斜激波与内凹半圆柱面无粘相互作用

Inviscid interactions between an oblique shock wave and a concave cylinder

关键词:  内转式进气道  斜激波  内凹半圆柱面  三维激波干扰  马赫反射  规则反射  流向涡对

Key words:  Inward-turning inlet  Oblique shock wave  Concave cylinder  Three-dimensional shock interactions  Mach reflection  Regular reflection  Streamwise counter-rotating vortex pair

摘要:

针对三维内转式进气道流动中激波入射内凹壁面主导的复杂波系干扰问题，采用斜激波入射内凹半圆柱面的简化构型，在来流马赫数为6的条件下，通过无粘数值模拟结合理论分析，研究了激波角β_i=14°~29°的斜激波在内凹半圆柱面反射形成的三维流场。结果表明，流场对称面均会出现显著高于二维情况的逆压梯度。当β_i≤25°时，从侧壁到对称面，斜激波经历了从马赫反射（MR）到规则反射（RR）的转变，形成了MR-RR型流场，转变点处产生的桥激波向对称面延伸，桥激波在对称面反射后产生的压力峰值高于二维斜激波反射；当β_i≥25°时，斜激波在侧壁和对称面均发生马赫反射，形成了MR-MR型流场，两种马赫反射分界点处产生的桥激波向侧壁发展，侧壁气流在对称面相撞后产生的压力峰值高于正激波后的压力；当β_i=25°时，流场存在MR-RR型和MR-MR型双解现象。通过降维分析理论，揭示了两类流场中转变点和分界点的形成机制，并厘清了桥激波的产生原因和初期演化特征。当β_i ≥ 18°时，无粘激波干扰所主导的侧壁气流加剧向对称面汇聚，并在对称面附近产生流向涡对。无粘分析获得的认识，有助于揭示内转式进气道中流动汇聚和流向涡对等现象的形成机理。

Abstract:

Three-dimensional shock interactions dominated by the shock wave impinging on concave walls are commonly encountered in the three-dimensional inward-turning inlet. To reveal the flow physics of these interactions， a simplified model that consists of an oblique shock wave impinging on a concave cylinder was proposed. Inviscid numerical simulations and theoretical analysis were conducted at a freestream Mach number of 6 with a series of shock angles β_i ranging from 14° to 29° to investigate the three-dimensional flowfield generated by the oblique shock wave impinging on the concave cylinder. The results show that the adverse pressure gradient on the symmetry plane is significantly higher than that of the two-dimensional scenario. For β_i ≤ 25°， the transitions from the Mach reflection （MR） to regular reflection （RR） occur when the oblique shock sweeps from the sidewall to the symmetry plane， which forms the type MR-RR flow field. A bridge shock wave generated at the MR-RR transition point extends to the symmetry plane and then reflects on the symmetry plane， which generates a peak wall pressure higher than that of the two-dimensional oblique shock reflection on a flat plate. For β_i≥25°， the shock reflections on the sidewall and the symmetry plane are both MR， forming the type MR-MR flow field. The bridge shock wave generated at the dividing point of the two MRs develops towards the sidewall. The flow past the sidewall collides on the symmetry plane， resulting in a peak wall pressure higher than that of a normal shock wave. When β_i=25°， dual solutions of MR-RR and MR-MR of the flow field exist depending on different initial conditions. The formation mechanisms of the transition points and the dividing points in the two types of flow fields are revealed using a theoretical method， in which the three-dimensional shock interactions are transformed into a series of two-dimensional problems. The generation mechanisms and initial evolution characteristics of the bridge shock wave are clarified using this theoretical method. When β_i ≥ 18°， the convergence of flow past the sidewall dominated by inviscid shock interactions are intensified on the symmetry plane， forming a streamwise counter-rotating vortex pair near the symmetry plane. The knowledge gained from the inviscid analyses is helpful to address the mechanisms of flow convergence and counter-rotating vortex pair phenomena in the inward-turning inlet.