KR101175465B1 - method for calculating trajectory for dumping of charge of blast furnace - Google Patents

Abstract

The present invention relates to a method for calculating the drop trajectory of the blast furnace charge,
A hopper discharge speed calculating step of calculating a hopper outlet speed of the charge;
A feeder spout discharge rate calculating step of calculating a feeder spout outlet speed of the charge;
A chute discharge rate calculation step of calculating chute exit velocity of the charge;
A drop trajectory calculation step of calculating a position of the charge according to time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step;
.
Therefore, it is possible to calculate the angle of repose at the drop trajectory and the drop position, thereby enabling more efficient control of the distribution of the charged object.

Description

Method for calculating trajectory for dumping of charge of blast furnace}

The present invention relates to a method for calculating the drop trajectory of the blast furnace charges so that when the charge of the blast furnace charges, it is possible to easily and accurately know the drop trajectory of the charge.

A blast furnace is a facility for melting molten iron ore to manufacture molten iron (pig iron).

Iron ore and coke are sequentially charged and stacked in the blast furnace, and the hot air is blown from the lower tuyere to combust the coke. .

The invention provides an easy and accurate calculation of the drop trajectory (including the deposit form immediately after the fall) of a blast furnace in a blast furnace using a bellless top charging device, which can be usefully used for the control of the load distribution. The purpose is to provide a method of calculating the drop trajectory.

The present invention for achieving the above object,

A hopper discharge speed calculating step of calculating a speed of the charge discharged to the hopper outlet;

A feeder spout discharge rate calculation step of calculating a speed of the charge discharged to the outlet of the feeder spout using the hopper discharge rate of the charge calculated in the hopper discharge rate calculation step;

A chute discharge rate calculation step of calculating a rate of the charge discharged to the outlet of the chute using the feeder spout discharge rate of the charge calculated in the feeder spout discharge rate calculation step;

A drop trajectory calculation step of calculating a position of the charge according to time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step;

It includes.

In addition, the flow rate (G) of the charge in the hopper discharge speed calculation step,

이고,

ego,

The charge discharge rate (V _1v ) at the hopper outlet,

V _1v = G / A.

In addition, the feeder spout outlet speed (V _2v ) of the charge in the feeder spout discharge rate calculation step is characterized in that V _2v = [V _1v ² + 2gH _d ] ^0.5 K _f .

In addition, the chute exit speed (V ₃ ) of the charge in the chute discharge rate calculation step is

V ₃ = [ω ² cosα (cosα + μsinα) L ² + 2g (sinα-μcosα) L + (V _2v sinα ) ² ] ^0.5 It is characterized by that.

In addition, in the drop trajectory calculation step, the position during the drop according to the time of the charge is made of the horizontal and vertical coordinates (X, Y) of the charge particles,

,

인 것을 특징으로 한다.The coordinate value (X, Y) is

,

It is characterized by that.

In addition, the coordinates (X, Y) is characterized in that it calculates the drop trajectory of the charge by continuously repeating the calculation over time.

The method may further include a repose angle calculation step of identifying a drop position of the charge from the drop trace calculated in the drop trajectory calculation step and calculating a repose angle of the charge at the drop position.

In addition, in the angle of repose of the charge,

이고,The angle of repose (α) in the center of the furnace is

ego,

인 것을 특징으로 한다.The angle of repose (β) in the furnace wall direction is

It is characterized by that.

In addition, the present invention includes a chute discharge rate calculation step of calculating the speed of the charge discharged to the outlet of the chute;

A drop trajectory calculation step of calculating a position of a charge according to time during the drop using the chute discharge rate;

. ≪ / RTI >

According to the present invention as described above,

The drop trajectory of the charges and the form of deposition (left and right angle of repose) at the dropping position can be easily and accurately understood, so that the distribution of the charges in the blast furnace can be more accurately understood. By doing so, the blast furnace operation efficiency and productivity can be improved.

1 is an installation state of the bell tower charging apparatus in the upper part of the blast furnace,
2 is a block diagram showing the configuration of the present invention;
Figure 3 is a schematic diagram showing the force acting on the particles passing through the chute and the factors affecting it,
Figure 4 is a graph showing the stacking form of ore and coke obtained through the blast furnace scale model experiment,
5 is a schematic view showing the drop trajectory and the angle of repose at the dropping position of the charge.

