Continuous casting of steel involving different grades in the same casting sequence remains a challenge to billet caster operators. The intermixed composition obtained during the grade change does not meet the specification of either grade and must be downgraded. Incorrect identification of this intermixed region may result in non-conforming products reaching the customer. In this study, a numerical model based on CFD (computational fluid dynamics approach) has been developed which predicts the start and end of the intermixed composition and the tonnage to be downgraded under different casting conditions. This model was validated and the results were in good agreement with the actual plant data for a 6-strand billet caster at LD-1 of TATA Steel, India. This model is used to calculate transition tonnage for different scenarios, e.g. when one of the outermost strands is not functional or some combinations are not functional and varying casting speed during operation. Furthermore, impact of different design of baffles on performance of Tundish has been evaluated to find a way to reduce transition or intermixed composition.
Continuous casting of steel involves liquid steel to be transferred from ladle to Tundish and finally to mould. The mould provides desired shape, where partial solidification of liquid steel happens. The Tundish works as a buffer between mould and ladle. Tundish provides two functional requirements: inclusion floatation and equal flow to the moulds [
When two heats of different composition are cast in a continuous sequence without replacing the Tundish produces intermixed products or grade transition. In such cases, products with intermixed composition are produced which are neither conformal to either composition and are needed to be diverted or downgraded [
For the prediction of the intermixed region due to the transition, different techniques have been developed [
Therefore, in the present work, a three-dimensional numerical model has been developed based on computational fluid dynamics (CFD) for the prediction of transition tonnage for 6 strands billet caster of Tata Steel India. The model is first validated with the available plant data and after the successful validation, the model is used to predict the transition tonnage under different plant conditions when one or more strand is non-functional or to find the effect of different casting speeds.
There is always an emphasis in the industry to reduce the transition tonnage to reduce the losses or diversions. Generally, baffles and weirs have proven to be a factor to reduce intermixed quantity [
As mentioned in the previous section, the scope of the study includes estabilishment of a well validated numerical model for grade transition for caster#3 (CC#3) of Tata Steel and further use this model to predict various scenarios existing in the plant. In addition, a means to minimize grade transition by using special baffle arrangement has also been evaluated.
In general, Tundish is a combination of plug flow reactor (PFR) and Continuously stirred tank reactor (CSTR) [
c * = c ( t ) − x y − x (1)
In the equation c* is dimensionless concentration, c(t) is the composition of given element in time t, x and y are the element composition for old and new grade respectively.
Using the above methodology, a concentration plot is obtained for Tundish using CFD model by tracking the concentration of tracer. This forms the basis for calculation of grade transition. The details are outlined in the next section where numerical approach and boundary conditions are provided.
CFD analysis has been performed to get the flow field and tracer evolution in the Tundish. The underlying equations used for the study are outlined as follows:
• For the mass conservation, continuity equation (Equation (2)) is solved
∂ ρ V ∂ t + ∇ ⋅ ( ρ V ) = 0 (2)
Here V is the velocity.
For the momentum balance and heat transfer, Navier-Stokes equation [
∂ ρ u ∂ t + ∇ ⋅ ( ρ V × V ) = − ∇ ⋅ p + μ ∇ 2 V − g α Δ T (3)
∂ ρ E ∂ t + ∇ ⋅ ( ρ V ¯ ( E + p ) ) = ∇ ⋅ k e f f ∇ T (4)
Here E is the energy , T is the temperature, t is the time, k is the effective diffusion term, p is the pressure, μ is the dynamic viscosity, g is the acceleration due to gravity, α is the thermal expansion coefficient.
Thermal induced buoyancy has been modelled using Boussinesq approximation [
• To model turbulence, realizable k-ε model with enhanced wall treatment has been used. The realizable k-ε model with enhanced wall treatment has been found to be better for Tundish flow simulations as mentioned in references [
∂ ∂ t ( ρ K ) + ∇ ⋅ ( ρ K V ) = ∇ ⋅ [ ( μ t σ K ) ∇ K ] + 2 μ S i j ⋅ S i j − ρ ε (5)
Here μ t = ρ C μ K 2 ε .
Here C μ is dimesionless constant and C μ = 0.09 .
∂ ∂ t ( ρ ε ) + ∇ ⋅ ( ρ ε V ) = ∇ ⋅ [ ( μ t σ ε ) ∇ ε ] + ρ C 1 S ε − ρ C 2 ε 2 K + ν ε + C 1 ε ⋅ ε K C 3 ε G b (6)
where C 1 = [ 0.43 , η η + 5 ] , η = S ⋅ K ε and S = 2 S i j S i j .
And value of C 1 ε = 1.44 , C 2 = 1.9 , σ K = 1.0 and σ ε = 1.2 .
