Transient Fluid Flow and Inclusion Motion in the Mold Using LES Models

Transcription

1 Transient Fluid Flow and Inclusion Motion in the Mold Using LES Models Quan Yuan Department of Mechanical Engineering University of Illinois at Urbana-Champaign September 5,

2 Acknowledgements Professor B.G.Thomas Professor S.P. Vanka AK Steel Allegheny Ludlum Corp. Columbus Steel ISPAT Inland Steel LTV Steel Stollberg, Inc National Science Foundation

3 Objective Investigate transient flow structure in continuous casting nozzles; Investigate the effect of inlet flow structure on - Flow pattern of the jet in the mold; - Velocity on the top surface; - Transient flow characteristics; - Validation of LES models; - Particle behavior.

4 Previous Work Two-phase fluid flow in continuous casting nozzles using k-ε model (Hua Bai); Two-phase flow in molds using k-ε model ( Tiebiao Shi) Investigation of transient flow in.4 scale water model with inlet generated from a fully developed duct using LES (Sivaraj Sivaramakrishman).

5 Investigation of.4 Scale Water Model

6 x y z Water 4 o opened flow rate:.756m 3 /s Slip free.8m 3mm.37m.75m 3 o down 3 o down.95m Left half region * (LES simulation domain) Right half region Symmetry Outlet port.73m Sketch of.4 scale water model and simulation domain

7 LTV.4 scale water model and nozzle Dimension/Condition* Value SEN length 344 SEN bore diameter SEN submerged depth Port width x height Port angle Recessed bottom well depth Water model height Water model width Water model thickness 3mm 7-8mm 3mm x 3mm 4 o upper edge 5 o upper edge 4.8mm 95mm 735mm 95mm (top) to 65mm (bottom) Liquid flow rate 3.53 x -4 m 3 /s Gas injection % *From: () Hua Bai, Argon Bubble Behavior in Slide-gate Tundish Nozzle during Continuous Casting of Steel Slab, Ph.D thesie; () Sivaraj Sivaramakrishnan et al, Transient Flow Structures in Continuous Casting of Steel, 83th Steelmaking Conference Proceedings, Poittburgh PA, March 6-9

8 Table Dimensions and conditions of the nozzle and.4 water model Dimension/Condition Simulated length of upper nozzle Truncated length Diameter of upper nozzle Inlet velocity of upper nozzle Height thickness(y z) of bottom nozzle Simulated length (x) of bottom nozzle Truncated length (x) of the bottom nozzle Value 437 mm 3 mm 3 mm.56 m/s 7mm x 3mm 66 mm 54 mm Port opening of.4 water model 3mm x 3mm Water model height 95 mm Water model width 365 mm Water model thickness 8 mm Averaged inlet velocity at port.44 m/s Averaged jet angle at port 3 o Liquid flow rate through each port m 3 /s Casting speed.78 m/min Liquid density kg/m 3 Liquid material viscosity. Pa/m * The dimensions of the case are to match the LTV.4 water model

9 Model assumptions - uniform vertical flow entering domain from slide gate bottom; - pi-shaped slide gate opening - one-way coupled flow between nozzle top and bottom and between nozzle bottom and mold; - no gas injection or mod air pockets (fully primed) flow; - flow angled exiting ports simulated by coordinates transformation of horizontal port results; - Smagorinsky subgrid scale model employed in transient LES solution of N-S equations; - steel shell neglected; - top surface level in mold is a horizontal plane; - free slip along top surface; - mold bottom holes are modeled as square ports with fixed outlet velocity.

