# Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles

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1 Model Studies on Slag-Metal Entrainment in Gas Stirred Ladles Anand Senguttuvan Supervisor Gordon A Irons 1

2 Approach to Simulate Slag Metal Entrainment using Computational Fluid Dynamics Introduction & Objective Governing equations and methods for solving the multiphase fluid flow problem Various modeling approaches used to supply appropriate boundary conditions for the system The approach applied to a case published in literature 2

3 Slag-Metal Entrainment in Gas Stirred Ladles Open Eye SLAG Plume METAL Rate of entrainment Size of entraining droplets Residence time of entrained droplets Gas injection 3

4 Objective Simulate slag-metal entrainment using multiphase computational fluid dynamics Use appropriate fluid properties, boundary and initial conditions solve momentum conservation equations to calculate two phase fluid flow use Volume-Of-Fluid (VOF) method to trace the location of slag metal interface 4

5 Generic Transport equation: Governing Equations 5 S D u t k j i w v u u k j i z y x i j k dv

6 Governing Equations Generic Transport equation: t u D S Production or destruction of ϕ Transport of ϕ due to Diffusion Transport of ϕ due to Convection Time Rate of Change of ϕ j dv k i 6

7 Governing Equations Momentum conservation Navier Stokes Equation three equations for a 3-D problem Transported quantity Diffusivity Source term u D S - (Pressure Gradient) (Surface Conservation of Volume fraction of phases F D S Momentum (per unit volume) Kinematic Viscosity (Buoyancy) tension) Volume fraction field F 0 u F t 0 Appropriate boundary and initial conditions 7

8 Volume Of Fluid (VOF) Method Solution of Navier-Stokes equation F t u F 0 F( x, y, z, t) Interface Reconstruction - To locate the interface Stephane Popinet, 2011, Lecture notes Calculate slope of the interface normal F tan F Adjust the interface location based on volume fraction of phases in the cell containing interface 8

9 Some CFD terminologies Discretization Mesh Boundary Conditions (BC) Initial codition Wall BC 0 cell Inlet BC f ( x, y, z, t) Outflow BC Symmetry BC 0 n 9

10 Open Source Package Gerris Flow Solver Developed by Stephane Popinet, NIWA New Zealand Has VOF method Good surface tension model - Important for shapes Adaptive Mesh Refinement Entrainment in ladles is multiscale phenomena small droplets vs large ladle dimensions. Meshing the whole domain with the same mesh to capture droplets will prohibitively increase computation time 10

11 Solution of Navier-Stokes Equations The difficulty in solving these equations arises due to turbulence - characteristic of Reynolds number DNS LES RANS Re Three approaches based on resolution of turbulent length and time scales DNS Direct Numerical Simulation - resolve (calculate) all the length and time scales by using very fine mesh and very small time steps LES Large Eddy Simulation - resolve the larger turbulence structures (eddies) and model only the small ones requires relatively coarse mesh and time steps RANS Reynolds Averaged Navier Stokes equations - model all the scales coarse mesh most affordable for industrial scale problems. UL 11

12 Solution of Navier-Stokes Equations Choose LES Narrow the domain of interest 12

13 Inlet Conditions for Large Eddy Simulation 13

14 Modeling Steel Flow in Ladle SLAG Reduced scale Water Model Without Upper Phase Plume METAL P.E. ANAGBO and J.K. BRIMACOMBE, 1990 Time & Area Averaged gas volume fraction Time averaged Plume Radius Unified Plume Model Kumar and Irons, 2007 R A P 0.55Q 0.49Q z z Enormous DATA 14

15 Modeling of plume Gas-Injection rate (Q) Inlet BC for this problem R P 0.49Q 0.2 z 0.5 Gas-Liquid mixture density A 0.55Q 0.63 ( 1) z G L 1.57 z r S g Buoyancy term Add as source term to Navier-Stokes equation 15

16 Solve Navier-Stokes Equations by RANS RANS incorporates the effect turbulent fluctuations by solving two more equations u t k D D D S S k S k k - Turbulent kinetic energy D D S S ε - Dissipation of turbulent kinetic energy Popularly known as the k-ε turbulence models Output : Time steady, Spatial distributions of u, v, w, k, However, LES needs, not just the effect, but fluctuating velocities too: u, v, w 16

17 Synthesize Turbulence Synthetic Eddy Method Turbulence is not some random fluctuations; the fluctuations are due to coherent structures known as eddies of various length scales. Virtual eddy box 3D channel N. Jarrin, R. Prosser, J.C. Uribe, S. Benhamadouche, D. Laurence,

18 Synthesize Turbulence Synthetic Eddy Method Turbulence is not some random fluctuations; the fluctuations are due to coherent structures known as eddies of various length scales. Virtual eddy box 3D channel N. Jarrin, R. Prosser, J.C. Uribe, S. Benhamadouche, D. Laurence,

19 Synthetic Eddy Method - Verification RANS simulation of Plane Channel Flow (2D) at Re = 6800 Results validated against literature values L = 25D Type of Mesh employed Axial velocity distribution across the channel width Total cells ~ 10,000 19

20 Synthetic Eddy Method - Verification Distributions across the channel width Axial Velocity Shear Stress Normal Stress Synthetic Eddy Method OUTFLOW 3D, time varying Plane Channel Flow with ~ 0.8 Million cells 20

21 Movies 21

22 Comparison of profiles input to and output from Synthetic Eddy method Axial Velocity Shear Stress -1 Axial Stress 22

23 Summary of the Approach Aim to simulate entrainment using multiphase fluid dynamics Use VOF method to track interface Solve Navier-Stokes equation for fluid flow RANS not dynamic; do LES Cannot afford LES for whole domain; narrow the domain of interest Do RANS simulation to generate inlet condition for LES - use RANS profiles RANS SLAG LES as time averaged inlet condition as input to Synthetic eddy method to synthesize turbulence Supply fluctuating components to inlet METAL Plume 23

24 Entrainment Test Case Simulation of a case from literature experimental work by Savolainen et al, 2009 for various oils and water 10 cm 50 cm 15 cm 30 Split the domain into two: Right half do single phase, 3D RANS get flow profiles Left half where entrainment takes place do LES 24

25 Single phase, RANS Simulation of right half of the domain < u < v 0 < <-0.75 w < < 0.05 k 0 < < < <

26 3D LES of left half of the domain 26

27 Movies 27

28 Simulated DATA Entrainment Test Case - Results Frequency Average droplet size Droplet size, mm From simulation 5.2mm Data: 8.5mm Discrepancy due to unaccounted droplets?? 28

29 Acknowledgements Dr. Gordon Irons Dr. Ken Coley Dr. Stephen Tullis Ed McCaffery Md Kashif 29

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