NUMERICAL SIMULATION OF NON-EQUILIBRIUM FLOW-RADIATION CHARACTERISTICS AT HYPERSONIC SPEEDS
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摘要: 飞行器高超声速飞行过程中所承受对流加热和辐射加热可能具有相当的量级, 因此合理准确预测气动加热需要将二者进行综合考虑. 文章发展了具有非玻尔兹曼电子能级分布和振动能级分布的高温空气碰撞辐射模型, 并耦合一维激波后流动方程计算不同飞行条件下激波后的非平衡流动特性, 采用逐线辐射输运模型计算获得激波后非平衡辐射特性、辐射强度和辐射输运通量, 深入比较分析了不同飞行高度和马赫数对非平衡流动和辐射输运过程的影响. 计算结果表明对于高空高马赫飞行条件, 其波后流动存在显著的热力学非平衡、化学非平衡和能级非平衡特征, 在近激波区域高振动能级和原子高束缚电子激发态明显低于玻尔兹曼分布. 在高空高马赫条件下真空紫外辐射占据主导地位, 主要是由高能原子束缚−束缚跃迁造成的. 随着高度和马赫数的下降, 激波层内气体解离和电离程度降低, 原子辐射贡献下降, 分子辐射贡献增加, 导致红外、可见光和紫外波段的辐射输运增强, 真空紫外辐射输运过程减弱.Abstract: The convective and radiative heating to which a hypersonic vehicle is subjected during hypersonic flight may be of comparable order of magnitude, so reasonably accurate prediction of aerodynamic heating requires a combination of both. In this paper, a high temperature air collisional-radiative model with non-Boltzmann electronical energy levels and vibrational energy levels distribution is developed, and coupled with the one-dimensional post-shock flow equations to calculate the non-equilibrium flow characteristics behind the shock front. The non-equilibrium radiation property, radiation intensity and radiation transfer of the post-shock flow are calculated by using the line-by-line radiation transfer model, which considers the bound-bound, bound-free, free-free radiative mechanisms of atoms and molecules in detail. The effects of flight altitudes and Mach numbers on non-equilibrium flow and radiation transfer process are deeply analyzed. The calculative results indicate that there are significant thermal non-equilibrium effect, chemical non-equilibrium effect and energy levels non-equilibrium effect existed in the post-shock flow for the high altitude and high Mach flight, and there are obvious under-population of the high vibrational energy levels and the high-lying electronical excited states in the near shock region, which are respectively caused by the rapid dissociation reaction of high vibrational states and the ionization processes of high-lying electronical states. Under the high altitude and high Mach conditions, the vacuum ultraviolet radiation is main contributor of radiative transfer process, which is mainly caused by the high energy atomic bound-bound radiative transition processes. With the decrease of altitude and Mach number, the degree of gas dissociation and ionization in the shock layer decreases, leading to the corresponding decrease of atomic radiative emission. Meanwhile, the number density of molecules increases and the contribution of molecular radiation increases, which leads to the enhancement of radiation transfer in infrared, visible and ultraviolet spectral bands, and the weakening of vacuum ultraviolet radiation transfer process.
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图 4 计算结果(线)与Cruden测量(点)得到的电子数密度结果比较
Figure 4. Comparison of the calculated electron density (lines) with experimental data (points)
图 5 平板模型累积辐射通量分布与文献比较
Figure 5. Comparison of the calculated radiative flux (solid lines) with literature (dot dash lines)
图 6 FIRE II驻点处2.2 ~ 4.1 eV积分辐射强度与飞行试验数据比较
Figure 6. Comparison of the stagnation point frequency-integrated radiative intensity with the flight data
图 7 激波后特征温度演变
Figure 7. The spatial evolution of characteristic temperatures behind the shock front
图 10 高温空气辐射系数分布
Figure 10. Distribution of radiative coefficients of high temperature air
表 1 碰撞辐射模型考虑的组分与能级
Table 1. Species and energy levels involved in CR model
Types Species Energy levels molecules N2 $ {X}^{1}{\sum }_{\mathrm{g}}^{ + } $(v = 0→67),$ {A}^{3}{\sum }_{u}^{ + } $, $ {B}^{3}{\prod }_{\mathrm{g}} $,
$ {W}^{3}{\Delta }_{u} $, $ {B{'}}^{3}{\sum }_{u}^{-} $, $ a{{'}}^{1}{\sum }_{u}^{-} $, $ {a}^{1}{\prod }_{\mathrm{g}} $,
