16 singh varun user-friendly model of heat transfer in...

ANNUAL REPORT 2010ANNUAL REPORT 2010UIUC, August 12, 2010

User-friendly model of heat transfer in submerged entry nozzles duringsubmerged entry nozzles during

preheating, cool down and casting

Varun Kumar Singh, B.G. Thomas

Department of Mechanical Science and Engineering

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Lance C. Hibbeler • 1

Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-Champaign

Objectives

• Develop a user friendly spreadsheet based tool tol l t th h t t f ffi i t d flcalculate the heat transfer coefficients and flame

temperature during preheating of the nozzle.

D l f i dl d h t b d t l t• Develop a user friendly spreadsheet based tool tomodel the heat transfer in submerged entry nozzlesduring the three stages: preheat cool down andduring the three stages: preheat, cool down andcasting.

University of Illinois at Urbana-Champaign • Metals Processing Simulation Lab • Varun Kumar Singh • 2

Model & computational domain

Model of Nozzle exposed to ambient

Gas

Molten SteelTundish

1. Preheat

2. Cool down

Nozzle Layers

Insulation layer

Gas Burner

Nozzle Insulation

AmbientAmbient

Ambient

Flux Submerged Entry Nozzle

Slide Gate (Flow Control)

Tundish Nozzle

Clog

3. Casting

Layers layer

Ambient

Nozzle Layers

Insulation layer

Solid Steel Clog

Liquid

Steel

Molten Steel

M d l f N l b d i l

Molten Steel Jet

Submerged Depth

Flux Submerged Entry NozzlePlane of Symmetry

Insulation Layer1. Preheat Ambient

Nozzle Layers

Insulation layer

Gas Burner

Model of Nozzle submerged in steel

Copper Mold

Solidifying Steel

Liquid Steel

Pool3. Casting

2. Cool down Ambient

Nozzle Layers

Insulation layer

Ambient

Molten Steel

NozzleLiquid

Molten Steel


Continuous Withdrawl

Solidifying Steel Shell

Nozzle Layers

Insulation layer

Liquid

Steel

Models Developed

• Flame Temperature Calculation Model

• Heat Transfer Coefficients Calculation Model

• Model for heat transfer in the refractoryModel for heat transfer in the refractory during the three stages: – preheatpreheat,

– cool down

casting– casting• Ambient slice

• Submerged sliceSubmerged slice.


Flame Temperature Calculation Model – Input PageCalculation Model Input Page


Calculation of Flame temperature and heat transfer coefficients

• User can select from the following gases as fuel: Methane, hydrogen,propane, natural gas, blast furnace gas and acetylene.propane, natural gas, blast furnace gas and acetylene.•The species considered are: CO2, O2, O, CO, H2O, N2, NO, OH, H, H2

• For natural gas and blast furnace gas, user can specify the percentageof various constituents (natural gas: mathane – 94%, ethane – 3%,propane – 1%, butane – 0%, CO2 – 1%, O2 – 0%, N2 – 1%)•Reactants temperature and pressure need to be entered.•The reaction is a constant pressure process.•The user can choose between excess air and oxygen enrichment.•The amount of excess air or air enrichment needs to be specified.•The flame temperature calculated for the above composition of naturalgas with 50% excess air was found to be 1510 °Cgas with 50% excess air was found to be 1510 °C.


Heat Transfer Coefficients


Heat Transfer Coefficients

• Free Convection to ambient:– The Churchill and Chu [1] equation for flow over a vertical flat plate is usedThe Churchill and Chu [1] equation for flow over a vertical flat plate is used

2

1 / 6

8 / 2 79 / 1 6

0 . 3 8 70 . 8 2 5

0 . 4 2 91P r

a v g

R aN u

= + + P r

• Forced Convection from flame:The Petukhov, Kirillov, and Popov [1] is used

[ ]1/ 2 2/3

( / 8) Re Pr1.07 12.7( /8) (Pr 1)

DfNu

f= + −

Th f d h t t f ffi i t l l t d t b 72 5 W/ 2K• The forced heat transfer coefficient was calculated to be 72.5 W/m2K. • The free heat transfer coefficient was calculated to be 7.6 W/m2K

• Sleicher and Rouse equation was used to calculate the forced


qconvection heat transfer coefficient from molten steel flowing on the inside of the nozzle.

