Can a faster quench buy axial order?
To grow lamellae along a cuvette you want the first crystals to nucleate at the closed end and grow up the axis. The obvious lever is a harder quench. We imposed cooling rates from 1 to 50 °C/min on the end plate and measured whether the thermal field develops a directional preference. It does not. The axial-to-lateral gradient ratio moves from 1.61x to 1.68x across a fiftyfold change in rate.
| rate °C/min | time to seed | undercooling at face | wall margin | G axial K/mm | G lateral K/mm | ratio | heat load |
|---|---|---|---|---|---|---|---|
| 1 | 114 s | 2.01 K | +8.65 K | 2.88 | 1.79 | 1.61x | 0.004 W |
| 2 | 60 s | 2.02 K | +8.74 K | 3.15 | 1.95 | 1.62x | 0.005 W |
| 5 | 28 s | 2.13 K | +8.83 K | 3.38 | 2.07 | 1.64x | 0.007 W |
| 10 | 16 s | 2.19 K | +8.91 K | 3.69 | 2.23 | 1.66x | 0.010 W |
| 20 | 10 s | 2.38 K | +8.94 K | 4.89 | 2.92 | 1.68x | 0.015 W |
| 50 | 6 s | 2.84 K | +8.91 K | 12.23 | 7.30 | 1.68x | 0.029 W |
Wall margin is how far the coldest wall liquid still sits above its own nucleation threshold at the moment the end face crosses its. Positive at every rate means the end plate seeds first, which is the entire point of the sequence.
Same model, run forward in time. The charge starts molten at 22 °C, the end plate is ramped at 5 °C/min, and the bore is soaked above the melt point so the end panel is the only heat sink. The front nucleates at the closed end and advances up the axis at about 11 µm/s.
Latent heat is ON in these runs, injected as a source term with a per-step release cap. That cap leaves small ripples near the front; they are the numerical signature of the release schedule, so read the front position from them, not their amplitude.
Rate does not buy order
Both gradients scale together, so the ratio is stuck near 1.6x. That is far too weak to select grain orientation, and no achievable cooling rate changes it. Geometry has to do the selection, which makes a grooved end face a requirement rather than an optimization.
Sequencing beats power
The end plate wins the race at every rate and the heat load never exceeds 0.03 W. What matters is quenching while the cold zone is still warm. Quench after a cold soak and the walls have already passed threshold at any rate.
Corner sensors are invisible here
Run with and without the four corner thermocouples, the end-face temperature differs by 7×10-11 K. Their tips sit 40–55 mm away while nucleation happens in the first 2 mm, so sensor placement and nucleation are independent decisions.
This is a conduction and phase-change model. It carries no crystal orientation, no anisotropic attachment kinetics and no grain competition, so it cannot predict epitaxy. It reports whether the thermal field favours axial growth, which is necessary but not sufficient. The nucleation undercoolings that set the thresholds, 2 K textured and 10 K smooth, are labelled estimates; the verdict was checked to be robust to any pair where textured beats smooth, because those thresholds move the timestamps rather than the outcome. End-panel thickness is assumed equal to the wall at 1.25 mm.
Method: liquid-only pre-nucleation melt, backward-Euler transient on the v3 cuvette network, end plate driven as a prescribed ramp through a penalty Dirichlet so a single factorization serves the whole run. The cold zone is warm-soaked to 18 °C first so nothing is undercooled at t=0.