Thermodynamic Database Guide

This document describes the thermodynamic databases integrated into Prometheus, their polynomial formats, and the reference-state calibration logic used to ensure cross-database consistency.

Overview

Database

Primary Source

Polynomial Format

Reference State

Calibration

NASA-9

NASA CEA (NRL 2002)

9-coefficient NASA

H_f°(298.15) = 0

Standard

TERRA

Bauman MSTU (Trusov)

Shomate (converted)

H(0) = 0 (raw)

Dynamic stoichiometric shift

AFCESIC

US Air Force

θ-based AFCESIC

Mixed / arbitrary

Hybrid NASA/TERRA calibration

NASA-9 / NASA-7

The gold standard for Prometheus. These databases use piecewise polynomials for Cₚ/R, H/RT, and S/R.

  • Reference point: elements in their standard states have H_f°(298.15) = 0.

  • Format: multi-segment (usually 2 or 3) polynomials covering 200 K – 6000 K.

TERRA

Contains approximately 2,600 species. Originally uses a reduced Gibbs energy (Φ*) polynomial; converted to NIST Shomate form (t = T/1000) internally:

\[C_p^\circ(t) = A + Bt + Ct^2 + Dt^3 + E/t^2\]

Calibration: TERRA raw data is referenced to 0 K. A dynamic stoichiometric shift is applied:

  1. The parser identifies the most stable state for every element in the TERRA binary.

  2. For every species, the weighted sum of its constituent elements’ raw enthalpies at 298.15 K is subtracted.

  3. This aligns TERRA enthalpies exactly with the NASA-9 formation enthalpy scale.

See TERRA Database Integration for the full derivation and accuracy tables.

AFCESIC

Contains specialised ionic and condensed species for metalized propellant studies.

  • Format: θ = T/1000 based polynomials with forward powers (low-T range) and inverse powers (high-T range).

  • Calibration (hybrid):

    1. NASA point-match — if a species exists in NASA-9/7, the AFCESIC integration constants (RF and CH) are adjusted to match NASA H and S at 1000 K.

    2. TERRA-stoich calibration — for species unique to AFCESIC, the stoichiometric shift is calculated using TERRA element reference enthalpies. This ensures that even unique AFCESIC species (e.g. Al₂MgO₄(s)) are correctly referenced to the same elemental baseline as the rest of the project.

Reference Enthalpies

Prometheus uses a unified set of element reference enthalpies (H_raw at 298.15 K) derived from the TERRA database to normalise any database that does not follow the H_f°(298.15) = 0 convention.

Key element references:

  • H₂ (gas): 7.45 kJ/mol

  • O₂ (gas): −2.33 kJ/mol

  • C (graphite): 0.00 kJ/mol

  • e⁻ (electron): 0.00 kJ/mol

Loading and Priority

Source priority

When multiple databases cover the same species Prometheus uses a priority-based selection (highest to lowest):

  1. NASA-9

  2. NASA-7

  3. JANAF

  4. TERRA

  5. AFCESIC

Override the priority at load time:

db.load(source_priority=["JANAF", "NASA-9", "NASA-7", "TERRA", "AFCESIC"])

Rebuilding from raw data

Regenerate the translated TERRA/AFCESIC databases from raw binaries:

uv run prometheus-build-legacy all

Regenerate all thermo databases (NASA/JANAF + TERRA/AFCESIC) in one step:

uv run prometheus-build-all-thermo