Fig.1.Evolution of the iron and slag levels in the hearth during the tap cycle.
Fig.2.Simulated iron and slag levels during a typical tap cycle
with a sitting dead man (ca 1, solid lines) and a ca
where the effective cross ctional area A e is 20% small-
er (ca 2, dashed lines).
Table1.Effect of production, initial iron level, dead-man voidage, hearth diameter and tap interval on the slag delay for the ca with
a sitting dead man.
h is the immersion depth of the dead man in the liq-uid pha (slag or iron). If the downward-acting pressure profile, the iron and slag levels and the dead-man voidage are known, the vertical position of the dead-man bottom,, can be calculated at each point of the cross-ctional area from
(5)
p b,sl max ϭr sl g (1Ϫe )(z sl Ϫz ir ) and p b,ir max
ϭr ir g (1Ϫ). Introducing A dm as the cross-ctional area of the dead man, the volumes of iron and slag in the hearth as well as the free volume can be calculated by
..................(6a)
..................(6b)
.......................(6c)
佐治亚理工
where superscripts max and min denote the maximum or minimum values of the variables. The areas A and A illustrated in Fig. 4. Given the iron and slag levels and a pressure profile p d , the dead-man position can be straight-forwardly determined by Eq. (5), and the volumes by Eqs.(6a)–(6c) if the hearth geometry is known. The inver problem, however, where the volumes of iron and slag are known, but their levels as well as the dead-man position are not, is considerably more complicated. As a rule, iterative techniques have to be applied to solve the unknowns.The Downward-acting Pressure
Equation (5) shows that the downward-acting pressure,, has a strong influence on the position of the
dead man. It consists of the pressure of the burden, p s , reduced by the lifting pressure of the gas flow D p g and the supporting ef-fect of the wall, D p w , i.e.,
p d ϭp s ϪD p g ϪD p w (7)
迈克尔杰克逊英文The burden pressure can be estimated if the (average) posi-tion of the cohesive zone and the holdups of iron and slag below the cohesive zone are known. Denoting the liquid holdup (volume fraction) by x , the bulk densities of the bur-den and coke by r s and r c , respectively, and the vertical po-sitions of the cohesive zone and the stock level by z , respectively, the static pressure of the burden at the dead-man bottom is
p s ϭr s g (z top Ϫz cz )ϩ(r c ϩr ir x ir ϩr sl x sl )g (z cz Ϫz sl )
ϩr c g (z sl Ϫz dm )..................................................(8)The lifting pressure of the gas flow can be calculated from the blast pressure (measured in the bustle main), p bl , and at the top gas pressure, p top , considering the pressure loss in the tuyere (no)
(9)
where r g is the density of the blast, w t is the (computed) gas velocity in the tuyere no and z t £1.1
is the loss factor of the outlet. The supporting effect of the wall is difficult to determine accurately; here it is roughly estimated by as-suming that it reduces the downward-acting pressure by a certain fraction, g , i.e.
D p w ϭg (p s ϪD p g ) (10)
The radial distribution of p d at the bottom of the furnace is also difficult to estimate, since it is affected by the radial distributions of burden and liquid holdup, wall friction, ef-fect of the raceways, etc . However, from disctions of quenched furnaces it is known that the dead man is likely to float higher near the wall beneath the raceway zones.Therefore, instead of attempting to rigorously estimate the
radial distribution of the pressure, an overall term, p
¯d , (inde-pendent of r ) is calculated from Eq. (7) and ud in a sim-ple parameterized model to describe the radial profile of the downward-acting pressure that shapes the bottom of the dead man:陶喆i love you
D p p p w g bl top t g t 2
2
ϭϪϪζρV A A dz z z fr dm hb
min dm
max ϭ
冠词练习题
Ϫ∫
[]V A A dz z z sl dm ir
sl
residual
ϭ
ϪϪ∫
英标读音
[()]1εV A A dz z z ir dm hb
min ir
o bϭϪϪ∫[()]1εz p p p z z z p p p p z p p p sl d sl d b,sl max
ir sl ir sl ir d
ir b,sl max d b,sl max hb d b,sl max b,ir max if 0if if ϭϪϪՅՅϩϪϪϪϽՅϩϾϩρερρρεg g ()
()()11听录音
exerci怎么读Fig.3.Forces acting on the dead man.
