Prediction of Limiting Casting Speed in a Horizontal Direct-Chill Casting through Numerical Modeling and Simulation
Abstract
:1. Introduction
2. Numerical Modeling Protocol
2.1. Protocol for Non-Dimensionalization of the Governing Equations
Description of the Mushy and Slurry Zone
2.2. Specification of the System, Boundary Conditions, and Materials Properties
3. Solution Methods
4. Results and Discussion
4.1. Numerical Model Validation
4.2. Influence of Different Casting Speeds on the Flow Characteristics, Temperature Distribution, Turbulent Viscosity Ratio, Dimensionless Temperature, and Velocity
4.3. Influence of Different Cooling Conditions on the Solid Fraction, Dimensionless Temperature and Velocity, Viscosity, and Sump Length
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Nomenclature
c | specific heat capacity (J/Kg/K) | fluctuating velocity in the i-direction (m/s) | |
constants in the -equation | fluctuating velocity in the j-direction (m/s) | ||
constant in the constitutive equation of eddy viscosity model | x | x-coordinate distance m | |
constants in the V2F length scale | X | X-coordinates dimensionless distance | |
f | elliptic relaxation | y | y-coordinate distance m |
liquid mass fraction | Y | Y-coordinates dimensionless distance | |
solid mass fraction | dimensionless wall distance | ||
g | acceleration due to gravity (m2/s) | W | width m |
volume fraction | Greek Symbols | ||
buoyant production | eddy thermal diffusivity (m2/s) | ||
h | heat transfer coefficient (W/) | thermal expansion coefficient | |
k | turbulent kinetic energy (m2/s2) | turbulence dissipation rate (m2/s2) | |
effective thermal conductivity (W/.K) | ϵ | small number to avoid zero division (0.001) | |
K | Permeability coefficient () | relative viscosity (kg/m. s) | |
partition coefficient | turbulent viscosity | ||
latent heat of fusion (J/Kg) | ρ | density (Kg/) | |
turbulent length scale (m) | turbulent flux Prandtl number | ||
P | pressure in (pascal) | turbulent Prandtl number for k and | |
production of turbulent energy | Reynolds stresses | ||
Turbulent Reynolds Number | Subscripts | ||
T | temperature (K) | c | casting |
turbulence time scale | cr | critical | |
t | time (seconds) | Eff | effective |
velocity variance (m2/s2) | liquid | ||
average velocity (m/s) | inl | inlet | |
casting velocity vector (m/s) | r | relative | |
V | velocity vector (m/s) | reference | |
Gr | Grashof number | s | solid |
Da | Darcy number | t | turbulent |
Pe | Péclet number | Superscripts | |
Re | Reynolds number | * | dimensionless |
St | Stefan number |
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Equations | |
---|---|
Continuity: | |
(1) | |
Momentum: | (2) |
Energy: | (3) |
Kinetic turbulent energy: | |
(4) | |
Turbulent dissipation rate of energy: | (5) |
Velocity variance: | (6) |
Elliptic relaxation: . | (7) |
where: , , , , |
Boundary | Flow Velocity | Thermal |
---|---|---|
Inlet | ||
Refractory | 0 | |
Top mold | Slip boundary | is a function of [2] |
Down mold | Slip boundary | The same with the top mold |
Top direct-chill | is a function of T [2] | |
Down direct-chill | ||
Outlet |
Properties | Values | Unit | References |
---|---|---|---|
Viscosity of the liquid, | 0.0013 | kg/m/s | [1] |
Liquid density, | 2460 | kg/ | [1] |
Liquid thermal expansion coefficient, | 1.17 × | [1] | |
Specific heat, | 1070 | J/kg/K | [1] |
Thermal conductivity of the liquid, Thermal conductivity of the solid, Solid density, | 95 180 2750 | W/m/K W/m/K kg/ | [1] [1] [1] |
Nu | Heat Transfer Coefficient h (W/m2K) |
---|---|
10 | 11,875 |
20 | 23,750 |
30 | 35,625 |
40 | 47,500 |
50 | 59,375 |
60 | 71,250 |
70 | 83,125 |
Sump Length (mm) | |
---|---|
10 | 150.57 |
20 | 126.33 |
30 | 117.91 |
40 | 113.95 |
50 | 111.04 |
60 | 109.58 |
70 | 108.34 |
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Ufodike, C.O.; Nzebuka, G.C.; Egole, C.P. Prediction of Limiting Casting Speed in a Horizontal Direct-Chill Casting through Numerical Modeling and Simulation. Metals 2023, 13, 1071. https://doi.org/10.3390/met13061071
Ufodike CO, Nzebuka GC, Egole CP. Prediction of Limiting Casting Speed in a Horizontal Direct-Chill Casting through Numerical Modeling and Simulation. Metals. 2023; 13(6):1071. https://doi.org/10.3390/met13061071
Chicago/Turabian StyleUfodike, Chukwuzubelu Okenwa, Gaius Chukwuka Nzebuka, and Chijioke Peter Egole. 2023. "Prediction of Limiting Casting Speed in a Horizontal Direct-Chill Casting through Numerical Modeling and Simulation" Metals 13, no. 6: 1071. https://doi.org/10.3390/met13061071