10 x z Water Upper nozzle y 3mm 37mm d=3mm Transient velocities truncated here and employed as the input of the bottom nozzle. Transient velocities truncated here and employed as the input of the mold. Outflow for bottom nozzle 54mm 7mm 3mm Bottom nozzle Outflow for upper nozzle Simplified nozzle simulation

11 Simulation Procedure The nozzle was divided into pieces: upper nozzle and bottom nozzle, Flow in the pieces were simulated separately using LES Simulation in the upper nozzle was performed with a grid consisting of nodes in the direction of y, θ and r; Transient velocities in the upper nozzle were truncated 3mm below the inlet opening every.75s for.875s after flow reached stationary state (.875s prior simulation) and employed as the input of bottom nozzle, the simulation takes CPU s per time step or 4 days on Pentium 45 for the total.75s; Simulation in the bottom nozzle was performed with a grid consisting of nodes in the direction of x, y and z; Transient velocities in the bottom nozzle were truncated every.5s for.75s after flow reached stationary state (.75s prior simulation),the simulation takes 8.6 CPU s per time step or 7 days for the total 3.5s. The truncated velocities at the left port were then rotated an angle of 3.4 o to generate the 3 o down inlet jet for the model.

12 Instantaneous flow in the upper nozzle (top) A' z (m) A.. A' z (m) A.m. A' z (m) A..m/s:.3 A.3 A'.3 A' inlet A y (m) y (m) y (m) (a) t=t (b) t= t +.s (c) t= t +s.

13 Instantaneous flow in the upper nozzle (middle) A' z (m) - A y (m) A' z (m) - A y (m) A' z (m) - A y (m) A'.m/s: inlet A (a) t=t (b) t= t +.s (c) t= t +s.

14 Instantaneous flow in the upper nozzle (lower) A' z (m) - A.6 A' z (m) - A.6 A' z (m) - A.6.m/s: A' inlet A y (m) y (m) y (m) (a) t=t (b) t= t +.s (c) t= t +s.

15 Time averaged flow in the upper nozzle (top) z (m) y (m).m/s: z(m) z(m) u (m/s) (a)velocity vector (b) streamline and (c) axial velocity contour

16 Time averaged flow in the upper nozzle (middle) z(m) m/s:. z(m) z(m) u (m/s) (a)velocity vector (b) streamline and (c) axial velocity contour.6.6

17 Time averaged flow in the upper nozzle (lower) z(m) m/s: z(m) m. z(m) (m/s) u (a)velocity vector (b) streamline and (c) axial velocity contour

18 Time averaged axial velocity at the truncation plane between upper and bottom nozzle. z (m) -. Contour unit: m/s. z (m) A' A x(m) A'.. A x (m) (a) Cylinder coordinates Through interpolation (b) Cartesian coordinates Contour lines of axial velocity at the trunction port

19 Upper Nozzle Validation Axial velocity V y (m/s) LES simulation, 37mm below slid gate CFX prediction, 37mm below slide gate LES simulation, 3mm below silde gate. z(m) -. *CFX Prediction: HuaBai, Transient Flow Structures in in Continuous Casting of of Steel, Steelmaking Conference Preceedings and unpublished results.

20 Upper Nozzle Observations LES simulation matches CFX prediction (validated with PIV); Recirculation region in the upper nozzle is located at -mm below the the blocked half side of the slide gate; the transient flow structures in the recirculation region include small transient swirls which have changing location; while the time-averaged flow structure in the upper nozzle only contains rolls in the region; No negative time averaged axial velocity was found mm below the slide gate; Axial velocity is consistently larger on the opening side than the other side; this asymmetry is still apparent at the truncation plane where the maximum of the axial velocity is displaced at 3mm from the center line of the bore; Turbulent flow in the nozzle is very large and significant: maximum timeaveraged secondary flow speed at the truncation plane is only.5% of the mean axial velocity while the maximal transient secondary flow speed is 68% of the mean axial velocity.

21 Bottom nozzle time averaged secondary flow z(m)..m/s:. -. View into port: center plane between the truncation planes

22 Bottom nozzle transient secondary flow. z(m) -..5m/s. z(m) Secondary flow at the left truncation port at two different instant

23 Bottom nozzle time averaged secondary flow Slice5 Slice4 Slice3 Slice Slice z(m) z.m/s: View into port: (a) left truncation plane (b) right truncation plane* Observations:The time averaged flow contains almost symmetrical rolls at both of the truncation planes corresponding to the physical outlet ports; no apparent flow pattern difference was found between the ports. *The two planes are 6.5mm from the center line of upper nozzle.