Hereinafter, with reference to the accompanying drawings the present invention will be described in detail.

1 is a schematic installation state diagram of a bell tower charging device, as shown in the bell tower charging device is installed in the furnace of the blast furnace 1, the hopper (3) receiving the charge from the bunker (2), and the hopper (3) a feeder spout (4) connected to the bottom and a chute (5) connected to the feeder spout (4) and adapted to allow for turning and tilting angle adjustment.

In the bell tower charging device the charge is continuously moved from the hopper 3 through the feeder spout 4 to the chute 5.

As shown in Figure 2, the present invention is a hopper discharge speed calculation step (S1) for calculating the speed of the charge supplied from the bunker 2 and discharged to the outlet of the hopper 2 via the hopper (3) Wow,

The hopper is supplied from the hopper 3 and discharged to the outlet of the feeder spout 4 via the feeder spout 4 by using the hopper discharge speed of the charge calculated in the hopper discharge speed calculation step (S1). Feeder spout discharge rate calculation step (S2) for calculating the speed of the water,

Using the feeder spout discharge rate of the charges calculated in the feeder spout discharge rate calculation step (S2), it is supplied from the feeder spout (4) is discharged to the outlet of the chute (5) via the chute (5) Chute discharge rate calculation step (S3) for calculating the speed of the charge,

It includes a drop trajectory calculation step (S4) for calculating the position of the charge according to the time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step (S3).

In addition, the present invention further includes a repose angle calculation step (S5) for calculating the drop position of the charge from the drop trajectory calculated in the drop trajectory calculation step (S4), and calculates the angle of repose of the charge accumulated in the drop position.

Now, each step of the method for calculating the drop trajectory of the blast furnace charge according to the present invention will be described in detail.

The hopper outlet speed of the charge in the hopper discharge speed calculation step (S1) is calculated as follows.

The charge flow in the hopper 3 is then regarded as funnel flow.

The charge stored in the hopper 3 moves through the orifice inside the hopper to the feeder spout 4, where the flow rate of the charge passing through the orifice affects the rate of drop at the outlet of the hopper 3.

The flow rate G of the charge is influenced by the inclination angle of the hopper 3, the diameter of the orifice and the density of the charge particles, and can be expressed as in the following equation (1).

--------------(1)

--------------(One)

G: mass flow rate, kg / s

ρ _s : density of particles. kd / m ³

d _eff : effective diameter of the discharge orifice, m

g: accelation due to gravity, m / s ²

β: acute angle between the cone wall and the horizontal, radian

In Formula (1), the flow rate G of the charge discharged from the hopper 3 can be known. In general, the flow rate is expressed as the product of the cross-sectional area A and the flow rate V, and thus the charge discharge rate at the hopper outlet. (V _1v ) can be calculated from the following equation (1-1).

V _1v = G / A -------------- (1-1)

(A; Hopper exit cross section)

Next, the feeder spout outlet speed of the charge in the feeder spout discharge rate calculation step (S2) is calculated as follows.

The charge discharged from the hopper 3 falls freely by gravity inside the feeder spout 4 at an initial speed V _1v .

The collision between the charge particles and the collision between the particles and the inner wall of the feeder spout 4 reduces the final speed (outlet speed of the peter spout) by Newton's law (in feeder spout 4). The horizontal speed is regarded as 0.)

The feeder spout outlet speed (V _2v ) of the charge is represented by the following equation (2).

V _2v = [V _1v ² + ² gH _d ] ^0.5 K _f ------------------------------- (2)

V _1v , V _2v : velocity at the entrance and exit of the down comer, respectively (m / s)

g: Accelation due to gravity, cm / sec ²

H _d : height of feeder spout, m

K _f : correction factor for collisions

Next, the chute exit (end) speed of the charge in the chute discharge rate calculation step (S3) is calculated as follows.

The charge discharged from the feeder spout (4) is discharged through the chute (5), the charge particles passing through the chute (5), as shown in Figure 3, the frictional force (Frictional force F _F ; parallel to the chute surface ), Gravity (gravitational force m _g ; acts vertically downward), centrifugal force (F _T ; acts in the tangential direction of chute pivot), reactive force F _R (acts in the direction of chute surface) This works.

