The present invention relates to a process for determining charging schedule of
a blast furnace for controlling stable operation thereof. In particular, it relates
to simulation of the burden distribution in blast furnaces, so as to obtain a
satisfactory charging schedule, that will provide stable operation.
BACKGROUND OF THE INVENTION
The operation of blast furnaces is largely governed by the distribution of the
gas flow inside the furnace. This has a pronounced effect on the reactions, the
thermal conditions as well as the pressure gradients in the lumpy zone. These
factors in turn affect the smooth working of the furnace. Control of the blast
furnace operation thus vests in the gas flow pattern which can be only
indirectly manipulated by the distribution of the burden, so as to adjust the
distribution of the porosity in the various layers. In addition, the burden
distribution directly influences the structure of the cohesive zone, where most
of the chemical reactions occur.
Direct measurement of various in-furnace phenomena has been studied with the aid of
advanced monitoring and recording techniques. The iron and steel institute of Japan1 have
reported this. Data is required from comprehensive instrumentation for measuring (1) the
geometry of the cohesive zone, (2) the distribution of the gas velocity, (3) the flow of the
molten hot metal and slag, (4) the movement of the cohesive zone. Detectors to measure
some of these furnace variables have been developed, such as (1) vertical probes for the
cohesive zone, (2) sampling of the ascending reducing gases and (3) the descending
solids, (4) profilometers for the blast furnace burden1 etc. The above-burden and in-
burden probes record temperatures and gas compositions at different radial positions, from
which information about the gas and burden distribution can be inferred. Measurements
from such detectors have enabled stable operation of large blast furnaces.
However, the instrumentation cited in the previous paragraph is not available in most
commercial blast furnaces. A number of experimental results have been reported. Small-
scale experiments, with a sector of the blast furnace2, 3 constructed according to
dimensional similarity, provide an insight into the process of burden formation. Full-scale
models2, 4 provide more reliable results, but even here a degree of approximation is
inevitable, as it is necessary to work with a sector model (in order to obtain a view of the
burden section). This effectively precludes experimental models of a rotating chute,
because the swirling component of the discharge velocity cannot be accommodated in a
sector model.
The large quantities of the charge materials required in full-scale experiments, means that
such studies are expensive and time consuming. Scaled down experiments are simpler,
but a fresh experiment has to be performed for every change in the charging pattern,
material properties such as particle size, or the position of the stock-line, or in the rate of
descent of the burden (matl, T, rev, dprt, helll, hell2, rdchlst, dscnlst).
The most convenient approach is to simulate the trajectories of the charge particles as they
fall from the chute, by numerical calculation. After the particles have been tracked to the
point of impact with the stock-line, the formation of the heap has to be computed,
considering segregation of the material and rolling of the particles1,5. Since this is a purely
numerical technique, specific values have to be assigned to a large number of parameters
such as the coefficient of restitution and the coefficient of friction of individual particles
with individual surfaces, repose angles, particle sizes etc. (corr, mu, rpang, dprt (1/2/3).
The specific values required for the numerical solution, such as the coefficients of
restitution and friction, and the repose angles of the various charge materials have to be
experimentally determined. In addition there are a number of empirical parameters, such
as the radial distribution of the burden descent rate, whose value has to be given. For this
reason, pilot experiments are required to validate the theoretical solution. However once
that is done a programmed processor can be used to predict the burden distribution for
different charging schedules, on line.
The high temperatures and abrasive nature of the materials in an operating
blast furnace make direct measurement of the internal state of the furnace
difficult, although some modern furnaces have been equipped with
sophisticated instrumentation for this purpose.
SUMMARY OF THE INVENTION
The main object of the present invention is to provide a convenient way to
quickly explore the effect of changing parameters on the burden distribution.
The applicability of this approach is confined within a judicious range of the
bench marked condition. For example the value assigned to the blockage
parameter of the dynamic arch holds good only within a reasonable range of
the charge weight.
The present invention thus provides a process for determining charging
schedule of a blast furnace for controlling stable operation thereof by obtaining
information regarding prediction of concomitant gas distribution in the shaft of
the blast furnace for controlling the blast operation, said process comprising
the steps of determining the initial discharge velocity for charging material in
incremental steps, determining the bounced trajectory of the particles of the
burden after striking the throat armor or furnace walls estimating heap
formation after the charge particles reach the stock-line, estimating ore/coke
ratios along the radius of the blast furnace and obtaining a charging schedule
based on the determined parameters.
BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS
The invention can now be described in detail with the help of the figures of the
accompanying drawings in which:
Figure 1 shows nomenclature of geometric variables.
Figure 2 shows the initial discharge velocity in the dynamic arch theory, and in the
hydrostatic head formulation.
Figure 3 shows bounced velocity in the Paul Wurth rotating chute.
Figure 4 shows heap formation at the stock-line (kase = 0,-2).
Figure 5 shows a simulated burden distribution, together with calculated ratios.
Figure 6 Enlarged view of the simulated burden distribution, showing the charges filled
with close packed circles of the particle sizes.
DETAILED DESCRIPTION
The simulation of the burden distribution can be done by tracing the path of descent of the
charge, and the formation of the heap at the stock-line in a processor (computer). This
method can be used to simulate the burden distribution in any blast furnace. The
geometrical and other operating parameters are specified through a set of interactive
menus. The list of variables for the geometrical parameters (hell to horl6) have been
shown in Table 1 and shown schematically in Figure 1.
The processor can be programmed to simulate the burden for a single charge or for a set
of upto 10 individual charges. This has been shown in the charging schedule in the list of
variables (Table 3) (Mat I, kolr, T, Rev, 10-0), with a provision to repeat the set a number
of times. Calculations of both the movable throat armor as well as the Paul Wurth rotating
chute are supported, which includes the effect of the swirling component of the velocity.
The radial distribution of the burden descent can be specified in the program (Table 4).
The system automatically lowers the burden by an appropriate amount between charges
(rdchlst, dscnlst), so as to retain the vertical probe at a constant level (horl6, hell/12).
The individual ore, coke, sinter layers, as well as the ore/coke ratios are graphically
displayed (Figure. 5).
A provision has been kept to incrementally change some of the empirical parameters (e.g.
kfact in Table 1 and vfact in Table 2). This is required in order to calibrate these
parameters against observed results.
The procedure followed is described in the following sections. Section (1) describes the
initial discharge velocity. Section (2) describes the bounced path of the particles after
striking the throat armor or the walls. Section (3) treats the formation of heaps at the
stock-line. Section (4) describes the ore/coke ratio.
1. INITIAL DISCHARGE VELOCITY
This can simulate the particle trajectories, based on two theories. The theory for the
discharge velocity based on the dynamic arch is described in Appendix 1. Under this
theory, the discharge velocity is governed by the opening of the large bell. It is possible to
simulate the effect of increasing bell opening, by adjusting the values for the initial, final
and incremental bell opening. The software will then show the trajectories of the particles,
starting from the initial bell opening and incrementing the bell opening in step upto the
final bell opening. As the bell opening increases, the discharge velocity is predicted to
increase, causing the trajectory to spread further outwards from the center.
The program can alternatively be switched, to calculate the initial discharge velocity based
on the hydrostatic head of the burden materials in the hopper. When the burden begins to
flow out, the particles are assumed to be ejected with a velocity governed by the pressure
of the material in the hopper (the hydrostatic head). As the hopper empties, the
hydrostatic head falls, so that the discharge velocity is reduced, and the trajectory comes
closer to the centre. This process is discretised into steps, and the velocity for each step is
assumed constant throughout that step. The volume discharged in each step is assumed
constant, neglecting the effect of the sloping hopper wall, and is taken as a proportion of
the full hopper volume multiplied with the ratio of the step increment to the total hopper
height. The trajectory of the particles is calculated for each step, from the full hopper
condition (maximum velocity), to the empty hopper condition (minimum).
Passing through the bell opening, the particles move along the large bell to its edge, and
attain an initial velocity for free fall in the throat space. The materials then strike the
burden surface, the throat wall or the movable armor, to form a burden profile. The
incremental discharge volume is shown at each step. Since the material discharged in the
previous steps governs the burden profile, this shows the skewing of the peak away from
the centre as the bell opening increases for the dynamic arch theory. For the hydrostatic
head formulation, the skewing is towards the centre, as the velocity of discharge tapers off
as the hopper empties. This has been shown in Figure 2.
