Speaker
Description
TOPIC:
Experimental and numerical modelling improvements of radiative heat transfer: refinement, verification, validation and comparison for space object re-entry simulation tools
BACKGROUND
Radiative heating dominates the total heat load for vehicles entering planetary atmospheres above 10 km/s. The FIRE II flight experiment [1] measured stagnation-point radiative fluxes of 1100–1530 W/cm² at 67–77 km altitude, exceeding 70% of total heating. High-fidelity codes (VSL2T–NEQAIR, LAURA–HARA, DPLR–NEQAIR) solve viscous shock-layer equations coupled with line-by-line radiation transport but require HPC resources and demand expert setup. Engineering correlations such as Tauber–Sutton [4] provide rapid estimates but return only a single wall-flux value without spectral or spatial resolution. A tool filling this gap — spectrally resolved shock-layer radiation in seconds — would benefit parametric pre-design, mission trade studies, and arc-heater ground-test correction, where facilities (NASA Ames IHF, JAXA JXWT) reproduce convective but not radiative heating.
METHODOLOGY
This paper presents two coupled analysis tools: psf2t, a 1-D post-shock two-temperature (2-T) ODE solver, and SPIRE (SPectral Inviscid Radiation for Entry), a coupled spectral radiation code.
psf2t implements Park's [2] 2-T model with 11-species air, 11 reaction sets, Millikan–White–Park relaxation, and Gupta et al. [5] thermodynamic coefficients for all species including molecular ions. A key innovation is the use of spatial coordinate x as the independent variable, guaranteeing uniform resolution throughout the shock layer. The integration terminates at the boundary-layer edge (estimated via a Reynolds-number correlation), not at the vehicle wall.
SPIRE integrates the 1-D radiative transfer equation from the shock to the BL edge with four-angle Gauss–Legendre quadrature. Spectral contributions include: 57 atomic/ionic lines (NIST ASD) with per-line RTE, full electronic partition functions from NIST energy levels, and Doppler broadening; bound-free and free-free continuum at T_ve; N2+ Meinel bands; and N2 LBH + NO molecular continua. The output is the spectrally resolved q_rad,BLE — the physically correct outer boundary condition for coupled radiation–convection–ablation BL analysis.
To compare with Cauchon's [1] wall measurements, BL transmittance factors (τ_lines = 0.783, τ_cont = 0.526) are applied. The overall 22–25% BL absorption is consistent with Johnston's [3] prediction of 20–40%.
RESULTS
Validation uses three FIRE II trajectory points at approximately 11.3 km/s. Flow field: BL-edge temperature predicted within +5 to +21% of reference values; pressure within ±16%. The x-based formulation achieves 0.007 cm maximum spatial gap versus 0.07 cm for time-based integration.
Radiation: Shock-layer q_BLE = 1428, 1975, and 1912 W/cm² for the three cases. Wall fluxes after BL transmittance are 1110, 1488, and 1447 W/cm², yielding errors of +0.9%, −2.7%, and +2.6% versus Cauchon [1].
Key findings from error structure analysis: (1) Full electronic partition functions reduce atomic line emission by 16–18%, shifting τ_lines from 0.630 (two-level) to 0.783 (full), demonstrating that the two-level approximation was being absorbed by the transmittance. (2) Temperature sensitivity analysis (±10% perturbation) reveals extreme sensitivity: a 10% reduction in T causes q_BLE to fall below Cauchon's [1] measurements, yielding non-physical τ > 1. This proves that the fitted τ is an integrated correction factor absorbing genuine BL absorption, flow-solver overestimate, and limited line-database compensation simultaneously. (3) Gupta [5] thermodynamic coefficients for molecular ions correct a significant high-temperature extrapolation error, reducing N2+ peak concentration by 22%.
Computation time is under 5 seconds on a standard laptop.
CONCLUSION
A coupled 1-D 2-T flow solver and spectral radiation code have been established and validated against FIRE II within ±3% at the wall. The error structure analysis demonstrates that the fitted transmittance is not a pure BL transmittance but an integrated correction factor whose components cannot be separated without independent q_BLE or τ_BL calculations. This finding motivates ongoing work on viscous BL solver coupling and expanded line databases. The transparent reporting of error structure, rather than claiming accuracy, is central to the present work.
REFERENCES
[1] Cauchon, D. L., NASA TM X-1402, 1967.
[2] Park, C., Nonequilibrium Hypersonic Aerothermodynamics, Wiley, 1990.
[3] Johnston, C. O., Ph.D. Dissertation, Virginia Tech, 2006.
[4] Tauber, M. E. and Sutton, K., J. Spacecraft and Rockets, 28(1), 1991.
[5] Gupta, R. N. et al., NASA RP-1232, 1990.
ACKNOWLEDGMENT
This work was supported by the SNU Aerospace Integrated Wind Tunnel Center
Summary
A coupled 1-D two-temperature post-shock flow solver (psf2t) and spectral radiation code (SPIRE) are presented and validated against FIRE II stagnation-point radiative heating within ±3% at the wall. Error structure analysis reveals that the fitted boundary-layer transmittance is an integrated correction factor, motivating independent validation via viscous BL solver coupling and EAST shock-tube data.