Properties of mixture of gases in combustion productsp

ni iy λλ

• Thermal conductivity of the mixture of gases is calculated using Saxena and Mason [3]:

λ

1

1

i im n

ij ij

j

y

y A=

=

λ =

Where = the thermal conductivity of the gas mixture

[ ]

mλWhere = the thermal conductivity of the gas mixture= the thermal conductivity of pure i

= mole fractions of component i and jiλ

,i jy y

21 / 2 1 / 41 ( / ) ( / )M M + η η 1 / 2 1 / 4

1 / 2

1 ( / ) ( / )[ 8 ( 1 / ) ]

i j j i

i ji j

M MA

M M

+ η η =+

j ij i i j

MA A

M

η=j i i j

i jMη

Where are the viscosities of pure i and j respectively

And are the molecular weights of pure i and j

jη,iη

,iΜ jΜ


i j

• Thermal diffusivity, kinematic viscosity, density and specific heat are calculated using the particle mixture rule.

Heat Transfer Model for the refractory – Main Pagerefractory Main Page


Heat Transfer Model for the refractory – Featuresrefractory Features

• User can enter the number of layers he wants in the model.

• Each layer can have different thickness and ydifferent number of nodes.

• The user can choose at what times theThe user can choose at what times the results have to be plotted.

• User can select the nodes where the results• User can select the nodes where the results are to plotted.


Heat transfer model – assign refractory propertiesrefractory properties

• The table gets populated based on the number of layers entered by the modelentered by the model.

• User can select which material should be assigned to each layer by choosing from the drop down menu (which get


automatically populated to show all the materials in the excel file)

Governing Equation and finite difference equation for interior nodesq

I f

AmbientGas Burner

• Heat conduction equation in cylindrical co–ordinates [1]

Inner surface refractory layer

Insulation layer

Bulk refractory layer

Outer surface refractory layer

i+1ii-1

q y [ ]

1p

T TC kr

t r r r

∂ ∂ ∂ρ =∂ ∂ ∂

• Using Taylor series [1] expansion the equation is discretized

2

2pT T

rr r

T kC

t r ∂ ∂+ ∂ ∂

∂ρ =∂

2

2

1 T T

r r r

Tt

∂ ∂+ ∂ ∂

∂ = α∂

• Using Taylor series [1] expansion, the equation is discretized as:

11 1 1 1

2

212

n n n n n n ni i i i i i iT T T T T T

r r r

Tt

++ − + − − − − ++ Δ Δ

= αΔ

21 1 1 1 nT


11 12 2 2

21 1 1 12 2

nn n n n i

i i i i

TT T t T T

r r r r r r r+

+ −

+ Δ + + − − Δ Δ Δ Δ Δ = α

Finite Difference Equations (Side nodes with convection))

1 2Inner surface

AmbientGas Burner

B lk f

• Heat balance on side half cell gives:

Side Half CellInner surface refractory layer

Insulation layer



T T∂ ∂2 2 1 1pV kA hA T

T TC

t r− ⏐ + Δ ⏐∂ ∂ρ =

∂ ∂

( )1

1

2 2

n n n nni i i i

ambient ipT T Tr r r

k r hr T Tr

TC

t

++ − −Δ Δ + + − Δ

ρ =Δ

( )1 12 22

n nn n ni i

i i ambient ip

T Tt r thrT T r T T

r r r r rC+ + −αΔ Δ Δ + + + − Δ Δ Δ

=ρ


Finite Difference Equations (Interface Nodes))

