Study on the evolution of non-modal disturbances in hypersonic boundary layer based on HLNS approach
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摘要: 高超声速边界层转捩是航天飞行器设计中的基础难题, 发生在线性失稳区上游的亚临界转捩是常规风洞实验中常见的现象. 亚临界转捩一般是由非模态扰动的演化及二次失稳触发的, 为了揭示局部突变对高超声速边界层亚临界转捩的影响机理, 发展了基于谐波型线性化Navier-Stokes (HLNS) 方程及其伴随系统的描述非模态扰动演化的求解框架. 该框架的优点是不改变原始系统的椭圆型特性, 因而可以处理非模态扰动 (条带) 在局部突变附近的快速畸变. 针对马赫数为5.96、攻角为
$ - 4^\circ $ 的高超声速钝平板边界层, 研究了不同深度凹槽对条带幅值的影响. 数值结果表明凹槽对条带有促进作用, 这与实验中发现的规律定性相符, 且存在使促进作用最大的最优凹槽深度.Abstract: Laminar-turbulent transition in hypersonic boundary layers is of fundamental importance in the design of aerospace vehicles. Subcritical transition, occurring upstream of the linear instability region, appears frequently in conventional wind-tunnel experiments. The subcritical transition is usually triggered by the evolution of non-modal disturbances and their subsequent secondary instability. In order to reveal the inherent mechanisms governing the impact of abrupt changes on hypersonic subcritical transition, a numerical framework describing the evolution of non-modal disturbances based on the harmonic linearized Navier-Stokes (HLNS) equation and its adjoint system is developed. The advantage of this framework is that the elliptic nature of the original system is retained, leading to the ability to deal with the rapid distortion of the non-modal disturbances (streaks) in the vicinity of the local abrupt changes. For a hypersonic blunt-plate boundary layer with an oncoming Mach number 5.96 and an angle of attack$ - 4^\circ $ , the impact of the cavities with different depths on streak amplitude is studied. Numerical solutions indicate that streaks are enhanced by the cavities, which agrees with the experimental observations in quantity. Moreover, the enhancement effect peaks at a particular cavity depth.-
Key words:
- hypersonic boundary layer /
- cavity /
- optimal perturbation /
- subcritical transition
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