24 Bottom nozzle time averaged velocities (sideview) x(m).5.m/s: (a) Slice. - x y.5.m/s: (b) Slice. - x(m).5.m/s:..5 5 (c) Slice 3.

25 Bottom nozzle time averaged velocities (sideview) x(m).5.m/s:..5 5 (d) Slice 4. x(m).5.m/s:..5 5 (e) Slice 5. What is jet angles exiting the two ports: Using Equations at the truncation cross planes: u = [ ui, j, ku i, j, k yi, j, k zi, j, k ] [ U i, j, k yi, j, k zi, j, k ] α = a tan( u / v) ; ; v = [ vi, j, ku i, j, k yi, j, k zi, j, k ] [ U i, j, k yi, j, k zi, j, k ] i, j, k ui, j, k + vi, j, k wi, j, k U = +. u and v are weighed velocity component in x and y direction respectively at the planes; α is the weighed flow angle with horizontal plane; The flow is.37 o up at the left plane and.3 o up at the right plane; Transient velocities were translate 3.4 o to generate the 3 o down angle to the mold. ;

26 Bottom nozzle observations The outflow of the simplified bottom nozzle contains turbulent transient swirls The flow at the port outlets contains important transient swirls and similar velocity variations along the vertical direction, which affects the flow pattern in the mold The time-averaged outflow contains almost symmetrical swirls which have been observed sometimes (<s) by Hershey; however this does not match the k-ε model s prediction for the PIV modeled nozzle (validated by experiments). The reason may be()the downstream's effect on the up-stream () insufficient simulation time for both upper nozzle and bottom nozzle and (3) geometry simplification Longer simulation time needed to get the low-frequency transients More accurate geometry should be molded to get the full swirl observed

27 .4 water model time averaged velocity vector (a) LES simulation (b) PIV measurements Center plane between wide faces

28 .4 water model instantaneous velocity vector (a) LES simulation (b) PIV measurements Center plane between wide faces

29 Flow near the nozzle port in the mold Time-averaged Time-averaged PIV PIV Measurements Measurements University of Illinois at Urbana-Champaign Computational Fluid Dynamics Lab/Metals Processing Simulation Lab Quan Yuan

30 Flow near the nozzle port in the mold.m/s: x y (b) transient velocity (c)time-averaged velocity

31 Flow near the nozzle port in the mold Distance from the bottom of the port (mm) PIV measurement CFX prediction Inlet for LES simulation Fluid velocity (m/s) Comparison of inlet fluid velocity (u +v ) / along the center line of the port

32 Horizontal velocity towards SEN -U (m/s) PIV:casting speed=.554m/min PIV:casting speed=.79m/min CFX: casting speed=.663m/min LES: casting speed=.78m/min *Casting speed refers to that in the.4-scale water model SEN Distance from SEN (m) Horizontal velocity towards SEN -U along the center line on the top surface NF *PIV and CFX results: Sivaraj Sivaramakrishnan et al, Transient Flow Structures in Continuous Casting of Steel, 83th Steelmaking Conference Proceedings, Poittburgh PA, March 6-9

33 PIV measurements LES simulation. Horizontal velocity towards SEN -U (m/s) Time (s) Variation of horizontal velocity towards SEN -U at the point on the top surface half way between SEN and NF

34 Mold Flow Observations LES simulation compares reasonably with PIV measurements and has better agreement at top surface with new inlet condition Constant symmetrical inlet swirls allow jet to bend upwards and cause higher surface velocity and generate greater velocity fluctuation on the top surface (relative to Sivaraj Sivaramakrishnan s LES simulation*, fully developed pipe inlet) The staircase flow pattern of the jet is not obvious in LES simulation, which is likely due to symmetrical swirls in this inlet flow instead of a single strong swirl; further study needs to be conducted about this. * Transient Flow Structures in in Continuous Casting of of Steel, 83th Steelmaking Conference Proceedings, Poittburgh PA, March 6-9