In the case of simulating the Paul Wurth mechanism, the flags are set to bypass the
process of incremental volume discharges, and the entire charge volume is set to follow a
single trajectory.
The quantities (halbl/2/3) in the dynamic arch theory can be assigned suitable values in
the operating menus (Table 1), depending on the user perception of the accuracy required.
A larger number of steps (with a smaller step increment) will increase the computation
time. A similar consideration applies to the quantities (hh 1/2/3), in the hydrostatic head
theory.
The quantities (kfact 1/2/3) are the empirical blockage parameters in the dynamic arch
theory, and (vfact 1/2/3) are the velocity factors in the hydrostatic head formulation. The
software can be programmed to increment these parameters in small increments and show
the concomitant trajectories. This provision is provided in order to calibrate with observed
data. Once an appropriate values for these factors have been finalized, the process for
incremental checking of these values can be bypassed.
Thus the changed trajectories for each incremental step are computed. By this means, the
observed splaying of the descent trajectory ran be faithfully simulated.
2. THE BOUNCED TRAJECTORY
The trajectory of the particles in the throat is assumed to be governed by the equations of
free fall, neglecting the effects of the gas velocity. The procedure is straightforward in the
case of the movable throat armor, as the particles follow a parabolic path in 2 dimensions.
The total distance of fall is divided into segments of equal vertical drops of
(dfytot/nstept=9048/50=180.96=181 mm). As long as there are no impacts, the vertical
component of the velocity is incremented, depending on the total distance of fall (dfystp).
In case of impacts and subsequent bouncing off, the vertical step is adjusted so that the
following step commences from an equal segment spacing. The point of the start of free
fall is updated, and dfystp is computed from this updated start of free fall. The time in this
vertical segment is computed, depending on the incoming velocity and the drop in the
segment. This time is then used to derive the position increments from the updated start
of free fall (dfx/dfy). This will continue till all the (ntstep = 50) segments have been
completed, or the particle comes to rest on the stock-line. In each segment, the particle is
assumed to move in a straight line. The total number of steps (ntstep) is user specified.
While each segment of the trajectory is being computed, it Is checked for intersection with
the armor, the throat wall, and the stock-line. An intersection indicates an impact of the
particles with an obstruction. A normal to the surface of impact is constructed, and the
tangential and normal components of the incoming velocity are computed. The bounced
trajectory is calculated in the software, by reversing the direction of the normal component
and multiplying it with the appropriate coefficient of restitution (corsll-33), as shown in
Appendix 2.
The procedure is more complicated in the case of the Paul Wurth chute. The Corriolis
forces drive the charge particles up the side of the rotating chute, so that the discharge
point changes from the default location at the bottom of the chute. Moreover, since the
chute is rotating there is a swirling velocity, which is indicated by the Vz value (Vx is radial
and Vy is taken as the vertical component of the velocity). With only the radial and vertical
components (Vx, Vy), the particle trajectory will be confined to a radial section. Because of
the swirling component (Vz) however, the trajectory plane will be out-of-center (Figure 3).
The swirling component will increase, with increasing (nrpm), the speed of rotation of the
chute.
If the particle impacts against the wall of the furnace, the swirling velocity will result in the
particle bouncing into a trajectory whose plane is different from that of the incoming
trajectory. Depending on the magnitude of the swirling velocity (nrpm), this can result in
the particle bouncing repeatedly against the wall and tracing a spiral trajectory as it
descends.
The simulation of the trajectories in such cases is done with an appropriate modification to
the procedure shown in Appendix 2, as the path still lies in a vertical plane (albeit being
out-of center). The coordinates of the particle in its trajectory (PCENT 1) will contain
(X and Z) values. The elevation (Y) remains the same as in the axis symmetric case for the
movable throat armor, with the total distance of fall (dfystp) continuing to be incremented
in steps of (dfytot/nstep = 181 mm), till the particle bounces against an obstruction.
However, the calculation of the point of impact with the sloping walls of the furnace is an
exercise in solid geometry, involving the intersection of a line in 3D with the frustum of a
cone. When there is an obstruction, the bounced velocity has to be evaluated which
involves calculating the normal to the surface.