When l = 0 (shoot inlet), V = V _2v sinα (speed of chute inlet), and l = L (suit exit), and V = V ₃ (speed of chute exit), The speed can be expressed by the following equation (3).

V ₃ = [ω ² cosα (cosα + μsinα) L ² + 2g (sinα-μcosα) L + (V _2v sinα ) ² ] ^0.5 --- (3)

ω: angular velocity, radian / s

μ: Coefficient of friction between the particles and the chute surface.

V _2v : velocity at the exit of the down comer, m

On the other hand, in the drop trajectory calculation step (S4) it is calculated as follows.

The charge velocity V ₃ at the chute exit, obtained through equation (3), consists of a radial component, a vertical component, and a tangential component, as shown in the following equations (4), (5) and (6). Is displayed.)

V _x = V ₃ cosα ------------------------------------------- ( 4)

V _y =-V ₃ sinα ------------------------------------------ ( 5)

V _θ = r _c ω -------------------------------------------- -(6)

(r _c ; radius to the tip of the chute)

The drop trajectory of the charge is calculated by considering only the vertical component (V _y ) and the horizontal component (V _x ) (two-dimensional modeling).

The drop trajectory is composed of the vertical and horizontal coordinates of the charged particles per unit time, and the calculation is performed by the following equations (7) and (8).

--------------------------------------(7)

-------------------------------------- (7)

---------------------------------(8)

---------------------------------(8)

V _t : Particle velocity at the chute tip (V ₃ ), (cm / sec)

α _s : Angle between the main principal stress and the shear line

g: Accelation due to gravity, (cm / sec ² )

After the drop of the charge in the chute (5) by the formula (7), (8) it is possible to know the horizontal and vertical coordinates of the charge particles over time, so that the position of the charge particles can be known, connected (I.e., repeating the calculation over time), the drop trajectory of the charge can be known.

In addition, when the charge falls, it falls with a certain thickness, so in order to take this into consideration, the flow of the charge is divided into upper and lower portions (the drop trajectory of the upper and lower flows is changed by the coefficient of friction). The middle part between the two flows is set to a high density flow, and the trajectory of the high flow is regarded as the drop trajectory of the charge.

On the other hand, the charged object falling on the calculated drop trajectory and dropped on the uppermost laminated surface is deposited by the charging continuation.

At this time, the angle of inclination in which the particles of the charge may be accumulated without flowing down from the deposition slope is called an angle of repose, and the angle of repose of the charge has a great influence on the shape of the charge stack.

The angle of repose consists of an angle of repose (center angle of retreat; α) of the furnace center slope and an angle of repose of furnace wall slope (the angle of repose angle (β)) with respect to the top of the charge deposit.

In order to develop a mathematical model for calculating the angle of repose (α, β), an experimental experiment using a blast furnace reduction model and a simulation using EDEM, a particle dynamics simulation tool (commercial program), were performed.

In the experiment using the blast furnace reduction model, a chute of 90 cm in length and 20 cm in diameter was used on a 1/5 scale of the actual blast furnace. The distance between the chute and the laminated surface was 50 cm, and the tilt angle was changed without the chute rotation. The charge amount was set to 25 kg, and the angle of repose of ore and coke was measured when the tilt angle was 45 °, 40 °, 35 °, 30 °, and 0 °.

Figure 4 shows the stacking shape of ore and coke according to the tilt angle change.

As a result, the maximum angle of repose was 35 ° for ore and 38 ° for coke.

The average values of the angle of repose angle α and the angle of repose angle β of ore and coke are shown in Table 1 below.

division
α
β
ore
34 °
17 °
cokes
37 °
28 °

In general, the value of the repose angle β in the furnace wall is small because the moving distance increases as the particles slide to the slope of the furnace wall due to the horizontal velocity of the charged particles.

Next, the angle of repose was measured using an EDEM.

Since EDEM can analyze individual particles, results similar to actual particle behavior can be expected. Particles have different moving distances depending on their shape factors. In the case of EDEM, since the spherical particles are analyzed, it is necessary to apply shape factors by adjusting the friction coefficient.

