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CHAM's Final Report on its contribution to the OSIRIS Project; December, 1998

SAFIR

A computer model of flow, heat and mass transfer, phase change and chemical reaction in the blast furnace, with injected coal or oil

by

D.B.Spalding and S. V. Zhubrin

[Concentration, Heat and Momentum Ltd, i.e. CHAM]


Summary

A steady-state three-dimensional four-phase model of blast-furnace behaviour has been developed by CHAM within the framework of the EC-funded OSIRIS project.

The four thermodynamic phases in question are:-

  1. gas, i.e. air and combustion products;
  2. the fast-moving particles of coal, coke, liquid-droplets and other "fines" which are suspended in the gas;
  3. the slower-moving solids consisting of iron-ore and coke,
  4. the faster-moving liquid metal.

The processes accounted for are:-

The model is embodied in a special version of the CFD code PHOENICS, called SAFIR, which makes extensive use of two techniques which are unique to that code, namely:-

  1. MUSES, which is an acronym for MUltiply-SharEd Space; and
  2. PLANT, which allows all the relevant special-modelling features to be supplied compactly by way of formulae inserted into the input file (Q1);the corresponding Fortran-coding counterparts of these formulae are then created automatically.

The report provides the problem specification and a description of the computer model.The developed prediction procedure, consisting of the mathematical model and solution algorithm, is applied to study the operational behaviour of a typical blast furnace.

Solutions are presented that predict the three-dimensional velocity, temperature, transfer mass flow rates between phases and concentration distributions of gaseous, solid and liquid phases, under different operating conditions of the furnace; and their realism is discussed.


Contents of the report

  1. The modelling features
  2. The equations solved
  3. Chemical reactions
  4. Phase transformations
  5. Interphase transport
  6. Physical properties
  7. The blast furnace considered
  8. Presentation of results
  9. Discussions of the results
  10. Remaining tasks
  11. Concluding remarks
  12. References

1. The modelling features

Contents

1.1 The general idea
1.2 Physical aspects
1.3 Computational aspects

The general idea

The blast furnace is, and has been for many hundreds of years, one of the most important items of industrial equipment; yet its inner workings are remarkably little understood; and its development therefore has had to proceed by trial and error.

It is therefore highly desirable that a computer model should be created which would have sufficient qualitative realism to aid understanding and sufficient quantitative accuracy to enable design and operating decisions to be safely made.

Such a model would enable the effects of varying geometrical configurations, and of blast and burden conditions, to be assessed easily, quickly, economically and reliably; it would reduce considerably the amount of physical-model and full-scale testing required to achieve satisfactory design.

The present report concerns the development and testing of such a model, based upon established principles of computational fluid dynamics. It is applicable to one-, two- and three-dimensional representations of the furnace geometry and is valid for both steady and transient conditions.

The model recognises that the space within the furnace is shared by four distinct kinds of material, namely gas, fine particles, lump solid and liquid, and that each of these has its own temperature, chemical composition and velocity components.

It is therefore, in CFD parlance, a "four-phase" model.

The model is being configured as a special version of the well established PHOENICS VFD code, which solves the relevant concervation equations and is able to take full account of interphase mass, momentum and heat transfer. An additional coal fines-fraction equation is solved to account for the diminishing radii of the burnt coal particles.

In order to assess the potential of the model, one-, two- and three-dimensional simulations have been performed for a typical blast furnace under different operating conditions. The results are presented and discussed.

1.2 Physical

The blast furnace is represented, in the current model, as a counter-current heat-and-mass exchanger and chemical reactor, having as its main purpose the reduction of (i.e. removal of oxygen from) iron oxide to produce liquid iron.

The major materials within the furnace are considered to be:-

  1. gases,
  2. particles (fines) carried by gas,
  3. lump solids, and
  4. liquids.

The gases are supposed to be the products of combustion of pulverised coal fines and lump coke, the oxygen being obtained both from the air and from the iron-oxide in the ore. They are represented as comprising a mixture of oxygen, nitrogen, carbon dioxide, carbon monoxide, hydrogen and water vapour.

The fines are supposed to consist of oil droplets or coal particles and to contain carbon, C, hydrogen, H, and nitrogen, N, as well as ash constituents.

The lump solids are supposed to contain ore, assumed to be pure iron oxide, Fe2 O3, lump coke of pure carbon, C, and inert ashes.

The liquids are supposed to be a mixture of molten iron and slag.

1.3 Computational

To simulate the four-phase relative motion, by means of the built-into-PHOENICS IPSA two-phase algorithm, a "two-space" version of the Multiply-SharEd Space (MUSES) technique is used.

Specifically, the gases and the fines are treated as respectively the "first" and "second" phases (in IPSA terms) of the space-share 1, while the lump solids and the liquids are treated as the corresponding phases of space-share 2.

The proportions in which the space is shared may vary from place to place, and must be computed as part of the overall calculation; and all the physical and thermal reactions between the sharing fluids are taken rigorously into account, by means of PLANT-type formulae.

The manner in which MUSES was first implemented was as follows:

Although this was perfectly satisfactory from the computational point of view, it did not lend itself easily to visual display of the results; nor would it have been convenient for the intended "parallelization" of the computer program.

Therefore an alternative geometrical "doubling" has been employed, in which computation is confined to a 45-degree sector of the furnace; then two such sectors are considered, one being devoted to phases 1 and 2 and the other to phases 3 and 4.


2. The equations solved

The three-dimensional mathematical model solves the equations of conservation of

for each of the four phases in the steady state (although it may be remarked that extension to transient operation will not be hard to make, when the time comes).

