WO2020045544A1

WO2020045544A1 - Method for starting continuous casting of steel

Info

Publication number: WO2020045544A1
Application number: PCT/JP2019/033828
Authority: WO
Inventors: 晃史原田; 章敏松井; 佑介渡邉; 敬一東
Original assignee: Ｊｆｅスチール株式会社
Priority date: 2018-08-31
Filing date: 2019-08-29
Publication date: 2020-03-05
Also published as: BR112021001763A2; CN112584947B; JP6841386B2; JPWO2020045544A1; CN112584947A

Abstract

In order to reduce the oxygen concentration of the atmosphere in a tundish efficiently and in a simple manner before injection of molten steel, provided is a method for starting continuous casting of steel in which continuous casting is started by injecting molten steel into the tundish in a state in which the oxygen concentration of the atmosphere has been reduced by replacing the gas in the atmosphere in the tundish before injection begins, wherein one or more gas discharge holes for replacing the gas in the atmosphere in the tundish are provided in the tundish cover in addition to a hole for injecting molten steel from the ladle, the molten steel injection hole and the gas discharge holes are arranged such that the distance therebetween satisfies a fixed relationship in relation to the long-side length of the tundish, and an inert gas for atmosphere replacement is supplied so as to satisfy a prescribed flow rate with respect to the volume V in the tundish.

Description

How to start continuous casting of steel

(4) The present invention relates to a method for starting continuous casting of steel, and more particularly to a method for starting continuous casting through appropriate replacement of an atmosphere gas in a tundish prior to the start of pouring into a mold.

In recent years, the requirements for the quality and characteristics of steel materials have been increasing year by year, and techniques for producing more clean steel are required. In particular, non-metallic inclusions (hereinafter, referred to as “inclusions”) in steel materials greatly affect quality and characteristics, and thus reduction is required. Inclusions present in steel include sulfides and nitrides, but most are oxides generated during the deoxidation process of the steelmaking process.

Therefore, conventionally, various technologies have been developed in the secondary refining process to remove inclusions generated in the deoxidation process. As a result, even for materials requiring high cleanliness, such as bearing steel, those having a single oxygen level of about 1 ppm in steel can be stably manufactured.

On the other hand, molten steel after secondary refining passes through a tundish for dispensing into a continuous casting mold, but if there is air in the tundish before molten steel injection, the injected molten steel and air The oxides react with oxygen to generate oxide-based inclusions, so that there is a problem that the tundish is again contaminated despite the reduction of inclusions in the steel during the secondary refining.

Conventionally, in Patent Document 1, the inside of the tundish is purged with an inert gas, and when the oxygen concentration in the tundish becomes 1 vol% or less, molten steel is injected into the tundish. Suggests how to get started.

Patent 3642284 (Japanese Patent Application Laid-Open No. 2002-254148)

However, the above prior art has the following problems. According to the technology disclosed in Patent Document 1, it is unclear how to reduce the oxygen concentration in the tundish to 1 vol%, and depending on the flow rate of the inert gas and the form of the tundish at that time, the atmosphere in the atmosphere may be reduced. There is a problem that it takes a long time to lower the oxygen concentration and the operation efficiency is poor.

The present invention has been developed in view of the above problems of the prior art, and aims to efficiently reduce the oxygen concentration in the atmosphere in a tundish before injecting molten steel in a continuous casting process. It is another object of the present invention to propose a method that can easily reduce the amount.

The method according to the present invention developed in order to solve the above-mentioned problems,
Injecting the molten steel into the tundish interposed between the ladle holding the molten steel and the continuous casting mold of the molten steel, the oxygen concentration in the atmosphere was reduced by replacing the gas in the atmosphere in the tundish before starting the injection. When injecting molten steel in the state and starting continuous casting,
In the lid of the tundish, in addition to the hole for injecting molten steel from the ladle, one or more gas exhaust holes for replacing atmospheric gas in the tundish are provided, and the hole for injecting molten steel and the gas exhaust hole are provided. The distance L to the hole is arranged so as to satisfy the following expression (1), and an inert gas for atmosphere replacement is supplied into the tundish space from one or more supply pipes installed around the molten steel injection hole. A method for starting continuous casting of steel, characterized in that a flow rate Q is supplied such that a flow rate Q satisfies the following expression (2) with respect to the total area A of the gas discharge holes and the volume V of the tundish.
W / 4 ≦ L ≦ 2W / 3 (1)
2.0 ≦ Q ² / (A · V) (2)
However,
W: Inner length (m) of the long side of the tundish,
L: Shortest distance (m) between the center of the molten steel injection hole and the center of the gas discharge hole of the atmosphere replacement gas,
Q: total blowing flow rate of the inert gas for atmosphere replacement per unit time (Nm ³ / min),
A: Total area of gas discharge holes (m ² )
V: Internal volume of the tundish (m ³ ).

