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质量引射会对高超声速边界层稳定性和转捩产生显著影响. 本文采用多组分Navier-Stokes求解器, 计算了不同气体质量引射的流场, 在此基础上分析了质量引射对流动稳定性的影响, 区分了引射气体不同性质的作用. 研究表明, 质量引射排挤主流流体, 形成引射层, 令边界层变厚, 显著降低壁面摩阻和热流. 引射气体的黏性系数、相对分子质量及扩散作用主要影响边界层厚度, 而热传导系数和比热容则主要影响温度分布. 线性稳定性分析结果表明, 质量引射激发多个高阶模态失稳, 但第二模态仍起主导作用, 且质量引射减小第二模态失稳区域, 令扰动积分幅值显著减小, 进而抑制转捩. 引射气体性质的变化通过两条路径影响稳定性: 1)改变基本流剖面; 2)改变混合气体性质. 其中引射气体的输运系数(黏性、扩散)主要通过路径一改变失稳特征, 比热容主要通过路径二起作用, 相对分子质量则通过双路径共同作用.Active mass injection is an effective thermal protection technique that can significantly reduce wall heat flux. However, it inherently changes the stability characteristics of boundary layer, substantially affecting the laminar-to-turbulent transition process. Crucially, the underlying mechanisms of controlling how different injected gases regulate flow stability are still unclear. In order to systematically analyze the effects of different gas injections on flow stability, the gas-specific mass injection effects are investigated in this work by employing a multicomponent Navier-Stokes solver to compute flow fields with air, argon, and nitrogen injections. The influence of mass injection on flow stability is analyzed using linear stability theory, followed by distinguishing the different effects of various injectant properties. The result shows that mass injection can displace the freestream gas, forming an injection layer near the wall and increasing the thickness of the boundary layer. Herein, the properties of the main boundary layer are still similar to those of the original boundary layer, while the injection layer exhibits significantly reduced temperature and velocity gradients, resulting in decrease of wall heat flux and surface friction. Linear stability analysis reveals that when mass injection excites multiple higher-order instability modes, the second mode is still dominant. Notably, mass injection reduces the unstable region of the second mode and significantly lowers the integrated disturbance amplitude, thereby suppressing the transition. This stabilizing effect is more pronounced with lighter gases. The differences in injected gas properties are mainly reflected in the viscosity coefficient, thermal conductivity, relative molecular weight, and diffusivity. Among these, the boundary layer thickness is primarily affected by the viscosity coefficient, relative molecular weight, and diffusivity of the injected gas, while the temperature within the boundary layer decreases with the increase of thermal conductivity and specific heat capacity of the injected gas. The influence of injected gas properties on flow stability is manifested in two different ways: 1) modification of basic flow profile and 2) change of mixed gas properties. Specifically, the transport coefficients (viscosity and diffusivity) of the injected gas mainly affect unstable characteristics through way 1), while the specific heat capacity mainly works through way 2). The relative molecular weight plays a combined role in the two ways.
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Keywords:
- mass injection /
- linear stability theory /
- hypersonic boundary layer
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图 1 混合气体模型下基本流程序验证 (a) 空气质量引射; (b) 氩气质量引射
Fig. 1. Validation of the base flow program under the mixed gas model: (a) Air mass injection; (b) argon mass injection.
图 2 LST程序验证 (a) 混合气体模型; (b) 热化学非平衡模型
Fig. 2. LST program validation: (a) Mixed gas model; (b) thermochemical non-equilibrium model.
图 3 (a) 钝锥模型示意图; (b) 网格示意图
Fig. 3. (a) Blunt cone model schematic; (b) computational grid schematic.
图 5 网格无关性验证 (a) 基本流剖面; (b) 稳定性分析结果
Fig. 5. Grid independence verification: (a) Base flow profiles; (b) stability analysis results.
图 6 质量引射对基本流场的影响 (a) 空气质量引射流场云图; (b) 引射区域流场云图
Fig. 6. (a) Flow field contours for air mass injection; (b) flow field contours in the injection region.
图 7 不同气体质量引射壁面量对比 (a) 壁面法向速度; (b) 壁面压力; (c) 引射气体的壁面质量分数
Fig. 7. Comparison of wall quantities for mass injection of different gases: (a) Wall normal velocity; (b) wall pressure; (c) wall mass fraction of the injected gas.
图 8 x = 508 mm处不同气体质量引射的温度 (a) 流向速度 (b) 法向速度 (c) 引射气体质量分数 (d) 剖面比较
Fig. 8. Comparison of profiles at x = 508 mm for mass injection of different gases: (a) Temperature; (b) streamwise velocity; (c) normal velocity; (d) mass fraction of the injected gas.
图 9 不同气体质量引射的边界层厚度 (a) 边界层厚度$ \delta $; (b) 引射层厚度$ {\delta _{ {\text{inj}}}} $; (c) 主流边界层厚度$ {\delta _{ {\text{mf}}}} $对比
Fig. 9. Comparison under different injection conditions: (a) Boundary layer thickness $ \delta $; (b) injection layer thickness $ {\delta _{ {\text{inj}}}} $; (c) mainstream boundary layer thickness $ {\delta _{ {\text{mf}}}} $.