The Pressure-Implicit with Splitting of Operators (PISO) [
• The strategy to mimic transition of grades during Tundish operation is realized via injecting a tracer for one second (pulse injection of the tracer) and then tracking the evolution of the tracer for longer duration. Note that the tracer is tracked on a developed flow field that is after solving the flow field for more than two times of theoretical residence time [
∂ ρ c C ∂ t + ∇ ⋅ ( ρ V C ) = ∇ ⋅ ( ρ c D e ∇ C ) (7)
where, C is the species mass fraction De is effective diffusion which is sum of molecular diffusion and turbulent diffusion. The turbulent diffusion coefficient is determined the turbulent diffusion coefficient is determined from the following relationship (assuming that the turbulent Schmidt number equals unity):
∂ ρ D e μ e ~ 1 (8)
As mentioned above, the tracer is tracked on the frozen flow field till most of the injected tracer leaves the Tundish via strands/outlets. For each strand/outlet, the concentration variation of the species is tracked with respect to time. This history of concentration variation with respect to time is called RTD (Residence time distribution) curve. In general, aRTD curve is a characteristic function of continuous process system and provides information on malfunction(s) if any and flow pattern i.e. degree of mixing [
This RTD curve is further normalized to get the Exit Age distribution curves (E-Curve) [
E ( t ) = c ( t ) − c ( t = 0 ) ∫ 0 n [ c ( t ) − c ( t = 0 ) ] d t (9)
Such that
∫ 0 n E i ( t ) d t = 1 (10)
where, i = 1 , 2 , ⋯ , n , ci(t): tracer concentration obtained either from experiment or numerical models and Ei(t): residence time distribution function.
After getting the E curve, further normalization of E curve is done to get normalized concentration C as follow:
C ( t ) = 1 − ∫ 0 n E i ( t ) d t (11)
where C(t) represents the normalized concentration of tracer at time t. This normalized concentration C(t) forms the basis for predicting the transition tonnage.
The 3-D design of Tundish is as shown in
Mass flow rate based on casting speed has been provided at the inlet with turbulence intensity of 5% [
For the heat transfer calculation, the boundary conditions include the incoming liquid steel temperature as 1823 K. The heat losses were supposed to be taking place through the walls, bottom and free surface of fluid in the Tundish. The heat transfer coefficient at the top surface is taken as 15 W/m2K and for Tundish walls heat transfer coefficient is taken as 3.46 W/m2K [
Further detailed boundary conditions are listed in
A grid independence study has been performed to find the appropriate grid for the Tundish flow. The results were assessed for four different grids: 81,470, 333,320, 5,076,362 and 9,466,023 elements with maximum element size varying from 100 mm, 75 mm, 45 mm and 25 mm respectively.
Parameter | Unit | Tundish |
---|---|---|
No. of strands | [-] | 6 |
Casting speed | [m/min] | 3 |
Mass flow rate | [Kg/s] | 36 |
Mass flow rate | [Metric Ton/minute] | 2.16 |
Volume | [m3] | 4.1 |
Total liquid steel | [Metric Ton] | 32 |
Theoretical residence time | [s] | 900 |
Shroud internal diameter | [m] | 0.067 |
Outlet nozzle diameter | [m] | 0.018 |
Submergence depth of the shroud | [m] | 0.05 |
Temperature of inlet stream (Tin) [*during trial] | [K] | 1823 |
Heat transfer coefficient at Tundish top (htop) | [W/m2K] | 15 |
Heat transfer coefficient at Tundish top (hwalls) | [W/m2K] | 3.46 |
Temperature of top wall (Ttop) | [K] | 1200 |
Temperature of side walls (Tsides) | [K] | 523 |
Density of liquid stream and Tracer | [kg/m3] | 7200 |
Conductivity of liquid steel | [W/mk] | 35 |
Specific heat capacity of liquid steel | [J/kg∙k] | 640 |
No. of Cells | Velocity at Outlet 3 (m/s) | Temperature at outlet 3 (K) |
---|---|---|
81470 | 3.528 | 1815.255 |
333320 | 3.411 | 1816.047 |
5076362 | 3.248 | 1816.871 |
9466023 | 3.235 | 1817.298 |
This section will describe the important results and validation aspects of this work.
To understand the general flow feature of the Tundish, flow pattern, temperature field contours and velocity vectors are visualized at different planes. Figures 4-6 show the velocity contour, vectors, and streamlines respectively for 3 m/min (0.05 m/s) casting speed for 28 Ton (28,000 kg) Tundish weight (total liquid steel content in the Tundish).
