Appearance

Tutorial: cryogenic line chilldown ​

The Cryogenic line cooldown example is the most demanding of the shipped models. In one run it combines real-fluid two-phase flow, a moving quench front, temperature-dependent wall properties, and film boiling (manual §7.11).

Open "Cryogenic line cooldown" in the app →

What it reproduces ​

The example is built on the configuration of NBS Report 9264, Figure 2 (Brennan et al., 1966, Cooldown of Cryogenic Transfer Lines), which C&R Technologies uses as a SINDA/FLUINT validation case. Saturated liquid hydrogen at 75 psia enters a long copper transfer line that starts at room temperature. The liquid boils on the hot wall, and the wall chills station by station from inlet to outlet.

From sindaFluintCryoLineCooldown in src/ui/examples.ts and its header comment:

ItemValue
FluidCoolProp Hydrogen (normal hydrogen), real-fluid model
Inlet boundary517 kPa (75 psia), quality 0 (saturated liquid, Tsat ≈ 27.3 K)
Outlet boundary83 kPa (0.82 atm, Boulder CO), 300 K
Line61 m copper, 15.9 mm ID, 19 mm OD, roughness 1.5 µm
Discretization20 axial segments of 3.05 m: 22 fluid nodes, 20 wall solid nodes, 21 pipe branches, 20 convection conductors
Per segmentfluid volume ≈ 6.05×10⁻⁴ m³, copper wall mass ≈ 2.32 kg, wetted area ≈ 0.152 m²
Initial statewalls and internal fluid at 300 K, internal nodes at outlet pressure
Wall cpcatalogue material ofhc-copper (NIST cryogenic fit, 4–300 K)
ConvectionMiropolskii correlation on every conductor; no fixed h
Time steppingfixed dt = 1 s, end time 80 s

Formula bindings tie the geometry together (manual §3.10). Each node volume is pipe('segN').volume, each conductor area is pipe('segN').surfaceArea, and the correlation diameter and flow area come from the same pipe. Segments 2–21 inherit length, diameter, and roughness from segment 1, so editing segment 1 reshapes the whole line consistently.

The physics ​

Two-phase flow: homogeneous equilibrium ​

Hydrogen in the line passes from subcooled liquid through the saturation dome to superheated vapor. OpenFLUME treats the two-phase region with the homogeneous equilibrium model (HEM) (manual §4.2): both phases move at the same velocity and are in thermodynamic equilibrium at the local pressure.

  • State from P and h. Inside the dome T is fixed by P, so nodes evaluate their state from pressure and enthalpy (statePH), which fixes quality x.
  • Coupled enthalpy. The network is solved as an extended [P, ṁ, h] system with nodal enthalpy as a coupled unknown, which lets a node sit on the saturation line for many steps without oscillating across it.
  • Pipe friction uses the HEM mixture density and the McAdams mixture viscosity, 1/μ = x/μ_g + (1−x)/μ_f.

Wall-to-fluid heat transfer: Miropolskii film boiling ​

Each wall segment is a lumped solid node (mass × cp(T)) tied to its fluid node by a convection conductor using the Miropolskii dispersed-flow film-boiling correlation (manual §4.4):

Nu = 0.023 · [Re_g · (x + (ρ_g/ρ_f)(1 − x))]^0.8 · Pr_g^0.4 · Y
Y  = 1 − 0.1 · (ρ_f/ρ_g − 1)^0.4 · (1 − x)^0.4
h  = Nu · k_g / D

Vapor properties are taken at saturation, and quality is clamped to [0.01, 0.99] at the edges of the dome. When a node is single-phase, the correlation falls back to Dittus–Boelter on that state, so one conductor can follow a segment through the whole chilldown. The mass flux follows the GFSSP convention: G is half the sum of |ṁ| over the node's attached branches, divided by the flow area. Manual §8.5 records Miropolskii as "as used by GFSSP for chilldown", citing Cross, Majumdar et al. (2002).

Wall thermal mass ​

Copper's specific heat drops steeply on cooling. The header comment quotes about 385 J/(kg·K) at 300 K, about 90 at 80 K, and order 1 near 20 K, so each segment cools faster the colder it gets. Per the same comment, a constant 385 J/(kg·K) "materially over-predicts the cold-end cooldown time". The material catalogue and its validity ranges are in solid-properties-results.md.

The comment also notes that for hydrogen most of the cooling comes from the sensible heat of the cold vapor, at about 14:1 relative to latent heat.

Run it and read the results ​

Click Run. This model takes much longer than the other examples because every step is a real-fluid two-phase solve across 20 coupled segments. The toolbar shows t = … s / 80 s progress; Cancel stops the run and keeps the trajectory, labelled as partial.