Inner surface

AmbientGas Burner

B lk f tinterface

1p

T TC kr

t

∂ ∂ ∂ρ =∂ ∂ ∂

Inner surface refractory layer

Insulation layer



interfacei i+1i-1

p t r r r

ρ∂ ∂ ∂

1

1/2 2 1/2 1/2 1 1/21n n

i ii i i i

ip

T T Tr k r k

r r

TC

t rr

+

+ + − −− ∂ ∂ ⏐ − ⏐ ∂ ∂

ρ =Δ Δ

11 1

2 12 21n n n n n n

i i i i i i

ip

T T T T Tr rr k r k

r r

TC

t rr

++ − − − −Δ Δ + − − Δ Δ

ρ =Δ Δ i

12 1 1 1( ) ( )n n n n n n

i i i i i i

r rT T r T T r T T

t+ Δ Δ + α + − − α − − Δ= 2 1 1 12 ( ) ( )

2 2i i i i i ii

T T r T T r T Tr r + −+ α + α Δ


Steel Shell Solidification Model

• Enthalpy formulation of the transient 1-D heat conduction equation is solved:equation is solved:

1H Tkr

t r r r

∂ ∂ ∂ρ =∂ ∂ ∂

• Top row temperatures:

i pourT T= p

• Top row enthalpies [2]:

* *int pourTH C T L

= + inti p pour f

solidus

H C T LT

= +

where Lf is the latent heat of fusion.


Steel Shell Solidification Model

• Enthalpy of interior nodes:

11 12 2 2

Δ 1 1 1 1 2ρ Δ 2 Δ Δ 2 Δ Δ

n n n n ni i i i i

k tH H T T T

r r r r r r r+

+ − + + + − −

=

1 1Δ 2 Δ ΔΔ Δ 2 Δ

2 n nn n n i ii i steel i

T Tt k t rH H T T r

h+ + − + − + + =

• Enthalpy of side nodes with convection:

Δ Δ 2 Δρ ρi i steel ir r r r

• After the enthalpy has been calculated the temperatures are then calculated i [2]

min ,max ,i fii sol

p p

H LHT T

C C

− =

using [2] :


Validation of Steady State Aspect of the Model

• Compared the results of the simulation when it reaches steady state with analytical Solution.

Governing equation for Analytical solution [1]:• Governing equation for Analytical solution [1]:

01 Tkr

r r r =

∂ ∂∂ ∂ Tflame

r

• Heat flux through the nozzle is calculated using:

r r r ∂ ∂hflame, T1

z

ln( / )1 1flame ambient

o i

flame i ambient o

T Tq

r r

h r k h r

−=

+ +

hambient, T2

Tambient

Refractory, kir orT , r

• Finally, the temperatures in the nozzle are : f

1 flame

qT T

h r= −

i or r t= −

q r


fflame ih r

2 ambientambient o

qT T

h r= +

1 lni

q rT T

k r

= −

Simulation conditions for validation of steady state aspect of the model

Label Symbol Value Units

Outer Radius of Refractory ro 67.5 mm

Bulk Refractory Wall Thickness t29.5 mm

Initial Nozzle TemperatureTintital 27* °C

Ambient Temperature T 27 °CTambient 27 C

Flame Temperature Tflame 1460 °CInternal Convection heat transfer

Coefficient (Forced) hflame 50 W/(m2K)

External Convection heat transfer Coefficient (Free)

hambient 7.3 W/(m2K)

Thermal ConductivityK 18.21 W/m-K

Specific Heat Cp 804* J/kg-Kp p g

Density ρ 2347 kg/m3

Stefan Boltzman's Constantσ 5.67E-8

Emmissivity ε 0.96


* Parameters required by transient simulation method

Validation – Steady state aspect of the model

• The results of the simulation are in good agreement with that of the analytical solution

Single Layer, No radiation Single Layer, with radiationg y , g y ,

Four Layers, No radiation Four Layers, with radiation


Validation of transient aspect of the model

• Compare the results of the simulation with that of the lumped thermal heat capacity model.

• System undergoing a transient thermal response to a heat transfer process has a nearly uniform temperature and small differences of temperature within the system can be ignored.

Th d l i lid l if th Bi t b (hL/k) 0 1• The model is valid only if the Biot number (hL/k) < 0.1

• The governing equation is [1]

( )p e

dTVC hA T T

dtρ = − −p edt

• To solve this equation, one initial condition is required:

t=0: T=To.

