1 Validation map
This document records how physical claims in the theory track are checked. Each row names the claim, the independent reference it is compared against (an analytic relation, an equilibrium calculation, or a published case), and the test or example that runs the comparison. The tables are grouped by mean flow, thermochemistry, and acoustics with its inverse; where no check exists, the gap is marked openly rather than left unstated. Broader consistency evidence and named literature cases appear in verification and benchmarks.
The test names are the routines in the codebase and can be run as written.
1.1 Mean-flow claims
| Claim | Reference | Check |
|---|---|---|
| Density recovery exists and is unique for any flow state with p, h_t > 0 | analytic monotonicity of F(\varrho) | test_real_root_matches_brentq, test_round_trip_physical_state |
| The recovered state is direction-independent where it must be | p_t, T_t depend on M^2 | test_round_trip_physical_state |
| An isentropic area change reproduces the classical jump | analytic compressible-flow relations | test_subsonic_nozzle_matches_isentropic |
| A sudden expansion loses the Borda–Carnot total pressure | momentum balance | test_expansion_unaffected_by_cc |
| A sudden contraction loss follows K_c = (1/C_c - 1)^2 | vena-contracta model | test_contraction_loss_matches_Kc, test_contraction_lossless_default_conserves_pt |
| Element residuals are invariant to an edge-arrow flip | direction-convention algebra | test_edge_direction_invariance |
| A long chain converges from exactly zero flow | continuation well-posedness | test_long_serial_chain_cold_start |
| A pressure-driven quiescent network converges | artificial-resistance continuation | test_quiescent_cold_start_converges |
| A symmetric branching network resolves its split | Levenberg–Marquardt damping | test_many_parallel_branches_converge |
| Choking saturates the mass flow at the sonic value | critical mass flux | test_choked_nozzle_saturates_mass_flow |
| The critical pressure ratio is the knee of the operating map | p^\ast/p_t \approx 0.528 | test_critical_pressure_ratio_is_the_knee |
| A choked orifice discharge detaches its exit pressure upward | underexpanded discharge | test_choked_nozzle_outlet_critical_mass_flux |
1.2 Thermochemistry claims
| Claim | Reference | Check |
|---|---|---|
| The equilibrium engine matches an independent equilibrium solver | Cantera oracle (needs a Cantera + numba env) | test_cantera_validation; public/solver packings agree via test_public_and_solver_paths_agree, test_frozen_from_xi_matches_properties |
| The kinetic-energy-coupled reacting state is exact | equilibrium oracle at the KE-coupled enthalpy | test_ke_burnt_static_matches_oracle |
| A transported passive scalar mixes as the mass-weighted donor | convex-combination mixing | test_passive_tracer_mixes_mass_weighted |
| A passive scalar does not perturb the mean flow | scalar-registry squareness | test_passive_tracer_does_not_perturb_mean_flow |
| A carried scalar stays realizable in [0,1] | convexity of the donor mix | test_passive_tracer_realizable |
| The marker gate selects the frozen/burnt closure and self-corrects | bimodal-marker convergence | test_auto_reacting_network_is_marker_gated, test_marker_self_corrects_any_seed |
| The marker-blended mean flow matches the hard closure | frozen/equilibrium limits | test_mean_flow_matches_hard_closure |
1.3 Acoustic and identification claims
| Claim | Reference | Check |
|---|---|---|
| The operator reduces to the base Jacobian at zero frequency (passive) | \mathbf{A}(0) = \overline{\mathbf{J}} | test_zero_frequency_operator_equals_jacobian |
| A duct carries the lossless propagation phase | e^{-\mathrm{i}\omega\tau_+} | test_meanflow_duct_tau_plus_phase, test_duct_scattering_is_lossless_phase |
| A cavity stamps the finite-volume compliance | C = V/\overline{\varrho}\,\overline{c}^{\,2} | test_cavity_storage_is_the_compliance |
| A choked-nozzle outlet reflects with the Marble–Candel coefficient | compact-nozzle reflection + entropy coupling | test_choked_nozzle_outlet_marble_candel |
| The characteristic maps are exact and invertible | linearized state definitions | test_characteristic_maps_are_inverse, test_characteristic_amplitude_relations |
| Transfer and scattering matrices round-trip, and across flavors | closed-form conversions | test_transfer_scattering_round_trip, test_flavor_round_trip |
| An n–\tau flame drives a self-excited instability | analytic dispersion root | test_n_tau_flame_drives_self_excited_instability |
| The modal frequency and growth rate of a published combustor are reproduced | OSCILOS (Li et al. 2017) on the EM2C combustor (Palies et al. 2011) | test_dominant_mode_matches_oscilos, test_mean_flow_matches_the_reported_operating_point |