Fortunately, this procedure is simplified as the possible obstructing surfaces (Figure 1.
stock shield line, ring platform line, and the stock-line), are all axis symmetric.
1. Stock shield line p 103 (hor 9, hel 1) - p 104 (hor 9, hel 9)
2. Ring platform line p 104 (hor 9, hel 9) - p 105 (hor 10, hel 10)
3. Stock-line (hel 11, hel 12)
After calculating the normal, the tangential and the normal components of the incoming
velocity are evaluated. For this purpose the angle of incidence is found from 3 points, a
point on the incoming trajectory, the point of intersection and the point where the
normal intersects the centerline. Since these points do not lie in a radial plane, the
angle is estimated from the triangle defining the 3 points. The normal component of
the incoming velocity is modified by the appropriate coefficient of restitution of the
charge material and the obstructing surface, to give the normal component of the
velocity after bouncing. The transversal incoming velocity of the particle remains
unchanged. With these two velocity components, the straight segment of the trajectory
after bouncing is constructed. The procedure has been shown in Figure 3 and Appendix
3.
Checking for obstructions is performed during the calculation of each segment of the
trajectory. The stock-line is initially defined as a straight line, which may be horizontal
or tilted at an angle (hel 11, hel 12). However, as fresh material is dumped on the
stock-line, the corresponding line segments of the heaps are added into an array, which
represents the changed stock-line. The checking for intersections is done against each
of these line segments. If there is intersection here, then the trajectory is terminated
(corr = 0). The point of impact is stored, for use in the calculation of the burden heap.
When the path from the initial discharge impinges on an obstruction the particles trace
a bounced path. For the 2 dimensional case with a movable throat armor, this has
been described in the section 2. (THE BOUNCED TRAJECTORY) and in (Appendix.2).
For calculation of the bounced trajectory in 3 dimensions. This occurs with a Paul
Wurth discharge mechanism. This requires modification of the method in claim 2. It
has been described in the section 2. (THE BOUNCED TRAJECTORY) and in (Appendix.
3).
3. FORMATION OF HEAPS AT STOCK-LINE
The stock-line is defined as a list of points comprising the boundary of the previous charges
deposited on the initial stock-line (hel 11, hel 12). This list is updated each time a fresh
charge is added. There is a provision to consider the burden decent, which is specified as
a set of points in the input menus (rdchlst, dscnlst). At the end of the simulation of a
discharge, the updated stock-line list is lowered by the amount specified in the burden
descent, to form the current stock-line. The procedure for tracing the trajectory of the
particle upto intersection with the stock-line was described in the previous section.
Several rases can arise, depending on the angle of the stock-line segment at the point of
impingent. The particles will stick to the point of impingement (kase = 0, 1, -1) if the
stock-line slope is less than or equal to the repose angle, but in the case that it exceeds
the repose angle of the material, the particles will roll down the slope, either towards the
center-line side (kase = 2) or towards the wall side (kase = -2). The points where the
particles will come to rest are determined,
For (kase = 0, 1, -1) a cone defined by the repose angle (rpang), is constructed at the
point where the particle trajectory impinges on the stock-line, by measuring a distance of
(defdis = 100 mm) vertically upwards on the trajectory segment (ptrj 0-ptrj 1). The
intersection of the two sides of the cone with the stock-line list is also determined. The
charge is assumed to form an annular ring on the stock-line, with a cross section of the
cone.
The volume of material in this cone is estimated by drawing vertical slices and multiplying
with the circumference of the circle centered at the centre-line. This slicing procedure is
required, as the stock-line can comprise of numerous peaks and shallows. A sufficiently
large number of slices (100 say) are made, the depth from the repose cone to the
underlying stock-line is calculated for each slice, and multiplication with the circular
perimeter of each slice gives the incremental volume due to that slice. If the computed
volume (vdschrg 3) is less than the charge volume (vdschrg 1), the apex of the cone is
incremented by a further step increment (defdis), and the procedure is repeated, till the
entire charge volume is accounted for. The accuracy of this procedure is governed by the
setting of this parameter (defdis). A smaller value will require a larger number of
iterations, but will provide better accuracy.
