Reattachment streaks in hypersonic compression ramp flow: an input–output analysis

Abstract

We employ global input-output analysis to quantify amplification of exogenous disturbances in compressible boundary layer flows. Using the spatial structure of the dominant response to time-periodic inputs, we explain the origin of steady reattachment streaks in a hypersonic flow over a compression ramp. Our analysis of the laminar shock/boundary layer interaction reveals that the streaks arise from a preferential amplification of upstream counter-rotating vortical perturbations with a specific spanwise wavelength. These streaks are associated with heat flux striations at the wall near flow reattachment and they can trigger transition to turbulence. The streak wavelength predicted by our analysis compares favorably with observations from two different hypersonic compression ramp experiments. Furthermore, our analysis of inviscid transport equations demonstrates that base flow deceleration contributes to the amplification of streamwise velocity and that the baroclinic effects are responsible for the production of streamwise vorticity. Finally, the appearance of the temperature streaks near reattachment is triggered by the growth of streamwise velocity and streamwise vorticity perturbations as well as by the amplification of upstream temperature perturbations by the reattachment shock.

Stochastic receptivity analysis of boundary layer flow

“…This trend is reminiscent of the various flow structures resulting from the eigenvalue decomposition of the steady-state covariance matrix (cf. Section IV) and has been also recently observed in spatio-temporal analysis of hypersonic boundary layer flows [60].…”

“…Previously, tools from sparse linear algebra in conjunction with iterative schemes have been employed to analyze the eigenspectrum of the governing equations and provide insight into the dynamics of transitional flows [50][51][52][53][54]. Efforts have also been made to conduct non-modal analysis of spatially evolving flows including transient growth [55,56] and resolvent [57][58][59][60] analyses. In particular, for the flat-plate boundary layer flow, the sensitivity of singular values of the resolvent operator to base-flow modifications and subsequent effects on the TS instability mechanism and streak amplification was investigated in [57].…”

Transition scenario in hypersonic axisymmetrical compression ramp flow

“…Yet it did not discuss from a physical viewpoint the nature of the linear amplification mechanism of streaks, which plays a central role in the overall dynamics of the flow. Even if good candidates for the linear amplification of longitudinal structures would be the centrifugal effect linked to Görtler instabilities (Navarro-Martinez & Tutty 2005;Benay et al 2006;Murray et al 2013) or the lift-up effect such as pointed out by Bugeat et al (2019) (albeit only for boundary layer flow), a recent study by Dwivedi et al (2019) tends to show that they are due to baroclinic effects. The work of Dwivedi et al (2019) focuses on a laminar flow and does not address directly the question of transition, but nonetheless, it provides insights about the amplification mechanism of so-called 'reattachment vortices' in an hypersonic compression ramp flow.…”

“…However, the mechanism proposed by Görtler (1940) is not the only one that can lead to the amplification of steady vortices. For instance, Dwivedi et al (2019) showed that a baroclinic mechanism could also lead to the growth of such structures. Another possible mechanism would be the 'lift-up' effect such as pointed out by the work of Bugeat et al (2019) (albeit for an attached boundary layer only).…”

Stochastic Dynamical Modeling of Turbulent Flows

“…2. Turbulence modeling for complex fluids and flows in complex geometries (101,102,103,104,105,106,107,108) requires dealing with a large number of degrees of freedom. Since improving upon current algorithms that require O(n 3 ) computations for a model with n states is challenging, a possible direction is to examine physical approximations (109,110,111,112) and model reduction techniques (13,15,16,17).…”