Flow-radiation coupling in ${\mathrm{CO}}_2$ hypersonic wakes using reduced-order non-Boltzmann models

The current work presents a computationally tractable simulation methodology combining different model-reduction techniques for resolving non-Boltzmann thermodynamics, chemical kinetics, and radiative transfer in complex three-dimensional flows. The empiricism associated with conventional multitemperature nonequilibrium models is abandoned in favor of the multigroup maximum entropy method combined with kinetics-informed adaptive binning. This group-based approach allows for time-varying optimal reduced-order representation of the internal state population distribution while accounting for all collisional processes included in the state-to-state model. Similarly, radiative transfer calculations are performed efficiently by discretization in the spectral, angular, and spatial spaces using the smeared band, discrete ordinate, and finite-volume methods, respectively. This reduction in computational overhead allows truly non-Boltzmann simulations with two-way coupling between the flow and radiation fields to be realized without simplifying approximations based on the tangent-slab method or local escape-factors. The simulation procedure is used in conjunction with the US3D flow solver to investigate the impact of vibrational nonequilibrium on ${\mathrm{CO}}_2$ wake flows and resultant infrared radiation around the Mars 2020 vehicle. This involves comparing predictions for flow-field properties and radiative transfer obtained using the conventional two-temperature model, the multigroup non-Boltzmann model, and for decoupled/coupled flow-radiation calculations. Conventional two-temperature models overestimate the rate of thermal equilibration in the near-wake region resulting in the population of midlying and upper ${\mathrm{CO}}_2$ vibrational levels being underpredicted by multiple orders of magnitude. Additionally, the two-temperature approach (in comparison to bin-based StS) overpredicts the rate of ${\mathrm{CO}}_2$ dissociation thereby leading to erroneous estimates for flow properties in the postshock region (primary source of afterbody radiative emission). This results in inflated values for surface radiative heat flux with two-temperature modeling, although overall differences in radiative behavior are tempered by the fast characteristic relaxation times for ground vibrational levels.

Figure 1

Comparison of rate coefficients for intermode ${\mathrm{VV}}_{m-k}$ and vibrational-translational ${\mathrm{VT}}_2$ excitation processes with $M={\mathrm{CO}}_2$.

Figure 2

Nonequilibrium ${\mathrm{CO}}_2$ vibrational population at $t={10}^{-4}\text{s}$ computed using the full StS model in an ideal chemical reactor [10]. The inset figure magnifies the distinct comblike structure of the nonequilibrium region.

Figure 3

Chemical reactor predictions for full StS, and reduced-order models based on 30 adaptive and energy bins [10].

Figure 4

Comparison of reduced-order model characteristics with experimental data (dashed lines represent extrapolated values).

Figure 5

Normalized emission coefficients for the $4.5\mu \mathrm{m}$ band originating from a Boltzmann distribution at $T_V=4100\mathrm{K}$.

Figure 6

Computational mesh for modeling the Mars 2020 wake flow.

Figure 7

Distribution for $T$, $T_V$, and ${\rho }_{{\mathrm{CO}}_2}$ along the $y=0\mathrm{m}$ plane for the 10 bin-based StS model. Individual streamlines and LOSs for analyzing flow-field and radiative intensity, respectively, are also defined.

Figure 8

Percentage difference in predicted translational-rotational temperature $T$ between bin-based StS and 2-T models: $(T^{\mathrm{StS}}-T^{2-\mathrm{T}})/T^{2-\mathrm{T}}\times 100\%$.

Figure 9

Percentage difference in predicted partial densities of ${\mathrm{CO}}_2$ vibrational bins 1, 2, 5, and 8 between bin-based StS and 2-T models: $({\rho }_{\text{bin}}^{\mathrm{StS}}-{\rho }_{\text{bin}}^{2-\mathrm{T}})/{\rho }_{\text{bin}}^{2-\mathrm{T}}\times 100\%$.

Figure 10

Distribution of $T$ (black) and $T_V$ (red) along streamlines 2 and 3. Solid and dashed lines represent bin-based StS and conventional 2-T models, respectively.

Figure 11

Partial densities of ${\mathrm{CO}}_2$ vibrational bins along different streamlines. Solid and dashed lines represent bin-based StS and conventional 2-T models, respectively.

Figure 12

Non-Boltzmann factor [Eq. (36)] for ${\mathrm{CO}}_2$ vibrational bins 1–4 along streamline 2.

Figure 13

Non-Boltzmann factor [Eq. (36)] for ${\mathrm{CO}}_2$ vibrational bins 5–10 along different streamlines.

Figure 14

Flow factors [Eq. (39)] for the first four ${\mathrm{CO}}_2$ vibrational bins along LOS 1.

Figure 15

Temperatures $T$ and $T_V$ (solid and dashed lines correspond to bin-based StS and conventional 2-T models, respectively), $\%\mathrm{\Delta }{F}_{i-j}$, and total radiative intensity along different LOSs. Percentage difference is computed as $(Q^{\mathrm{StS}}-Q^{2-\mathrm{T}})/\left|Q^{2-\mathrm{T}}\right|\times 100\%$.

Figure 16

Percentage difference in total ${\mathrm{CO}}_2$ density between bin-based StS and 2-T models: $({\rho }_{{\mathrm{CO}}_2}^{\mathrm{StS}}-{\rho }_{{\mathrm{CO}}_2}^{2-\mathrm{T}})/{\rho }_{{\mathrm{CO}}_2}^{2-\mathrm{T}}\times 100\%$.

Figure 17

Negative value of volumetric radiative heating term. Percentage difference computed as $(\mathbf{\nabla }·{\mathbf{q}}_{\text{rad}}^{\mathrm{StS}}-\mathbf{\nabla }·{\mathbf{q}}_{\text{rad}}^{2-\mathrm{T}})/|\mathbf{\nabla }·{\mathbf{q}}_{\text{rad}}^{2-\mathrm{T}}|\times 100\%$ (right).

Figure 18

Total radiative surface heat flux $q_{\text{wall}}$ from bin-based StS and 2-T models. Percentage difference computed as $(q_{\text{wall}}^{\mathrm{StS}}-q_{\text{wall}}^{2-\mathrm{T}})/q_{\text{wall}}^{2-\mathrm{T}}\times 100\%$.

Figure 19

Escape factor and total radiative intensity along different LOSs. Percentage difference is computed as $(Q^{\mathrm{StS}}-Q^{2-\mathrm{T}})/\left|Q^{2-\mathrm{T}}\right|\times 100\%$.

Figure 20

Percentage difference in total radiative surface heat flux coupled/uncoupled bin-based StS and 2-T models along the $y=0\mathrm{m}$ edge: $(q_{\text{wall}}^{\mathrm{StS}}-q_{\text{wall}}^{2-\mathrm{T}})/q_{\text{wall}}^{2-\mathrm{T}}\times 100\%$