R Agarwal et al, tation and equal flow to the moulds 1 and 2 for multi strand caster configu. rations The number of moulds is in general 1 to 2 for slab casters 2 to 4 for. bloom casters and 2 to 8 for billet caster 3, When two heats of different composition are cast in a continuous sequence. without replacing the Tundish produces intermixed products or grade transi. tion In such cases products with intermixed composition are produced which. are neither conformal to either composition and are needed to be diverted or. downgraded 4 5 6 The casting operators need to know the location and. extent of the intermixed region and how it is affected by grade specifications and. casting conditions 3 5 With the strict norms for steel grades with specific. composition there is a consequent rise of grade transitions in the casting se. quence thus giving a further increase in the cost associated with the intermixed. For the prediction of the intermixed region due to the transition different. techniques have been developed 1 2 Water models 1 2 7 3D numerical. models 6 8 and semi empirical numerical models 3 are the typical tools to. address this problem But each of the method has its own limitations for exam. ple the water model fails to satisfy both Froude and Reynolds similarity criteria. on scaled models to predict the transition In the three dimensional numerical. modelling 8 9 10 it requires an injection of tracer but the credibility of the. model is based on the validation with the plant data 8 11 12 13 14 Third. case of semi empirical model is based on experiment on real plant conditions. where billet slab composition is tracked with time to predict transition tonnage. The strong point of this approach is that it is based on real plant condition. however for multi strand casting especially in billet and bloom casting it is dif. ficult to perform experiments for different plant condition It is also important. to note that design of Tundish also plays a major role in this and a model devel. oped for a design of Tundish may not be valid for other Tundish designs. 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 condi. tions 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 6 7 10 In this study two designs of. baffles have been analysed to find the efficiency regarding intermixed quantity. 2 Problem Definition, As mentioned in the previous section the scope of the study includes estabi. lishment of a well validated numerical model for grade transition for caster 3. DOI 10 4236 wjm 2019 92003 30 World Journal of Mechanics. R Agarwal et al, CC 3 of Tata Steel and further use this model to predict various scenarios ex. isting in the plant In addition a means to minimize grade transition by using. special baffle arrangement has also been evaluated Figure 1 a shows general. schematics of a Tundish with 6 strands Tata Steel India produces around 3 5. million tons of long products and out which 1 million tons is produced via cas. ter 3 CC 3 route The Caster 3 covers the range from low carbon to Ther. mo mechanical treatment TMT bars to high carbon grades processing wire. and wire rods, In general Tundish is a combination of plug flow reactor PFR and Con. tinuously stirred tank reactor CSTR 14 15 16 During sequence change of. the casting grade change leads to mixing of grades which may be undesirable for. critical grades Grade change leading to transition can be explained as follows. suppose a grade with x Composition Chemistry is being casted and after a. certain time the other grade with Composition y is poured in the Tundish with. y x 3 A general picture regarding concentration variation at a strand out. let from Tundish to inlet of mould with time can be plotted as shown in Figure. 2 a The concentration plot can be made dimensionless using Equation 1 as. shown in Figure 2 b, Figure 1 Geometry and boundary conditions for 6 strand Tundish a Schematics of a. 6 Strand Tundish b Boundary conditions for 6 strand billet caster. DOI 10 4236 wjm 2019 92003 31 World Journal of Mechanics. R Agarwal et al, Figure 2 Concentration variation from grade x to grade y a Concentration vs time b. Normalised concentration vs time, 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. 3 Numerical Approach,3 1 Governing Equations, 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. Here V is the velocity, DOI 10 4236 wjm 2019 92003 32 World Journal of Mechanics. R Agarwal et al, For the momentum balance and heat transfer Navier Stokes equation 11. 