For (kase = 2, -2), the slope of the stock-line at the point of impingement exceeds the
repose angle of the material, and slopes towards the center-line or towards the wall side.
The point where the particles will come to rest are determined by tracking the stock-line till
an opposing slope is encountered, where the particles can come to rest. As the particles
accumulate at this local minimum elevation, the profile of the accumulated charge is
constructed by drawing parallel lines at the slope of the repose angle. These lines are
drawn by measuring off (defdis) distances from the lowest point, along the incoming stock-
line slope. The slicing procedure is repeated to calculate the incremental volumes. As
before, the process continues till the entire charge volume is accounted for. Figure 4
illustrates the procedure for two cases (kase = 0, -2).
Estimating the heap formation after the charge particles reach the stock-line involves
estimating the change in the inter-surface between successive charges for ail the previous
charges, as the burden descends in the blast furnace, to arrive at the current stock-line.
4. ORE COKE RATIO
Figure 5 illustrates a burden distribution that has been simulated by the software. There is
a provision to draw the distribution with each charge color coded to a pre-selected
specification. Where monochromatic representation is required, the individual charges may
be filled with circles drawn to the specified particle sizes (dprt). This has been shown in
Figure 6, which is an enlarged representation of the burden in Figure 5.
The simulated burden distribution makes it possible to obtain various other numerical
values that are useful for predicting the behavior of the blast furnace. The Figure by the
side of the burden distribution has been obtained by segregating the individual ore, coke
and sinter charges. This makes it possible to see at a glance the total height of any of
these materials, at a specific radius. In the composite Figure of these individual
segregations, the final profile is the same as the top of the burden distribution, but the
arrangement below groups the charges so that all the ore, coke, and sinter layers are
together.
The set of 4 Figures at the top, display the segregated charge data scaled as a ratio with
the total height of materials at a radius. This means that the top line will be flat at 100 %.
The set of 4 Figures at the bottom displays the ratio of a particular material to the amount
of coke at a particular radius. Such visual representations of numerical data, are
particularly useful to experienced operators, and enable them to anticipate problems. In
addition, various combinations of charges can be simulated, in order to form a strong
centre.
The simulation exercise demonstrates the sensitivity of the burden profile to changing
notch positions of the throat armor, or the chute angle of a Paul Wurth mechanism. A
heap discharged at mid radius in one of the initial charges can seriously influence the
subsequent burden distribution by blocking the trajectory of subsequent charges. This
further increases the height of the heap at mid radius thus compounding the effect.
A logical extension of this work would be to use the simulation procedure, to conjure up a
charging schedule that matches a preset ore/coke radial distribution. This would eliminate
the trial and error simulation of various charging schedules in order to arrive at an
acceptable solution. Instead the operator would specify the central working condition that
was desired, and the software would provide the ideal charging schedule.
We consider burden materials present in a large bell hopper. The large bell lowers at a
prescribed speed from a closed position to reach a position corresponding to a
prescribed large bell stroke. According to experimental results, at an early stage of this
large bell descent, there exists a period when no particles flow out. This period lasts
until the horizontal clearance at the lower edge of the hopper wall reaches about four
times the mean size of the burden to be discharged. When the burden begins to flow
out of this hopper, a dynamic arch contacting both the hopper wall and the large bell, is
formed at a level close to the edge of the hopper wall. Above the dynamic arch,
particles constituting the burden interfere with each other as they descend slowly
towards this arch. Passing through this dynamic arch, the particle fall freely, till they
reach and strike the large bell. Subsequently they move along the large bell to its
edge, and attain an initial velocity for free fall in the throat space.
It is assumed that the average fall distance is 0.5*hh. Assuming non-elastic collision of
particles with the large bell surface, we obtain the initial velocity ue*sin (thetarl) of
particles moving along this surface, and the velocity at the edge of the large bell as
follows.
Xx=sin (thetarl) -muf*cos (thetarl)
muf dimensionless [Coeff friction particle / bell surface ]
yy=2.0*g (lsld+0.5*hh*sin (thetarl))
lsld mm [Sliding dist after strike bell]
vd=sqrt (ue*sin (thetarl) * ue sin (thetarl) + yy*xx)
Apendix 2. Procedure for calculating the bounced path in 2D.
