§ 1
Scope of this document
Dynamica is an engineering screening and design-support tool. Every calculator below has a validated envelope outside of which results may carry undocumented error. Outside-envelope inputs are accepted to support what-if exploration but are not certified.
§ 2
Property packages
| Package | Standard | Validity envelope | Notes |
|---|---|---|---|
| Water/steam (IF97) | IAPWS-IF97 (2007) | 273.15–2273.15 K, up to 100 MPa; saturation up to 22.064 MPa / 647.096 K | Backward equations used; reverse-call max error vs forward eqs < 0.025 % on h,s |
| Psychrometrics | ASHRAE Fundamentals 2021 ch. 1, Hyland-Wexler | T_db = −40 … +120 °C, P = 50 … 110 kPa | Above 100 °C dry-bulb the saturation extrapolation is flagged |
| Ideal gases | NASA Glenn 7-coeff polynomials | 200 … 6000 K | Real-gas departure not applied |
| Refrigerants | REFPROP-style cubic-EOS fit, 10 fluids: R134a, R1234yf, R1234ze(E), R32, R290, R600a, R744 (CO₂), R717 (NH₃), R718, R410A (blend) | T_r ∈ [0.45, 0.99]; outside the two-phase dome only above NBP | R410A treated as pseudo-pure; glide < 0.2 K not modelled |
§ 3
Combustion & flue-gas
- Dry-basis stoichiometric calc valid for any C/H/O/N/S fuel; excess-air range tested 0 – 200 %.
- LHV/HHV correlations: Dulong, Boie, Channiwala-Parikh — agreement within ±2 % for coals, ±3 % for biomass on the BIBLIO-Phyllis2 reference set.
- NOₓ output is thermal-NOₓ only (extended Zeldovich, Re-Norby tube fit). Fuel-NOₓ and prompt-NOₓ are not modelled.
§ 4
Heat-transfer correlations
| Geometry / regime | Correlation | Validity |
|---|---|---|
| Forced convection, smooth tube, turbulent | Gnielinski | 0.5 < Pr < 2000, 3 000 < Re < 5×10⁶ |
| Forced convection, laminar | Sieder-Tate | Re < 2 300, L/D > 60 |
| Free convection, vertical plate | Churchill-Chu | 10⁻¹ < Ra < 10¹² |
| Tube bank, cross-flow | Žukauskas | 10 < Re < 2×10⁶, 0.7 < Pr < 500 |
| Boiling, pool | Rohsenow | Up to peak heat flux; correlation constant C_sf only tabulated for water/steel, water/copper, refrigerants/copper |
§ 5
Two-phase flow
- HEM, Lockhart-Martinelli, Friedel, Müller-Steinhagen-Heck implemented.
- Friedel valid for μ_l/μ_g < 1000, G > 100 kg/m²·s. MSH valid for horizontal/near-horizontal pipes, all flow regimes.
- Choked-flow detection assumes homogeneous equilibrium; metastable / frozen-flow models not provided.
- Regime maps: Mandhane (horizontal), Hewitt-Roberts (vertical). 3D pipework, bends < 5 D, and helical coils are out of scope.
§ 6
Power cycles
- Carnot / Otto / Diesel / Brayton / Rankine / Reheat / Regen / CCGT / Advanced Rankine.
- All cycles assume steady-state, lumped-parameter, single working fluid per loop. No transient start-up, no off-design turbine maps.
- CCGT topping cycle uses ISO-2314 gas-turbine reference conditions (15 °C, 60 % RH, 101.325 kPa); deviations applied via the user-supplied ambient block only.
§ 7
Biomass module
- Ultimate analysis must total 100 % ± 0.5 %; ash chemistry expected as oxide mass fractions.
- Slagging/fouling/agglomeration indices (Fu, Folgueras, R_b/a, Bed-Agglomeration Index) are empirical screening only — derived from Nordic and Iberian fuel sets; tropical (sugar-cane, palm) fuels carry ± 25 % index uncertainty.
