Transient growth analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92

Hildebrand, Nathaniel; Nichols, Joseph W.; Candler, Graham V.; Jovanović, Mihailo R.

doi:10.1103/physrevfluids.5.063904

Cited by 14 publications

(9 citation statements)

References 45 publications

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“…While low wavenumbers exhibit a modal and localised (around the bubble) dynamics, optimal responses at larger wavenumbers have been shown to ignore the recirculation region as they are driven by a convective instability growing downstream in the boundary layer, as a result of non-modal effects. These findings are consistent with those of Dwivedi et al (2020), who recently carried out a transient growth analysis in a SWBLI at M = 5.92. Such analysis also embeds the non-modal effect and can in fact be seen as the temporal counterpart of the resolvent analysis (Sipp et al 2010).…”

Section: Discussionsupporting

confidence: 92%

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Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

et al. 2022

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Resolvent analysis is used to study the low-frequency behaviour of the laminar oblique shock wave/boundary layer interaction (SWBLI). It is shown that the computed optimal gain, which can be seen as a transfer function of the system, follows a first-order low-pass filter equation, recovering the results of Touber & Sandham (J. Fluid Mech., vol. 671, 2011, pp. 417–465). This behaviour is understood as proceeding from the excitation of a single stable, steady global mode whose damping rate sets the time scale of the filter. Different Mach and Reynolds numbers are studied, covering different recirculation lengths $L$ . This damping rate is found to scale as $1/L$ , leading to a constant Strouhal number $St_{L}$ as observed in the literature. It is associated with a breathing motion of the recirculation bubble. This analysis furthermore supports the idea that the low-frequency dynamics of the SWBLI is a forced dynamics, in which background perturbations continuously excite the flow. The investigation is then carried out for three-dimensional perturbations for which two regimes are identified. At low wavenumbers of the order of $L$ , a modal mechanism similar to that of two-dimensional perturbations is found and exhibits larger values of the optimal gain. At larger wavenumbers, of the order of the boundary layer thickness, the growth of streaks, which results from a non-modal mechanism, is detected. No interaction with the recirculation region is observed. Based on these results, the potential prevalence of three-dimensional effects in the low-frequency dynamics of the SWBLI is discussed.

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Section: Discussionsupporting

confidence: 92%

“…These findings are consistent with those of Dwivedi et al. (2020), who recently carried out a transient growth analysis in a SWBLI at . Such analysis also embeds the non-modal effect and can in fact be seen as the temporal counterpart of the resolvent analysis (Sipp et al.…”

Section: Discussionsupporting

confidence: 90%

Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

et al. 2022

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“…Another convective mechanism leading to the formation of streamwise streaks is transient growth, as shown in Dwivedi et al. (2020) for the case of shock impingement on a flat plate.…”

Section: Introductionmentioning

confidence: 94%

“…However, they demonstrated that baroclinic effects arising from the interaction of upstream pressure perturbations with base-flow density gradients, rather than centrifugal effects near reattachment, are responsible for the production of streamwise vorticity. Another convective mechanism leading to the formation of streamwise streaks is transient growth, as shown in Dwivedi et al (2020) for the case of shock impingement on a flat plate.…”

Section: Introductionmentioning

confidence: 99%

Transition to turbulence in hypersonic flow over a compression ramp due to intrinsic instability

et al. 2022

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In this work, a transition process in a hypersonic flow over a cold-wall compression ramp is studied using direct numerical simulation (DNS) and global stability analysis (GSA). The free-stream Mach number and the Reynolds number based on the flat-plate length are 7.7 and $8.6 \times 10^5$ , respectively. The shock-induced pressure rise causes the boundary layer to separate on the flat plate, forming a separation bubble around the corner. Without introducing any external disturbances, the DNS captures the transition to turbulence downstream of flow reattachment. The DNS results agree well with the experimental data as well as theoretical predictions. To uncover the intrinsic instability in the flow system, GSA is employed to investigate the three-dimensionality of the two-dimensional base flow. Several stationary and oscillatory unstable modes are revealed, which result in spanwise periodicity inside and downstream of the separation bubble. The GSA and DNS results indicate that the intrinsic instability of the flow system triggers the formation of streamwise counter-rotating vortices and boundary-layer streaks near reattachment. The downstream transition to turbulence starts from the breakdown of the streamwise vortices and streaks. Moreover, the second harmonic of the most unstable global mode and a broadband low-frequency unsteadiness occur in the saturated flow, which has a significant influence on the transition process. In summary, the present study demonstrates a transition process in a hypersonic compression-ramp flow as a result of the intrinsic instability of the flow system.

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“…2019), and small fluctuations around the laminar 2-D base flow can experience significant non-modal amplification that leads to the appearance of steady reattachment streaks (Dwivedi et al. 2020 b ). Furthermore, recent experiments on the cone-flare configurations (Benitez et al.…”

Section: Introductionmentioning

confidence: 99%

Oblique transition in hypersonic double-wedge flow

Sidharth

Jovanović

2022

J. Fluid Mech.

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We utilize resolvent and weakly nonlinear analyses in combination with direct numerical simulations (DNS) to identify mechanisms for oblique transition in a Mach $5$ hypersonic flow over an adiabatic slender double wedge. Even though the laminar separated flow is globally stable, resolvent analysis demonstrates significant amplification of unsteady external disturbances to the linearized flow equations. These disturbances are introduced upstream of the separation zone and they lead to the appearance of oblique waves further downstream. We demonstrate that the large amplification of oblique waves arises from the growth of fluctuation shear stress due to streamline curvature of the laminar base flow in the separated shear layer. This is in contrast to the attached boundary layers, where no such mechanism exists. We also use a weakly nonlinear analysis to show that the resolvent operator associated with linearization around the laminar base flow governs the evolution of steady reattachment streaks that arise from quadratic interactions of unsteady oblique waves. These quadratic interactions generate vortical excitations in the reattaching shear layer which lead to the formation of streaks in the recirculation zone and their subsequent amplification, breakdown and transition to turbulence downstream. Our analysis of the energy budget shows that deceleration of the base flow near reattachment is primarily responsible for amplification of steady streaks. Finally, we employ DNS to examine latter stages of transition to turbulence and demonstrate the predictive power of a weakly nonlinear input–output framework in uncovering triggering mechanisms for oblique transition in separated high-speed boundary layer flows.

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Transient growth analysis of oblique shock-wave/boundary-layer interactions at Mach 5.92

Cited by 14 publications

References 45 publications

Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

Low-frequency resolvent analysis of the laminar oblique shock wave/boundary layer interaction

Transition to turbulence in hypersonic flow over a compression ramp due to intrinsic instability

Oblique transition in hypersonic double-wedge flow

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