Liu, Jianxin; Marensi, ElenaISTA; Wu, Xuesong
Sherwin, Spencer; Schmid, Peter; Wu, Xuesong
Streaky structures in the boundary layers are often generated by surface roughness elements and/or free-stream turbulence, and are known to have significant effects on boundary-layer instability. In this paper, we investigate the impact of two forms of streaks on the instability of supersonic boundary layers. The first concerns the streaks generated by an array of spanwise periodic and streamwise elongated surface roughness elements, and our interest is how these streaks influence the lower-branch viscous first modes, whose characteristic wavelength and frequency are on the classical triple-deck scales. By adapting the triple-deck theory in the incompressible regime to the supersonic one, we first derived a simplified system which allows for efficient calculation of the streaks. The asymptotic analysis simplifies a bi-global eigenvalue problem to a one-dimensional problem in the spanwise direction, showing that the instability is controlled at leading order solely by the spanwise-dependent wall shear. In the fundamental configuration, the streaks stabilize first modes at low frequencies but destabilize the high-frequency ones. In the subharmonic configuration, the streaks generally destabilize the first mode across the entire frequency band. Importantly, the spanwise even modes are of radiating nature, i.e. they emit acoustic waves spontaneously to the far field. Streaks of the second form are generated by low-frequency vortical disturbances representing free-stream turbulence. They alter the flow in the entire layer and their effects on instability are investigated by solving the inviscid bi-global eigenvalue problem. Different from the incompressible case, a multitude of compressible instability modes exists, of which the dominant mode is an inviscid instability associated with the spanwise shear. In addition, there exists a separate branch of instability modes that have smaller growth rates but are spontaneously radiating.
IUTAM Laminar-Turbulent Transition
The work is supported by the National Key Research and Development Program of China (No. 2016YFA0401200), the National Natural Science Foundation of China (Grant Nos. 91952202 and 11402167).
2019-09-02 – 2019-09-06
Liu J, Marensi E, Wu X. Effects of streaky structures on the instability of supersonic boundary layers. In: Sherwin S, Schmid P, Wu X, eds. IUTAM Laminar-Turbulent Transition. Vol 38. 1st ed. IUTAM Bookseries. Cham: Springer Nature; 2022:587-598. doi:10.1007/978-3-030-67902-6_51
Liu, J., Marensi, E., & Wu, X. (2022). Effects of streaky structures on the instability of supersonic boundary layers. In S. Sherwin, P. Schmid, & X. Wu (Eds.), IUTAM Laminar-Turbulent Transition (1st ed., Vol. 38, pp. 587–598). Cham: Springer Nature. https://doi.org/10.1007/978-3-030-67902-6_51
Liu, Jianxin, Elena Marensi, and Xuesong Wu. “Effects of Streaky Structures on the Instability of Supersonic Boundary Layers.” In IUTAM Laminar-Turbulent Transition, edited by Spencer Sherwin, Peter Schmid, and Xuesong Wu, 1st ed., 38:587–98. IUTAM Bookseries. Cham: Springer Nature, 2022. https://doi.org/10.1007/978-3-030-67902-6_51.
J. Liu, E. Marensi, and X. Wu, “Effects of streaky structures on the instability of supersonic boundary layers,” in IUTAM Laminar-Turbulent Transition, 1st ed., vol. 38, S. Sherwin, P. Schmid, and X. Wu, Eds. Cham: Springer Nature, 2022, pp. 587–598.
Liu J, Marensi E, Wu X. 2022.Effects of streaky structures on the instability of supersonic boundary layers. In: IUTAM Laminar-Turbulent Transition. vol. 38, 587–598.
Liu, Jianxin, et al. “Effects of Streaky Structures on the Instability of Supersonic Boundary Layers.” IUTAM Laminar-Turbulent Transition, edited by Spencer Sherwin et al., 1st ed., vol. 38, Springer Nature, 2022, pp. 587–98, doi:10.1007/978-3-030-67902-6_51.