The dependent variables are therefore, for each of the four phases:-

The equations governing the sharing of space, which will in due course lead to predictions of the locations and sizes of the so-called "raceway" (where space-share 1 is 100%) and "dead man" (where it is 0%), have not yet been incorporated. Therefore these proportions have been allocated on the basis of experimental observations.

The following chemical species are supposed to be present in the various phases:-

The gas temperature, Tgas, is calculated from the equation which relates the total gas enthalpy, Hgas, to composition and temperature as follows:-

Hgas = CPgas*Tgas + HCOCO2*YCO + HHH2O*YH2,

where:

CPgas is the gas heat capacity,
YCO and YH2 stand for mass fractions of CO and H2,
HCOCO2 stands for the heat of combustion per unit mass of CO and
HHH2O is the heat of reaction H2 + 0.5*O2 -> H2O.

The fines temperature, Tfin, is calculated from the equation which relates the total fines enthalpy, Hfin, to its temperature as follows:

Hfin = CPfin*Tfin + HCC

where:

CPfin is the solid heat capacity and
HCC stands for the heat of carbon combustion.

The solid temperature, Tsol, is calculated from the equation which relates the total solid enthalpy, Hsol, to coke mass fraction and temperature as follows:-

Hsol = CPsol*Tsol + Ycoke*HCC

where:

CPsol is the solid heat capacity and
Ycoke stands for mass fractions of coke.

The liqud temperature, Tliq, is calculated from the equation which relates the total liquid enthalpy, Hliq, to liquid composition and temperature as follows:-

Hliq = CPliq*Tliq + Hfm*Yliro + Ham*Yslag

where:

Yliro and Yslag stand for mass fractions of liquid iron and slag,
HFM stands for the heat of iron melting and
HAM is the heat of ash melting.


3. Chemical reactions

Contents

3.1 Coal and coke combustion
3.2 Ore-reduction reaction

3.1 Coal and coke combustion

The 7GASES model of PHOENICS is used to simulate the combustion of pulverised-coal fines with the gas phase absorbing the carbon from both fines and coke.

The effective (ie laminar-plus-turbulent) diffusion coefficients of the gaseous species are all taken as equal, and the reaction rates are supposed diffusion-limited; consequently all gas species concentrations depend on carbon mass fraction, in piecewise-linear fashion.

The oxidation of carbon is presumed to proceed in two stages, viz:

Reactions:

The gas-phase equilibrium-composition diagram, taking account of the elemental mass fractions of O, C and H, is supposed to have three regions:

Gaseous N2 can be found in any region, and is related to Fcl by:

YN2 = NINCL * Fcl + AirN2 * (1-Fcl)

Any location on the diagram is characterised by the element mass fractions of oxygen, carbon and hydrogen. These sum to 1.0 minus the element mass fraction of nitrogen.

The three regions are represented by the following:

In (1) - (3):

and

3.2 Ore-reduction reaction

For simplicity, the real blast-furnace chemistry is represented by a single-step global reaction:

Fe2O3 + 3 CO -> 2 Fe + 3 CO2.

The rates, per unit area, of consumption and creation of chemical species involved in the reaction can be expressed via the global reaction rate, Ro, as follows:


Rfe = Ro * (1+3 * Mco/Mfe2o3) * 2Mfe/(2 * Mfe+3 * Mco2)
Rco2 = Ro * (1+3 * Mco/Mfe2o3) * 3Mco2/(2 * Mfe+3 * Mco2)
Rco = 3 * Ro * Mco/Mfe203

where


Mco stands for molecular mass of CO , kg/kmol,
Mco2 stands for molecular mass of CO2 , kg/kmol,
Mfe stands for molecular mass of Fe , kg/kmol,
Mfe2o3 stands for molecular mass of Fe2O3, kg/kmol, and
Ro is the global reaction rate per unit area, kg/m^2/s.

The global reaction rate is deduced from the consideration of mass balances at the solid surface which is supposed to be pure iron oxide.

In the limit of physically-controlled reaction, its global rate can eventually be expressed as proportional to the mass fraction of carbon monoxide in the gas phase as follows.

Ro = hgs * YCO/CPgas, kg/m^2/s

where hgs stands for gas solid heat transfer coefficient, W/m^2/s.

Here, it is supposed that the mass transfer coefficient is equal to the heat transfer coefficient divided by the specific heat of the gas.

Multiplication of Ro by specific area of solid lumps gives the volumetric reaction rate

Rov = Ro * Ags, kg/m^3/s

where Ags stands for the coke lump area per unit volume, m^2/m^3.


4. Phase transformations

Two phase transformations considered in the present model are as follows:


Fe (solid) -> Fe (liquid) and
Ash (solid) -> Slag (liquid).

The liquid fraction of the solid is determined from the following equation:

Fliq = max (0., min (1., (Tsol-Tlqs)/(Tlqs-Tsls))

where


Tsls is the solidus temperature of either Fe or ash and
Tlqs is their liquidus temperatures.

The melting rate of solid Fe is assumed proportional to liquid fraction times the rate of reduced iron.

The melting rate of ash is assumed proportional to liquid fraction and mass inflow of ash.

More details will be given in section 5.3


5. Interphase transport

Contents

5.1 Sources related to fines - gas mass transfer
5.2 Sources related to solid - gas mass transfer
5.3 Sources related to solid - liquid mass transfer
5.4 Convective heat transfer
5.5 Frictional momentum transfer

Preliminary Note:-
Because ther are four phases , and transfer of heat mass and momentum can take place between any two of them, there are in principle thirty six interphase-transport terms to be described. Section 5 is therefore very long.

