Simulation of Steel Casting Thermal Behavior

Start with the Single
Governing Idea:
Energy + Latent Heat

Every continuous casting simulation ultimately begins with one governing principle: energy conservation. Heat flows through the material according to classical conduction laws, but at the solid-liquid interface an additional phenomenon emerges. As liquid metal transforms into solid, enormous quantities of latent heat are released. The interaction between heat transport and phase transformation creates a moving boundary problem known as the Stefan problem, which forms the foundation of modern solidification modeling.

Four Core Physical Concepts

Within both the fully liquid steel and the growing solid shell, thermal energy transport is governed by Fourier heat conduction. This equation describes how temperature changes over space and time as energy flows from hotter regions toward cooler regions.

The complexity arises because liquid steel and solid steel possess different thermal properties. Thermal conductivity, density, and specific heat vary across the phase boundary, requiring simulation algorithms to update material properties continuously as solidification progresses.

Properties That Change Across The Interface

At the moving solid-liquid boundary, a special energy balance known as the Stefan condition must be satisfied. This relationship links interface velocity directly to the difference in heat flux arriving from the liquid side and leaving through the solid side.

The resulting energy imbalance cannot disappear. Instead, it is consumed by the phase transformation process itself, driving movement of the solidification front and controlling shell growth throughout continuous casting.

Stefan Energy Balance

During solidification, steel releases enormous quantities of latent heat. For typical steel grades, latent heat is approximately 270 kJ/kg, making it one of the largest energy contributions in the entire casting system.

This energy release strongly influences shell growth, temperature gradients, mold heat flux, and cooling behavior. Any simulation that neglects latent heat or models it inaccurately will significantly underestimate solidification rates and shell thickness development.

Latent Heat Controls

Classical heat-transfer problems typically involve fixed boundaries whose positions are known in advance. Continuous casting is fundamentally different. The location of the solid-liquid interface is unknown and must be determined simultaneously with the temperature field.

This moving interface is described as a free boundary. Every change in temperature influences interface position, while every movement of the interface alters the temperature field. The two quantities remain tightly coupled throughout the entire solution process.

Coupled Solution Process

Why “Solidification” Breaks Simple Simulations

The elegance of the Stefan formulation conceals a profound numerical challenge: once the interface position becomes an unknown, the problem becomes inherently nonlinear.

In a standard conduction problem, the computational mesh is fixed and temperatures are solved at known node locations. In a moving-boundary problem, the interface position changes with every time step — and its position depends on the very temperature field you are trying to solve.

This circular dependency makes explicit time-stepping schemes unstable, while implicit schemes require careful treatment to avoid oscillation or non-convergence. Mesh-tracking approaches can be accurate but become computationally expensive and prone to mesh distortion over large displacements.

Why Generic Thermal Solvers Are Not Enough

These numerical challenges explain why industrial casting simulators require significantly more sophisticated code architecture than generic thermal solvers.

Connecting Temperature to Fraction Solid

Capturing the mushy zone correctly requires coupling the thermal solver to thermodynamic databases such as IDS or Thermo-Calc, which compute equilibrium or non-equilibrium fraction solid as a function of temperature and alloy composition.

From Sharp Boundary to Physical Reality

The Thermal Detail That Damages Parts

The shell/mold thermal interaction is a micron-scale phenomenon with meter-scale consequences: a flux gap of 0.1–0.3 mm can halve heat flux and double shell temperature, directly triggering cracks and breakouts.

Online Era: Fast Coupled
Heat Transfer + Solidification
+ Microstructure

The ultimate objective of casting simulation is not simply offline analysis but active process control. Advances in computational speed, validated physical models, and industrial-scale data integration have enabled simulation systems capable of supporting real-time operational decisions. Modern online-capable environments combine thermal modeling, solidification prediction, microstructure evolution, and cooling optimization into a unified framework that continuously guides production toward defined quality targets.

Three Core Digital Platforms

CastManager is designed specifically for continuous casting environments where calculations must be completed fast enough to support operational decisions. The software computes thermal behavior from mold entry through secondary cooling and up to the final solidification point along the strand.

Its primary challenge is balancing computational speed with physical accuracy. Advanced numerical optimization techniques allow the system to produce accurate shell thickness, mold heat-flux, and temperature predictions while remaining suitable for real-time control environments.

CastManager Computes

IDS (Interdendritic Solidification) converts thermal predictions into metallurgical outcomes. Using alloy chemistry and local cooling conditions, it calculates fraction-solid evolution, solidification paths, partition coefficients, and equilibrium or non-equilibrium transformation behavior.

The software transforms temperature histories into practical quality indicators, allowing engineers to predict casting performance before defects become observable in production.

IDS Predicts Quality Risks

Tempsimu focuses on the secondary cooling region where most solidification is completed. Before engineers implement changes on the caster, the software evaluates proposed modifications such as spray-zone redesign, nozzle adjustments, altered water distributions, roll configuration updates, or revised cooling-zone boundaries.

By evaluating these changes virtually, engineers can identify undesirable thermal consequences before operational deployment, reducing production risk and protecting product quality.

Tempsimu Evaluates

Online Control Architecture

From Equations to Reality: Continuous Casting Is Not Just Heat

While the Stefan problem captures essential solidification physics, a real continuous casting machine demands far more. High-fidelity simulation couples turbulent fluid flow, thermal transport, and solidification into a computationally demanding multi-physics problem.

Liquid steel flowing through the submerged entry nozzle (SEN) and into the mold pool is turbulent, highly inertial, and thermally stratified. High-fidelity studies solve the full three-dimensional, time-dependent Navier–Stokes equations coupled to the energy equation.

Turbulence models such as k-ε, LES, or hybrid approaches capture the flow structures that directly influence shell formation and inclusion transport.

At the point where the liquid steel jet strikes the solidifying shell — the jet impingement zone — local heat fluxes reach extraordinary magnitudes. These extreme values drive rapid initial shell formation and influence whether the nascent shell can withstand ferrostatic pressure as it exits the mold.

Grid Resolution Demands

Steep thermal and velocity gradients near the jet impingement zone and solidification front demand very fine computational grids. Industrial-scale molds can therefore push simulations into high-performance computing territory.

Why Flow Cannot Be Ignored

A purely conductive thermal model of the mold pool dramatically misrepresents the temperature distribution. Turbulent convection by the steel jet homogenizes much of the liquid pool, elevating temperatures in recirculation zones and maintaining superheat deeper into the strand than conduction alone would predict.

Simulation Becomes a Process-Design Tool

Coupled flow-thermal simulations reveal how SEN geometry, mold electromagnetic stirring configurations, and casting speed influence the process. This enables virtual prototyping of new nozzle geometries before costly physical trials.

Continuous Casting Is a Coupled Physics Problem

Accurate simulation must connect turbulent flow, heat transfer, and solidification. Only by resolving their interaction can engineers predict shell formation, superheat penetration, heat-flux distribution, and the process response of a real continuous casting machine.