Based on the contours, vectors and streamlines, it is visible that flow is predominantly surface driven; this is evident by the presence of high velocity near top of the Tundish spanning across the width. Just below this high velocity zone, there exist many slow-moving zones or say slow moving islands (see the blue coloured region in the contour plots and the recirculation loop marked by arrows in the vector plot (
To understand flow and short-circuiting phenomena, snapshots of streamline are plotted for different intervals as shown in
streamline paths that there are heavy recirculation zones near inlet due to special curved refractory design near the inlet part. Based on streamline, a fair judgment can be done on short circuiting, see
that the strands closest to the inlet are receiving the material first. This will have consequences in the grade transition and will be more evident during tracking of tracer which has been covered in the next section.
To characterize Tundish behaviour, many authors [
The RTD parameters are obtained from tracer concentration evolution as described in Section 3.1. Here analyses have been performed to find these parameters for 3 different scenarios: when all strands are working, when the one of the outermost strand is off (6th off) and when one of the strands closest to inlet is off (4th off). To find a single RTD curve for a given Tundish, Tracer concentrations at respective outlets (strands) are averaged with respect to number of strands.
It will also be interesting to find if above volumes was impacted by change in casting speed.
All strand working | 6th strand off | 3rd strand off | ||
---|---|---|---|---|
θmin | Dimensionless minimum residence time | 0.05 | 0.025 | 0.02 |
θmean | Dimensionless mean residence time | 0.72 | 0.63 | 0.55 |
VDead (%) | Dead volume | 25.65 | 37.6 | 41.87 |
VDPlug (%) | Dispersed plug flow volume | 32.25 | 25.11 | 16.44 |
Vmix (%) | Well mixed volume | 42.1 | 37.8 | 41.01 |
All strand working (casting speed: 3 m/min) | All strand working (casting speed: 3.5 m/min) | |
---|---|---|
Plug flow region (%) | 17.51 | 17.82 |
Dead regions (%) | 28.70 | 27.16 |
Well mixed region (%) | 53.73 | 55.08 |
This shows short-circuiting phenomenon as mentioned in literature [
To predict the transition tonnage during the grade change, the exit age distribution, E-curve, obtained for each strand is normalized on the scale of 0 to 1 by using Equation (8), Equation (9) and Equation (10). The curve thus obtained is called C-curve as shown in
In real plant scenario, transition tonnage is predicted by comparing transition of critical elements (e.g. C, Mn, Si, Cr, Vetc.) during grade change. This requires transition percentage to be calculated based on the limiting element. Based on the band of acceptable composition of a grade (e.g. 80%, 90%, 95%), the corresponding transition time and transition tonnage is predicted.
As shown in
To get the confidence in the grade transition model, a plant trial was executed. The trial casting conditions and grade composition are shown in
Grade1 | Grade2 | |
---|---|---|
PC No. 479―M75480 | PC No. 975―Heat Id M75483 | |
Critical element―Carbon | 0% - 0.06 % | 0.0% - 0.07% |
Actual % C | 0.03% | 0.068% |
Critical element―Manganese | 0.5% - 0.55 % | 0.27% - 0.35% |
Actual % Mn | 0.504% | 0.335% |
Critical element―Silicon | 0.018% - 0.028 % | 0.035% - 0.07% |
Actual % Si | 0.024% | 0.047% |
Casting Speed, m/min (Avg.) | Strd1 | Strd2 | Strd3 | Strd4 | Strd5 | Strd6 |
---|---|---|---|---|---|---|
Tundish weight at ladle open = 23.7 T | 2.71 | 2.71 | 2.71 | 2.71 | 2.71 | 2.71 |
Time (mins) | C | Mn | Si | |||
---|---|---|---|---|---|---|
Non-Normalized % | Normalized | Non-Normalized % | Normalized | Non-Normalized % | Normalized | |
10 | 0.06 | 0.741935 | 0.4 | 0.443 | 0.032 | 0.653846 |
13.25 | 0.06 | 0.741935 | 0.39 | 0.384 | 0.034 | 0.576923 |
16.41 | 0.054 | 0.548387 | 0.375 | 0.325 | 0.034 | 0.5 |
19.66 | 0.053 | 0.516129 | 0.37 | 0.236 | 0.039 | 0.5 |
22.83 | 0.06 | 0.741935 | 0.362 | 0.207 | 0.039 | 0.307692 |
26.083 | 0.06 | 0.741935 | 0.35 | 0.159 | 0.04 | 0.307692 |
29.5 | 0.044 | 0.225806 | 0.345 | 0.088 | 0.043 | 0.269231 |
32.5 | 0.042 | 0.16129 | 0.335 | 0.059 | 0.043 | 0.153846 |
35.75 | 0.039 | 0.064516 | 0.4 | 0 | 0.043 | 0.153846 |
transition according to CFD analysis is around 28 minutes while plant trial composition variation reveals it is around 29.5 minutes. Looking at the validation plot (
In this section, various ifs and buts for numerous plant conditions will be presented. Due to breakout or other mechanical failures of strands during casting, numerous scenarios may prevail. For example, outer strand may become non-functional or one of the inner strands may be closed or any of the two strands may become non-functional. As known from previous section about RTD analysis that the closure of strands with respect to inlet position changes the flow characteristics as well as RTD features. Therefore, it is suspected that the above scenarios may impact the transition tonnage generated during the grade change. To understand that, here numerous situations are analysed. This exercise in essence can provide a guideline to plant in taking proper action to cut the transition tonnage at accurate time. In addition, casting speed during grade change may vary. This also needs a deep evaluation to find if there is impact of casting speed on grade transition tonnage or not.