5.1 Sources related to fines - gas mass transfer

Gas phase absorbs carbon and hydrogen from particles of fines and lumps of coke, as they engage in combustion.

The corresponding sources are all handled by built-in coding and therefore require no special treatment.

For completeness, however, they are as follows.

(a) Mass transfer rates

The mass is transfered from "fines" phase leading to:

at volumetric rate

m21 = coef12 * VPOR * R2 * (Fs-Fmix), kg/m^3/s,

where Fs is the mass of coal per unit mass of air/fuel mixture to convert all carbon and oxygen to carbon monoxide.

Fs = AirO2/(AirO2 + CINCL * MO2/(2 * MC))

(b) Mixture fraction source

Transfer of carbon from fines leads to increase of gas mixture fraction at the same rate.

This is effected by the following built-in source for gas phase mixture fraction equation.

Sf21 = m21 * (1.-Fmix)

The unity in brackets signifies that mass transfer brings in material which is 100% particulate carbon.

(c) Enthalpy transfer

Transfer of enthalpy and heat is handled by the setting


PHINT(H1) = GRND7 and
PHINT(H2) = GRND7.

(d) Momentum transfer

It is effected by the default settings.

5.2 Sources related to solid - gas mass transfer

Solid phase is also engaged in combustion along with the ore reduction process. The resulting mass transfer is associated with

(a) Mass transfer rates

The volumetric rate of coke burning is taken as proportional to its mass fraction of the solid flow. This enters as a mass source of gas phase

m31c = coef13 * VPOR * Ycoke * R1 * (Fs-Fmix) and

sink of solid mass phase

m13c = -coef13 * VPOR * Ycoke * R1 * (Fs-Fmix), kg/m^3/s.

The gas phase supplies carbon monoxide for ore reduction and recieves the carbon dioxide with the net volumetric rate of gas mass phase

m31o = Ags * Yore * (Rco2-Rco), kg/m^3/s

This enters as a mass source of gas phase.

The sink of solid phase is of the same rate:

m33o = -m31o.

(b) Gas mixture fraction source

Transfer of carbon from coke leads to increase of gas mixture fraction at the same rate.

This is effected by the following source for gas phase mixture fraction equation.

Sf31 = m31 * (1.-Fmix)

The unity in brackets signifies that mass transfer brings in material which is 100% carbon.

(c) Gas carbon dioxide content

The carbon dioxide content of gas phase is supplied by both combustion of fines\coke and ore reduction.

The total CO2 gas phase content is, therefore, taken as

Yco2,tot = Yco2 + Rco2 * Ags * Yore * cell volume/in-cell gas mass

(d) Gas carbon monoxide content

The carbon monoxide content of gas phase is also supplied by both combustion of fines\coke and ore reduction.

The total CO gas phase content is, therefore, taken similarly

Yco,tot = Yco + Rco * Ags * Yore * cell volume/in-cell gas mass

(e) Ore mass fraction sink

The global reaction volumetric rate, Ro * Ags * Yore, leads to decrease of ore content of solid phase at the same rate.

This is effected by the following volumetric source of ore mass fraction conservation:

Sore = -Ro * Ags * Yore

(f) Solid Fe mass fraction source

The volumetric rate of Fe production, Rfe, leads to increase of the iron content of solid phase at the same rate.

This is effected by the following volumetric source of solid iron mass fraction conservation:

Ssiro = Rfe * (1.-Ysiro)

where

Ysiro stands for mass fractions of solid iron.

(g) Coke mass fraction sink

The transfer of coke carbon from solid phase leads to decrease of its coke content at the volumetric rate m31c.

This is effected by the following volumetric sink of coke mass fraction conservation:

Scoke = -m31 * Ycoke

(h) Enthalpy transfer

The transfer of carbon from coke leads to increase of gas enthalpy at the volumetric rate m31c.

This is effected by the following volumetric source of gas enthalpy conservation:

Shgcok = m31c * (Hsol - Hgas)

The consumption of CO by iron reduction leads to decrease of gas enthalpy at the volumetric rate Rco * Ags * Yore.

This is effected by the following volumetric sink of gas enthalpy conservation:

Shgco = -Rco * Ags * Yore * (CPgas * Tgas+HCOCO2)

The CO2 supply by iron reduction leads to increase of gas enthalpy at the volumetric rate Rco2 * Ags * Yore.

This is effected by the following volumetric source of gas enthalpy conservation:

Sghcoo = Rco2 * Ags * Yore * (CPgas * Tsol-Hgas)

The transfer of carbon from coke leads to decrease of solid enthalpy at the volumetric rate m31c.

This is effected by the following volumetric sink of solid enthalpy conservation:

Sshcok = -m31c * Hsol

(i) Momentum transfer

The momentum transfer associated with mass tarnsfer is ignored, because it appears to be much less than frictional momentum transfer.

5.3 Sources related to solid - liquid mass transfer

The ash in solid state, and the solid iron which is the product of iron oxide reduction, are supposed to be engaged in phase transformations.

The resulting mass transfer is associated with

The liquid phase receives the related mass sources from solid flow.

(a) Liquid mass transfer rates

The volumetric rate of solid Fe melting is taken as follows:

MRfs = const * Rfe * Yore * Fliq * Ags,

where MRfs stands for Fe melting rate per unit volume, kg/m^3/s.

