Mei C., Zhou J., Peng X. Simulation and Optimization of Furnaces and Kilns for Nonferrous Metallurgical Engineering

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6 Simulation and Optimization of Electric Smelting Furnace 

1.5m, the centre of the temperature curve at the top of the furnace forms a

concave surface. If the fin is insulated and only the casing conducts electric

current (Cavigli,1978), the temperature distribution in the electrode is similar to

Fig. 6.7 (d).

From the above analysis, it can be found that increasing the current density of

the electrode, the electric resistance of the casing and the fin, as well as the

thermal conduction of the paste will effectively make the 300

ć isothermal line

rise, whilst cause little changes for the 500

ć isothermal line. The main reason for

it is because a big temperature difference exists between the electrode above the

furnace roof and the ambient, which causes great heat losses (Fig. 6.4 (b)). If a

refractory fiber sleeve can be mounted on the outer surface (or on the interior

Fig. 6.7



Influence of various parameters on temperature field of electrode (T

=1500ć)

(a) Current density of electrode is 3Acm

;(b) Temperature in furnace chamber is 700ć;

(e) Thermal insulation measures are taken between clamp and the top of the furnace;

(f) Thermal insulation measures are taken, and electrode current is 25kA

  Jiemin Zhou and Ping Zhou

surface) of the electrode packing gland, to increase the thermal resistance between

the electrode surface and the ambient, the heat dissipation through the electrode

surface will be remarkably reduced, and the heat will be forced to flow upwards so

that the baking condition of the electrode will be improved. The thermal insulation

sleeve can be made of two semicircle rings for convenient mounting and uninstall.

The temperature field in the electrode with this reform is shown in Fig.6.7(e). It

can be seen that the 500

ć isothermal line has been located at the lower margin of

the clamp, and the danger of soft-broken of the electrode between furnace roof and

clamp will be greatly reduced. In order to reduce the heat carried away by cooling

water and to improve the baking condition, the vaporization cooling method can

be considered. If the electrode can still bear a relatively big current as No. 3

furnace when it is insulated, the temperature curves on the electrode plane will be

distributed as shown in Fig. 6.7 (f). Under this kind of electric regime, the 300

isothermal line is approaching to the upper margin of the clamp, which decreases

the flowing of the paste, and the 500

ć isothermal line is fully in the clamp, so

that the electrode has relatively high mechanical intensity when it leaves the clamp.

The smooth and uniform ascent of temperature in the electrode is helpful to

improve of the baking quality. However, because the slag around the electrode is

exposed to gas, the temperature in the furnace chamber is very high, and the seal

of the furnace is poor, the baked electrode will be quickly oxidized at conditions

of high temperature and sufficient oxygen. Or even worse, as the electrode falls

very slowly and stays for several days inside the furnace hearth, it will not only

consumes more electrodes, but also results in the hard-broken of the electrode.

Therefore, more modification of the furnace should aim for the fully covering of

slag with furnace charge, decreasing furnace temperature, improving the air

lightness of the electrode hole or painting antioxidation coating on the electrode

surface. In this situation, improving the baking of the electrode above the furnace

roof may remarkably enhance the electrode intensity, reduce accidents of electrode

and decrease the consumption of energy and material.

6.3



Modeling of Bath Flow in Electric Smelting Furnace

The bath movement in the electric smelting furnace has a great influence on the

smelting process. So many scholars in the world have carried out a lot of

researches into the movement rules of the bath.

Giomidovskij systematically observed and analyzed the movement of the molten

slag in the electric smelting furnace by substantial model (Giomidovskij, 1959).

Moreover, he studied the quantitative relationship between the flow path and

the heat transfer in the furnace, based on the simplified flow path of the molten

slag. Although these empirical formulas have taken some guide roles in

6 Simulation and Optimization of Electric Smelting Furnace 

practices, they could not be used to understand the movement of the molten

slag in the furnace.

In 1980s, Jia Di et al. established mathematical models of steady state electric

field, temperature field and velocity field for the single electrode smelting furnace,

taking account of the coupling influence of velocity field on the temperature field.

These researches became the base of numerical simulation on the velocity field in

the furnace.

Here, the electric cleaning furnace, which was a type of the electric smelting

furnace, was taken as an example, and the numerical simulation for the velocity

field in the furnace was introduced.