$ {w}^{1}{\Delta }_{u} $, $ {G}^{3}{\Delta }_{\mathrm{g}} $, $ {C}^{3}{\prod }_{u} $, $ {E}^{3}{\sum }_{\mathrm{g}}^{ + } $O2 $ {X}^{3}{\sum }_{\mathrm{g}}^{-} $(v = 0→46),$ {a}^{1}{\Delta }_{\mathrm{g}} $,$ {b}^{1}{\sum }_{\mathrm{g}}^{ + } $,
$ {c}^{1}{\sum }_{u}^{-} $,$ {A{'}}^{3}{\Delta }_{u} $,$ {A}^{3}{\sum }_{u}^{ + } $,$ {B}^{3}{\sum }_{u}^{-} $,$ {f}^{1}{\sum }_{u}^{ + } $NO $ {X}^{2}\prod $,$ {a}^{4}\prod $,$ {A}^{2}{\sum }_{}^{ + } $,$ {B}^{2}\prod $,$ {b}^{4}{\sum }_{}^{-} $,
$ {C}^{2}\prod $,$ {D}^{2}{\sum }_{}^{ + } $,$ {B{'}}^{2}\Delta $,$ {E}^{2}{\sum }_{}^{ + } $,$ {F}^{2}\Delta $molecular ions N2+ $ {X}^{2}{\sum }_{\mathrm{g}}^{ + } $,$ {A}^{2}{\prod }_{u} $,$ {B}^{2}{\sum }_{u}^{ + } $,
$ {a}^{4}{\sum }_{u}^{ + } $,$ {D}^{2}{\prod }_{\mathrm{g}} $,$ {C}^{2}{\sum }_{u}^{ + } $O2+ $ {X}^{2}{\prod }_{\mathrm{g}} $,$ {a}^{4}{\prod }_{u} $,$ {A}^{2}{\prod }_{u} $,$ {b}^{4}{\sum }_{\mathrm{g}}^{-} $ NO+ $ {X}^{1}{\sum }_{}^{ + } $,$ {a}^{3}{\sum }_{}^{ + } $,$ {b}^{3}\prod $,$ {W}^{3}\Delta $,
$ {b{{'}}}^{3}{\sum }_{}^{-} $,$ {A{'}}^{1}{\sum }_{}^{ + } $,$ {W}^{1}\Delta $,$ {A}^{1}\prod $atoms N $ {{}_{}{}^{4}S}^{0} $, $ {}_{}{}^{2}D $, $ {}_{}{}^{2}P $, ··· (46 levels) O $ {}_{}{}^{3}P $, $ {}_{}{}^{1}D $, $ {}_{}{}^{1}S $, ··· (40 levels) atomic ions N+ $ {}_{}{}^{3}P $ O+ $ {{}_{}{}^{4}S}^{0} $ electron e− — 
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表 2 FIRE II飞行状态
Table 2. Flight conditions of FIRE II vehicle
Time/s Height/km Temperature/K Velocity/(m·s−1) 1634 76.42 195 11360 1643 53.04 276 10480 1648 42.14 267 8300
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表 3 碰撞辐射模型考虑的辐射跃迁过程
Table 3. Radiative processes involved in CR model
Species Types Radiative transitions N bound-bound N(i)$ \leftrightarrow $N(j < i) + hv bound-free N+ + e−$ \leftrightarrow $N(i) + hv free-free N(i) + e−$ \leftrightarrow $N(i) + e− + hv O bound-bound O(i)$ \leftrightarrow $O(j < i) + hv bound-free O+ + e−$ \leftrightarrow $O(i) + hv free-free O(i) + e−$ \leftrightarrow $O(i) + e− + hv N2 bound-bound N2($ {B}^{3}{\prod }_{\mathrm{g}} $)$ \leftrightarrow $N2($ {A}^{3}{\sum }_{u}^{ + } $) + hv N2($ {C}^{3}{\prod }_{u} $)$ \leftrightarrow $N2($ {B}^{3}{\prod }_{\mathrm{g}} $) + hv N2($ {c}_{4}^{\text{'}}{\sum }_{u}^{ + } $)$ \leftrightarrow $N2($ {X}^{1}{\sum }_{\mathrm{g}}^{ + } $) + hv N2($ {c}_{3}^{\text{'}}{\prod }_{u} $)$ \leftrightarrow $N2($ {X}^{1}{\sum }_{\mathrm{g}}^{ + } $) + hv N2($ {b}^{1}{\prod }_{u} $)$ \leftrightarrow $N2($ {X}^{1}{\sum }_{\mathrm{g}}^{ + } $) + hv N2($ {b}_{}^{\text{'}1}{\sum }_{u}^{ + } $)$ \leftrightarrow $N2($ {X}^{1}{\sum }_{\mathrm{g}}^{ + } $) + hv N2($ {o}_{3}^{1}{\prod }_{u} $)$ \leftrightarrow $N2($ {X}^{1}{\sum }_{\mathrm{g}}^{ + } $) + hv bound-free continuum N2+ bound-bound N2+($ {B}^{2}{\sum }_{u}^{ + } $)$ \leftrightarrow $N2+($ {X}^{2}{\sum }_{\mathrm{g}}^{ + } $) + hv N2+($ {A}^{2}{\prod }_{u} $)$ \leftrightarrow $N2+($ {X}^{2}{\sum }_{\mathrm{g}}^{ + } $) + hv N2+($ {C}^{2}{\sum }_{u}^{ + } $)$ \leftrightarrow $N2+($ {X}^{2}{\sum }_{\mathrm{g}}^{ + } $) + hv NO bound-bound NO($ {B}^{2}\prod $r)$ \leftrightarrow $NO($ {X}^{2}\prod $r) + hv NO($ {A}^{2}{\sum }_{}^{ + } $)$ \leftrightarrow $NO($ {X}^{2}\prod $r) + hv NO($ {C}^{2}\prod $r)$ \leftrightarrow $NO($ {X}^{2}\prod $r) + hv NO($ {\mathrm{D}}^{2}{\sum }_{}^{ + } $)$ \leftrightarrow $NO($ {X}^{2}\prod $r) + hv NO($ {B{'}}^{2}\Delta $)$ \leftrightarrow $NO($ {X}^{2}\prod $r) + hv NO($ {E}^{2}{\sum }_{}^{ + } $)$ \leftrightarrow $NO($ {X}^{2}\prod $r) + hv O2 bound-bound O2($ {B}^{3}{\sum }_{u}^{-} $)$ \leftrightarrow $O2($ {X}^{3}{\sum }_{\mathrm{g}}^{-} $) + hv bound-free continuum
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