图 10 不同引射条件下的(a) 壁面摩阻和(b) 壁面热流对比
Fig. 10. Comparison under different injection conditions: (a) Wall friction; (b) wall heat flux.
图 11 不同引射条件下的中性曲线对比
Fig. 11. Comparison of neutral curves under different injection conditions.
图 12 $ \omega = 2.4 $时 (a) 扰动增长率沿流向变化; (b) 相速度沿流向变化; (c) N值曲线对比
Fig. 12. For $ \omega = 2.4 $: (a) Variation of disturbance growth rate along the streamwise direction; (b) variation of phase velocity along the streamwise direction; (c) N-factor curve.
图 13 $ \omega = 2.4 $时空气质量引射下 (a) 第二模态的特征函数; (b) 高阶模态的特征函数
Fig. 13. Air mass injection for $ \omega = 2.4 $: (a) Eigenfunctions of the second mode; (b) eigenfunctions of higher-order mode.
图 14 $ \omega = 1.5 $时时空气质量引射下 (a) 扰动增长率沿流向变化; (b) 相速度沿流向变化; (c) N值曲线对比
Fig. 14. Air mass injection for $ \omega = 1.5 $: (a) Variation of disturbance growth rate along the streamwise direction; (b) variation of phase velocity along the streamwise direction; (c) N-factor curve.
图 15 不同引射条件下的N因子包络线对比
Fig. 15. Comparison of N-factor envelopes under different injection conditions.
图 16 引射气体的黏性系数、热传导系数对基本流的影响 (a) 壁面速度; (b) 壁面密度
Fig. 16. Effect of viscosity and thermal conductivity of the injected gas on the base flow: (a) Wall velocity; (b) wall density.
图 17 引射气体的黏性系数、热传导系数对基本流的影响 (a) 法向速度剖面; (b) 密度剖面; (c) 温度剖面
Fig. 17. Effect of viscosity and thermal conductivity of the injected gas on the base flow: (a) Normal velocity profile; (b) density profile; (c) temperature profile.
图 18 引射气体的黏性系数、热传导系数对基本流的影响 (a) 边界层厚度$ \delta $; (b) 引射层厚度$ {\delta _{{\text{inj}}}} $; (c) 主流边界层厚度$ {\delta _{{\text{mf}}}} $
Fig. 18. Effect of viscosity and thermal conductivity of the injected gas on the base flow: (a) Boundary layer thickness $ \delta $; (b) injection layer thickness $ {\delta _{{\text{inj}}}} $; (c) mainstream boundary layer thickness $ {\delta _{{\text{mf}}}} $.
图 19 引射气体的黏性系数、热传导系数对流动稳定性的影响 (a) 中性曲线对比; (b) 混合气体模型下不同流向位置的增长率随频率变化; (c) 完全气体模型下不同流向位置的增长率随频率变化
Fig. 19. Effect of viscosity and thermal conductivity of the injected gas on flow stability: (a) Comparison of neutral curves; (b) variation of growth rate with frequency at different streamwise positions under the mixed gas model; (c) variation of growth rate with frequency at different streamwise positions under the perfect gas model.
图 20 引射气体的相对分子质量对基本流的影响 (a) 壁面速度; (b) 壁面密度
Fig. 20. Effect of the relative molecular mass of the injected gas on the base flow: (a) Wall velocity; (b) wall density.
图 21 引射气体的相对分子质量对基本流的影响 (a) 法向速度剖面; (b) 密度剖面; (c) 温度剖面
Fig. 21. Effect of the relative molecular mass of the injected gas on the base flow: (a) Normal velocity profile; (b) density profile; (c) temperature profile.
图 22 引射气体的相对分子质量对基本流的影响 (a) 边界层厚度$ \delta $; (b) 引射层厚度$ {\delta _{ {\text{inj}}}} $; (c) 主流边界层厚度$ {\delta _{ {\text{mf}}}} $
Fig. 22. Effect of the relative molecular mass of the injected gas on the flow stability: (a) Boundary layer thickness $ \delta $; (b) injection layer thickness $ {\delta _{ {\text{inj}}}} $; (c) mainstream boundary layer thickness $ {\delta _{ {\text{mf}}}} $.
图 23 引射气体的相对分子质量对流动稳定性的影响 (a) 中性曲线对比; (b) 混合气体模型下不同流向位置的增长率随频率变化; (c) 完全气体模型下不同流向位置的增长率随频率变化
Fig. 23. Effect of the relative molecular mass of the injected gas on flow stability: (a) Comparison of neutral curves; (b) variation of growth rate with frequency at different streamwise positions under the mixed gas model; (c) variation of growth rate with frequency at different streamwise positions under the perfect gas model.
图 24 引射气体的比热容对基本流的影响 (a) 壁面速度; (b) 壁面密度
Fig. 24. Effect of the specific heat capacity of the injected gas on the base flow: (a) Wall velocity; (b) wall density.