Friction coefficients used in EDEM include Coefficient of static friction and Coefficient of rolling friction. In EDEM, the value of the two coefficients is not determined, so it is necessary to find an appropriate value.

In order to measure the angle of repose according to the two coefficients, coefficient values were set as shown in Table 2 below.

division
Static friction coefficient
Cloud friction coefficient
case1
0.5
One
case2
0.76
One
case3
One
One
case4
One
2.5

The angle of repose was measured for each case. The particles dropped in the vertical direction.

Lamination of the particles was made in the shape of the largest angle of repose in case4, the largest value of the two coefficient of friction. The angle of repose for each case is case1; 26 °, case 2; 38.5 °, case 3; 44 °, case 4; It is calculated as 46 °, and the friction coefficient of case 2 is the most appropriate when compared with the actual lamination phenomenon.

Among the factors influencing the angle of repose, the variables applied to the mathematical model are shown in Table 3.

Angle of repose (°)
A _masx
Particle size (m)
D
Shape factor
F _s
Horizontal speed (m / s)
V _v
Blast furnace opening diameter (m)
d
Horizontal position when falling
X
a constant
C

In Fig. 5, the charge drop path and drop position (horizontal coordinate X) from the chute 5, the center direction angle α and the furnace wall direction angle β at the drop position can be confirmed.

The final angle of repose including the variables is shown in the following equations (9) and (10). The angle of repose cannot exceed the maximum angle of repose and is proportional to the particle size (D) and inversely proportional to the shape factor (F _s ). At this time, the index of particle size and shape coefficient was obtained from the scale model test results.

----------------------------------(9)

---------------------------------- (9)

---------------------------(10)

--------------------------- (10)

As mentioned above, in the case of the furnace wall repose angle β, there is an additional term. This is because when the charges fall from the furnace wall is accumulated in contact with the furnace wall, the angle of repose is reduced than normal. To take this into account, a term was added, with the dropping position of the charge as a variable.

Therefore, the drop trajectory from the time point at which the charge is discharged from the chute 5 to the position falling on the surface of the accumulated charge according to the above formulas (7) and (8) can be known accurately and easily. By (9) and (10), the blast furnace center direction angle α and the furnace wall direction angle angle β at the dropping position can be known accurately and easily.

The calculation of the equation is performed using a computer. When a user inputs a variable, a computer inputs and executes a program that performs a calculation using the formula. Therefore, the user can easily and accurately know the drop trajectory and the angle of repose of the charge by simply inputting a variable into the computer.

In this way, the drop trajectory and the angle of repose of the charges can be easily and accurately understood, and thus the distribution of the charges in the blast furnace can be more accurately understood. Accordingly, the charging of the charges can be properly controlled according to the operation conditions of the blast furnace, thereby making the blast furnace operation efficiency and productivity more accurate. This is improved.

1: blast furnace 2: bunker
3: Hopper 4: Peter Spout
5: suit

Claims (9)

delete A hopper discharge speed calculating step of calculating a speed of the charge discharged to the hopper outlet;
A feeder spout discharge rate calculation step of calculating a speed of the charge discharged to the outlet of the feeder spout using the hopper discharge rate of the charge calculated in the hopper discharge rate calculation step;
A chute discharge rate calculation step of calculating a rate of the charge discharged to the outlet of the chute using the feeder spout discharge rate of the charge calculated in the feeder spout discharge rate calculation step;
A drop trajectory calculation step of calculating a position of the charge according to time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step;
Including;
In the hopper discharge speed calculation step, the flow rate of the charge (G),