In the above method according to the present invention, the shortest distance from the center of the molten steel injection hole provided on the lid of the tundish to the center of the gas replacement hole of the atmosphere replacement gas is further defined by the range of the above formula (1). In addition to the inert gas blown from around the molten steel injection hole of the lid of the tundish, the inert gas is blown from at least one or more positions within a range of 2 L / 3 when L is expressed as It is more preferable that the inert gas is blown into the gas discharge hole at an inclination of 10 to 80 °.

Further, in the above method according to the present invention, it is more preferable that the molten steel in the ladle is started to be injected into the tundish after the oxygen concentration in the tundish atmosphere satisfies the following expression (3). Can be
0.3 × M / V ≧ (O ₂ ) (3)
M: Amount of molten steel in a tundish when full (ton)
V: Tundish inner volume (m ³ )
(O ₂ ): oxygen concentration in tundish atmosphere (vol%)

According to the method of starting continuous casting of steel according to the present invention having the above-described configuration, the installation position of the gas discharge hole for the atmosphere replacement gas provided on the lid of the tundish, the total area of the gas discharge hole, and the inertness By properly controlling the gas injection angle, etc., it is possible to effectively prevent the contamination of molten steel due to reoxidation, and to provide an extremely effective method especially for continuous casting of highly clean steel. Can be.

(A), (b), (c), (d) is a schematic diagram showing a tundish embodiment. It is a partial cross section of a tundish. FIG. 3 is a schematic diagram of a tundish for explaining an inert gas blowing angle.

The inventors of the present invention have prepared various types (a) to (d) of the tundish 1 as shown in FIG. 1 as a process prior to continuous casting. A preferred method for preventing molten steel contamination by re-oxidation by blowing was investigated. 2 and 3 show the specifications (I type) of the tundish used as the premise of this experiment. In these various tundishes, gas sampling holes were installed, and the oxygen concentration in the tundish atmosphere was measured by a gas oxygen concentration meter using a vibration type suction pump and an electrochemical oxygen sensor. At the stage of this examination, the inventors determined the presence or absence of the gas discharge hole 3 for the atmosphere replacement gas in the tundish 1, its size and installation position, the blowing angle and the blowing flow rate of the replacement inert gas. It was confirmed that the replacement time for reducing the oxygen concentration in the atmosphere in the tundish 1 was changed. As the inert gas for replacing the atmosphere in the tundish, an argon gas, a nitrogen gas, or the like can be used.
In addition, although a weir for controlling the flow of molten steel for accelerating the floating of inclusions may be installed in the tundish 1, especially when the weir plate 6 is installed downward from the tundish lid 1 t, the tundish 1 Even if the storage amount of the molten steel in the inside increases and the lower end of the weir plate 6 is immersed in the molten steel, the flow of gas in the tundish 1 is not obstructed so that the flow of gas in the tundish 1 is not obstructed. It is desirable to provide a gap in at least a part of the tundish 1 so as to communicate the space inside the tundish 1 before and after the weir plate 6.

According to an experiment conducted by the inventor at this time, the inert gas used for atmosphere replacement was simply blown in, and if the gas exhaust hole for properly discharging the gas was not provided, the blown inert gas was used. And the like remain in the tundish 1 and are eventually discharged from the molten steel injection hole 2. As a result, unexpected movement and stagnation of gas occur in the tundish 1, resulting in a decrease in oxygen concentration. On the contrary, it was found that it was impossible to proceed, and that a long time was required for atmosphere replacement.

On the other hand, a gas discharge hole 3 for discharging the atmosphere replacement gas is provided at an appropriate position on the tundish lid 1t, that is, the gas discharge hole 3 is placed on the tundish lid 1t at a position satisfying the following expression (1). When one or more holes 3 are provided, a stable flow is formed in a certain direction without stopping the flow of gas from the position where the inert gas is blown for replacing the atmosphere to the gas discharge hole 3. It was found that the atmosphere in the tundish could be replaced with a low oxygen concentration in a short time.

