Numerical investigation of the laminar-turbulent boundary-layer transition for a circular cone at Mach 5: Wind tunnel and flight conditions

Direct Numerical Simulations (DNS) were carried out to investigate the laminar-turbulent boundary-layer transition process for a 7◦ half-angle cone with a circular cross section and a 2.5 mm nose radius at Mach 5.2 and zero angle of attack. The free-flight flow conditions used in the simulations match the conditions at a time instant during the ascent trajectory of the Hypersonic International Flight Research Experimentation (HIFiRE-1) tests as closely as possible. The ground based wind tunnel conditions are based on the test conditions of the Hypersonic Wind Tunnel 5 (HWT-5) at Sandia National Laboratories. The wall is considered to be isothermal with a temperature distribution considering the heating of the nose region of the cone for the flight conditions and a constant wall temperature for the wind tunnel conditions. Linear Stability Theory (LST) investigations revealed that for all cases axisymmetric second mode waves were the dominant primary instability. While for the wind tunnel conditions first mode waves were also amplified according to LST, the strong wall cooling for the flight conditions completely stabilizes the first mode. Secondary instability investigations indicated that for all cases a strong fundamental resonance with respect to second mode waves can be observed. Subsequently, so-called “controlled” fundamental breakdown simulations were carried out, which confirmed that fundamental resonance is a viable nonlinear mechanism to lead to laminar-turbulent boundary-layer transition for wind tunnel as well as flight conditions.