Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models
Abstract
:1. Introduction
2. Physical Models and Numerical Methods
2.1. Flow Governing Equations with Thermochemical Nonequilibrium Models
2.2. Flowfield Solver
2.3. Step Models for Radiation Properties
2.4. Tangent Slab (TS) Approach for RTE
2.5. Radiation–Flowfield Uncoupling Algorithm
3. Results and Discussion
3.1. Convective Heating
3.2. Thermochemical Nonequilibrium Flowfield
3.3. Radiative Heating
3.4. Radiation Field
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Nomenclature
e | total energy |
eve | vibrational-electronic energy |
h | total enthalpy |
hs | enthalpy for the species s |
hve,s | vibrational-electronic enthalpy for the species s |
kf,r | forward reaction rate coefficients of the r-th reaction |
kb,r | backward reaction rate coefficients of the r-th reaction |
p | pressure |
q | total heat flux |
qve | vibrational-electronic heat flux |
qcw,stag | convective heat flux at stagnation point |
qrw,stag | radiative heat flux at stagnation point |
Bj | j-th component of the unit directional vector |
H | altitude |
Hw | enthalpy at the wall |
He | enthalpy at the outer edge of the boundary layer |
Iν | spectral radiative intensity at frequency ν |
Ibv | blackbody radiative intensity at frequency ν |
Js,j | mass diffusion flux of the species s in the j-th direction |
Ms | molecular mass per mole of species s |
Ns | total number of air species |
Nr | total number of chemical reactions |
Rs | gas constant for the species s |
RN | nose radius |
Ttr | translational-rotational temperature |
Tve | vibrational-electronic temperature |
Tw | wall temperature |
T∞ | freestream temperature |
εw | wall emissivity |
κm | absorption coefficient for the m-th spectral step |
κP | Planck-mean absorption coefficient |
κν | absorption coefficient at frequency ν |
ν | radiation frequency |
stoichiometric coefficient of the species s in the r-th backward reaction | |
stoichiometric coefficient of the species s in the r-th forward reaction | |
ρs | density of the species s |
ρ∞ | freestream density |
τij | viscous stress tensor |
τν | optical thickness at frequency ν |
ωr | radiative source term |
ωs | mass production rate of the species s |
ωve | vibrational-electronic energy source term |
Appendix A. Nongray Two-, Five- and Eight-Step Models
Appendix A.1. Two-Step Model
Appendix A.2. Five-Step Model
Appendix A.3. Eight-Step Model
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Model | Step No. | Wavelength (Å) | Spectral Band |
---|---|---|---|
Two-step | 1 | 0–1100 | VUV (vacuum ultraviolet) |
2 | 1100–∞ | Visible | |
Five-step | 1 | 620–1100 | VUV continuum |
2 | 1100–1300 | VUV continuum | |
3 | 1300–1570 | VUV lines | |
4 | 1570–7870 | Visible | |
5 | 7870–9552 | IR (infrared) lines | |
Eight-step | 1 | 400–852 | VUV continuum |
2 | 852–911 | VUV continuum | |
3 | 911–1020 | VUV continuum | |
4 | 1020–1130 | VUV continuum | |
5 | 1130–1801 | Continuum + line wings | |
6 | 1130–1801 | Line “centers” | |
7 | 1801–4000 | Visible | |
8 | 4000–∞ | Visible + infrared |
Time (s) | H (km) | V∞ (km/s) | Ma | RN (m) | ρ∞ (kg/m3) | T∞ (K) | Tw (K) |
---|---|---|---|---|---|---|---|
1634 | 76.42 | 11.36 | 40.58 | 0.935 | 3.72 × 10−5 | 195 | 615 |
1636 | 71.02 | 11.31 | 38.94 | 0.935 | 8.57 × 10−5 | 210 | 810 |
1637 | 67.05 | 11.25 | 37.17 | 0.935 | 1.47 × 10−4 | 228 | 1030 |
1640 | 59.62 | 10.97 | 34.34 | 0.935 | 3.86 × 10−4 | 254 | 1560 |
1643 | 53.04 | 10.48 | 31.47 | 0.805 | 7.80 × 10−4 | 276 | 640 |
1645 | 48.37 | 9.83 | 29.05 | 0.805 | 1.32 × 10−3 | 285 | 1520 |
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Yang, X.; Wang, J.; Zhou, Y.; Sun, K. Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models. Aerospace 2022, 9, 219. https://doi.org/10.3390/aerospace9040219
Yang X, Wang J, Zhou Y, Sun K. Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models. Aerospace. 2022; 9(4):219. https://doi.org/10.3390/aerospace9040219
Chicago/Turabian StyleYang, Xinglian, Jingying Wang, Yue Zhou, and Ke Sun. 2022. "Assessment of Radiative Heating for Hypersonic Earth Reentry Using Nongray Step Models" Aerospace 9, no. 4: 219. https://doi.org/10.3390/aerospace9040219