The object chosen for analysis was the cleaning electric furnace that was used

to tackle the slag in Noranda’s copper smelting furnace. Its rated electrical power

is 6,300kV

• A and its frequency of the alternating current is 50Hz. Three

cylindrical carbon electrodes with 1,000mm diameter were fixed in the furnace

with 9,200mm diameter.

6.3.1



Mathematical model for velocity field of bath

The controlling equations and boundary conditions to solve the bath velocity field

in aluminum cell are introduced as follows.

6.3.1.1



Basic equations

The following assumptions were used:

a)The electrodes were in a stable work condition;

b)The turbulent viscosity of the molten slag was isotropic;

c)The influences of the molten slag dumping into the furnace on the fluid flow

and of magnetic field on the fluid fluctuating were neglected;

d)The matte was in a relative stationary state.

The equations for the molten slag flow in furnace are expressed by:

()0U

∇=• (6.4)

eff

() [()]

p μ

ρρ

∇×=−∇+ ∇+∇• UU F U U (6.5)

where variables are defined the same as in Section 2.3.1.

Generally, the bath velocity in the electric smelting furnace was small, so the

turbulent model with low Reynolds number was suitable for the simulation. In the

computation of bath velocity field in the cleaning electric furnace, the k-

two-equation model with low Reynolds number supposed by Launder (Launder,

1974) was adopted. There is:

t μμ

μ cfρ

(6.6)

  Jiemin Zhou and Ping Zhou

The k-

equation were modified by:

()

ρ k μ kGρε

⎡⎤

⎛⎞

⎢⎥

⎜⎟

⎢⎥

⎝⎠

⎣⎦

∇=∇+∇+−−••U (6.7)

122

() ( )

ρμ CG Cfρε E

εε

⎡⎤

⎛⎞

⎢⎥

⎜⎟

⎢⎥

⎝⎠

⎣⎦

∇=∇+∇+− +••U (6.8)

()[()]=+∇∇+∇

G μμ UU U (6.9)

where

f , f

, D and E are respectively defined by

10.3exp( )f= Re−−

)(2 U∇∇=

μμ

με

ρk

The values of the empirical constants refer to Table 2.5.

6.3.1.2



Boundary conditions

The computational region is the molten slag layer in the electric cleaning furnace,

which is shown in Fig.6.8. The boundary conditions are listed as following:

a) The top surface (W

) in molten slag was taken as free surface. i.e.

UV k

ZZ ZZ

∂∂ ∂∂

=====

∂∂ ∂∂

b) The velocity of molten slag at the solid wall surfaces (W

) was zero. i.e.

U=V=W=0

c) The velocity of molten slag at the electrode surfaces (W

) was assumed to be

zero too.

d) The velocity of matte at the bottom boundary (W

) was motionless. i.e.

U=V=W=0

e) k and

near the wall were treated as wall function (Fig. 6.8).

6.3.2



The forces acting on molten slag

The flow pattern of the molten slag is complex as it is affected by a number of

forces simultaneously. By analyzing the physical and chemical process occurring

in the electric cleaning furnace, it can be concluded that four forces acting

6 Simulation and Optimization of Electric Smelting Furnace 

mutually on molten slag are electromagnetic force, buoyancy force, gravitational

force and drag force caused by bubbles. The bubbles in the furnace mainly result

from reduction reaction. As the quantity of reactants is 3

%∼4% of molten slag and

most reactions are carried out at the top layer of the bath, it is reasonable to

neglect the drag forces of bubble in this model.

Fig. 6.8 Schematic of Analytical Zone and its Corresponding Cross Section

of the Electric Field

(a)Transect; (b)Vertical section of plane a-a.

6.3.2.1



Computation of electromagnetic force

The electromagnetic forces acting on the molten slag with high electric

conductivity take the form:

E+jhB (6.10)

where

F is the electromagnetic force per volume; E is the electric field intensity

vector;

is the residual charge density; j is the current density vector; B is the

magnetic induced intensity vector;

Although there are a lot of positive and negative ions and free charges in the

electric cleaning furnace, the whole number of positive charges balances with that

of negative charges, that is

= 0. Then Eq. 6.10 can be written as:

F=jhB (6.11)

The magnetic field is induced from the electrode current and distributing

current in the slag. The latter has only an effect on compressing the molten slag.

As, it is much smaller than the former. It can be neglected in computation of the

electromagnetic field.