35 Transient Flow and Particle Motion in a Full Scale Water Model

36 Sketch of the full scale water model and simulation domain Water x y z.38m Free slip.965m Inflow: V=.69m/s 5 degree down Inlet jet: 5 degree down.5m A' A Inlet Port Outflow Symmetry 5mm A-A' 56mm Outlet port (a) (b)

37 Table Conditions for LES Simulation Parameter Case Case Domain Length.5m - Domain Width.965m - Domain Thickness.38m - SEN Submerged Depth.5m - Averaged Jet Angle (match port angle) 5 o down - Inlet port 5mm x 56 mm oval 5mm x 5mm circular Averaged Inlet Velocity.69m/s.56m/s Model Inlet Velocity Profile transient, interpolated from upper nozzle simulation uniform Inlet flow rate (each port) Simulated Casting Speed.344m 3 /s (corresponding to 4.5kg/s of 7kg/m 3 density steel) 5.mm/s (35.9inch/min or.9m/min).4(m 3 /s) (corresponding to 5.kg/s of 7kg/m 3 density steel) 9.3mm/s (.97inch/min or.558m/min)) Laminar Kinematic Viscosity. -6 m /s - Inlet Reynolds number Liquid Density kg/m 3 - Particle's Material Density 988kg/m 3 998kg/m 3 Particle's Material Diameter 3.8mm.5mm Corresponding Inclusion Density in Steel Caster Corresponding Spherical Inclusion Diameter in Steel Caster Simulation Mesh ( x y z) Simulation Speed on Pentium 75MHz 7 kg/m 3 7 kg/m 3 3µm µm CPU s/ time-step (3.s /day) Case is to match the experiment in references 5 CPU s/ time-step (3.5s /day) - : same as Case () R.C.Sussman et al, Inclusion Particle Behavior in a Continuous Slab Casting Mold, Iron and Steel Society, Warrendale, PA, 99, pp.9-34

38 Instantaneous velocity profile (case ) x(m) m/s:. y (m) Center plane between wide faces, instant

39 Instantaneous velocity profile (case ).8 x(m) y (m) Center plane between wide faces, instant

40 Instantaneous velocity profile (case ) x(m).5.5 y (m).5 Center plane between wide faces

41 Time averaged velocity profile (case ) m/s: Velocity vector profile at the center plane between wide faces

42 Time averaged velocity profile (case ).8 x(m) m/s: Velocity vector profile at the center plane between wide faces

43 Time averaged velocity profile (case ) x(m) Velocity vector profile at the center plane 34mm from wide face

44 Validation of flow in the mold 5 mm from SEN mmfromsen 46mm from SEN 9mmfromSEN velocity (m/s) velocity(m/s) velocity (m/s) velocity (m/s) Distance below the top surface (m) LES Simulation Experiment, Set Experiment, Set Comparison of velocity (V x + V y ) / between LES simulation and measurements Experiment results: B.G.Thomas, Simulation of of Argon Gas Flow Effects on a Continuous Slab Caster, Metallurgical and Material Transaction B, Volume 5B, August 994, pp

45 Comparison of nondimensionalized top surface velocity Nondimensionalized horizontal velocity towards SEN (-U / V inlet) Case : casting speed=5.mm/s Case : casting speed=9.3mm/s Distance from SEN (m)

46 Mold Flow Observations LES simulation matches the hot-wire anemometry speed measurements and was validated Time averaged jet in case bends upward a little while it is straight in case ; related to.4 scale water mold results, transient second flow, especially swirls, with considerable magnitude, is likely the reason to allow jet to bend upward Horizontal velocity at meniscus nondimensionalized with inlet velocity is consistently greater in case than that in case ; as found in.4 scale water model, the transient of inlet flow has an important influence on meniscus speed

47 Particle simulation assumptions Particles are sphere and have uniform size; Only drag force, buoyancy and gravity force act on each particle; Particles are small enough to achieve their local terminal velocity everywhere they move; Particle interaction neglected; Particles don t affect flow pattern (case ).