The melting rate, per cell, of ash is calculated as follows:

MRash = const * inflow solid velocity * solid density * free face area * solid volume fraction * ash mass fraction * Fliq,

where MRash stands for ash melting rate, kg/s

(b) Liquid iron mass fraction source

The volumetric rate of solid Fe melting, MRfs, leads to increase of the iron content in liquid phase at the same rate.

This is effected by the following volumetric source of solid iron mass fraction conservation:

Sliro = MRfs * (1.-Yliro)

where

Yliro stands for mass fractions of liquid iron.

(c) Solid ash mass fraction sink

The volumetric rate of solid ash melting, MRash, leads to decrease of the ash content in solid phase at the same rate.

This is effected by the following sink of solid ash mass fraction conservation:

Sash = -MRash * Yash

where

Yash stands for mass fractions of ash in solid phase.

(d) Slag mass fraction source

The volumetric rate of solid ash melting, MRash, leads to increase of the slag content in liquid phase at the same rate.

This is effected by the following sink of solid ash mass fraction conservation:

Sash = MRash * (1.-Yslag)

where

Yslag stands for mass fractions of slag in liquid phase.

(e) Enthalpy transfer

The transfer of melted ash from its solid state leads to increase of liquid enthalpy at the volumetric rate MRash.

This is effected by the following source of liquid enthalpy conservation:

Shslag = MRash * (CPliq * Tlqs + Ham-Hliq).

The transfer of melted ash from its solid state leads to decrease of solid enthalpy at the volumetric rate MRash.

This is effected by the following sink of liquid enthalpy conservation:

Shsash = -MRash * CPsol * Tsol.

The transfer of melted iron from its solid state leads to increase of liquid enthalpy at the volumetric rate MRfs.

This is effected by the following volumetric source of liquid enthalpy conservation:

Shliro = MRfs * (CPliq * Tlqs + Hfm-Hliq).

The transfer of melted iron from its solid state leads to decrease of solid enthalpy at the volumetric rate MRfs.

This is effected by the following volumetric sink of liquid enthalpy conservation:

Shsash = -MRfs * CPsol * Tsol.

(f) Momentum transfer

The momentum transfer associated with mass transfer is ignored, because it appears to be much less than frictional momentum transfer.

5.4 Convective heat transfer

Enthalpy transfer between the various phases occurs due to convection. The rate of enthalpy transfer, per unit volume, between each phase generally takes the form :

Ecij = hij * Aht * (Ti-Tj), W/m^3

In which, Aht is the heat transfer area per unit volume, 1/m, hij is a heat transfer coefficient determined by an empirical correlation for the transfer from phase i to j.

The model considers gas-solid, gas-liquid, fines-solid, liquid-solid and gas-fines heat transfer modes.

The expressions used for these are set out below.

(a) Gas-solid heat transfer

The gas-solid heat transfer coefficient, hgs, is determined by the Ranz-Marshall equation:

hgs = gamma * (kg/Ds) * (2.0+0.6 * Regs^0.5 * Prg^1/3)

in which the Reynolds number

Regs=Ss * rhog * * Ds/emug

Here,


gamma stands for scaling factor,
kg stands for gas thermal conductivity, W/m/K,
Ds stands for solid lump diameter, m,
Ss stands for the shape factor of solid lump, <Vg-Vs> stands for the relative velocity magnitude between gas and solid, m/s,
Prg gas Prandtl number,
rhog stands for gas density, kg/m^3 and
emug stands for gas dynamic viscosity, kg/m/s.

The gas-solid specific contact area is calculated as

Ags = (Rg/(1-Rs)) * 6. * Rs/Ss/Ds, 1/m

where

Rg is the volume fraction of space available for gas flow and Rs is the volume fraction of space available for solid flow.

The heat transfer is effected by following source terms.

For solid enthalpy, Hsol, conservation equation:

Shsg = hgs * Ags * (Tgas - Tsol), W/m^3

For gas enthalpy, Hgas, conservation equation:

Shgs = hgs * Ags * (Tsol - Tgas), W/m^3

(b) Gas-liquid heat transfer

The expression for hgl times Aht comes from Mackey and Warner:

hgl * Agl = 4.18E-4 * (Rg * rhog * ) * Cpg * (Rl * rhol * )^0.35 * Regl^-0.37 * (Schg/Prg)^2/3

in which the Reynolds number for liquid

Regl= * rhol/emul * Dl and

the gas Schmidt number

Schg=emug/rhog * Difg.

Here,


rhol stands for liquid density, kg/m^3,
<Vg-Vl> stands for the relative velocity magnitude between gas and liquid phases, m/s,
Cpg stands for gas specific heat, J/kg/K
Rl stands for volume fraction available for liquid flow and
Difg stands for diffusion coefficient, m^2/s.

The heat transfer is effected by following source terms.

For gas enthalpy, Hgas, conservation equation:

Shgl = hgl * Agl * (Tliq - Tgas), W/m^3

For liquid enthalpy, Hliq, conservation equation:

Shlg = hgl * Agl * (Tgas - Tliq), W/m^3

(c) Fines-solid heat transfer

The fines-solid heat transfer coefficient utilises an expression for heat transfer between fluidised bed and wall as follows:

hfs = he * (Rf/(1-Rs)), W/m^2/K.

In which,

Rf stands for the volume fraction available for fines flow and

he = 2. * sqrt(ke * rhoe * Cpe/(3.14159 * tce)), W/m^2/K.

Where,

tce = (Rg + Rf)/(Vele * Ags), s.

Here,

VARe=(Rg * VARg+Rf * VARf)/Rg+Rf

for VAR= k, rho, Cp and velocity magnitude, Vel.