12 13 Equation 3 and thermal energy equation Equation 4 are solved. respectively,V V p 2V g T 3,V E p keff T 4, Here E is the energy T is the temperature t is the time k is the effective dif. fusion term p is the pressure is the dynamic viscosity g is the acceleration due. to gravity is the thermal expansion coefficient, Thermal induced buoyancy has been modelled using Boussinesq approxima. tion 11 This has been added as a source term in the momentum equation. Equation 3 see the rightmost term of Equation 3 The reference density of. steel in Boussineq approximation is taken as 7200 kg m3. To model turbulence realizable k model with enhanced wall treatment has. been used The realizable k model with enhanced wall treatment has been. found to be better for Tundish flow simulations as mentioned in references. K KV t K 2 Sij Sij 5,Here C is dimesionless constant and C 0 09. t C1 S C2 C1 C3 Gb,where C1 0 43 S and S 2 Sij Sij. And value of C1 1 44 C2 1 9 K 1 0 and 1 2, The Pressure Implicit with Splitting of Operators PISO 17 algorithm was. used for the pressure velocity coupling and Quadratic Upstream Interpolation. for Convective Kinematics QUICK 17 scheme was used for the discretization. of momentum energy turbulent kinetic energy and turbulent dissipation rate. The strategy to mimic transition of grades during Tundish operation is real. ized 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 3 7 The concentra. tion equation Equation 7 is solved to track species concentration over. time The tracer study is similar to injecting a dye in a water models for an. DOI 10 4236 wjm 2019 92003 33 World Journal of Mechanics. R Agarwal et al, instant of time and tracking the evolution of dye with time 6. VC c De 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 follow. ing relationship assuming that the turbulent Schmidt number equals unity. 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 2 8 15 18, This RTD curve is further normalized to get the Exit Age distribution curves. E Curve 2 8 15 19 20 as follow,0 Ei t dt 1, 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 nor. malized concentration C as follow,C t 1 0 Ei t dt, where C t represents the normalized concentration of tracer at time t This. normalized concentration C t forms the basis for predicting the transition ton. 3 2 Geometry and Boundary Conditions, The 3 D design of Tundish is as shown in Figure 1 b It is a six strand Tundish. with a turbo stop just beneath the inlet to control turbulence. Mass flow rate based on casting speed has been provided at the inlet with tur. bulence intensity of 5 9 The no slip condition was employed on each wall. surface with the zero velocity at the wall The outflow boundary condition was. taken at each outlet The top surface was assumed as a free surface with the. zero shear stress The acceleration due to gravity was taken as 9 81 m s2. For the heat transfer calculation the boundary conditions include the incom. DOI 10 4236 wjm 2019 92003 34 World Journal of Mechanics. R Agarwal et al, ing liquid steel temperature as 1823 K The heat losses were supposed to be tak. ing 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 9 The higher heat trans. fer at top surface is due to extra radiative heat transfer taking place as compared. to walls of Tundish where only conductive heat transfer happens. Further detailed boundary conditions are listed in Table 1 The commercial. ANSYS Fluent V 15 has been used in this study,4 Grid Independence Study. 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, Table 2 shows the temperature and velocity at outlet number 3 for the above. four meshes Figure 3 shows the temperature value on a line passing through the. cross section of the Tundish along X axis 6 34 m domain The difference in. average results for velocity at outlet 3 for 81 470 elements and 9 466 023 ele. ments is about 10 while the difference in the results for 5 076 362 elements and. 9 466 023 elements is about 1 Therefore in the present study the 3 D compu. tational grid having 5 076 362 has been considered. Table 1 Boundary conditions for 6 strand Tundish,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,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 m K 2. Heat transfer coefficient at Tundish top hwalls W m K 2. 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, DOI 10 4236 wjm 2019 92003 35 World Journal of Mechanics. R Agarwal et al, Figure 3 Temperature on a line along length of Tundish for the grid independence. Table 2 Mesh validation for Tundish grade transition. 