48 Numerical settings for particle simulation Table 4 Simulation settings for particles, case Particle group Amount of particles Input time index 5 s-.6s 5 s-.4s 5 4s-4.4s 3 5 6s-6.4s 4 5 8s-8.4s 5 5 s-.4s Table 5 Simulation settings for particles, case Particle group Amount of particles Input time index 5 s 5 s 5 4s 3 5 6s 4 5 8s 5 5 s Particles were input at random position at the inlet port and initialized with local transient velocity: z (m)

49 Typical particle trajectories x (m)... z(m) x(m)... z (m) (a) Moving to the meniscus without going through lower roll

50 Typical particle trajectories x(m)... z(m) x(m)... z(m) (b) Moving to the meniscus after going through lower roll

51 Typical particle trajectories x(m)... z(m) x(m)... z(m) (c) Moving out of the domain through outlet port

52 Typical particle trajectories x(m)... z(m) x(m)... z(m) (d) Recirculation between upper and lower rolls

53 Particle transport in mold x(m) Time=.seconds 5 particles X Z Y x(m) Time=.4seconds 5 particles X Z Y (a) (b)

54 Particle transport in mold -.. Time=.4seconds 5 particles X Z -.. Time= 4.seconds 5 particles X Z...3 Y.3 Y x(m) x(m).3.. (c) (d)

55 Particle transport in mold x(m) Time=.seconds 5 particles X Z Y x(m) Time= 5.seconds 5 particles X Z Y (e) (f)

56 Particle transport in mold -.. Time=.secon 5 particles X Z -.. Time= 4.secon 5 particles X Z...3 Y.3 Y x(m) x(m).3.. (g) (h)

57 Validation and results particle simulation: Table 6 Statistic of particles moving to the meniscus within s after each group's input, case Particle group Particles moving to the meniscus index Amount Percentage Average % 6.96% 36 7.% % % 5.56% % % Statistic result in experiment measurements:.3%. Table 7 Statistic of particles moving to the meniscus within s after each group's input, case Particle group Particles moving to the meniscus index Amount Percentage Average % 5.6% 45 9.% 96 9.% %.8% % 5 5.%

58 Particle Behavior Observations Typical particle trajectories in LES simulation were similar as found in the experiment*; The percentage of particle moving to the meniscus in the simulation case matches the experiment measurements*, in which 3.% particles moving into meniscus within seconds after the particle injection; the mathematical model was validated; In case, different particle input time can lead to statistic results with considerable differences, while the averaged results converges to a constant number; this may imply that transient structures near the inlet have an important influence of particle motions and thus sufficient input time is required to get accurate statistic results; the big discrepancy in case may be due to the too short input time; More particles consistently move to the top surface in case within seconds after their input; this suggests that jet flow pattern has an important influence on particle motions in the mold; the transient "wiggling" of the jet may contribute to the particle moving to meniscus. *R.C.Sussman et et al, Inclusion Particle Behavior in in a Continuous Slab Casting Mold, Iron and Steel Society, Warrendale, PA, 99, pp.9-34

59 Conclusions LES results match PIV measurements (LTV) in top surface velocity and jet bending; Transient swirls in inlet are likely an important parameter affecting both the time averaged and transient variation of the velocity on the top surface; Transient secondary flows, especially swirls, are likely the main reason allowing jet bending upwards; Particle simulation using LES matches experiment measurements (AK Steel) in the statistic of particle moving to the meniscus within the starting seconds; 4 typical particle trajectories were found in the water model matching observations in the experiment (AK Steel); Transient flow in the inlet and jet have an important influence on particle motions in the mold; wiggling of the jet likely transport more particles to the meniscus than straight jet does.

60 Future Work Model both left and right sides of the caster Model the open bottom mold side face curvature Investigate the behavior of a range of particles Investigate heat transfer in the mold