Casting Solidification Analysis
Theory: latent heat and heat flow into the mould
Overview
How does solidification analysis differ from ordinary heat conduction?
Two things: the latent heat released on freezing and the treatment of the mould boundary. Metals release a lot of heat as they freeze (about 270 kJ per kg for steel), so temperature lingers near the melting point. Alloys freeze gradually between liquidus and solidus, releasing latent heat according to solid fraction over that range. Numerically, enthalpy is used as the unknown instead of temperature, or latent heat is treated as extra specific heat. As for the boundary, in sand moulds the mould's own resistance to heat flow sets the freezing rate, whereas in permanent moulds the casting-mould interface heat transfer (which drops sharply when a shrinkage gap opens) controls it. Which one dominates decides which inputs need the most care.
Enthalpy method
H is enthalpy, c specific heat, L latent heat and f_l liquid fraction. Solving for H instead of temperature handles latent heat release stably.
Chvorinov constant for sand moulds
ρ_m, L and T_m are metal density, latent heat and melting point, T₀ the initial mould temperature, and k, ρ, c (subscript mo) the mould's conductivity, density and specific heat. It assumes a semi-infinite mould controlling heat flow and ignores superheat.
A square law found by a Czech engineer
The law that freezing time scales with the square of the modulus was published in 1940 by the Czech foundry engineer Nicolas Chvorinov. Measuring freezing times for castings of many shapes, he showed they collapse onto volume ÷ surface area regardless of shape. In the pre-computer era it became a powerful tool for sizing risers, and it is still used for estimates before simulation and for checking results.
Worked examples
The table substitutes constant assumed properties into an ideal model, not a guaranteed freezing time for a particular alloy. The aluminium row assumes a single melting temperature close to pure aluminium. Real alloys require freezing ranges, superheat, finite mould thickness and interface thermal resistance.
Example: freezing times of steel and aluminium alloy in silica sand
Silica sand: conductivity 0.6 W/(m·K), density 1,600 kg/m³, specific heat 1,170 J/(kg·K). Steel: liquid density 7,000 kg/m³, latent heat 272 kJ/kg, melting point 1,810 K. Aluminium: density 2,385 kg/m³, latent heat 398 kJ/kg, melting point 933 K. Initial mould temperature 300 K.
| Metal | Chvorinov constant B | 20 mm plate | 50 mm plate |
|---|---|---|---|
| Steel | 1.11 s/mm² | 111 s (1.9 min) | 695 s (11.6 min) |
| Aluminium alloy | 1.57 s/mm² | 157 s (2.6 min) | 983 s (16.4 min) |
An infinite plate's modulus is half its thickness; 2.5 times the thickness means 6.25 times the freezing time. Adding superheat lengthens it further.
I plan to make the same shape in a permanent mould and used this sand constant to estimate freezing time. Is that a problem?
It will be far off. The constant was derived for sand — a mould that conducts heat poorly and controls the heat flow — and does not carry over to metal moulds. Mould steel conducts heat tens of times better than sand, so the casting-mould interface heat transfer controls the flow, and freezing time tends toward being roughly proportional to the modulus rather than its square. The interface coefficient is also large right after pouring (thousands of W/(m²·K)) and drops to hundreds when the casting shrinks and a gap opens. In simulation, supplying this interface heat transfer as a function of time, temperature or gap size drives the result most. For permanent moulds, identify it by matching measured cooling curves.
Practical workflow
- Prepare liquidus, solidus, latent heat and solid-fraction curve of the alloy, and mould properties as functions of temperature.
- Estimate freezing times of main sections with Chvorinov's rule as a magnitude check.
- Start solidification from the filling analysis temperatures.
- Check last-to-freeze regions, isolated liquid and gradients; adjust risers and chills.
- Compare with thermocouple cooling curves and tune interface heat transfer and mould properties.
“The flat part of the cooling curve”
A thermocouple in a casting shows a plateau near the melting point where temperature barely falls — latent heat is being released, and its length roughly equals the local freezing time. Overlaying simulated cooling curves and checking that plateau length and level match verifies latent heat, solid-fraction curve and interface heat transfer together.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Forgetting latent heat | Freezing far too fast | Check enthalpy data |
| Using sand constants for metal moulds | Freezing time far off | Model interface heat transfer |
| Constant interface coefficient | Gap effect missed | Function of time or temperature |
| Linear solid-fraction curve | Wrong last-to-freeze region | Use the alloy's curve |
| Skipping filling, uniform start temperature | Wrong freezing order | Start from filling results |
I'd like to learn related topics.
Related pages include casting filling analysis, casting defect prediction, investment casting simulation and casting residual stress analysis.
Frequently asked questions
What does casting solidification analysis solve?
Heat conduction in metal and mould with the release of latent heat on solidification added. In the mushy zone latent heat is released according to solid fraction, handled by the enthalpy or apparent-heat-capacity method. Interface heat transfer between mould and casting and heat loss from the mould exterior are boundary conditions, and the analysis gives when each point freezes (order and time) and the thermal gradients.
How is solidification time estimated?
By Chvorinov's rule, time scales with the square of the modulus (volume ÷ cooling area). For sand moulds, where the mould controls heat flow, the constant B can be computed from mould conductivity, density and specific heat and from the metal's latent heat and melting point. In silica sand it is about 1.11 s/mm² for steel and 1.57 s/mm² for aluminium alloy, so a 50 mm plate takes about 12 min in steel and 16 min in aluminium.
Why does lower-melting aluminium take longer to freeze?
In sand moulds the mould sets the rate of heat removal. Aluminium's low melting point gives a small temperature difference to the mould, so the mould draws heat less strongly; with its latent heat per volume, freezing takes longer than for steel. In permanent moulds that conduct heat well, the situation changes and interface heat transfer controls freezing time.
References and scope of verification
Numbers are educational reference calculations under the stated assumptions. Sources document theory and setup, not proof that these numerical values were reproduced in each package. Engineering decisions require validation for the actual conditions.
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