Solving the equation, the temperature at any time,t can be calculated from:Solving the equation, the temperature at any time,t can be calculated from:

( / )phA VC te

o e

T Te

T T− ρ− =

−


where To is the initial surface temperature, Te is the ambient temperature.

Simulation Parameters – Validation of transient aspect of the modelp

Label Symbol Value Units

Outer Radius of Refractory ro 67.5 mmOuter Radius of Refractory ro 67.5 mm

Bulk Refractory Wall Thickness t29.5 mm

Initial Nozzle TemperatureTintital 1100 °C

Ambient Temperature Tambient 27 °C

External Convection heat transfer Coefficient (Free) hambient 7.3 W/(m2K)Coefficient (Free) ambient

Thermal ConductivityK 1000 W/m-K

Specific Heat Cp 804 J/kg-K

Density ρ 2347 kg/m3

Stefan Boltzman's Constantσ 5.67E-8

Emmissivity ε 0.96Emmissivity ε 0.96


Comparison of Results of lumped model and transient simulation

• The results of the simulation are in good agreement with that of the lumped thermal heat capacity model


Output page of the tool


Comparison with measurements (inside heat transfer coefficient = 72 W/m2-K))


Comparison with measurements (inside heat transfer coefficient = 18 W/m2-K, emissivity = 0.5)


Parametric Study

Parameters Highest Temperature Difference in temp. between inner and outer

surface

Forced Convection = 72 W/m2-K, emissivity = 0.5

920 °C 90 °C

Forced Convection = 18 W/m2-K, emissivity = 0.5

585 °C 30 °C

Thermal Conductivity is 954 °C 150 °Chalved

Emissivity increased to 0.9

850 °C 100 °C

Specific Heat is doubled 954 °C 100 °C


Conclusions

• The temperature in the inner surface of the nozzle reached 900 °C after a preheat time of 2 hours If the inside heat900 C after a preheat time of 2 hours. If the inside heat transfer coefficient is reduced to 18 W/m2-K the temperature in the inner surface of the nozzle is 585 °C. Results from

i l i l ti t h th f i t f thinumerical simulation match those of experiments for this case.

• The tool can be used to predict the temperatures in theThe tool can be used to predict the temperatures in the nozzle during different stages of preheat, cool down and casting.

Th l b d l l h fl d• The tool can be used to calculate the flame temperature and heat transfer coefficients for different fuels and varying composition.


p

• Air entrainment should be decreased, because excess air reduces the flame temperature.

References

1. Incropera, F.P., and Dewitt, P.D., 2002, Fundamentals of Heat and Mass Transfer, John Wiley and Sons, New York.Mass Transfer, John Wiley and Sons, New York.

2. Thomas, B.G. and B. Ho, "Spread Sheet Model of Continuous Casting," Journal of Engineering for Industry, ASME, New York, NY, Vol. 118, No. 1, 1996, pp. 37-44.No. 1, 1996, pp. 37 44.

3. Poling, B.E., O’Connell J.M., and Prausnitz, J.M., 2001, The Properties of Gases and Liquids, McGraw-Hill, New York.

4 Moran J M and Shapiro H N 2004 Fundamentals of Engineering4. Moran, J.M., and Shapiro, H.N., 2004, Fundamentals of Engineering Thermodynamics, John Wiley and Sons, New York.

5. Report on “Modeling of Tundish Nozzle Preheating” by J. Mareno and B G ThomasB.G. Thomas.


Acknowledgementsg

• Continuous Casting Consortium Members(ABB A l Mitt l B t l C LWB(ABB, Arcelor-Mittal, Baosteel, Corus, LWB Refractories, Nucor Steel, Nippon Steel, Postech, Posco ANSYS-Fluent)Posco, ANSYS Fluent)

• Rob Nunnington LWB Refractories• Rob Nunnington, LWB Refractories

University of Illinois at Urbana-Champaign • Mechanical Science & Engineering • Metals Processing Simulation Lab • Lance C. Hibbeler • 30

16 singh varun user-friendly model of heat transfer in...

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