Better understanding the onset of turbulence approaching Mach 5

Aircraft designers and scientists are trying to understand the relation between supersonic modes and the hypersonic flows around aircraft or projectiles at hypersonic speeds, specifically regarding the transition from smooth laminar flow to irregular turbulence. The onset of turbulence generally leads to increased drag and heating, which impair engine performance and control. The rapidly rising temperature at Mach 5 and above is particularly challenging, and solutions such as incorporating thermal protection materials add weight, thus reducing payloads.

The new research by Knisely and Zhong sought to better understand how this transition to turbulence occurs and how to more accurately predict the phenomenon. They built on previous studies and applied a new approach that uses both mathematics-based Linear Stability Theory (LST) and Direct Numerical Simulation (DNS) to analyze supersonic modes during these transitions. These supersonic modes were experimentally observed for the first time, over a blunt wall cone with thermochemical nonequilibrium effects.

They attributed the mechanism of the supersonic mode to the interactions among the unstable subsonic mode S, stable supersonic mode F1, and the slow acoustic spectrum. Since LST analysis assumes each mode to act independently, the supersonic mode cannot be adequately resolved in this way. Therefore, the authors conclude, both LST and DNS analyses must be performed to reliably assess the impact of the supersonic mode on transition to turbulence.

“This study is novel in that it confirms the existence of the supersonic mode on a blunt axisymmetric cone,” said Knisely. “Furthermore, this work is significant in that new LST boundary conditions incorporating the effects of an oblique shock are developed and verified, leading to a more accurate physical representation of the flow.”

Source: “Sound radiation by supersonic unstable modes in hypersonic blunt cone boundary layers. I. Linear stability theory,” by Carleton P. Knisely and Xiaolin Zhong, Physics of Fluids (2019). The article can be accessed at https://doi.org/10.1063/1.5055761 .