Let us assume that in the 31st segment of the parabolic trajectory [PO-P1], there is an
impact with the wall of the furnace [P2-P3]. The drop in each segment [181 mm] is
obtained from the total distance of fall and the number of specified steps [dfytot=9048,
nstept = 50], and the drop from the bell lip to the start of this segment [PO] is
dfystp = (31-l)*9048/50=5429 mm].
+
PI gives the Cartesian coordinates of the planar projection, at the termination of the
31st segment. The planar coordinates of the point of intersection, is updated as the
end point of the trajecectory before impact [PI]. The free fall upto the point of impact
had started at an elevation of [hel40=36583 mm], [at the lip of the bell].
The vertical component of the velocity depends on the initial vertical
Velocity [2597 mm / sec], and the distance of free fall upto the point of impact (36583-
[31288=5295 mm] [vdy3=sqr (2.597 A 2+2 * 9.81 * 5. 295.) = 10. 518 m / sec]
The planar total velocity is the vector sum of the X & Y components:
[vd3=sqr (2.029 A2+10.518A2) = 10.711 m / sec]
The angle from the trajectory at the point of impact, to the impeding wall is:
[pangle2=169 deg; measured in the anticlockwise direction]
And the angle from the positive X axis to the normal to the wall is:
[panglen=186 deg; measured in the anticlockwise direction]

The bounced trajectory is obtained by measuring a line along the furnace wall from the
impact point P1, proportional to the transverse velocity [vdt 3] and then measuring a
line normal to the wall proportional to the normal velocity [vdn 3]. Extending this line
till intersection with the end segment horizontal, gives the point PO' which is the start of
the next section of the trajectory.
Appendix 3. Procedure for calculating the bounced path in 3D.
Let there be an impact in the 31st segment. The starting point of the 31st segment
corresponds to the termination point of the 30th segment, and this is stored as the
point (PCENTO: 3103, 31335, 22311. The termination point of the 31st segment is
calculated [PCENT1=3137, 31154, 22781]. A point on the line [PCENTO-PCENT1] can
be expressed parametrically as: X=3103+34*kl; Z=2231+47*kl : Y = 31335 -
181*kl
The radius of the wall at any level can be obtained form the geometrical parameters of
the furnace.

A value of (0<= kl <= 1), and (0<= k2 <=l), would indicate and intersection of the
trajectory segment with the frustum of the cone defining the furnace wall. Otherwise,
the segment does not intersect, and the simulation can proceed to the following
segment. In this case we have: kl= .2480; k2= .2049. Solving for the point of
intersection we have:
X = 3112; z = 2243; Y = 31288
The normal to the surface of the cone at a level (Y = 34575 - 16032 - 16032*k2) will
meet the centre line at (PNCNT) : X = 0; Z=0, Y = 34575 - 16032*K2-(3487+1701*
k2)*(5188-3487) / (34575-18543) = 34205-16212*k2 = 30883
Now 3 points are known, the starting point of the segment of the trajectory (PCENTO),
the point of impact (PCENT1) and a point on the normal (PNCNT). This defines the
plane of the incoming particle trajectory, and also the plane of the bounced centrifugal
trajectory. The angle of incidence is evaluated from the triangular area (PCENTO-
Now the bounced velocity, after impact, can be calculated. Prior to impact, the velocity
components were evaluated as: (VDX1 / VDY30 / VDZ1 = 2029, 10518, 2778 mm / sec
say). The total = sqrt (2029**2 +10518**2 + 2778**2) = 11.066 m / sec.
The tangential component parallel to the impeding wall, remains unchanged after
impact, and is: vdt 3=vd30*sin (panginc) = 11066*sin (84.29) = 11.011 m/sec. And
the component normal to the impeding wall, after impact is: vdn3=cors*vd3*cos
(panginc)=0.3*11066*cos (84.29)^0.330 m/sec.