(Equation 1)
W / 4 ≦ L ≦ 2W / 3 (1)
here,
W is the inner length of the long side of the tundish (m),
L is the shortest distance (m) between the center of the molten steel injection hole and the center of the gas discharge hole of the atmosphere replacement gas.
Note that the center of the molten steel injection hole and the center of the gas discharge hole of the atmosphere replacement gas are the positions of the centers of gravity of the respective tundish lid openings in the horizontal plane.

In the present invention, when the gas discharge hole 3 for the atmosphere replacement gas is provided at a position outside the condition of the above formula (1), that is, when L <W / 4, the inert gas blown for the atmosphere replacement is provided. The gas does not reach the entire area of the tundish 1 and the short-circuit gas flow toward the gas discharge hole 3 increases. Therefore, it is preferable that L ≧ W / 4. On the other hand, when L> 2W / 3, the installation position of the gas discharge hole 3 for discharging the atmosphere replacement gas is on the end side (outside) of the tundish, and there is a possibility that an appropriate opening area cannot be secured. , L ≦ 2W / 3.

Further, in the present invention, it is effective to control the total flow rate of the inert gas for atmosphere replacement blown into the tundish 1 per unit time. That is, the flow rate of the inert gas blown into the tundish from one or more supply pipes installed around the molten steel injection hole per unit time should satisfy the following equation (2). is necessary. The reason is that when replacing the atmosphere in the tundish before casting, particularly when replacing a ladle during continuous casting, it is necessary to efficiently perform gas replacement within a limited time. That is, in order to perform the atmosphere replacement from the air atmosphere to a low oxygen concentration in a short time, especially within about several minutes, the gas discharge hole area and the tundish inner volume should satisfy the following expression (2). This is because it is necessary to supply the flow rate of the inert gas per unit time into the tundish. If the condition of the formula (2) is not satisfied and Q ² /(A·V)<2.0, the inert gas used for the atmosphere replacement is replaced with respect to the total area of the gas discharge hole and the volume of the tundish. And the flow rate of the inert gas in the gas discharge hole cannot be secured, so that the influence of the inflow of the atmosphere is increased and the atmosphere replacement does not proceed efficiently.

(Equation 2)
2.0 ≦ Q ² / (A · V) (2)
here,
Q is the total blowing flow rate (Nm ³ / min) of the inert gas for atmosphere replacement per unit time,
A is the total area of the gas exhaust holes (m ² )
V is the volume in the tundish (m ³ ).
Note that N in Nm ³ represents the standard state of the gas.

Here, the reason for limiting the total blowing flow rate of the inert gas for atmosphere replacement is that it is necessary to satisfy Q ² /(A·V)≧2.0 in order to realize sufficient atmosphere replacement. Preferably, Q ² /(A·V)≧6.0. For that purpose, it is effective to install one or more inert gas blowing pipes 4 described later in appropriate places.

If the gas discharge hole 3 for the atmosphere-replacement inert gas satisfies the expression (1), not only the tundish lid 1t but also an overflow gutter opening 5 for emergency use (FIG. 1D) ) May be substituted. In this case, L indicates the distance between the molten steel injection hole 2 and the overflow gutter opening 5. Also, in an actual tundish, there may be a gap between the lid and the lid or between the lid and the tundish skin, which may cause inflow of air or blown inert gas from the gap. Since the gas flows out and an appropriate gas flow cannot be formed, the effect of the present invention may not be sufficiently obtained. For this reason, it is desirable to carry out curing with a heat-resistant sheet or an amorphous refractory before casting. When the overflow gutter opening 5 is not used as a discharge hole, it is desirable to cure the steel sheet with a heat-resistant sheet or the like so as not to hinder the flow of molten steel in an emergency.

