heattransfer is taking place. Heat flux along the narrow face wall,

which is our area of interest for getting good casting is found

out for all port angles and was shown in Figure 7. Dirrerent

port angle cases results different values of heat fluxes. It is

because of the variation of the velocity discharge angles,

which invariably changes the momentum. It also varies with

the turbulent kinetic energy. Great reduction in the values of

heat flux is observed for low values of turbulent kinetic energy

and high values for higher turbulent kinetic energy. Maximum

heat flux is observed in case of lower port angles. Maximumheat flux results in maximum heat transfer rates. It greatly

affects the quality of casting. This may causes the hot spots,

which is not desirable and is a casting defect.


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Figure 6: wall shear stress along the center of narrow face wall

Figure 7: Total surface heat flux along the center of narrow

face wall

CONCLUSIONSA three dimensional computational model which can be used

to study the flow behavior of liquid steel inside the continuous

casting unit is presented in the present paper. Following

conclusions can be drawn:

The bulk steel flow from the port of the SEN whereentering into the mould , splits into two, giving to

upper and lower recirculation zones in the mould.

Surface heat flux is found maximum at impingementpoint and this results in casting defects.

300

downward port angle gives minimum wall shearstress than the existing parallel port , which greatly

effects the casting quality

REFERENCES[1] Kadir Ali Gursoy and Mehmet Metin Yavuz.;

Mathematical modeling of liquid steel flow in

continuous casting machines, International Iron &

Steel Symposium, 02-04 (April 2012), Karabuk,Turkiye.

[2] Brian G. Thomas; Modeling of continuous-castingdefects related to mold fluid flow; 3rd Internat.

Congress on Science & Technology of Steelmaking,

Charlotte, NC, May 9-12, AIST, Warrendale, PA,(2005), pp. 847-861.

[3] Chaudhary.R, Go-gi lee, B.G. Thomas, and Seon-Hyo Kim; Transient Mold Fluid Flow with Well- and

Mountain-Bottom Nozzles in Continuous Casting of

Steel; The Minerals, Metals & Materials Society and

ASM International (2008); DOI: 10.1007/s11663-

008-9192-0.

[4] Gupta D. and Lahari A. K. Met. & Mats Trans. B,Vol. 27B, Aug 1996, pp. 695-697.

[5] Gupta, D and Lahiri, A.K.(1992): Water modelingstudy of the jet characteristics in a continuous casting

mould, Steel Research, Vol.63 No.5, pp.201-204.

[6] Gupta, D and Lahiri, A.K. (1994): Water modellingstudy of the surface disturbances in continuous slab

caster, Metallurgical and Materials Transactions B.Volume 25 B, pp.227-233

[7] Glitz K. L. Z, Silva A. F. C, Maliska C. R, Borges R.N, Soprano A. B, Vale1 B. T; Modeling the interface

dynamics in continuous casting molds employing

ANSYS CFX.

[8] Rajat Kumar das, Sukanta kumar Das; NumericalAnalysis of Free Surface in Water Model for Design

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Documents

Simulation of Liquid Steel Flow Inside the Mould- Effect of Submerged Entry Nozzle