Next, a point on the normal is located by dropping a perpendicular from the start point
PCENTO, on to the normal. This will simply divide the line PCENT1-PNCNT, in a ratio
of: = 49.3356*0.0994626/3857.4108=0.001272
The normal point (PNCNT) is now updated in proportion to: Pncnt [x] = PCENT1 [x]+
(PNCNT [x]-PCENTl [x]) * prp = 3112+ ( 0- 3112) *0.001272=3108
Pncnt [Y]=PCENT1 [Y] = (pncnt [YJ-PCENTl[Y])*prp
= 31288+ (30883- 31288)*0.001272=31287
Pncnt [Z]=pcentl [z]+ (PNCNT [Z]-PCENT1 [Z])* prp
= 2243+ ( 0- 2243)* 0.001272 = 2240
The distances, are also updated.
a3 (distance PCENT1 PCENT1 Pncnt) = 5.0990
a4 (distance Pncnt PCENTO) 49.6588
In the case of perfectly elastic impact [cors=l], the angle of incidence becomes equal
to the angle of reflection. However, for non-elastic impact, the angles are unequal.
The plane of the incident segment of the trajectory, the normal, and the reflected
trajectory segment, is coplanar. To find the reflected line, the points PCENTO and
Pncnt are used. The point Pncnt was redefined as the foot of the perpendicular from
PCENTO onto the normal. This line is extended to Prefl [say], so that PCENTl-Prefl
defines the reflected path. Then, the ratio of the line PCENT-Pncnt / PCENTl-Pncnt will
equal the ratio of the transversal velocity to the normal velocity before impact. On
similar lines, the ratio of the line Prefl-Pncnt / PCENTl-Pncnt will equal the ratio of the
transversal velocity to normal velocity after impact.
Prefl-Pncnt-Pcentl-Pncnt = Prefl-Pncnt / a3 = vdt3 / vdn3
Prefl-Pncnt = a3 * vdt3 / vdn3 = 5.0990 * 11011 / 330 = 170.1366
The points Prefl, Pncnt & PCENT0 are collinear. The length of the line Prefl-Pcent 0 =
the line Prefl-pncnt + the line Pncnt-PCENTO
= Prefl=Pncnt + a4 = 170.1366+49.6588 = 219.7954
The ratio of Prefl - Pcent 0 / Pncnt - Pcent 0 = prpl. Then Prpl = 219.7954 / a4 =
219.7954 / a4 = 219.7954 / 49.6588 = 4.4261
The coordinates of the point Prefl, defining the reflected path, can now be calculated,
as PCENT0 and Pncnt are known.
PCENT0 [3103, 31335, 2231], Pncnt [3108, 31287, 2240]
Prefl [X] = 3103+ (3108 - 3103 + 4.4261 - 3125
Prefl [Y] = 31335 + (31287-31335) * 4.4261=31123
Prefl [Z] = 2231 + (2240 - 2231) * 4.4261 = 2271
Since the point of impact [PCENTl 3112, 31288, 2243], and the point on the reflected
trajectory [Prefl 3125, 3125, 31123, 2271] are known, and also the total velocity after
impact [vd3 11016 mm/sec, the Cartesian components of the velocity can be evaluated:
a3 = (distance PCENTl-Prefl) = 167.8630 mm
dum - (Prefl [Y] - PCENTl [Y]) / a3 = 931123-31288) / 167.8638—0.982939
vdy3 = vd3*dum = 11016* (-0.982939) = - 10828 mm/sec
dum = (Prefl [Z] - Pcentl [Z]) / a3 = (2271-2243) / 167.8630=0.1668026
vdz3=vd3* dum = 11016* (0.1668026) = 1837 mm/sec
The coordinates of the point of impact are stored in horO, helO, helO, hzcO. This is also
updated into the new start point of the next segment of the trajectory [PCEIMT0]. The
velocities after impact are similarly also updated into the starting velocity of the next
segment [vdxl / yl / zl].
+
The trajectory in each segment is checked for intersection with each of the following
lines. It is possible that the trajectory impacts against more than one of these lines, in
which case, the first [closest] impact point is considered, as the others will be masked.
FLGINT is a flag, which indicates the active surface against which impact has occurred.
FLGINT =
1; Check intersection with Movable armour line pl01-pl02
2; Check intersection with Stock Shield line pl03-pl04
3; Check intersection with Ring Platfrm line pl04-pl05
Charging Schedule Variables:
5C# : Indicates the serial number of the charge
Matl : Indicates the nature of the charged material with the code
Ore=l, Coke=2, Sinter=3.