Next, the inventors of the present invention have proposed a method of blowing an inert gas into the tundish 1, in particular, one or a plurality of inert gas blowing pipes 4 provided separately from the blowing of the inert gas along the molten steel injection hole 2. The blowing angle (θ) was also examined. As a result, for example, in the example shown in FIG. 2, by giving a predetermined inclination from at least one location toward the gas discharge hole 3 of the atmosphere gas (inert gas), the oxygen concentration in the atmosphere can be more efficiently reduced. Could be reduced. Here, as shown in FIG. 3, the blowing angle θ of the inert gas is based on a straight line ab in a plane passing vertically through the inert gas blowing point a and the center b of the gas discharging hole 3. This is a downward angle toward the gas discharge hole 3. Basically, the inert gas is blown downward, but a part of the gas is inclined by 10 to 80 ° toward the gas discharge hole 3 so that the gas flow in the tundish 1 can be reduced. Propulsion is applied, and atmosphere adjustment (substitution of gas) can be performed more efficiently.

At this time, the reason why the blowing angle of the inert gas from the blowing pipe 4 is inclined by 10 to 80 ° is that when the blowing angle is smaller than 10 ° (θ), the blown gas is Flows along the lid and does not work effectively. On the other hand, if the blowing angle is larger than 80 °, the water flows almost directly below, and this is not effective from the viewpoint of the propulsion. Further, depending on the blowing position, it is preferable to set the inclination angle to be smaller than 80 ° in order to act to obstruct the flow of the inert gas blown from around the molten steel injection hole 2.

The position of the inclined inert gas injection pipe 4 is defined as L, where L is the shortest distance between the center of the molten steel injection hole 2 of the tundish lid 1t and the center of the atmosphere replacement gas gas discharge hole 3. It is desirable to install it within a range of 2 L / 3 or less from the center of the molten steel injection hole 2. If the installation location is larger than 2 L / 3, the gas discharge hole 3 is not provided before the inert gas blown through the inert blow pipe 4 ′ from around the molten steel injection hole 2 is given a propulsive force. And the expected effect cannot be obtained.

Therefore, in a range of 2 L / 3 or less from the center of the molten steel injection hole 2 of the tundish lid 1t, apart from the inert gas injected from around the molten steel injection hole 2, at least one or more inert gas injection pipes are provided. Inert gas is blown through 4. In addition, the effect of the present invention can be obtained if the horizontal component of the inert gas injection is within 20 ° left and right with respect to the straight line ab.

In the above description, although the opening area of the gas discharge hole 3 for the atmosphere replacement gas provided in the tundish lid 1t is not particularly defined, the opening area of the gas discharge hole 3 is set to π (H / 4). ^When it is larger than ² , the influence of the air inflow becomes large. Therefore, in order to carry out the present invention more efficiently, the opening area of the gas discharge hole 3 is preferably set to π (H / 4) ² or less. Here, H is the internal length (m) on the short side of the tundish. At this time, when the emergency overflow gutter provided in the tundish 1 is used as one of the gas discharge holes 3, the same effect can be obtained if the opening area is π (H / 4) ² or less. It is possible to obtain

Furthermore, as a result of various experiments and studies, it was found that the reoxidation amount of the molten steel was affected by the oxygen concentration in the tundish, the weight of the molten steel in the tundish when full, and the volume in the tundish. That is, when the oxygen concentration in the tundish when the molten steel in the ladle is started to be injected into the tundish satisfies the following equation (3), the increase in oxygen in the molten steel due to reoxidation can be greatly reduced, and the oxygen concentration in the molten steel can be reduced. It is possible to increase the amount below 1 mass ppm. On the other hand, when the expression (3) is not satisfied, the influence of the oxygen concentration in the tundish atmosphere on the molten steel increases, and there is a possibility that inclusions due to reoxidation increase.
Therefore, when the oxygen concentration in the tundish atmosphere satisfies the expression (3), it is preferable to start injecting molten steel from the ladle into the tundish.

(Equation 3)
0.3 × M / V ≧ (O ₂ ) (3)
M: Amount of molten steel in a tundish when full (ton)
V: Tundish inner volume (m ³ )
(O ₂ ): oxygen concentration in tundish atmosphere (vol%)
Here, “full” refers to the case where the amount of molten steel contained in the tundish is maximum during steady casting of the continuous casting machine.