ego,
The charge discharge rate (V _1v ) at the hopper outlet,
A drop trajectory calculation method for a blast furnace charge, wherein V _1v = G / A.
(G: mass flow rate, kg / s
ρs: density of particles. kd / m ³
d _eff : effective diameter of the discharge orifice, m
g: accelation due to gravity, m / s ²
β: acute angle between the cone wall and the horizontal, radian
A: hopper exit cross section, m ² ) A hopper discharge speed calculating step of calculating a speed of the charge discharged to the hopper outlet;
A feeder spout discharge rate calculation step of calculating a speed of the charge discharged to the outlet of the feeder spout using the hopper discharge rate of the charge calculated in the hopper discharge rate calculation step;
A chute discharge rate calculation step of calculating a rate of the charge discharged to the outlet of the chute using the feeder spout discharge rate of the charge calculated in the feeder spout discharge rate calculation step;
A drop trajectory calculation step of calculating a position of the charge according to time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step;
Including;
The feeder spout outlet speed (V _2v ) of the charge in the feeder spout discharge rate calculation step is V _2v = [V _1v ² + 2gH _d ] ^0.5 K _{f The} method of calculating the drop trajectory of the blast furnace charge.
(V _1v , V _2v : velocity at the entrance and exit of the down comer, respectively), m / s
g: accelation due to gravity, m / s ²
H _d : height of feeder spout, m
K _f : correction factor for collisions A hopper discharge speed calculating step of calculating a speed of the charge discharged to the hopper outlet;
A feeder spout discharge rate calculation step of calculating a speed of the charge discharged to the outlet of the feeder spout using the hopper discharge rate of the charge calculated in the hopper discharge rate calculation step;
A chute discharge rate calculation step of calculating a rate of the charge discharged to the outlet of the chute using the feeder spout discharge rate of the charge calculated in the feeder spout discharge rate calculation step;
A drop trajectory calculation step of calculating a position of the charge according to time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step;
Including;
In the chute discharge rate calculation step, chute exit velocity (V ₃ ) of the charge is
V ₃ = [ω ² cosα (cosα + μsinα) L ² + 2g (sinα-μcosα) L + (V _2v sinα) ² ] ^0.5 .
(ω: angular velocity, radian / s
μ: Coefficient of friction between the particles and the chute surface.
V _2v : velocity at the exit of the down comer, m) A hopper discharge speed calculating step of calculating a speed of the charge discharged to the hopper outlet;
A feeder spout discharge rate calculation step of calculating a speed of the charge discharged to the outlet of the feeder spout using the hopper discharge rate of the charge calculated in the hopper discharge rate calculation step;
A chute discharge rate calculation step of calculating a rate of the charge discharged to the outlet of the chute using the feeder spout discharge rate of the charge calculated in the feeder spout discharge rate calculation step;
A drop trajectory calculation step of calculating a position of the charge according to time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step;
Including;
In the drop trajectory calculation step, the position of the drop according to the time of the charge is made of the horizontal and vertical coordinates (X, Y) of the charge particles,
The coordinate value (X, Y) is

,

Drop trajectory calculation method of blast furnace charge, characterized in that.
(V _t : Particle velocity at the chute tip (V ₃ ), (cm / sec)
α _s : Angle between the main principal stress and the shear line
g: Accelation due to gravity, (cm / sec2)) The method according to claim 5,
The method for calculating the drop trajectory of the blast furnace charge, characterized in that to calculate the falling trajectory of the charge by repeatedly calculating the coordinate values (X, Y) continuously with time. A hopper discharge speed calculating step of calculating a speed of the charge discharged to the hopper outlet;
A feeder spout discharge rate calculation step of calculating a speed of the charge discharged to the outlet of the feeder spout using the hopper discharge rate of the charge calculated in the hopper discharge rate calculation step;
A chute discharge rate calculation step of calculating a rate of the charge discharged to the outlet of the chute using the feeder spout discharge rate of the charge calculated in the feeder spout discharge rate calculation step;
A drop trajectory calculation step of calculating a position of the charge according to time during the drop using the chute discharge rate of the charge calculated in the chute discharge rate calculation step;
And a repose angle calculating step of grasping the drop position of the charge from the drop trajectory calculated in the drop trajectory calculating step and calculating a repose angle of the charge at the drop position. The method of claim 7,
In the angle of repose of the charge,
The angle of repose (α) in the center of the furnace is

ego,
The angle of repose (β) in the furnace wall direction is

Drop trajectory calculation method of blast furnace charge, characterized in that.
(A _mas : maximum angle of repose (°), D: particle size (m), F _s : shape factor, d: blast furnace diameter (m),
X: Horizontal position when falling, C: Constant) delete

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