2.4.2. Hearth Wear Profile

The internal geometry of the scale models and the computational domains that represent the hearth profile have usually been simple and regular in physical experiments and in CFD simulations. However, as discussed above, the inner hearth profile may assume different states, partly as a result of the dead-man state. When the hearth lining is cooled at the cold face, the local temperature and velocity of liquid iron in the vicinity of the hot face could become insufficient to keep the iron in liquid form. As a result, the iron may gradually solidify, forming a skull layer on the hot surface of the remaining lining. Therefore, as is often seen by observing the evolution of thermocouples embedded in the hearth lining, the internal geometry of the hearth varies during the campaign [54].

In view of the inherent coupling between liquid flow and heat transfer, an intensive circumferential flow leading to severe erosion is usually linked with an increased heat load on the hearth lining materials. Temperatures measured by thermocouples embedded in the hearth lining can therefore be utilized to predict the hearth wear profile. In practice, the 1150 ◦C isotherm is often regarded as the internal liquid–solid interface in the hearth. In order to estimate this isotherm, mathematical models where an inverse problem of heat transfer is solved have been proposed [31,54]. It should be stressed that 1150 ◦C is the lowest temperature at which carbon-saturated iron is present in liquid form, and consequently only heat conduction is solved in this kind of hearth wear profile model. A basic algorithm for estimating the hearth wear profile is outlined in Figure 10.

**Figure 10.** Basic algorithm of a hearth wear profile estimation model.

As a rule, wear models detect the inner profile of the intact lining by matching the most severe erosion experienced during the campaign. If later points correspond to less severe erosion, this is taken as an indication of the formation of a skull layer. It is still a complicated task to accurately identify the remaining sound lining and the skull thickness, particularly for cases wherein the historical thermocouple readings are not available for the whole furnace campaign. A systematic and two-dimensional approach is needed in order to estimate the progress of erosion, and also the formation of skull, during the campaign [31,54,55]. The erosion and skull lines estimated with such an approach for two different BFs (unpublished results using the model outlined in [55]) are presented in Figure 11. It can be seen that the two furnaces have different but characteristic wear profiles, i.e., bowl-shaped and elephant-foot-shaped profiles, which are likely to reflect the state of the iron flow in or below the dead man during the campaigns.

Hearth wear profile estimation models are commonly implemented as monitoring and diagnosis tools to aid the operation of BFs. By analyzing the estimated hearth wear profile, indications may be obtained pertaining to the need to adjust the operation towards conditions less prone to cause erosion, e.g., by reducing the production rate or by blanking tuyeres. The latter means both reducing the local inflow of iron "from above" and suppressing a possible local floating of the dead man. On the other hand, it may be argued that such blanking may instead promote liquid flow, as the liquid holdup decreases at a lower local bosh gas flow. It seems that the efficiency of such actions depends on the state of the furnace when the change is implemented.

The estimated erosion profile can be used to support the interpretation of the liquid flow pattern and dead man floating state that are intimately related to hearth erosion. For instance, a too strong peripheral flow or too low carbon content of the hot metal may be counteracted by the center charging of strong and large coke, which (in the long run) will promote a more uniform flow of iron through the dead man, enhancing the contact of it with the hearth wall. Still, it should be kept in mind that the accuracy of erosion models depends on the validity of the modeling assumptions. In particular, brittle lining layers of low conductivity may lead to inaccurate estimates of the progress of the erosion profile, and the occurrence of such should be detected by other means [56,57].