图 25 引射气体的比热容对基本流的影响 (a) 法向速度剖面; (b) 密度剖面; (c) 温度剖面
Fig. 25. Effect of the specific heat capacity of the injected gas on the base flow: (a) Normal velocity profile; (b) density profile; (c) temperature profile.
图 26 引射气体的比热容对流动稳定性的影响 (a) 中性曲线对比; (b) 混合气体模型下不同流向位置的增长率随频率变化; (c) 完全气体模型下不同流向位置的增长率随频率变化
Fig. 26. Effect of the specific heat capacity of the injected gas on flow stability: (a) Comparison of neutral curves; (b) variation of growth rate with frequency at different streamwise positions under the mixed gas model; (c) variation of growth rate with frequency at different streamwise positions under the perfect gas model.
图 27 引射气体的扩散作用对基本流的影响 (a) 壁面速度; (b) 壁面密度
Fig. 27. Effect of the diffusion of the injected gas on the base flow: (a) Wall velocity; (b) wall density.
图 28 引射气体的扩散作用对基本流的影响 (a) 引射气体质量分数剖面; (b) 温度剖面
Fig. 28. Effect of the diffusion of the injected gas on the base flow: (a) Mass fraction profile of the injected gas; (b) temperature profile.
图 29 引射气体的扩散作用对基本流的影响 (a) 边界层厚度$ \delta $; (b) 引射层厚度$ {\delta _{{\text{inj}}}} $; (c)主流边界层厚度$ {\delta _{{\text{mf}}}} $
Fig. 29. Effect of the diffusion of the injected gas on the base flow: (a) Boundary layer thickness $ \delta $; (b) injection layer thickness $ {\delta _{{\text{inj}}}} $; (c) mainstream boundary layer thickness $ {\delta _{{\text{mf}}}} $.
图 30 引射气体的扩散作用对流动稳定性的影响 (a) 中性曲线对比; (b) 混合气体模型下不同流向位置的增长率随频率变化; (c) 完全气体模型下不同流向位置的增长率随频率变化
Fig. 30. Effect of the diffusion of the injected gas on flow stability: (a) Comparison of neutral curves; (b) variation of growth rate with frequency at different streamwise positions under the mixed gas model; (c) variation of growth rate with frequency at different streamwise positions under the perfect gas model.
i $ {\mu _{{\text{ref}}i}} $/(kg·m–1·s–1) $ {S_{\mu i}} $/K $ {T_{{\text{ref}}i}} $/K Ar 2.117×10–5 146.3 273.16 N2 1.656×10–5 104.7 273.16 O2 1.919×10–5 125 273.16 
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表 2 引射气体性质
Table 2. Properties of the injected gas.
引射气体 黏性系数 热传导系数 相对分子质量 比热容 扩散作用 Ar 不变 不变 40 $ \dfrac{3}{2}{R_{{\text{Ar}}}} $ 不变 Ar(μ*) $ \mu $下降, $ {\mu _{{\text{Ar}}\left( {\mu^*} \right)}} = {\mu _{{{\text{N}}_{2}}}} = 1.656 \times {10^{ - 5}}{\left(\dfrac{T}{{273.16}}\right)^{3/2}}\left(\dfrac{{273.16 + 104.7}}{{T + 104.7}}\right) $ Ar(k*) $ k $下降, $ {\kappa _{{\text{Ar}}\left( {k^*} \right)}} = {\kappa _{{{\text{N}}_{2}}}} = 1.656 \times {10^{ - 5}}{\left(\dfrac{T}{{273.16}}\right)^{3/2}}\left(\dfrac{{273.16 + 104.7}}{{T + 104.7}}\right)\left(\dfrac{5}{2}c_{{\text{v, tra}}}^{{\text{Ar}}} + c_{{\text{v, tor}}}^{{\text{Ar}}}\right) $ Ar(M*) $ M $下降, $ {M_{{\text{Ar}}\left( {M^*} \right)}} = {M_{{{\text{N}}_{2}}}} = {28} $ Ar(Cv*) $ {\text{Cv}} $上升, $ C_{\text{v},\text{Ar}\left( {C_{\text{v}}^*} \right)}= C_{\text{v},\text{N}_{2}} = \dfrac{5}{2}{R_{{\text{Ar}}}} $ Ar(D*) $ {D_{{\text{Ar}}\left( {D^*} \right)}} \to {0} $
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表 3 气体性质对流动稳定性的作用路径
Table 3. The pathway of gas properties on flow stability.
作用路径 主要影响
因素对第二模态影响 改变边界
层剖面相对分子
质量相对分子质量增大, 边界层厚度降低,
不稳定频率增大、最大增长率增大黏性系数 黏性系数增大, 边界层厚度降低,
不稳定频率增大、最大增长率降低扩散 扩散作用导致边界层厚度增大,
不稳定频率降低改变混合
气体性质相对分子
质量相对分子质量增大, 不稳定频率降低 比热容 比热容增大, 不稳定频率降低、
最大增长率增大
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