At time t, the electromagnetic force induced by electrode A at space point D (x,

y, z) is given by:

)()( tz,y,x,tz,y,x,

AyzAxt

BjF ×= (6.12)

)()( tz,y,x,tz,y,x,

AxzAyt

BjF ×= (6.13)

  Jiemin Zhou and Ping Zhou

)()()()( tz,y,x,tz,y,x,tz,y,x,tz,y,x,

AyzAxyAzt

BjBjF ×+×−= (6.14)

where

AytAxt

FF , and

Azt

F refer to electromagnetic force components in the three

coordinate directions respectively. B

(x,y,z,t) and B

(x,y,z,t) are the magnetic

induced intensity components in x, y directions, respectively (their magnitude and

direction are determined by Biot-Sevart law(Wang and Mei,1996)). Similarly,

)()( tz,y,x,,tz,y,x,

jj and )( tz,y,x,

j are current densities, which are given by

the results of the numerical simulation of the electric field.

During a period, the magnetic forces from electrode A are given by:

()

k1T

Ai Ait

∫

FF (6.15)

where i is taken as x, y and z, respectively. T is the periodic time and k is an

integer.

Similarly, at space point D, the magnetic field and electromagnetic force

produced by the electrode B and C can be computed. At an arbitrary point in the

furnace, the electromagnetic force acting on the molten slag is the sum of that

produced by the electrode A, B and C.

6.3.2.2



Buoyancy forces and gravitational forces

As mentioned above, the buoyancy forces will be generated by temperature

gradients in the furnace. The joint force including the buoyancy and gravitational

force is described as follows:

βρ

′

=Δ

•••FT (6.16)

where

β is the expansion factor of the molten slag;

Δ is the temperature

difference between local and down nodes;

g is the gravitational acceleration.

6.3.3



Solution algorithms and characters

The method of the staggered grid and the control volume was used to establish the

discrete equations and SIMPLE method was applied. Compared with a general

SIMPLE algorithm, the program has the following characters:

a) A cylindrical coordinate system and uneven grids were used.

b) A program for TDMA algorithm to the non-tridiagonal matrix was developed.

c) The pressure fields on the horizontal section were revised with that on the

vertical section.

Fig. 6.9~ Fig. 6.13 show the computational results of the velocity fields in the

typical sections. It can be found that, to the top layer (section

) of the molten

slag, two eddies are formed near each electrode due to the influence of

electromagnetic forces. Compared with section

, the velocity field in section

d-d (including electrodes) has similar flow pattern, while the eddies have different

sizes and directions. The reason for the differences is that the horizontal fluid flow

6 Simulation and Optimization of Electric Smelting Furnace 

is affected by the vertical flow in the bath depth that electrods were inserted. In

section

f-f (without including electrodes), a large circulation occurs in the lower

level of the molten bath, as electromagnetic forces drive the fluid flowing. This

type of the velocity field is advantageous to increasing collision among matte

particles in melting period, but it is disadvantageous in cleaning period to settling

matte particles and to forming an efficient gradient concentration field between the

inlet and the outlet of the molten slag. These are disadvantageous to improving the

recovery of valuable metals in the molten slag. In section

a-a (including an

electrode) three distinct circulations are produced. In section

b-b (without

including electrodes), four circulations are produced and two circulations are

formed near each electrode.

Fig. 6.9



Velocity at cross section W



Fig. 6.10 Velocity at cross section d-d Fig. 6.11 Velocity at cross section f - f

  Jiemin Zhou and Ping Zhou

The results mentioned above indicate that the fluid in longitudinal direction

near electrode is of large velocity. The material that is dumped into the region near

the electrode can be molten more quickly, which reduces the melting time of

material, increases the time for cleaning material and accelerates chemical

reaction in the furnace, which is helpful for cleaning the slag.

6.4



Heat Transfer in the Molten Pool and Temperature Field

Model of the Electric Smelting Furnace

Various technical and economic indices of the electric smelting furnace depend on

the electricity-heat conversion process, heat transfer process and temperature

distribution, which directly influence the smelting process. With the development

of productivity and the enlarging of furnace volume, it becomes more and more

important to understand the electricity and heat transfer in the smelting process,

and much work has been done to study mathematically the electric and heat

distribution in the electric smelting furnace. W. D. Heiss (Heiss,1978a,b,1980)

published several papers from 1975 to 1979 to introduce his research. For the

circular three-electrode furnace, he assumed that no furnace wall existed, and the

electrodes were simplified to be conducting wires without diameter. Besides,

physical parameters were set be constants. In this way, he got the analytic solution

of the current density. For the rectangular six-electrode furnace, an electric field

function was constructed and the distributions of electric field and power were

also calculated under similar assumptions. Then he obtained some useful

conclusions agreeing well with the real furnace. However, as he emphasized, such

simplifications differed greatly from the real situation, so its application was

limited, and it could be only used as a basis of other more advanced numerical

models.