Kolr : Indicates the colour in which the trajectory, and the burden heap for this
charge will be drawn. The colour code is: 1: Red, 2: Yellow, 3: Green, 4:
Cyan, 5: Blue, 6: Magenta, 7: White, 8: Black, 9: Matt, 10: orange.
T : Specifies the weight of this charge in metric tones
Rev : This is a reversing option, to indicate whether the charging should
proceed in the order of 10 to 0 [Rev=l], or from 0 to 10 [Rev=2].
10-0 : The program can simulate both the movable throat armour, as well as the
Paul Wurth rotating rotating chute. In the former case, the columns 10 to
0 indicate the north position of the armour, and the values in the columns
indicate the proportion of the total charge [T] to be discharged at these
notch settings. In the latter case, the column headings 10 to 0 indicate
equal annular area rings at the stock-line and the column values are the
respective proportions of the charge.
' Chute angle Variables:
The chute angles to form 10 equal annulus area rings at the stock-line, when simulating
the Paul Wurth Chute. These are the chute angles with the vertical, given in one tenth
of degrees. These can be specified by the user. There is also a provision for these
values to be automatically calculated by the program.
Chute Angles [banglst]:
Ring# 10 987 6 5 43210
(485 452 419 386 353 320 287 254 221 177 111 : onetenth dg)
Burden descent Variables:
The burden descent is specified by 2 parameters. The first gives the radii at which the
descent is specified, and the second gives the amount of descent at that radius. The
descent at intermediate radii is interpolated from the descents specified at the spanning
radii.
Radii for specifying burden descent [rdchlst]:
( 5188 3838 3637 3412 3165 2901 2620 2327 2024 1605 0 : mm hor rad )
Amount of burden descent at the specified radii [dscnlst]:
(1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 1000 : mm descent )
REFERENCES Blast Furnace Phenomenon
and modeling.
1. The iron and steel Institute of Japan (1987) Y. Omori
(1987) 302
2. Blast Furnace Iron Making. (1991) 121 (1991) Anjan De
3. Proc of 3rd Process Technology Conf.
Pittsburg (1982) 166 (1982) J.J. Proveromo & J.W. Hinka
4. Trans. ISIJ 19 (1979) 667 (1979) K. Narita etal
5. Proc of 49th Ironmaking
Conf. Detroit (1990) 263 (1990) T. Inada etal
WE CLAIM:
1. A process for determining charging schedule of a blast furnace
for controlling stable operation thereof by obtaining information
regarding prediction of concomitant gas distribution in the shaft
of the blast furnace for controlling the blast operation, said
process comprising the steps of :
- determining the initial discharge velocity for charging
material in incremental steps ;
- determining the bounced trajectory of the particles of the
burden after striking the throat armor or furnace walls
estimating heap formation after the charge particles reach
the stock-line;
- estimating ore/coke ratios along the radius of the blast
furnace; and
- obtaining a charging schedule based on the determined
parameters.
2. The process as claimed in claim 1, wherein said determination
step of initial discharge velocity comprises computation of
changed trajectory for each incremental step for simulating the
descent trajectory faithfully.
3. The process as claimed in claim 1, wherein the bounced
trajectory of the particles of the burden is determined in two
dimensions.
4. The process as claimed in claim 1, wherein the bounced
trajectory of the particle of the burden is determined in three
dimensions.
5. The process as claimed in claim 1, wherein estimating the heap
formation comprises estimation of the change in the inter-
surface between successive charges for all the previous charges,
as the burden descends down to arrive at the current stock line.
6. A process for determining charging schedule of a blast furnace
for controlling stable operation thereof, substantially as herein
described and illustrated in the accompanying drawings.

The invention provides a process for obtaining charging schedule for
improved operation of a blast furnace by simulating the burden
distribution therein. The burden distribution in the blast furnace is
simulated for determining the initial discharge velocity for charging
material in incremental steps. The bounced trajectory of the particles
of the burden is determined. Hcap formation after the charge
particles reach the stock line is estimated. The ore/coke ratios along
with the radius of the blast furnace are estimated for providing
information regarding prediction of concomitant gas distribution in
the shaft of the blast furnace for controlling the blast furnace
operation. A charge schedule is obtained based on the determined
parameters.