As stated earlier during casting operation, there is a possibility that certain strands are not operational. Here three scenarios are analysed for the six strands Tundish: first case where all 6 strands are functional, second case where number 6 strand is non-functional (farthest from the inlet) and the third case where number 4 strand is non-functional (nearest from the inlet), for nomenclature of strands see
Note that the casting speed and the weight of the steel in Tundish are based on real plant scenario. The transition tonnage is calculated as follows:
Transition Tonnage = casting speed × density of steel × area of the billet
× transition time × No. of strands running (15)
To predict transition tonnage for different plant scenarios, numerous permutations and combinations for strand unavailability is analysed.
tonnage is produced when closest strand to the inlet, strand (3 or 4) is non-operational. For two strand closure cases, the strand 1 and 2 closure leads to highest transition tonnage.
A pertinent question is that whether at different casting speed, the transition time and tonnage will be different. To answer this, transition tonnage and time is computed for two casting speeds, 3 and 3.5 m/min for all strand working scenario.
the operational people, transition tonnage is the deciding factor to remove the mixed composition. It can be stated that the CC#3 Tundish has nominal impact on transition tonnage due to increase in casting speed. The above fact essentially tells that there is no change in flow characteristics of Tundish due to change in casting speed. This was already obvious from the analysis of dead, plug and well mixed volume in Section 5.2.1 where no significant impact on the volumes was found due to change in the casting speed. Hence, this signifies that no. of rounds of billets which will be downgraded for transition remains same irrespective of casting speed.
There is always an emphasis to decrease the intermixed quantity. One of the methods is to provide special baffles. To study the impact of baffles on the transition tonnage, here two types of design of baffles for six strands Tundish have been performed. The two designs are shown in
To understand the impact of short circuiting,
On calculating the tonnage saving for Tundish with 2 baffles (Design 1) reveals that 21 tons material (3 rounds of 9 m billet) can be prevented from downgradation or diversion. This is a huge saving.
In this study, a model to predict transition tonnage and time for 6 strand billet caster Tundish of Tata Steel India has been developed using CFD methodology. The developed model in this study validates quite well with the plant trial findings. The model has been used to analyse different plant conditions e.g. if nearest strand to inlet or farthest strand to inlet has been non-operational; then what will be the impact on transition tonnage. The model has shown its efficacy to provide insights about what happens during grade change. The important conclusions from this study are outlined as follows:
• Flow field inside the Tundish is symmetrical and short circuiting phenomena are observed to happen for a strand nearest to inlet.
• Due to special curved design near inlet, high surface velocity regions directed towards long side wall away from strand outlets are found. This may lead to heavy erosion of Tundish refractory in the top region of rear wall area.
• The closure of the one or more strands plays a vital role for dictating the transition tonnage to be downgraded.
• For single strand closure situation, highest transition tonnage is produced when strand nearest to inlet is non-functional and minimum transition tonnage is achieved when all strands are functional.
• Casting speed plays a role in reducing transition time, but it does not have significant impact on transition tonnage. This was due to the fact that insignificant changes in the plug, dead and well mixed zones were found due to increase or decrease in the casting speed.
• Baffles improve the performance of Tundish and reduce the intermixed quantity.
A future study is underway to find the best baffle height, number of baffles and position of baffles to further reduce the intermixed quantity.
The authors are thankful to Tata Steel India Management for their support for carrying out research.
The authors declare no conflicts of interest regarding the publication of this paper.
Agarwal, R., Singh, M.K., Kumar, R.B., Ghosh, B. and Pathak, S. (2019) Extensive Analysis of Multi Strand Billet Caster Tundish Using Numerical Technique. World Journal of Mechanics, 9, 29-51. https://doi.org/10.4236/wjm.2019.92003