Nonlinear Evolution and Breakdown of Azimuthally Compact Crossflow Vortex Pattern over a Yawed Cone

Abstract

Hypersonic boundary-layer flows over a circular cone at moderate angle of incidence can support strong crossflow instability in between the windward and leeward rays on the plane of symmetry. Due to the more efficient excitation of stationary crossflow vortices by surface roughness, a possible path to transition in such flows corresponds to rapid amplification of the high-frequency secondary instabilities of finite amplitude stationary crossflow vortices. In the present paper, the previous analyses of crossflow instability over a 7degree half-angle, yawed circular cone in a Mach 6 free stream have been extended to the nonlinear evolution of azimuthally localized crossflow vortex packets and the amplification characteristics and nonlinear breakdown of high-frequency secondary instabilities associated with those packets. A comparison between plane marching PSE and direct Navier-Stokes simulations (DNS) reveals favorable agreement in regard to mode shapes, most amplified disturbance frequencies, and N-factor evolution. In contrast, the quasiparallel predictions are found to result in severe underprediction of the N-factors. The direct numerical simulations also indicate that the breakdown of secondary instabilities in a 3D hypersonic boundary layer shares certain common features with the previous computations of crossflow transition over subsonic swept wings.

Roughness-Induced Instabilities and Transition on a Generic Hypersonic Forebody at Mach 6

“…The N-factor at x = 0.180 m when transition occurs is equal to 8 in the DNS and 7.2 in the LST-2D. This was also observed in the work of Choudhari et al [16] and De Tullio et al [39], where the N-factor obtained with LST computations was below the one predicted by DNS and PSE. This is attributed to the high degree of non-parallelism taking place in the wake of a roughness immersed in a flow holding a spanwise component of the velocity.…”

“…In the works of [15], [11] and [16], the Mack modes appeared to be the only high-frequency traveling disturbances unstable at the initial stages of the growth of the crossflow vortices. As the crossflow vortices grew in the roughness wake, the Mack mode was found to be modulated by the crossflow vortex and to morph into the shear layer instability, such that it was not possible to differentiate between the Mack modes and the shear layer instabilities at the downstream locations.…”

“…The frequencies of the most amplified secondary disturbances were found to be in the range of 200 kHz to 360 kHz [11]. These configurations were also analyzed with PSE computations in both linear and non-linear stages [16]. Results showed the ability of the quasi-parallel stability analysis to predict the general topology of the instability modes and their associated dominant frequencies.…”

Effect of Distributed Patch of Smooth Roughness Elements on Transition in a High-Speed Boundary Layer

“…Effects of spanwise modulation of this type on the streak instabilities and the associated mode shapes have been studied in the context of crossflow instability evolution in the boundary layer flow over a swept wing 34 and a yawed cone. 35 Not unlike the findings in those papers, the differences in boundary layers crests near the spanwise end planes and the centerplane are significant enough to yield highly visible differences in the spanwise structure of the |u'| mode shapes in those regions as seen from Fig. 9.…”

Transition Delay via Vortex Generators in a Hypersonic Boundary Layer at Flight Conditions

“…Li et al [17] studied the interaction of Görtler vortices with Mack-mode instabilities on a flared cone, demonstrating a possible route to transition via this interaction. Li et al [18] studied the secondary instability of crossflow vortices in the hypersonic boundary layer over a yawed cone and found that nonlinearly saturated crossflow vortices destabilize the Mack modes, which dominate the onset of transition in comparison with the intrinsic secondary instabilities of crossflow vortices, i.e., instability modes that do not originate from the second mode instability [19,20]. Ren et al [21] studied the stabilizing effect of weakly nonlinear suboptimal streaks and Görtler vortices on the planar first-mode and Mack-mode instabilities.…”