Abstract
Hypersonic laminar flow over a canonical 25°–55° double cone is studied using computational fluid dynamics and global stability analysis (GSA) with a free-stream Mach number of 11.5 and various unit Reynolds numbers. Axisymmetric simulations reveal that secondary separation occurs beneath the primary separation bubble beyond a critical Reynolds number. The numerical results agree well with existing experiments and the triple-deck theory with the axisymmetric effect on the incoming boundary layer treated by the Mangler transformation. The GSA identifies a three-dimensional global instability that is azimuthally periodic immediately prior to the emergence of secondary separation. The criterion of the onset of global instability in terms of a scaled deflection angle established for supersonic compression corner flows (Hao et al., J. Fluid Mech., vol. 919, 2021, A4) can be directly applied to double-cone flows. As the Reynolds number is further increased, the flow is strongly destabilized with the coexistence of multiple stationary and low-frequency oscillating unstable modes. Direct numerical simulations confirm that the supercritical double-cone flow is intrinsically three-dimensional, unsteady and exhibits strong azimuthal variations in the peak heating.
Highlights
Hypersonic flow over a double cone represents a canonical case of shock-wave–boundarylayer interaction (Babinsky & Harvey 2011)
Robinet (2007) observed low-frequency unsteady characteristics of shock impingement on a Mach 2.15 laminar boundary layer using direct numerical simulations (DNS), which stemmed from a supercritical Hopf bifurcation of the separated flow
The global stability of a Mach 7.7 compression corner flow was parametrically studied by Hao et al (2021) with different ramp angles and wall temperatures, which was closely linked with the emergence of secondary separation beneath the primary bubble
Summary
Hypersonic flow over a double cone represents a canonical case of shock-wave–boundarylayer interaction (Babinsky & Harvey 2011). Robinet (2007) observed low-frequency unsteady characteristics of shock impingement on a Mach 2.15 laminar boundary layer using direct numerical simulations (DNS), which stemmed from a supercritical Hopf bifurcation of the separated flow. Hildebrand et al (2018) studied shock impingement on a Mach 5.92 laminar boundary layer They found a stationary global mode at a supercritical shock angle, which can lead to the formation of streamwise streaks downstream of reattachment. The global stability of a Mach 7.7 compression corner flow was parametrically studied by Hao et al (2021) with different ramp angles and wall temperatures, which was closely linked with the emergence of secondary separation beneath the primary bubble. DNS are performed to verify the GSA results and reveal the evolution of three-dimensional flow structures
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