J. H. Downing et al. (Kaiser and Douning, 1978; Douning et al.,1978,1980)

carried out numerical calculations of the heat transfer process at the bottom of the

circular electric smelting furnace with the help of computer in 1977. Their data

from the two-dimensional unsteady heat transfer model was then used as criterion

for design of the furnace hearth, and also used to predict the damage of the hearth

Fig. 6.12



Velocity at cross section a-a

Fig. 6.13



Velocity at cross section b-b

6 Simulation and Optimization of Electric Smelting Furnace 

and to determine the maintenance period. In 1978, they built a electric and thermal

analytical model of the furnace. They divided the circular three-electrode furnace

into six symmetric parts as analytical domain. Although the convection problem of

the slag could not be solved yet, and some physical parameters could not be

determined precisely either, the model calculated the electric and the thermal

fields in the circular furnace successfully, and predicted the furnace operation

character. Furthermore, it gave reasonable interpretation to some experiential

formula obtained by former researchers. In the following two years, J. H.

Downing et al. used this model to investigate the influence of various design and

operation parameter on the production process, and the result agreed with the

practical data very well.

For the circular single-electrode furnace, Esko Juuso (Esko, 1986) built a similar

model, but the study of A. Jardy et al. (Jardy et al., 1986) was more unique. They

solved the steady two-dimensional Maxwell, Navier-Stokes and Fourier equations

set, and analyzed the electric, flow and temperature fields in the single-electrode

furnace to make the calculation more perfect. There are still no very good models

reported for the three-electrode and six-electrode electric smelting furnaces. This

section is to systematically introduce the research of heat and temperature

distribution in the molten pool of rectangular six-electrode nonferrous metal sulfide

smelting furnace. Later in 1998, Y. Y. Sheng et al. (Sheng et al.,1998a, b)

investigated this kind of furnace, adopting a similar method to that introduced in this

book, to study the electric field of the molten pool. They studied the electric field,

temperature field and flow velocity field simultaneously, which furthered the

research on this subject.

6.4.1



Mathematical model of the temperature field in the molten pool

In the rectangular copper and nickel sulfide smelting furnace, the six electrodes

are mounted in a line, its configuration sketch is shown in Fig. 6.14. As a typical

example, the No. 2 furnace in Jinchuan Nonferrous Metal Company has a power

of 6500 kV

噝A, a dimension of 21.5mh5.5mh4m, and a electrode diameter of

1m (JNMC, 1981).

The composition of some charge (mainly sulfide calcine) and products (nickel

matte and slag) of the furnace is given in Table 6.4.

Table 6.4 Composition of charge, nickel matte and slag (%)

Component Ni Cu Co S Fe MgO

SiO

Charge 5~6 2.5~3.0 0.15~0.25 15~18 27~32 10~14 13~19 1~2

Nickel matte 12~15 6~8 0.4~0.6 25~28 46~50

Slag

İ0.2

0.1~0.2 0.8~1.0

İ18

40~42 1.5~2.5

  Jiemin Zhou and Ping Zhou

Fig. 6.14 Configuration sketch of rectangular six-electrode electric smelting furnace

(a) Longitudinal cross section; (b) Lateral cross section

Some physical properties of the slag, copper and nickel matte are listed in Table

6.5 and Table 6.6.

Table 6.5 Physical properties of slag and copper matte (Kyllo and Richards, 1998)

Physical properties Slag Copper matte

Density/kggm

−3

3297+128.5[FeO]

−0.115T

[SiO

]

3880+404[Cu]

+4590[Cu]

−3750[Cu]

Viscosity/Pags

s2s

[Fe]

9380

2.06 10 exp 0.714

[SiO ]T

−

⎡⎤

⎛⎞

×−×

⎢⎥

⎜⎟

⎢⎥

⎝⎠

⎣⎦

5000

3.36 10 exp

−

⎛⎞

⎜⎟

⎝⎠

Thermal conductivity

−1

2.09

1.34−17.9[Cu]

+25.6[Cu]

−13.7[Cu]

Note: The subscript S in the above table represents the slag phase; M represents the copper matte

phase; the value in [ ] represents the component mass percentage; and T is temperature, K.