Mean volumetric solid area exposed to fines phase is taken as:

Afs = (Rf/(1-Rs)) * 6. * Rs/Ss/Ds, 1/m

The heat transfer is effected by following source terms.

For fines enthalpy, Hfin, conservation equation:

Shfs = hfs * Afs * (Tsol - Tfin), W/m^3

For solid enthalpy, Hsol, conservation equation:

Shsf = hfs * Afs * (Tfin - Tsol), W/m^3

(d) Liquid-solid heat transfer

The liquid-solid heat transfer coefficient is based on correlation for liquid metals.

hls = gamma * (Kl/Ds) * (2 * (Resl * Prl)^0.5/(1.55 * (Prl)^0.5 +3.07 * (0.372-0.15 * Prl)^0.5)) , W/m^2/K

In which, the liquid Reynolds number is

Resl= Ss * rhol * /emul and

liquid Prandtl number, Prl.

Here,


rhol is density of liquid metal, kg/m^3,
emul is liquid metal dynamic viscosity, kg/m/s,
Kl is liquid metal heat conductivity, W/m/K and
<Vg-Vl> is relative velocity between gas and liquid phases, m/s.

Mean volumetric solid area exposed to liquid phase is taken as:

Als = (Rl/(1-Rs)) * 6. * Rs/Ss/Ds, 1/m

The heat transfer is effected by following source terms.

For liquid enthalpy, Hliq, conservation equation:

Shls = hls * Als * (Tsol - Tliq), W/m^3

For solid enthalpy, Hsol, conservation equation:

Shsl = hls * Als * (Tliq - Tsol), W/m^3

(e) Gas-fines heat transfer

It is effected by the default settings of 7GASES built-in model and is handled by the settings

PHINT(H1) = GRND7, PHINT(H2) = GRND7,

5.5 Frictional momentum transfer

The rate of frictional momentum transfer, per unit volume, between the phases generally takes the form :

Fij = Drag coefficient * density * relative velocity * (ui-uj), N/m^3

It is , here, determined by empirical correlations which are set out below.

(a) Gas to liquid momentum transfer.

The directional correlations used to calculate the volumetric drag forces between liquid and gas phases are given below for longitudinal velocity only.

Fglw = 0.75 * (Rl * rhog/(Sl * Dl)) * * (Wgas-Wliq) * Cdgl, N/m^3

In which,


Rl is the volume fraction available for liquid flow,
rhog is the gas density, kg/m^3,
Sl is the shape factor of liquid fragments,
Dl is the mean size of liquid fragments, m,
<Vg-Vl> is the gas-liquid relative velocity magnitude, m/s,
Wgas is axial velocity component of the gas, m/s,
Wliq is axial velocity component of the liquid, m/s, and
Cdgl is the drag coefficient.

The drag coefficients are calculated as follows:

Cdgl=[24./Regl * ((1+0.18 * Regl^0.65)+0.42/(1+6881/Regl))] * (Rl/(Rl+Rg))^-4.65

where the Reynolds number, Regl are :

Regl=Sl * rhog * * Dl/emug.

The momentum transfer is effected by following source terms.

For gas W-momentum, Wgas, conservation equation:

Sglw = 0.75 * (Rl * rhog/(Sl * Dl)) * * Cdgl * (Wliq-Wgas), N/m^3

For liquid W-momentum, Wliq, conservation equation:

Slgw = 0.75 * (Rl * rhog/(Sl * Dl)) * * Cdgl * (Wgas-Wliq), N/m^3

The similar correlations are used for other components of liquid and gas velocities.

(b) Solid to liquid momentum transfer.

The calculation of the lump solid -liquid drag forces are based on the Kozeny-Carman equation. In what follows, it will be detailed for longitudinal velocity components only.

Fslw = Cdsl * rhol * /Rh * (Wsol-Wliq), N/m^3

In which, the drag coefficient

Cdsl = 5./Resl + 0.4/Resl^0.1 ,

where the Reynolds number is taken as

Resl = rhol * * Rh/emul and

the size scale of liquid fragment is given by

Rh = Rl * Ss * Ds/(6 * Rs), m.

Here,


Rl is the volume fraction available for liquid flow,
Rs is the volume fraction available for solid flow,
rhol is the liquid density, kg/m^3,
emul is the liquid dynamic viscosity, kg/m/s,
Ss is the shape factor of solid lumps,
Ds is the mean size of solid lumps, m,
<Vl-Vs> is the solid-liquid relative velocity magnitude, m/s,
Wsol is axial velocity component of the solid, m/s,
Wliq is axial velocity component of the liquid, m/s.

The momentum transfer is effected by following source terms.

For solid W-momentum, Wsol, conservation equation:

Sslw = Cdsl * rhol * /Rh * (Wliq-Wsol), N/m^3

For liquid W-momentum, Wliq, conservation equation:

Slsw = Cdsl * rhol * /Rh * (Wsol-Wliq), N/m^3

The similar correlations are used for other components of liquid and solid velocities.

(c) Solid to fines momentum transfer.

The solid-fines frictional momentum transfer in axial direction is supposed to be governed by the following equation:

Fsf = Rf * Cdsf * rhof * /Ds * (Wsol-Wfin), N/m^3

In which,

Cdsf = 12. * Fr^-1.33,

the Froude number is taken as

Fr = g * Df/^2.