**Figure 11.** Erosion and skulllinesin twoindustrial furnacesestimated based oninverse heat transfer calculation.

#### 2.4.3. Drainage Behavior

In the BF hearth, the void space is occupied by the immiscible liquid iron and slag. As a result of gravity, the rivulets of molten iron and slag from the cohesive zone [58] will eventually separate into two different layers, i.e., the upper slag layer and the lower iron layer. Two interfaces, i.e., gas–slag and slag–iron, are thus formed in the hearth. In practice, a tap starts when one taphole is drilled open. A substantial pressure drop in the vicinity of the taphole can be formed as the high-viscosity slag is driven to flow through the dead man towards the taphole. As a result, the gas–slag interface is tilted down locally near the taphole [24,59–62]. Thus, the overall gas–slag interface is above the taphole level at the moment when gas bursts out and the tap is terminated. This is actually the reason why some amount of slag still remains in the hearth at the tap end, and a "dry hearth" is impossible in practice.

It was earlier commonly assumed that the slag–iron interface is horizontal at the level of the taphole when the slag phase approaches the taphole during tapping. Based on this assumption, extensive physical experiments were carried out by Fukutake and Okabe in order to estimate the tap end slag residual ratio [63–65]. By analyzing the experimental results mainly using the theories of fluid dynamics, the authors proposed a dimensionless flow-out coefficient that was found to correlate monotonically with the slag residual ratio defined. The flow-out coefficient is strongly affected by the state of the dead man, including its voidage and coke particle size. Later, the aforementioned assumption of a horizontal slag–iron interface was found to be incorrect, since both practical observations and physical experiments with two immiscible liquids indicated that the lower phase (liquid iron) can be pumped up from some level below the taphole during the period when slag and iron are drained out simultaneously [59,66,67]. In the BF hearth, a substantial pressure drop is induced in the taphole vicinity when the high-viscosity slag flows through the dead man. This large pressure drop is sufficient to compensate for the flow resistance of the low-viscosity iron, and to overcome the gravitational force when iron is drained up from some level below the taphole. The iron and slag levels at the end of a tap in the BF hearth are sketched in Figure 12, where the hearth internal profile is idealized.

The flow-out coefficient [63–65] was later modified by other authors [68,69] to take into account the non-horizontal slag–iron interface as it is depicted in Figure 12, the coke-free zone beneath the dead man, the varying drainage rates of iron and slag due to taphole erosion, and the continuous production of the liquids. Both observations in the practical operation of the hearth and CFD-based simulations [70,71] have shown that an increase in the slag residual ratio is often attributed to a decrease in dead man permeability, or an increase in draining rate or in slag viscosity. It has also been found that a coke-free zone beneath the dead man directly affects hearth drainage only if it extends close to or above the taphole level [32,68,72]. However, even a partial floating of the dead man may have implications for the drainage via the accumulation and depletion of liquid iron in the coke-free zone during the tap cycle, which affects the liquid levels [25,37,38] and therefore the pressure-loss terms of iron and slag in front of the taphole [24].

**Figure 12.** Schematic of the gas–slag and slag–iron interfaces at the end of a tap, where *z*sl,e, *z*th and *z*ir,e refer to the vertical distances from the overall gas-slag interface, centerline of taphole, and slag-iron interface to the hearth bottom, while *p*sl, *p*th and *p*ir,ft refer to the static pressure at the overall gas–slag interface, in front of the taphole, and at the overall slag–iron interface, respectively.

With reference to Figure 12, the asymptotic relation between the tap end iron and slag levels that are related to the dead man state can be derived based on a simplified pressure balance [66,67]:

$$\frac{\Delta z\_{\rm ir,c}}{\Delta z\_{\rm sl,c}} = \frac{\rho\_{\rm sl}}{\rho\_{\rm ir} - \rho\_{\rm sl}}\tag{4}$$

where *z* and ρ are the vertical distance and liquid density, and where subscripts ir, sl and e denote iron, slag and tap end, respectively.

Equation (4) has been adopted as an asymptotic relation in some hearth drainage studies to validate the calculated results [25,73]. It should, however, be noted that the end points of individual taps may depart considerably from the above relation, simply because the "initial" volume of slag is not sufficient: if too little slag is drained, the duration of the tap is not long enough for the liquids to reach this asymptotic state. The occurrence of local liquid levels in a BF with an impermeable dead man further complicates the general interpretation [62,74–76].