  1. Model tab: set Color by to Temperature and drag the time scrubber. The cold front moves down the line, turning the walls from red to blue one segment after another.
  2. Results tab, wall temperatures: add a plot, type wall in the channel search box, and pick temperature channels for a few stations, such as walls 1, 5, 10, 15, and 20. (The Node & solid temperature preset plots all 42 temperatures, which gets busy.) Each wall stays warm until the front reaches it, then falls steeply once it is cold enough for copper's low heat capacity to take over.
  3. Fluid quality: the Quality / front / wetted fractions preset shows each node's vapor quality as the two-phase region moves along the line.
  4. Flow: the Branch mass flow preset shows low flow while the warm line boils liquid into vapor, rising as the line chills and liquid reaches further downstream.

src/ui/tests/examples.test.ts checks the shipped example: every wall ends below its 300 K start, wall 1 ends below 50 K, and wall 1 drops below 50 K before wall 20 does. These checks are qualitative; they confirm the front is sequential and the inlet reaches cryogenic temperature.

Comparison with the experiment ​

  • The shipped example demonstrates the NBS Figure 2 configuration. The manual (§7.11) says chilldown time at the instrumented station "is compared with the NBS experiment and with GFSSP predictions in the validation suite". That comparison runs in the slow test tier on the repository's chilldown builders, not as a pass/fail on this exact model.
  • Validation corpus and trust levels (manual §8.4). From NBS Report 9264, Table 6 provides eighteen chilldown-time points for saturated and subcooled hydrogen and nitrogen, and eleven digitized oscillograph figures provide 44 station traces (10 195 samples).
    • Trusted (calibration grade): four saturated runs, sixteen traces.
    • Diagnostic only: seven subcooled runs. Their errors reach +80 % at coarse axial discretization, so they can inform a diagnosis but cannot be quoted as agreement.
    • CI acceptance band: computed chilldown time at the instrumented station within a factor of 1.6 of experiment, with mean absolute error under 25 % across the four-case slow suite. Two-phase chilldown energy and enthalpy balances close within 10 % and 12 %.
    • Single-phase chilldown surrogates reproduce the plateau-then-plunge shape but are not comparable on absolute times.
  • Fluid choice brackets the data. The example uses normal hydrogen. The header comment cites a C&R Technologies validation note (May 2009): normal-H₂ over-predicts and para-H₂ under-predicts by about 20 %, with the test data in between. The validation reports have not re-derived this.
  • "Chilldown time" has no unique definition. NBS 9264 defines it as the low-temperature knee of the wall-temperature curve 60.4 m from the supply dewar (quoted in src/validation/nbsChilldown.ts). In this model, wall 20 sits at x = 61 m and is the nearest station.

Together these support a factor-of-1.6 engineering band on trusted saturated runs, short of a precision prediction.

Things to try ​

  • Para-hydrogen. In Setup → Fluids, change the fluid to ParaHydrogen and run again. Use + Compare run… to overlay a wall temperature from both runs. Per the C&R note above, the two should bracket the experiment.
  • Resolution. A coarse version cannot resolve the front (manual §7.11), and diagnostic-run errors grow at coarse discretization (§8.4). Repeat… and Split… (manual §3.13) build finer chains; change one thing at a time and keep the formula bindings consistent.
  • Longer run. Raise End Time in Setup → Solver if the last segments haven't chilled by 80 s.
  • Other correlations. A convection conductor can use Darr–Hartwig, the 2020 cryogenic flow-boiling set with a regime map over film, nucleate, transition, and single-phase boiling. It needs an axial position, derivable from physical node positions. Its fitted envelope is LH₂ in vertical upward flow at 1 g, which excludes this horizontal line. The TT-WF closure is research status and not validated (manual §4.4, §8.5; fluid-front-transport.md).

Limitations ​

  • HEM only. No phase slip, stratification, or flow-regime map for horizontal two-phase flow, and no separated-flow pressure-drop multipliers such as Lockhart–Martinelli. HEM under-predicts pressure drop at high void fraction (manual §1.7).
  • Miropolskii is a film-boiling correlation with a single-phase fallback; it does not model nucleate or transition boiling, or wall rewet.
  • Lumped walls. Each 3.05 m segment is one temperature, with no axial conduction between wall segments and no radial gradient through the wall.
  • No pressure waves. Surges and oscillations in real chilldown tests depend on acoustic and inertial dynamics this model does not resolve (manual §1.7).
  • Alpha software. Treat results as engineering estimates within the evidence above. If you find a disagreement with a trusted reference, open an issue with the reference and tolerance.