Furthermore, as a result of various experiments and studies, it was found that the reoxidation amount of the molten steel was affected by the oxygen concentration in the tundish, the weight of the molten steel in the tundish when full, and the volume in the tundish. That is, when the oxygen concentration in the tundish when the molten steel in the ladle is started to be injected into the tundish satisfies the following equation (3), the increase in oxygen in the molten steel due to reoxidation can be greatly reduced, and the oxygen concentration in the molten steel can be reduced. It is possible for the increase to be below 1 mass ppm. On the other hand, when the expression (3) is not satisfied, the influence of the oxygen concentration in the tundish atmosphere on the molten steel increases, and there is a possibility that inclusions due to reoxidation increase.
Therefore, when the oxygen concentration in the tundish atmosphere satisfies the expression (3), it is preferable to start injecting molten steel from the ladle into the tundish.

(Equation 4)
0.3 × M / V ≧ (O ₂ ) (3)
M: Amount of molten steel in a tundish when full (ton)
V: Tundish inner volume (m ³ )
(O ₂ ): oxygen concentration in tundish atmosphere (vol%)

実施 Hereinafter, examples of the present invention will be described in comparison with comparative examples. In this example, the molten steel amount per charge is about 200 tons on a real machine, and it is listed as a representative of high cleanliness steel through each process of converter, ladle refining furnace, RH vacuum degassing furnace, and continuous casting. This is an example of producing bearing steel. The composition of the bearing steel is as follows: a carbon concentration of 0.90% by mass to 1.10% by mass; a silicon concentration of 0.15% by mass to 0.25% by mass; a manganese concentration of 0.45% by mass; 0.020 mass% or less, sulfur concentration 0.0050 mass% or less, aluminum concentration 0.030 mass% or less, chromium concentration 1.4 mass% or more and 1.7 mass% or less, nitrogen concentration 0.0050 mass% or less It is. In each method, after heating and stirring in a ladle refining furnace and RH vacuum degassing, a ladle, a tundish and a curved continuous caster (no vertical section directly under the mold) through a tundish The cross section perpendicular to the direction was 300 mm thick x 400 mm wide) at a slab drawing speed of about 0.70 m / min. At this time, tundishes of various forms (T type in FIG. 1 (a), I type in FIGS. 1 (b), (c) and (d)) were used, and were first provided at the heating position on the casting floor. The inside of the tank was heated to about 1000 ° C. by a flame obtained by burning coke oven gas with a burner. Next, the burner was extinguished and the inert gas was started to be blown into the tundish through a gas blowing pipe provided separately from the molten steel injection hole while moving the tundish to the casting position. Thereafter, the injection of molten steel in the ladle into the tundish was started through a long nozzle attached to a sliding nozzle on the bottom of the ladle. In addition, the index of the total oxygen concentration in the slab when the sum of the total oxygen concentration in the molten steel before the injection of the tundish, that is, the sum of the dissolved oxygen concentration and the oxygen concentration corresponding to inclusions, was set to 1. The sample for total oxygen analysis was collected from the center of the width of the bottom of the slab, which was cut at a position corresponding to about 3 tons from the casting start end, at the center of the width on the top side, and the inert gas was melted. The samples were analyzed according to the infrared absorption method.

Table 1 shows the form of the tundish, the total flow rate of the inert gas, and the oxygen concentration in the tundish atmosphere 3 minutes after the start of the blowing of the inert gas for the present invention example and the comparative example.

As shown in Table 1, in each of the examples of the present invention, the oxygen concentration in the atmosphere in the tundish at the start of the injection into the tundish is reduced to 2 vol% or less, and almost no reoxidation occurs even after the molten steel is injected. In addition to reaching the level, good results were also obtained regarding the total oxygen concentration in the slab. On the other hand, when a test using a tundish having no gas exhaust hole for the atmosphere replacement gas was performed, the oxygen concentration at the start of injecting molten steel into the tundish was as high as 2.9 vol to 6.2 vol%. . Further, even when the gas discharge hole is used, the distance between the molten steel injection hole and the inert gas discharge hole is shorter than the condition of the present invention, or the total flow of the inert gas blown is smaller than the tundish volume or gas. In the case where the discharge hole area was insufficient, the oxygen concentration at the start of molten steel injection into the tundish was 3 vol% or more, which did not reach a level at which reoxidation of molten steel could be suppressed. As a result, the total oxygen concentration in the slab was higher than before the injection of the tundish, and good results could not be obtained.

