HyFlux HX

HX Type

Flow Arrangement

Geometry (per module)

D_inner [mm]

D_inner_OD [mm]

D_outer [mm]

Length [mm]

N_tubes (bundle)

N_passes

System Scale

N_modules (for 3 MW)

He Flow (Hot)

ṁ [g/s]1200

T_in [K]55

Pressure [bar]

LH₂ Flow (Cold)

ṁ [g/s]55.0

T_in [K]21.0

Pressure [bar]

AM Production

Material

AM Printer

Build Orientation

3D CAD — Tube-in-Tube Geometry

Drag to rotate · Scroll to zoom

Temperature Profile

Q & ε vs He Mass Flow

ε-NTU Counterflow Map

Validation Checks

AM Build Analysis

3MW Optimizer — Tube-in-Tube Bundle

Find minimum module count for 3MW total duty · Each module = one AM-printed bundle fitting Renishaw 500Q

Module Architecture

⬡

1 Module = Nt parallel tubes (e.g. 37) in a hexagonal bundle, printed as one piece with integrated headers. LH₂ flows inside tubes, He flows in annuli around each tube.

⊞

System = N modules in parallel (identical, each gets 1/N of total flow). Common LH₂ + He manifolds distribute flow equally.

◊

Build constraint: Each module must fit 300×300×400mm (Renishaw 500Q). Bundle OD ≈ √Nt × D_outer. L ≤ 400mm.

System Flow Schematic

  LH₂ supply ──┬── Module 1 (Nt tubes) ──┬── GH₂ out
  (total ṁ_c)  ├── Module 2 (Nt tubes) ──┤  (total)
               ├── Module 3  ...         ├──
               ├── ...                   ├──
               └── Module N              └──

  He supply ───┬── Module 1 (annuli)  ───┬── He out
  (total ṁ_h)  ├── Module 2             ├──
               └── Module N             └──

  Per module: ṁ_c/N and ṁ_h/N
  Total Q = N × Q_per_module = 3 MW

D_inner [mm]

D_outer [mm]

Wall [mm]

k_wall [W/mK]

N_tubes

Max L [mm]

LH₂/mod [g/s]

He/LH₂ ratio

Grid

PARETO: N_modules vs Total ΔP

PARETO: N_modules vs ṁ_LH₂/module

Top 20 Designs — Minimum Module Count for 3 MW

#	Di	Do	Nt	L	ṁ_c/mod	ṁ_h/mod	Q/mod	ε	N_mod	Total ṁ_c	ΔP_c %	ΔP_h %	T_c_out	Bundle Ø	Load

✅ HyFlux HX — Validation Report

17-point physics cross-check for cryogenic heat exchanger design validation.

Correlations Used

Correlation	Application	Range
Gnielinski (1976)	Primary Nusselt number	2300 < Re < 5×10⁶, 0.5 < Pr < 2000
Dittus-Boelter (1930)	Cross-check Nusselt	Re > 10000, 0.6 < Pr < 160
Petukhov (1970)	Darcy friction factor	3000 < Re < 5×10⁶
Seban-McLaughlin	Curved tube enhancement	De > 11.6, spiral HX
Žukauskas (1987)	Shell-side cross-flow	Re 1–2×10⁵, spiral HX

Correlation

Application

Range

Gnielinski (1976)

Primary Nusselt number

2300 < Re < 5×10⁶, 0.5 < Pr < 2000

Dittus-Boelter (1930)

Cross-check Nusselt

Re > 10000, 0.6 < Pr < 160

Petukhov (1970)

Darcy friction factor

3000 < Re < 5×10⁶

Seban-McLaughlin

Curved tube enhancement

De > 11.6, spiral HX

Žukauskas (1987)

Shell-side cross-flow

Re 1–2×10⁵, spiral HX

Fluid Properties — REFPROP 9.0 + CoolProp 7.2 Validated

Helium (40–300 K): Ideal gas EOS (R=2077.1 J/kg·K), Cp=5193 J/kg·K. Viscosity and conductivity via ln-polynomial fits validated against CoolProp/REFPROP within 2–5%.

Para-Hydrogen (20–31 K liquid, 31–300 K gas): REFPROP 9.0 cross-validated with CoolProp 7.2.0 ParaHydrogen HEOS (<0.0001% agreement, Leachman 2009 EOS). LH₂ is >99.8% para-H₂ at 20K. T_sat(P) = quadratic in ln(P), error <0.07K across 1–12 bar. h_fg(P) pressure-dependent: 446→237→143 kJ/kg from 1→10→12 bar. Gas cp includes ortho→para conversion peak (~16 kJ/kgK at 150K). 4-segment Simpson integration for enthalpy accuracy. Total Δh 21→280K @10bar: 4145.2 kJ/kg (REFPROP) = 4145.2 kJ/kg (CoolProp).

Validation Checks (17 points)

Reynolds numbers in turbulent range (Re > 4000) for both streams

Prandtl numbers physical (0.1 < Pr < 1000)

Nusselt numbers match Gnielinski ±5% vs Dittus-Boelter cross-check

Energy balance to machine precision (|Q_hot − Q_cold|/Q_avg < 1e−10)

Effectiveness bounded (0 < ε < 1)

Second law satisfied (no temperature crossover)

Subcooling margin ≥ 5 K (LH₂ stays liquid at inlet and outlet)

Pressure drop < 10% of stream pressure

NTU in reasonable range (0.1 < NTU < 10)

Joule-Thomson coefficient sign check (He warms on expansion above inversion T)

LMTD positive and finite

Wall thermal resistance physically reasonable

Capacity ratio bounded (0 ≤ C_r ≤ 1)

Dean number check for spiral (De > 11.6 for enhancement)

Curvature ratio check for spiral (δ = d/D_coil < 0.1)

Surface density within AM limits

Build volume fit verification for selected printer

Property Backend Priority

1. ctREFPROP (NIST license) → 2. CoolProp + REFPROP → 3. CoolProp HEOS → 4. Built-in polynomial correlations

Test Coverage

78 tests passing: helium properties (μ, k, ρ, Cp) at multiple temperatures, LH₂ properties, Gnielinski/Dittus-Boelter Nusselt correlations, Petukhov friction factor, ε-NTU solver (energy balance, effectiveness bounds, second law), API endpoints, phase safety, property backend detection.

References

Gnielinski, V. (1976). New equations for heat and mass transfer in turbulent pipe and channel flow. Int. Chem. Eng., 16(2), 359-368.

Petukhov, B. S. (1970). Heat transfer and friction in turbulent pipe flow. Advances in Heat Transfer, 6, 503-564.

Lemmon, E.W., et al. NIST Standard Reference Database 23: REFPROP v10.0.

Bell, I.H., et al. (2014). Pure and pseudo-pure fluid thermophysical property evaluation: CoolProp. Ind. Eng. Chem. Res., 53(6), 2498-2508.

Mishra, P. & Gupta, S. N. (1979). Momentum transfer in curved pipes. Ind. Eng. Chem. Process Des. Dev., 18, 130-137.

Žukauskas, A. (1987). Heat transfer from tubes in crossflow. Advances in Heat Transfer, 18, 87-159.

HyFlux HX v2.0 — Vassal Enterprises / HyFlux Ltd — hyflux.aero
Python solver: 78/78 tests ✓ | Dashboard: Chart.js + Three.js | Backend: FastAPI