Three simulations of one process condition, CCN_600_5. All geometry goes through the experiment's own measuring function measure() (fusion line at peak temperature 1771 K, outer contour, symmetrisation and smoothing: the same ruler as the 0822 targets). Measured: fusion width 974.2 µm, depth 181.5 µm, bead height 98.4 µm, pool area 117 175 µm², dilution 0.677.
Steady S: a steady solution in the frame moving with the beam; the free surface is iterated to normal-stress (Young–Laplace) balance and then held fixed; the mixing of composition and heat by the flow fluctuations of the transient is compensated by an equivalent diffusion (D32). Transient: VOF free surface, powder feed and solidification, computed from rest to 250 ms. All three share the material properties, the σ(f, T) table, and the beam and powder rules.
| Model | Cells (half domain) | η (calibrated) | Compute | Case |
|---|
Sections are drawn at true aspect (one scale for both axes); z = 0 is the original substrate surface. The measurement is the 0822 curve (baseline frame); S is the fusion envelope and top surface at the outlet; each transient is one section in the middle of its solidified stretch. Dashed lines are the cold estimates of the transients (see "The transient reads a hot state" below).
| Model | Width W / µm | Depth D / µm | Bead height H / µm | Pool area / µm² | Bead area / µm² | Dilution | D/W |
|---|
One physical grid (every 25 µm in y and 10 µm in z; the half width mirrored). The transients average the fully solid sections 100–120 ms after the beam has passed; S takes the outlet. Only each model's fused zone and bead are drawn; white lines are that model's fusion line and outer contour.
| Model | Mean | SD | Pool bottom z −170…−100 | Lower −100…−50 | Upper −50…0 | Bead 0…100 | Point-wise difference from med |
|---|
Element mass fractions mix linearly between the two end members, w = f·wCoCrNi + (1 − f)·w4140, normalised without C as EDS reports them. A difference of 0.01 in f is about 1 wt% of Fe; EDS quantification is good to about 1–2 wt%. Both features in the table below differ between the three models by more than that, so measured line scans can tell the models apart.
| Model | Upper f | Lower f | Upper − lower, Fe wt% | Centre f | Edge f | Edge − centre, Fe wt% |
|---|
| f | Fe / wt% | Co / wt% | Cr / wt% | Ni / wt% |
|---|
06_对标/提取/预测EDS.py compare: it back-calculates f point by point and compares it with each model.The time-averaged flows of the two models agree; the transient has, in addition, fluctuations of the same order as the mean flow, driven by Marangoni stresses. S, with its fixed surface, is itself steady: where streamlines close, only molecular diffusion acts across them, and the composition map stratifies and does not converge under mesh refinement. The compensation restores the mixing by the fluctuations as an equivalent diffusion (of composition and heat); its value is taken from the fluctuation statistics of the transient, not fitted to the experiment (D32).
| Quantity (symmetry plane, liquid pool) | Coarse transient | Med transient | Steady S |
|---|---|---|---|
| Mean flow speed / (m/s) | 0.024 | 0.028 | 0.026 |
| Fluctuation rms / (m/s) | 0.030 | 0.059 | 0.09–0.16 × mean (detrended) |
| Vertical velocity changes sign between snapshots | 53% | 44% | 2–4% |
| Equivalent diffusivity u′ℓ / (m²/s) | 2–3×10⁻⁶ (both meshes agree; 2.5×10⁻⁶ used) | — | |
| Map SD without compensation (25 / 12 / 6 µm mesh) | med 0.045 | 0.157 / 0.209 / 0.188 | |
07_文档/推导/核算_S与VOF流动的时均与脉动.py, 核算_S非定常检验.py.In the transient the metal density depends on temperature. At the snapshot the solidified sections are still at about 1000–1400 K, expanded relative to the initial cold state (573 K), and the whole section is lifted towards the free surface; the experiment measures the cold state. S uses a constant density and has no such term.
Thermal expansion is removed column by column: lift = Σ dz·(1 − ρ/ρref) over the metal cells below that height, with ρref the initial cold state (A4140 not austenitised, 573 K). The outer contour is corrected with the section's current temperatures; after the correction the far field returns to near z = 0 (a check). The fusion line is moved down by the peak lift over the thermal cycle, which gives only an order of magnitude: the digest is cropped near the pool (z ≥ −585 µm), and heating below the crop would make the lift larger; the hot zone under the beam is local and part of the expansion goes sideways, which would make it smaller.
S is calibrated on the measured pool area to η 0.395; the transient uses 0.45. Calibrated on the same area, the transient's hot reading corresponds to η 0.456 and its cold estimate to about 0.438 (A ∝ η4.5). The transient must absorb 11–15% more power to melt a pool of the same size.
| Candidate | Check | Verdict |
|---|---|---|
| Surface losses (radiation, convection, evaporation) | below 10 W in both, against an absorbed power of about 240–275 W | not the cause |
| Energy taken by the powder | the same formula cp(T − Tp) + L and the same feed rate | identical |
| Laser power deposited on the gas side of the interface | 13–18% in the transient; the coarse mesh has a larger share yet melts more; the gas near the pool carries away only 0.03 W | ends up in the metal |
| Hot reading of the transient | the cold-estimate area is 13–18% larger than the hot reading | explains about a quarter |
| Heat transport by the fluctuations | added to S, it lowers the η that S needs | opposite direction |
| Remainder | with both calibrated and similar fusion areas (production S against med): the section area at ≥ 2000 K is 15 799 µm² in the transient and 2 500 µm² in S; inside the 1300 K isotherm the transient is 8% larger | the extra power absorbed by the transient goes into superheating the upper pool and heating its surroundings, not into more melting; the reason is open |
The second process condition. The absorptivity and all other settings keep the 612 W calibration, with no recalibration. The measured fusion width, 1929.7 µm, equals the 2 mm beam width (the 612 W pool is narrower than the beam), so this group also tests whether the shape deficit comes from the beam intensity profile. The criteria were written down before the transient started: an area within ±10% means η carries over across power; an aspect-ratio error of −20% to −35% means the deficit does not depend on power.
| Model | Width W / µm | Depth D / µm | Bead height H / µm | Pool area / µm² | Bead area / µm² | Dilution | D/W |
|---|
07_文档/推导/送粉与光束的能量账.md): surface losses in S are only 2.4% of the absorbed power, and light absorbed by the powder in flight can supply at most 29% of the net heat missing at 1188 W; neither is the main cause.