Prediction of laminar-turbulence transition of the hypersonic boundary layer has received much attention. Receptivity is the initial stage and key problem of transition, since it influences the parameters (frequency, amplitude and phase) of instability waves in the boundary layer triggered by free-stream disturbance. For hypersonic aircraft, the interaction between disturbance and oblique shock wave is the key to the receptivity, which also provides input information such as amplitude of waves for the eN method. Based on the conservative linearized Euler equations CLEE, the paper investigates interaction between free-stream disturbance and oblique shock. The three-dimensional CLEE is derived in the generalized curvilinear coordinate system, and the generalized conservative variables and inviscid flux of the governing equation are derived. The fifth order WENO scheme is utilized for spatial discretization. The three-step third-order Runge-Kutta method, is utilized for time marching. The non-reflective boundary condition is achieved using grid stretching techniques to eliminate the reflection of boundary disturbance waves. Further, interaction between free-stream disturbance and oblique shock is simulated. Two cases where flow behind the shock is subsonic and supersonic are studied, with different incident waves (entropy & vorticity). Satisfactory agreement is observed between our numerical results and theoretical result from linear interaction analysis (LIA). The current method can faithfully reproduce the interaction between shock and freestream disturbance.

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Numerical Investigation of Interaction Between Free-Stream Disturbance and an Oblique Shock Wave Based on Conservative Linearized Euler Equations

  • Chunhui Liu,
  • Liangjie Gao,
  • Zhansen Qian,
  • Pengbo Xu

摘要

Prediction of laminar-turbulence transition of the hypersonic boundary layer has received much attention. Receptivity is the initial stage and key problem of transition, since it influences the parameters (frequency, amplitude and phase) of instability waves in the boundary layer triggered by free-stream disturbance. For hypersonic aircraft, the interaction between disturbance and oblique shock wave is the key to the receptivity, which also provides input information such as amplitude of waves for the eN method. Based on the conservative linearized Euler equations CLEE, the paper investigates interaction between free-stream disturbance and oblique shock. The three-dimensional CLEE is derived in the generalized curvilinear coordinate system, and the generalized conservative variables and inviscid flux of the governing equation are derived. The fifth order WENO scheme is utilized for spatial discretization. The three-step third-order Runge-Kutta method, is utilized for time marching. The non-reflective boundary condition is achieved using grid stretching techniques to eliminate the reflection of boundary disturbance waves. Further, interaction between free-stream disturbance and oblique shock is simulated. Two cases where flow behind the shock is subsonic and supersonic are studied, with different incident waves (entropy & vorticity). Satisfactory agreement is observed between our numerical results and theoretical result from linear interaction analysis (LIA). The current method can faithfully reproduce the interaction between shock and freestream disturbance.