In the same manner as in Example 1, the same composition as in Example 1 was used in each process of the converter, the ladle refining furnace, the RH vacuum degassing furnace, and the continuous casting in an actual machine having a molten steel amount of about 200 tons per charge. Bearing steel was manufactured. At this time, injection of molten steel into the tundish was started using various types of tundishes defined by L and W.
Table 2 shows the form of the tundish, the weight of the molten steel when the tundish is full, the total flow rate of the inert gas blown, and the oxygen concentration in the tundish atmosphere at the start of injecting the molten steel into the tundish of the present invention. In addition, an index of the total oxygen concentration in the cast slab when the total oxygen concentration in the molten steel before the injection of the tundish, that is, the sum of the dissolved oxygen concentration and the oxygen concentration corresponding to inclusions, was set to 1. The sampling position of the slab sample for the total oxygen concentration and the analysis method are the same as those in the first embodiment.

As shown in Table 2, in each of the examples of the present invention, the oxygen concentration in the atmosphere in the tundish at the start of injecting molten steel into the tundish was reduced to 2 vol% or less, and the total oxygen concentration in the slab was good. Results were obtained. In Examples 15 to 18 of the present invention in which the gas discharge holes for the inert gas were installed and the inert gas was properly blown, the oxygen concentration in the tundish atmosphere at the start of injecting molten steel into the tundish was such that there was no slanting blow. Was able to be reduced more stably than the case of. Further, in addition to the oblique blowing, the oxygen concentration in the tundish atmosphere at the start of injecting the molten steel into the tundish is 0.3 × M / V (M: weight of the molten steel when the tundish is full (ton), V: internal volume of the tundish (M ³ )) In Examples 19 to 22 of the present invention satisfying the following, the oxygen concentration in the atmosphere in the tundish was reduced to 1 vol% or less. Very good results were obtained with 70% or less.

The effect of the present invention is not limited by the composition and concentration of the steel, and the present invention can be applied to steels of any composition.

Reference Signs List 1 tundish 1t tundish lid 2 molten steel injection hole 3 gas exhaust hole 4 inert gas injection pipe 5 overflow gutter opening 6 weir

Claims

Injecting the molten steel into the tundish interposed between the ladle holding the molten steel and the continuous casting mold of the molten steel, the oxygen concentration in the atmosphere was reduced by replacing the gas in the atmosphere in the tundish before starting the injection. When injecting molten steel in the state and starting continuous casting,
In the lid of the tundish, in addition to the hole for injecting molten steel from the ladle, one or more gas exhaust holes for replacing atmospheric gas in the tundish are provided, and the hole for injecting molten steel and the gas exhaust hole are provided. The distance L to the hole is arranged so as to satisfy the following expression (1), and an inert gas for atmosphere replacement is supplied into the tundish space from one or more supply pipes installed around the molten steel injection hole. A method for starting continuous casting of steel, characterized in that the gas is supplied so that the flow rate Q satisfies the following expression (2) with respect to the total area A of the gas discharge holes and the internal volume V of the tundish.
W / 4 ≦ L ≦ 2W / 3 (1)
2.0 ≦ Q 2 / (A · V) (2)
However,
W: Inner length (m) of the long side of the tundish,
L: Shortest distance (m) between the center of the molten steel injection hole and the center of the gas discharge hole of the atmosphere replacement gas,
Q: total blowing flow rate of the inert gas for atmosphere replacement per unit time (Nm 3 / min),
A: Total area of gas discharge holes (m 2 )
V: Internal volume of the tundish (m 3 ).
When the shortest distance from the center of the molten steel injection hole provided in the lid of the tundish to the center of the gas discharge hole of the atmosphere replacement gas is represented by L satisfying the range of the above formula (1), the shortest distance is within a range of 2 L / 3. In addition to the inert gas blown from around the molten steel injection hole of the lid of the tundish, the inert gas is blown from at least one or more positions, and the inert gas blow angle is adjusted by the gas discharge. 2. The method for starting continuous casting of steel according to claim 1, wherein the steel is blown into the hole with an inclination of 10 to 80 °.
3. The continuous casting of steel according to claim 1 or 2, wherein the molten steel in the ladle is started to be injected into the tundish after the oxygen concentration in the tundish atmosphere satisfies the following formula (3). Method.
0.3 × M / V ≧ (O 2 ) (3)
M: Amount of molten steel in a tundish when full (ton)
V: Tundish inner volume (m 3 )
(O 2 ): oxygen concentration in tundish atmosphere (vol%)