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 298,5 Results and Discussion, This section will describe the important results and validation aspects of this. 5 1 Flow Features in the Tundish, To understand the general flow feature of the Tundish flow pattern tempera. ture 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 pre. dominantly 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 ar. rows in the vector plot Figure 4 a A noteworthy observation is that see. Figure 5 a high velocity zone is present near the top surface of the rear end of. Tundish and this high velocity zone propagates very near to rear wall spanning. the whole width This can provide a clue that there can be erosion issue at rear. side of wall due to this high velocity, To understand flow and short circuiting phenomena snapshots of streamline. are plotted for different intervals as shown in Figure 6 It is evident from initial. DOI 10 4236 wjm 2019 92003 36 World Journal of Mechanics. R Agarwal et al, Figure 4 Velocity contours on various planes in 6 strands Tundish for all strands run. ning a Velocity field on a plane across the Tundish near three outlets for 6 strand Tun. dish b Velocity field on a plane passing through the inlet for 6 strand Tundish c Ve. locity field on a plane passing through all outlets for 6 strand Tundish. 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 Figure 6 b and Figure 6 c It is obvious. DOI 10 4236 wjm 2019 92003 37 World Journal of Mechanics. R Agarwal et al, Figure 5 Velocity vectors at various locations in 6 strands Tundish all strand functional. a Velocity vector field on a plane passing through the inlet for 6 strand Tundish b. Velocity vector field on a plane passing through all outlets for 6 strand Tundish. Figure 6 Streamline plot for 6 strands Tundish at various intervals. DOI 10 4236 wjm 2019 92003 38 World Journal of Mechanics. R Agarwal et al, 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, Figure 7 a and Figure 7 b show temperature distributions on two planes. along the width passing through inlet and all the outlets respectively Overall a. maximum drop of temperature in the Tundish is about 10 C To compare tem. perature at different strands the temperatures at all six strand outlets are shown. in Figure 8 with respect to inlet temperature As expected the farthest strand has. highest temperature drop Higher temperature is achieved in the nearest strands. from the inlet Predominantly two factors are responsible for this large tem. perature drop in the outer strands first one is presence of numerous slow mov. ing zones and seconds one is higher residence time However comparing nearest. to the farthest strands regarding temperature drop there is a minimal difference. of 2 C in the temperature, Figure 7 Temperature counters on various planes in 6 strands Tundish all strand func. tional a Temperature field on a plane passing through the inlet for 6 strand Tundish b. Temperature field on a plane passing through all outlets for 6 strand Tundish. DOI 10 4236 wjm 2019 92003 39 World Journal of Mechanics. R Agarwal et al, Figure 8 Comparison of Inlet temperature to outlet temperatures of strands for 6 strands. Tundish all strands functional,5 2 Characteristics of Tundish. 5 2 1 Residence Time Distribution RTD Curves, To characterize Tundish behaviour many authors 2 21 have used plug flow. dead volume and well mixed regions also called RTD parameters If the propor. tion of the well mixed region is higher this indicates adequate mixing in the. melt phase and hence better material and heat transport On the other hand a. large plug flow volume indicates better possibility of inclusion floatation In ad. dition higher the dead volume higher will be the heat loss and higher the tran. sition tonnage, The RTD parameters are obtained from tracer concentration evolution as de. scribed in Section 3 1 Here analyses have been performed to find these parame. ters 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. Figure 9 presents the dimensionless RTD plot for above mentioned three sce. narios The corresponding RTD values are presented in Table 3 The data about. volumes shows that when one of the strands is non functional the dead volume. increases while plug flow volume decreases, It will also be interesting to find if above volumes was impacted by change in. casting speed Table 4 compares these volumes for 3 and 3 5 m min casting. speed There is insignificant impact of casting speed change on the volumes In. other words increase or decrease in casting speed does not change the charac. teristics of the Tundish,5 2 2 Prediction of Grade Transition. Figure 10 a shows the concentration plot E Curve with respect to time for. two strands strand 4 nearest to the inlet and strand 1 farthest from the inlet. Looking at Figure 10 a it is evident that nearest strand is receiving the material. first red curve in the figure as well as the decay rate for this strand is faster. DOI 10 4236 wjm 2019 92003 40 World Journal of Mechanics. R Agarwal et al, Figure 9 RTD curves for different strand operational on