Fig.4.Cross-ctional areas in the ca of a floating dead man.
(11)
where R is a scaling factor, e.g., the radius of the unworn
hearth at the start of the furnace ’s campaign. Thus, the pres-sure is assumed to be constant within a central region and (for a Ͼ0) to decrea as the wall is approached. The ex-pression (11) is extremely flexible, which is en in Fig. 5that illustrates the arising dead-man bottom pro files (in the iron pha) for some parameter values.
2.4.
3.Illustrative Examples
To illustrate the effect of a floating dead man, a tap cycle with similar properties as the first example ca in Subc.2.3.2 (solid lines in Fig. 2) was simulated. The dead-man shape was modeled by the parameters a ϭ190kPa, r 0ϭ2ϭ4m and n ϭ2 in Eq. (11) to qualitatively mimic the find-ings from hearth disctions 20)and the hearth geometry was considered a cylinder with a diameter of 8m and sump depth of 1.5m. Two different floating states were simulated
with p
¯d ϭ120kPa (ca 1) and p ¯d ϭ100kPa (ca 2). The lower panel of Fig. 6depicts the predicted evolutions of the liquid levels (ca 1 with solid lines and ca 2 with dashed lines). As can be en, the slag delay in ca 2ϭ15.1min) is considerably shorter than in ca 1ϭ38.7min) and very much shorter than in the sitting dead-man reference ca of Subct. 2.3.2 (t sl ϭ50.9min).The liquid levels follow the general pattern illustrated in Fig. 1, but the amplitude clearly decreas with increasing dead-man floating degree. An interesting obrvation is that the descent rate of the iron level decreas as the level reaches the taphole even though the out flow rate is con-stant. The upper panel of Fig. 6 depicts the dead-man posi-tions at the start of slag out flow for the two cas. The re
a-son for studying the conditions at this moment is that the slag delay is mainly in fluenced by the difference in free vol-ume between the moment of slag flow start and the end of the tap.Simulation
Two industrial blast furnaces have been monitored and the erosion and buildup pro files of the hearths of the fur-ments in the lining since the campaign starts.5,21)Con-siderable variations in the slag delay were obrved in BF B, showing a strong negative correlation with changes in the volume of the hearth. In BF A no correlation between slag delay and hearth volume has been obrved, even though the hearth volume has varied considerably.21)The measured slag delays and the estimated hearth volumes of the furnaces have been depicted in Fig. 7. The difference between the furnaces is believed to depend mainly on the floating state of the dead men: In BF B indicators show that the dead man floats during parts of the campaign, while there are no such indications in the data from BF A.21)In what follows, the model described in Sec. 2 is applied on data from BF B.
3.1.Simplified Model 3.1.1.Setup影子内阁
A simple model of the hearth was formulated to be able
p r p r r p a r r R r r n
d d d ();;ϭՅϪϪϾ000
Fig.5.
Resulting dead-man bottom pro files for some parameter values in Eq. (11) for a dead man with e ϭ0.35 sub-merged in the iron bath.
Fig.6.
Upper panel: Hearth geometries and dead-man positions at slag flow start for two simulated examples, p ¯d ϭ120kPa (ca 1, left half) and p ¯d ϭ100kPa (ca 2, right half). Lower panel: Evolution of the iron and slag levels for ca 1 (solid lines) and ca 2 (dashed lines).
Fig.7.
Change in hearth volume (dotted line) and slag delay (solid line) for BF A (upper panel) and BF B (lower panel).
