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 = Target Q
| # | 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 |
|---|
Live ctREFPROP Fortran calls · Leachman 2009 EOS · Connecting...
17-point physics cross-check for cryogenic heat exchanger design validation.
| 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 |
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).
All thermodynamic property lookups are validated against published values from Cool Fuel: Hydrogen as a Combustion Fuel (Leachman & Jacobsen, 2022, Cambridge University Press). Both HyFlux and Cool Fuel use the Leachman (2009) para-hydrogen equation of state, ensuring exact thermodynamic consistency.
| Property | REFPROP API | Cool Fuel Published | Status |
|---|---|---|---|
| Normal Boiling Point | 20.271 K | 20.271 K | ✓ Exact match |
| Critical Temperature (Tc) | 32.938 K | 32.938 K | ✓ Exact match |
| Critical Pressure (Pc) | 1285.8 kPa | 1285.8 kPa | ✓ Exact match |
| Critical Density (ρc) | 31.32 kg/m³ | 31.32 kg/m³ | ✓ Exact match |
| Triple Point Temperature | 13.803 K | 13.803 K | ✓ Exact match |
| hfg at NBP | 446.1 kJ/kg | 448.7 kJ/kg (normal H₂) | ✓ Expected Δ (para vs normal) |
| ρliq at 20 K, 10 bar | 72.29 kg/m³ | 72.3 kg/m³ | ✓ <0.01% |
| cpliq at 20 K, 10 bar | 9541 J/(kg·K) | ~9500 J/(kg·K) | ✓ <0.5% |
The 0.6% difference in hfg is expected: Cool Fuel reports normal-hydrogen (75% ortho / 25% para), while REFPROP uses pure para-hydrogen (PARAHYD). At 20 K, equilibrium hydrogen is >99.8% para-H₂.
Both REFPROP 10 and CoolProp 7.2 implement the same Leachman et al. (2009) fundamental Helmholtz energy equation of state for para-hydrogen. This EOS covers 13.803 K (triple point) to 1000 K and pressures up to 2000 MPa. Cross-validation between REFPROP and CoolProp shows <0.0001% agreement across all properties, confirming identical EOS implementations.
Client-side polynomial correlations are calibrated against REFPROP 10 data to enable instant calculations when the API server is unavailable.
| Property | Range | Max Error vs REFPROP | Fit Type |
|---|---|---|---|
| ρliq | 14–30 K, 10 bar | 0.23% | Degree-4 polynomial |
| cpliq | 14–30 K, 10 bar | 3.1% | Degree-4 polynomial |
| kliq | 14–30 K, 10 bar | 0.28% | Degree-3 polynomial |
| μliq | 14–30 K, 10 bar | 0.97% | Degree-4 polynomial |
| cpgas | 50–300 K, 10 bar | 6.0% | Degree-4 polynomial |
| μgas | 50–300 K, 10 bar | 0.04% | Power + offset |
| kgas | 50–300 K, 10 bar | 11.6% | Sqrt model |
| Tier | Backend | Latency | Accuracy | Requirements |
|---|---|---|---|---|
| 1 | NIST REFPROP 10 | <0.5 ms/call | Reference standard | NIST license + librefprop.so |
| 2 | CoolProp 7.2 | ~1 ms/call | Same EOS as REFPROP | pip install CoolProp |
| 3 | Built-in Polynomials | ~0 ms (JS inline) | 0.04–11.6% vs REFPROP | Zero dependencies |
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.