| A shed entropy wave is inert at a pressure-release outlet | no entropy-to-acoustic conversion without acceleration | test_the_entropy_wave_is_a_spectator_at_an_open_end |
| The acoustic and intrinsic modes of a published combustor are reproduced and told apart | network analysis of the BRS rig (Emmert et al. 2017; Komarek and Polifke 2010), published eigenvalues read from vector figures | test_three_dominant_modes_match_the_published_frequencies, test_the_robust_growth_rates_match_the_published_values, test_the_passive_network_matches_the_published_acoustic_modes, test_the_flame_adds_one_mode_that_the_passive_network_does_not_have |
| The pure intrinsic system solves the reference’s dispersion relation, as a network and as a scalar | anechoic burner-and-flame system, with the FTF normalization bridge \alpha_2 | test_the_pure_ita_network_matches_the_dispersion_relation, test_the_pure_ita_relation_needs_the_normalization_bridge |
| An intrinsic mode grows when the outlet reflection that damps it is removed | reflection sweep to the published anechoic endpoint | test_reducing_the_outlet_reflection_destabilizes_the_intrinsic_mode, test_the_anechoic_outlet_endpoint_matches_the_published_track |
| A passive heat-addition jump keeps velocity continuity under the isentropic reduction | zero-Mach limit of a compact heat source | test_passive_temperature_jump_keeps_the_zero_mach_velocity_continuity |
| A sampled impulse response is entire, so it continues to complex frequency exactly | finite sum of exponentials | test_fir_is_entire_and_matches_its_definition_off_the_real_axis, test_fir_single_spike_is_an_n_tau |
| The eigensolver’s mode count is certified complete | argument-principle winding | test_eigenmodes_certified_count_matches |
| An eigenvalue-free region yields no modes, whatever the band | argument-principle winding as the Beyn rank | test_beyn_moment_rank_is_ambiguous_on_an_empty_contour, test_no_modes_survive_an_eigenvalue_free_region, test_eigenmodes_are_insensitive_to_the_band_edge |
| A mode is told from an arbitrary frequency on an ill-conditioned operator | residual on the equilibrated \mathbf{D}_r\mathbf{A}\mathbf{D}_c | test_equilibrated_residual_separates_a_mode_from_an_arbitrary_point |
| The search sub-contours cover the region they certify | elliptical tiling geometry | test_subcontours_cover_the_counted_region |
| The growth-rate sign matches the boundary energy budget | Myers acoustic energy | test_boundary_power_sign_matches_growth_every_mode |
| The Nyquist count agrees with the eigensolver | matrix-determinant lemma | test_unstable_count_matches_eigenmodes |
| A de-embedded element reproduces its measured response | Woodbury identity | test_identify_transfer_matrix_cascade, test_identify_single_input_ftf |
| The isentropic analysis omits indirect noise (as documented) | entropy-to-acoustic coupling | test_isentropic_analysis_misses_the_indirect_noise |
1.4 Coverage remarks
The entries above name one check per claim, not every check that backs it: many claims are tested several times, and the complete list lives in the tests themselves; this table is only a guide. The items left open in limitations (finite-rate chemistry, supersonic internal flow, and the compositional-noise gap at analytic terminal closures) are deliberately omitted here, because they mark what the present version does not yet cover or only approximates; where a partial check exists (for example a warning when compositional noise is dropped at a closure), it is noted in the limitations document, not counted as a proven result.
Basic consistency checks that support many of these entries are gathered in verification; the named literature cases and their quantitative agreement appear in benchmarks.
References
Emmert, Thomas, Sebastian Bomberg, Stefan Jaensch, and Wolfgang Polifke. 2017. “Acoustic and Intrinsic Thermoacoustic Modes of a Premixed Combustor.” Proceedings of the Combustion Institute 36 (3): 3835–42. https://doi.org/10.1016/j.proci.2016.08.002.
Komarek, Thomas, and Wolfgang Polifke. 2010. “Impact of Swirl Fluctuations on the Flame Response of a Perfectly Premixed Swirl Burner.” Journal of Engineering for Gas Turbines and Power 132 (6): 061503. https://doi.org/10.1115/1.4000127.
Li, Jingxuan, Dong Yang, Charles Luzzato, and Aimee S. Morgans. 2017. Open Source Combustion Instability Low Order Simulator (OSCILOS–Long) Technical Report. Department of Mechanical Engineering, Imperial College London. https://www.oscilos.com.
Palies, Paul, Daniel Durox, Thierry Schuller, and Sébastien Candel. 2011. “Nonlinear Combustion Instability Analysis Based on the Flame Describing Function Applied to Turbulent Premixed Swirling Flames.” Combustion and Flame 158 (10): 1980–91. https://doi.org/10.1016/j.combustflame.2011.02.012.