NUMERICAL MODELING OF THERMAL PROCESSES IN COMPLICATED REGIONS WITH LARGE CHANGES IN MATERIAL CHARACTERISTICS AND PROPERTIES

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1 NUMERICAL MODELING OF THERMAL PROCESSES IN COMPLICATED REGIONS WITH LARGE CHANGES IN MATERIAL CHARACTERISTICS AND PROPERTIES YOGESH JALURIA Department of Mechanical and Aerospace Engineering Rutgers, the State University of New Jersey New Brunswick, NJ IMECE, Anaheim, CA

2 Topics Considered Modeling and Simulation Material Properties, Complex Domains Polymer Processing Optical Fiber Drawing and Coating Solidification and Other Processes Validation Enclosure Fires, Electronic Systems Conclusions and Future Research Needs

3 Different Approaches COMPLICATED GEOMETRY Transformed Domain:. Simple Grids for FDM and FVM Physical Domain: Complex, Arbitrary Discretization for FEM, FVM VARIABLE MATERIAL PROPERTIES Properties at Previous Time Step or Iteration Extrapolated Values Iterative Property Correction

4 Twin-Screw Food Extruder Feed Hopper Rotating Screw Extruder Channel Heating/Cooling Arrangement Die

5

6 Sketch of Single-Screw Polymer Extruder

7 Model of Single-Screw Polymer Extruder

8 Material Properties Accurate Data on Material Properties Material Property Variations with Temperature, Shear Rate, Concentration, Pressure, etc. Link Between Properties and Process

9 Material Properties: Shear Stress Versus Shear Rate

10 Material Properties: Viscosity Variation GLASS ν = exp [ 32 (T melt /T - 1) ] POLYMER μ = μ o (. γ /. γ o ) n - 1 exp ( b /T ) REACTIVE POLYMER μ = μ o (. γ /. γ o ) n - 1 exp [ -b (T - T o )] exp [ -b m (C - C o )]

11 Chemical Kinetics FOOD d[(1-x)]/dt = -K (1 X) m with K = K T + K S where K T = K To exp ( - E T / RT ) K S = K So exp ( - E S /τ η ) X: Degree of Conversion CVD K = K o p SiH4 /[1 + K 1 p H2 + K 2 p SiH4 ]

12 Transport in the Channel of a Single-Screw Polymer Extruder

13 Model of Extruder with Arbitrary Screw Profile

14 Distributive Mixing in Extruder Channel

15

16 Measured and Calculated Temperature Profiles in Single- Screw Extruder 3D (FEM) 2D (FDM)

17 Modeling of Twin-Screw Polymer Extruder

18 Flow in NIP Region of Twin-Screw Extruder

19 Flow in the Region Between Two Co-Rotating Cylinders

20 Measured and Calculated Velocity Profiles in Polymer Extrusion

21 Modeling of Flow through Extrusion Dies

22 Optical Fiber Drawing System Drawing Furnace Fiber Cooling Coating Curing Take-Up

23 Sketch of Optical Fiber Drawing System

24 Material properties: Radiation Properties of Silica Glass

25 Cylindrical Draw Furnace and Finite Zones For Radiation Analysis

26 The Governing Equations for Glass and Inert Gas

27 Schematic Diagram of Double-layer Optical Fiber r (1), u, u (2) r, u a a z (1), v, v (2) z,va (2) r 0 V g (1) r 0 Core R F Cladding L Fiber (1) r f (2) r f Furnace V f

28 Landau s Transformations Glass Layer One Gl ass Layer Two Inert Gas Cylinders

29 Generation of Neck-Down Profile

30 Iterative Convergence Of Neck-Down Profile

31 Streamlines in Optical Fiber Drawing

32 Isotherms in Optical Fiber Drawing

33 Neck-Down Profile from Numerical Simulation and Experimentation

34 Calculated Versus Measured Tension in Optical Fiber Drawing

35 Flow in Fiber Coating Process Open-Cup Pressurized

36 Grid Generation in the Fiber Coating Process

37 Meniscus in Fiber Coating Process A, C: Unpressurized B, D: Pressurized

38 Effect of Meniscus

39 Pressure contours for v f =11 m/s Pressure distributions along the die wall for various fiber speeds Pressure Distributions in Coating Die

40 Melting in Enclosed Region

41 Solidification of Water in an Enclosure with Conjugate Effects

42 Melting of Gallium in Enclosed Region Streamlines Isotherms

43 Measured Versus Calculated Solid- Liquid Interface in Solidification

44 Solidification with Conjugate Transport at the Wall Isotherms Streamlines

45 Chemical Vapor Deposition

46 Contours in Horizontal TiN CVD Reactor

47 Film Growth in a Horizontal CVD Reactor

48 A Typical Room Fire

49 Room & Corridor System

50 Laminar Flow Generated by a Fire in a Room with an Opening

51 Flow and Thermal Fields for Turbulent Flow (a) Steady state flow and thermal Field, (a) Isotherms and (b) Streamlines. (b)

52 Flows in a Vertical Elevator Shaft and in a Stairwell From Marshall (1986)

53 Natural Convective Cooling of Electronic Equipment

54 Flow in an Enclosure due to Isolated Heat Sources

55 Governing Equations with Variable Properties

56 Governing Equations with Variable Properties

57 Governing Equations with Variable Properties

58 Steady Streamlines on Y-Z Planes for 3D Flow in a Channel

59 Isotherms on the Horizontal Midplane at τ=8.0 (Top Figure) and τ=24 (Bottom Figure) for Re=20, Gr=10000 and Ar=10.0

60 Conclusions Strong Need for Material Properties Must Model Changing Material Characteristics Use of Properties at Previous Time or Iteration Convenient Improved Accuracy and Convergence with Extrapolated Property Values Transformations, FEM, other Approaches for Complex Geometry

61 Conclusions (Contd.) Important to Employ Suitably Grid Critical to Represent Boundary Conditions Correctly Convergence Characteristics Strong Functions of Numerical Scheme Experimentation for Validation and Insight

62 Flow in Neck-Down Region During Optical Fiber Drawing

63 Viscous Dissipation and Temperature in Neck-Down Region During Optical Fiber Drawing

64 Flow and Temperature Fields in a Horizontal CVD System

65 Experimental and Numerical Results on Horizontal Channel Flow for CVD

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