Here,


Rf is the volume fraction available for fines flow,
rhof is the density of fines, kg/m^3,
Ds is the mean size of solid lumps, m,
<Vs-Vf> is the solid-liquid relative velocity magnitude, m/s,
Wsol is axial velocity component of the solid, m/s,
Wfin is axial velocity component of the fines, m/s.

The momentum transfer is effected by following source terms.

For solid W-momentum, Wsol, conservation equation:

Ssfw = Rf * Cdsf * rhof * /Ds * (Wfin-Wsol), N/m^3

For fines W-momentum, Wfin, conservation equation:

Sfsw = Rf * Cdsf * rhof * /Ds * (Wsol-Wfin), N/m^3

The similar correlations are used for other components of fines and solid velocities.

(d) Gas to solid momentum transfer.

The gas-lump solids frictional momentum transfer in axial direction is supposed to be calculated by the following equation:

Fgsw = rhog * Rs/(1-Rs) * Cdgs * /(Ds * Ss) * (Wgas-Wsol), N/m^3

In which, the drag coefficient is taken as

Cdgs = 1.75 + 150. * enug * Rs/( * (1-Rs) * Ds * Ss).

Here,


Rs is the volume fraction available for solid flow,
rhog is the density of gas, kg/m^3,
Ss is the solid lump shape factor,
enug is the kinematic viscosity of the gas, m^2/s,
Ds is the mean size of solid lumps, m,
<Vg-Vs> is the gas-solid relative velocity magnitude, m/s,
Wsol is axial velocity component of the solid, m/s,
Wgas is axial velocity component of the gas, m/s.

The momentum transfer is effected by following source terms.

For solid W-momentum, Wsol, conservation equation:

Ssgw = rhog * Rs/(1-Rs) * Cdgs * /(Ds * Ss) * (Wgas-Wsol), N/m^3

For gas W-momentum, Wgas, conservation equation:

Sssw = rhog * Rs/(1-Rs) * Cdgs * /(Ds * Ss) * (Wsol-Wgas), N/m^3

The similar correlations are used for other components of gas and solid velocities.

(e) Gas to fines momentum transfer.

The directional correlations used to calculate the volumetric frictional forces between fines and gas phases are similar to ones used for gas liquid drag terms above.

The momentum transfer is effected by following source terms.

For gas W-momentum, Wgas, conservation equation:

Sgfw = 0.75 * (Rf * rhog/(Sf * Df)) * * Cdfl * (Wfin-Wgas), N/m^3

For fines W-momentum, Wfin, conservation equation:

Sfgw = 0.75 * (Rf * rhog/(Sf * Df)) * * Cdfl * (Wgas-Wfin), N/m^3

In which, the drag coefficients are calculated as follows:

Cdfl=[24./Regf * ((1+0.18 * Regf^0.65)+0.42/(1+6881/Regf))] * (Rf/(Rf+Rg))^-4.65

where the Reynolds number, Regf are :

Regf=Sf * rhog * * Df/emug.

Here,


Rf is the volume fraction available for fines flow,
Rg is the volume fraction available for gas flow,
rhog is the gas density, kg/m^3,
emug is the gas dynamic viscosity, kg/m/s,
Sf is the shape factor of fines fragments,
Df is the mean size of fines fragments, m,
<Vg-Vf> is the gas-fines relative velocity magnitude, m/s,
Wgas is axial velocity component of the gas, m/s and
Wfin is axial velocity component of the fines, m/s.

The similar correlations are used for other components of fines and gas velocities.


6. Physical properties

Gas density is calculated from the ideal-gas state equation as a function of temperature and pressure. Gas heat capacity, thermal conductivities and viscosities are taken as constants.

For the solid, ore and coke, the densities, shape factors, thermal coductivities, heat capacities, thermal conductivities and viscosities are constant. Solid particle diameters are taken as constants.

Liquid density, heat capacity, thermal conductivity, and viscositiy are constant. Shape factor is constant and set to unity. Liquid fragment size is proportional to the local solid particle diameter.

Fines density, diameter, shape factor, thermal conductivity are constant. Heat capacity is also constant.

The heats of combustion are taken as for 7GASES model of PHOENICS. The latent heats of melting are taken as equal to 272000 J/kg.


7 The blast furnace considered

Contents

7.1 Geometry
7.2 Operating conditions
7.3 Boundary conditions
7.4 The grid and computational spaces

7.1 Geometry

Figures 1 and 2 illustrate the geometry of the blast furnace considered.

The furnace configuration chosen for present computations is an idealised one. However, it retains many features of practical equipment: coal and air input at the bottom at one end; combustion and reduction product gases discharge at the top; the coke and ore come in at the top; and liquid iron and slag extracted at the bottom.

7.2 Operating conditions

The main operational data of Austin et al's blast furnace from which all inputs have been deduced are as follows:


        Ore mass fraction                0.6
        Coke mass fraction               0.4
        Ash mass fraction                0.0
        Ore and coke size                5.e-2           m
        Solid inlet temperature          300             K
        Air blast rate                   847             Nm^3/min
        Air inlet temperature            1450            K
        Fines mass flow rate             5.7e5           kg/day
        Fines inlet temperature          1450            K
        Fines size                       0.1             mm

The gas and fines inlet conditions are defined in the region of nozzle, specifying the mass flow rates, inlet velocities and phase enthalpies. The gas/fines mass outflow conditions of fixed pressure type are specified over the top of the domain.

At the top of the furnace, the solid inlet conditions are defined, specifying the solid mass flow rates. However, the solid vertical velocity is allowed to vary freely at the top surface, to allow the model to predict non-uniform solid descent.

Free liquid and solid outflows are allowed at the bottom of the furnace.