dimensionless concentration. with dimensionless time, Figure 10 Prediction of grade transition at different level 50 80 and 95 for 6. strands Tundish a E Curve for strand 1 and 4 b Normalized concentration curve for. strand 1 and 4, Table 3 Comparison of RTD parameters of Tundish for different plant scenarios. All 6th 3rd,strand working strand off strand off, min Dimensionless minimum residence time 0 05 0 025 0 02. mean 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, DOI 10 4236 wjm 2019 92003 41 World Journal of Mechanics. R Agarwal et al, Table 4 Comparison for RTD for different casting speed. All strand working All strand working,casting speed 3 m min 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 7 10 and. as obvious from streamline plots see Figure 6, To predict the transition tonnage during the grade change the exit age distri. bution 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 Figure 10 b This C curve forms the basis of the. prediction of transition tonnage 7 The transition time and tonnage obtained. depends on the composition difference of the grades and acceptance criteria at. plant For example transition can finish at 50 or 80 or 95 as indicated by. horizontal lines in the plot of Figure 10 b is solely dictated by customer re. 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 corre. sponding transition time and transition tonnage is predicted. As shown in Figure 10 b the transition time for strand 4 is lesser than. strand 1 Here in LD 1 CC3 caster the strand with largest transition time. strand 1 or 6 is the limiting strand This is because the torch cutting system of. billets has certain limitations in its automation system However there is a pos. sibility to automate the transition cutting system for each strand to minimize. 5 2 3 Validation of the Grade Transition Model, To get the confidence in the grade transition model a plant trial was executed. The trial casting conditions and grade composition are shown in Table 5 and. Table 6 In the trial all the strands were functional and average casting speed. was in range of 2 71 m min Strand 6 was chosen for sampling of billets to track. the chemistry variation of elements C Mn Si with respect to casting time. Nine billet samples were collected from the strand 6 at different time intervals. after the Grade 2 ladle was opened to be poured into the Tundish Table 7 shows. the variation of Mn Si and C concentration both normalized and non normalized. with respect to casting time As it is evident from Table 7 that the critical ele. ment for the trial sequence is Mn since the transition of Mn is slowest among all. elements The normalized concentrations obtained from both CFD and plant is. compared as shown in Figure 11 The transition time to achieve 92 of. DOI 10 4236 wjm 2019 92003 42 World Journal of Mechanics. R Agarwal et al, Figure 11 Validation for 6 strands Tundish with experimental data points. Table 5 Grades used for validation during plant experiment. 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. Table 6 Casting speed for each strand during plant experiment. 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. Table 7 Elements variation with time during plant experiment. Time C Mn Si, mins 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, DOI 10 4236 wjm 2019 92003 43 World Journal of Mechanics.

keefektifan pembelajaran matematika model Taba dengan strategi Concept Mapping terhadap kemampuan berpikir kreatif siswa dan untuk mengetahui karakter siswa yang muncul dalam pembelajaran matematika model Taba dengan strategi Concept Mapping Kelas VIII SMP Negeri 1 Tulis.

Textbook: "Fundamentals of Materials Science and Engineering," William D. Callister, Jr.. 2nd Ed.(special edition) References: (available in Grainger) Foundations of Materials Science and Engineering, William F. Smith (McGraw-Hill, 1993). Engineering Materials and Their Applications, R.A. Flinn and P.K. Torjan (Wiley, 1995).

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dibuat setiap pembelajaran berlangsung. Berdasarkan hasil penelitian, diperoleh kesimpulan bahwa pelaksanaan pembelajaran matematika dengan menggunakan metode Mind Map(peta pikiran) guna meningkatkan motivasi belajar matematika siswa, dilakukandengan langkah-langkah pembelajaran sebagai berikut: (1) Mempelajari konsep suatu

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4. Langkah-langkah Pembelajaran Peta Konsep (Concept Mapping) Langkah-langkah dalam membuat peta konsep cukup sederhana, siswa harus menemukan kata kunci dan menghubungkannya dengan garis hubung sehingga membentuk suatu hubungan yang jelas. Pembuatan peta konsep dilakukan dengan membuat suatu sajian atau suatu diagram tentang