- FEGT margin band uses IDT/ST/HT ± 30 °C ASTM D1857 reproducibility; worst-case breach flagged when ST − FEGT < 50 °C.
- Co-firing blender is mass- or energy-basis linear mixing; non-linear ash-chemistry interactions (e.g. K-Si eutectics) not predicted.
- K-Cl-S speciation uses a pseudo-equilibrium logistic fit (Glarborg, Hindiyarti, Sengeløv) — not a Gibbs minimiser. Treat as ± 1 species-class qualitative.
§ 8
Wall thickness & life assessment
- Larson-Miller master curves: ASME II-D for A335-P11, P22, P91, P92, T22, T23, T91, 304H, 316H, Alloy 800H. All other grades return an error. Constant C calibrated per grade.
- Fatigue: ASME III Div 1, NH polynomial S-N curves; design margins of 2 on stress and 20 on cycles already embedded (per code).
- Creep-fatigue interaction envelope: bilinear D_c + D_f ≤ 1 (Appendix T) — no time-fraction or strain-range partitioning option.
- FFS (API 579-1 / ASME FFS-1, 2021):
- HTHA (RP 941, 8th ed.) — 8 grades; log-linear interpolation between published curve anchors.
- LTA — Part 5 Level 1 only; uniform-loss α = 1. Local-loss (α = 0.85), groove-like, and pitting flaws require Level 2.
- FAD — Part 9 Level 2A, Option 1 envelope. Residual stress and secondary-stress (Q-stress) terms must be added externally.
- UT trending — linear regression with 95 % one-sided conservative slope; non-linear corrosion mechanisms (under-deposit, dewpoint, MIC) need separate analysis.
§ 9
Steam piping
- Pressure-drop correlations: Darcy-Weisbach with Colebrook-White friction factor (implicit, Serghides solver, ≤ 10⁻⁹ residual).
- Fittings via 3-K (Hooper) and equivalent-length (Crane TP-410) — both available; results agree within ± 8 %.
- Steam-trap sizing is not provided.
§ 10
Units & assumptions baked into every page
- SI is canonical; US-customary conversions use NIST SP 811-2008 factors.
- Gauge ↔ absolute conversions assume 101.325 kPa unless the user supplies a local atmospheric pressure.
- Temperature differences in K and °C are interchangeable; temperatures themselves are not — the UI flags this mismatch.
§ 11
Benchmark deviations > 1 %
Tracked in the public validation corpus. Current outliers as of 2026-05-20:
| Case | Reference | Δ | Cause |
|---|---|---|---|
| R744 transcritical COP at T_evap = −10 °C / P_gas = 9 MPa | NIST REFPROP 10.0 | +1.4 % | Cubic-EOS fit under-predicts c_p near pseudo-critical |
| P91 LMP at 600 °C / 80 MPa·hr¹ | ASME II-D 2023 Table 1A | −1.2 % | Master-curve digitisation rounding |
| Mandhane regime boundary, slug → annular at G = 450 kg/m²·s | Mandhane 1974 fig. 5 | line offset 0.05 in log space | Spline knot placement |
| FEGT − ST margin, palm-EFB | EUBIONET-III lab tests | +18 °C | ash-chemistry index extrapolation outside calibration set |
§ 12
What Dynamica is not
- Not a CFD solver (no spatial discretisation, no turbulence model beyond bulk-property correlations).
- Not a transient/dynamic simulator (no integrator, no controller emulation).
- Not a code-stamped design tool — outputs support engineering judgement; the responsible engineer must sign off.
- Not a substitute for in-service inspection, NDE, or Level 2/3 FFS by a qualified body.
§ 13
Reporting an error or extending the envelope
Email contact@dynamicathermalscience.com with: inputs, expected value, reference (paper, code clause, certified test), and observed Dynamica output. Verified bugs ship in the next weekly release; envelope extensions go through the validation corpus PR template.