Wall heat losses are assumed to make a negligible contribution to the furnace heat balance. An axis symmetry is assumed.

7.3 Boundary conditions

(a) Coal and air inlet

At air and coal inlet, values are given of all dependent variables with prescribed flow rates.

(b) Ore and coke inlet

Fixed inlet pressure with prescribed ore/coke mass fraction ratio and their inlet temperatures. As the solids are, obviously, incompressible, this pressure is set equal to zero. The solid mass inflow rate is not known in advance. It is calculated so as to be in accord with interphase mass transfer.

(c) Outlets

Fixed exit pressures for gas, fines and liquid. They are set to zero for gas and fines. The appropriate outflow coefficient is set to provide free liquid outflow. No outlets are provided for solids.

(d) Impermeable walls

The furnace walls are free-slip boundaries for all phases except in one two-dimensional case of solids.

7.4 The grid and computational spaces

Most the computations reported here have been carried out with a uniform grids having 15x10x10 cells. They are arranged in two spaces of one computational domain as shown in Figure 3.

The two-phase flows are considered to take place in each space and, being linked together, they form the four interdispersed continua as follows:

the 1st phase of Space 1 is the gas flow (1);
the 2nd phase of Space 1 is the coal fines flow (2); the 1st phase of Space 2 is the solid lump flow of coke in ore (3)
and
the 2nd phase of Space 2 is the liquid flow of iron and slag (4).

All phases are linked to appropriate neighbours in a manner shown on Figure 3 for the interphase mass transfer links, where 2to1 link stands for mass flow rate governed by combustion of coal fines, 3to1 link is due to combustion of coke, 4to1 is related to reduction of ore and 4to1 appears as a result of ore fusion. The appropriate links are also provided for interphase momentum and heat transfer.

Since it is assumed that the flow pattern repeats itself in each 60 degree of the furnace cross-section, the each computational space is restricted to only 60 degree sector.

Although the grid is fairly coarse, it is sufficient to demonstrate the capabilities of the present model.

For two- and one-dimensional models, the number of intervals in X- and X- and Y-directions are taken as unity.


8. Presentation of computed results

A very large number of computations have been performed for the one-, two- and three-dimensional distributions of all dependent and auxiliary variables. It is impossible to display all the computed results here. Thus, only some selected profiles, contour and vector fields are displayed and discussed.

Figures 4, 5 and 6 present computed results for the one-dimensional test case in the form of longitudinal profiles of the dependent variables.

Figures 7, 8, 9, 10, 11, 12 and 13 display computed results for two-dimensional test cases in the form of velocity vectors and dependent-variables contours.

Figures 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 and 30 illustrate computed results for the three-dimensional base case in the form of velocity vectors and dependent variables contours.


9. Discussions of the results

Contents

9.1 One-dimensional simulation
9.2 Two-dimensional simulation
9.3 Three-dimensional simulation

9.1 One-dimensional simulation

The one-dimensional option of the model can be treated as a preparatory step towards the understanding of the results of multi dimensional ones. It has been used to perform the calculations which, being favourably compared with widely used typical distributions, would provide the confidence in the model and numerical method employed in its solution.

Figure 4, 5 and 6 show the longitudinal distribution for gas and solid, the phase mass fractions of solid and liquid components and the reaction rates of indirect reduction and coke burning.

They show typical progress of heat exchange and reduction of iron oxide, as observed in the blast furnace processes. It appears that they are fairly close to those reported by Omori et al, 1987.

9.2 Two-dimensional simulation

In the two-dimensional study attention was focussed on the influence of the downward-velocity distribution of the solid burden.

Two different cases were studied in the first, radial motion of the burden was prevented, and the zero-slip condition at the furnace wall was NOT applied. This resulted in a downward-velocity distribution having its maximum at the wall and its minimum at the axis.

In the second, radial motion was allowed and the zero-slip condition at the wall WAS applied. This resulted in a downward-velocity distribution with its maximum at the axis and its minimum (namely zero) at the wall.

The two cases are referred to as "base burden case" and "reverse case" in the legends of the following figures.

In the first case, the contours of burden mass flow rate are shown on Figure 7. The inlet mass flow rate exhibits an almost linear variation with radius, the smallest value being at the centreline.

In the second case, by contrast, the inlet burden distribution, as shown on Figure 8, is radially reversed from the base case, with mass flow rate of solid small at the wall and large near the axes.

The figures 9 and 10 show the temperature distributions of solid phase and gas for both cases. Figure 11 to 13 display the contours of ore reduction rate, mass fraction of coke in solid phase and distribution of iron mass for base burden case. From the inspection of these the following observations may be drawn:

(1) The temperature distributions, as shown on Fig.9 and 10 are significantly influenced by inlet distribution of solid mass inflow at the top of the furnace, with the temperature increase becoming small in the high mass velocity zone of burden descent.

(2) As the solid movement is small at the centerline for the first case, its temperature, in the upper part of the furnace, is kept there at high level. The temperature of the gas flowing out of the center region is high and this promotes melting of ore.

(3) The shape of stagnant region at the center of furnace has, in terms of coke mass fraction distribution shown on Fig.12, tendency to adopt the inverted V- shape since coke combustion proceeds within a limited peripheral space.

(4) The isothermal line of 1400 K, for the first case, also has inverted V-shape and this is nearly corresponds with the cohesive zone shape as it has been elucidated by investigation of quenched furnaces as reported by Omori et al, 1987.

(5) The distribution of reduction rate, Fig. 11, exhibits inverted V-shape in the upper part of the furnace with the maximum value at the boundary of the region of largest temperatures. There is also delay of the reduction reaction caused by lower temperatures near the furnace walls.

(6) The distribution of iron, Fig. 13, becomes inverted V-shape with the maximum corresponds to the outer boundary of high temperature region.

The above simulated observations are fully in accord with the results reported by Omori et al, 1987 and Austin et al, 1997,1998.

9.3 Three-dimensional simulation

All three-dimensional simulations have been performed with radial motion of the burden prevented. The main results are shown in Fig. 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 and 30 by way of contours of dependent variables at some of the cross-sectional planes.

Figures 14, 15 and 16 present the predicted distributions of longitudinal gas and fines velocities followed by volume fractions of coal fines contours. Significant slip is observed between the gas and coal particles. For the most of the furnace the coal motion appears to be more uniform than the gas motion with noticeable three-dimensionality of velocity distributions near the tuyere. The volume fraction of coal diminishes significantly due to combustion and is more sensitive to the three-dimensionality of the flow.

Figures 17 and 18 display the gas and fine temperature contours. It is evident that there are no significant temperature differences. The temperature distributions demonstrate the trends similar to those discussed above for two-dimensional model.

Figures 19 and 20 present the carbon monoxide, CO, and carbon dioxide, CO2, concentration contours in terms of corresponding mass fractions.The smallest CO concentration is observed next to the tuyere, as expected; increases significantly to a value of 0.35 as more coke is involved in combustion. The latter figure is close to observed CO concentrations in the top gas /Omori et al, 1987/. For the top half of the furnace, the concentration distributions are more or less unifiorm. Similar trends have been predicted for other components of the gas phase.

Figure 21 shows the distribution of liquid volume fraction. As expected, it has the highest value at the furnace bottom, exhibits most uniformity at the middle and diminishes significantly at the top with much greater non-uniformity due to both 3D effects and temperature distributions.

The distribution of the reduction rate depicted in Fig. 22 is affected by both CO concentration distributions discussed above and temperature distributions which will be discussed below. It is highly non-uniform with the highest level of reduction observed where expected on the basis of 2D model analysis above.

Comparison of the solid and liquid temperatures, shown in Fig. 23 and 24, reveals the expected realistic similarities as well as differences. Except the obvious three-dimensionality effects, the qualitative behaviour of those distributions is very much the same as for the 2D base case and the same comments can apply here.

The above arguments are applied also to the calculated results of solid and liquid compositions shown, in Fig.25, 26, 27 and 28. They extend to three-dimensions what has been observed in two-dimensional model.

Finally, the predicted results of slag and iron mass distributions within blast furnace are displayed in Fig. 29 and 30.

They may serve to assess the overall performance of the blast furnace in question. It can be seen, that the three-dimensionality of the furnace geometry greatly affect the "productivity" of the lower half of the shaft.


10. Remaining tasks

Although the satisfactory qualitative and quantitative working of the model has been proved, further work remains to be done. The following tasks can be distinguished:


11 Concluding remarks

This report has brought into existence a computer-based three dimensional model of blast furnace. It is based upon the consideration of four-phase motion and related heat and mass transfer processes. The model includes simple basic representation of the major chemical reactions and physical features of the furnace.

Results have been presented and are shown to indicate the correct trends. The predictions provide detailed information for each phase present, regarding three-dimensional fields of velocities, of temperatures and of phase compositions. Further work should consist of grid-independence studies and comparison with experimental data, in order to validate the model.

In order to extend the field of applications of the model, additional physical models should be included. The effect of additional chemistry may be introduced through either conventional or multi-fluid approaches. Similarly, radiation heat transfer may be handled by PLANTing the radiation models described elsewhere. The inclusion of any of these models merely increases the number of conservation equation to be solved, but otherwise incurs no significant modification to the present model.

It is expected that the model is flexible enough to allow the shape of, and conditions in, the raceway to be predicted rather than assumed. Similarly, the position and shape of the "dead man" can be calculated.

The model, as it now stands, represents a valuable tool which can be used by OSIRIS partners and others, in the future, to advance the state of knowledge significantly. It seems to be an appropriate base to include further multiphase interactions and chemistry.

However, since the velocity distribution int he downward-moving burden has been shown to influence performance significantly, a physically-based model of the burden motion should be provided, if possible.

Finally, more work is required to obtain reliable experimental correlations for the interphase heat-, mass-, and momentum transfer, which can then be used to improve the input of the model.


12 References

Spalding DB: Progress with SAFIR. Report to OSIRIS-project management, June 1998

Spalding DB and Zhubrin SV: SAFIR; A computer model of flow, heat and mass transfer, phase change and chemical reaction in the blast furnace, with injected coal or oil, CHAM Web-site report, October, 1998.

Spalding DB: Progress with SAFIR. Report to OSIRIS-project management, November 1998

Austin PR, Nogami H and Yagi J-i: A mathematical model of four-phase motion and heat transfer in the blast furnace. ISIL International Journal vol 37 (1997) no 5 pp 458 -467

Austin PR, Nogami H and Yagi J-i: A mathematical model for blast furnace reaction analysis based on the four-fluid model. ISIL International Journal vol 37 (1997) no 8 pp 748 -755

Austin PR, Nogami H and Yagi J-i: Analysis of actual blast furnace operation and evaluation of static liquid holdup effects by the four-fluid model. ISIL international Journal vol 38 (1998) no 3 pp 246 -255

Omori Y et al "Blast furnace phenomena and modelling", published by Elsevier, 1987