Abstract:In this work, the stability of hypersonic flow over a curved compression ramp is studied using several stability analysis tools and direct numerical simulations (DNS). The free-stream Mach number and the unit Reynolds number are 7.7 and
$4.2 \times 10^6$
m
$^{-1}$
, respectively. Corner rounding is considered to alter the separation bubble flow so as to suppress the intrinsic instability of the compression-ramp flow. The variation of intrinsic instability i… Show more
“…The interplay between the intrinsic instability and upstream disturbances was addressed in a companion study (Cao et al. 2023). Figure 10.Optimal responses (left) and forcings (right) associated with the most amplified streamwise streaks at ( a ) α = 0°, ( b ) α = 4°, ( c ) α = 8° and ( d ) α = 12°.…”
Section: Resultsmentioning
confidence: 99%
“…The interplay between the intrinsic instability and upstream disturbances was addressed in a companion study (Cao et al 2023).…”
Hypersonic flow over a two-dimensional compression corner is investigated using computational fluid dynamics and global resolvent analysis in this study, which is a continuation of the work done by Hao et al. (J. Fluid Mech., vol. 919, 2021, p. A4). The same baseline free-stream conditions with a Mach number of 7.7 and a unit Reynolds number of 4.2 × 106 m−1 are considered. The ramp angles range from 0° (equivalent to a flat plate) to 12° (slightly below the critical angle of global instability). During this process, the base flow evolves from no separation to incipient separation to large separation. The resolvent analysis reveals that the optimal response to upstream disturbances localised near the leading edge is in the form of steady streamwise streaks for all interaction strengths, which arise from transient growth in the flat-plate boundary layer due to the lift-up mechanism and significantly grow near the corner due to the Görtler instability. The most amplified spanwise wavelength decreases as the ramp angle is increased and scales with the incoming boundary-layer thickness.
“…The interplay between the intrinsic instability and upstream disturbances was addressed in a companion study (Cao et al. 2023). Figure 10.Optimal responses (left) and forcings (right) associated with the most amplified streamwise streaks at ( a ) α = 0°, ( b ) α = 4°, ( c ) α = 8° and ( d ) α = 12°.…”
Section: Resultsmentioning
confidence: 99%
“…The interplay between the intrinsic instability and upstream disturbances was addressed in a companion study (Cao et al 2023).…”
Hypersonic flow over a two-dimensional compression corner is investigated using computational fluid dynamics and global resolvent analysis in this study, which is a continuation of the work done by Hao et al. (J. Fluid Mech., vol. 919, 2021, p. A4). The same baseline free-stream conditions with a Mach number of 7.7 and a unit Reynolds number of 4.2 × 106 m−1 are considered. The ramp angles range from 0° (equivalent to a flat plate) to 12° (slightly below the critical angle of global instability). During this process, the base flow evolves from no separation to incipient separation to large separation. The resolvent analysis reveals that the optimal response to upstream disturbances localised near the leading edge is in the form of steady streamwise streaks for all interaction strengths, which arise from transient growth in the flat-plate boundary layer due to the lift-up mechanism and significantly grow near the corner due to the Görtler instability. The most amplified spanwise wavelength decreases as the ramp angle is increased and scales with the incoming boundary-layer thickness.
“…Regarding the numerical implementation, our in-house code CHASES is employed, which integrates the LST, LPSE, NPSE and sensitivity analyses. A series of validation cases for LST and LPSE have been carefully compared with both theoretical (Guo et al 2020(Guo et al , 2021(Guo et al , 2022a and DNS (Guo et al 2022b;Cao et al 2023) results. The validation of the NPSE code is shown in Appendix A.…”
“…This set-up allows adequate selection of additional potentially unstable frequencies and wavenumbers and tends to approach the flow state in a noisy environment. In DNS, the white noise term is added every 50 time steps for case A2 to allow its convection in the meshed domain (Cao et al 2023). This interval corresponds to an angular frequency of 20ω p , where ω p is the angular frequency of the optimal planar wave.…”
Section: A1mentioning
confidence: 99%
“…In DNS, the white noise term is added every 50 time steps for case A2 to allow its convection in the meshed domain (Cao et al. 2023). This interval corresponds to an angular frequency of 20 ω p , where ω p is the angular frequency of the optimal planar wave.…”
Section: Case Description and Simulation Strategymentioning
The present paper finds that the coexistence of multiple primary instability waves may cause a non-trivial nonlinear interaction and breakdown process, which has not been reported before. In the considered Mach 6 flat-plate boundary layer, a global resolvent analysis reports three optimal disturbances (local maxima): a high-frequency planar wave, a low-frequency oblique wave and a stationary streak. For the dominant planar and oblique waves, a parabolised stability equation analysis identifies the initial non-modal transient growth and downstream modal growth. Initiated by these two optimal disturbances jointly, the complete linear and nonlinear instability processes until breakdown to turbulence are shown with direct numerical simulation. Owing to the transient growth, the oblique wave may be more significant than the planar wave in the breakdown. The oblique wave and scales of nonlinear interactions are pronounced in the outer layer, whose significance may not be comprehensively characterised by the wall pressure measurement. Fourier modes characterising the oblique-wave oblique breakdown, the planar-wave fundamental resonance, the planar-wave subharmonic resonance and the combination resonance related to a detuned mode are observed successively. The detuned mode seems to dominate the near-wall dynamics in the late nonlinear stage, characterised by
$\varLambda$
-like structures. Meanwhile, the existence of this detuned mode is independent of the initial amplitude ratio and the absolute amplitude of the oblique and planar waves. Weakly nonlinear stability analyses demonstrate that the detuned mode is mainly a consequence of the secondary instability under the combination of planar and oblique primary waves. Wave vector plots reveal the resonant state of multiple triads. Energy budget and amplitude-correction analyses provide a clear physical image of energy transfer.
The detailed energy sources that sustain the eigenmodal exponential growth in boundary layers are currently unclear. In the present study, the phase of each term in the linear stability equation is examined to identify the significant physical sources for a wide range of Mach numbers and wall temperature ratios. The Tollmien–Schlichting mode for incompressible flows, the oblique first mode for supersonic flows and the Mack second mode and supersonic mode for hypersonic flows share some similar features. The unique appearance of obliqueness for the most unstable first mode is accompanied by the enhancement of Reynolds shear stress. By contrast, the weakened Reynolds thermal stress prevents the oblique second mode from being the most unstable state. Wall cooling stabilises the oblique first mode by rendering Reynolds thermal stress and dilatation fluctuations out of phase with the internal energy fluctuation. It destabilises the second mode by a newly generated pronounced region of wall-normal internal energy transport beneath the second generalised inflection point. In comparison, the porous coating destabilises the oblique first mode by significantly enhancing the mean-shear production while it stabilises the second mode similarly to wall heating. Finally, the relatively weak supersonic mode has the feature that the phase destruction of wall-normal transport near the critical layer results in a low contribution to the internal energy growth. Connections and consistencies are also highlighted with the previous inviscid thermoacoustic interpretation for the second mode (Kuehl, AIAA J., vol. 56, 2018, pp. 3585–3592) and for the supersonic mode. The pronounced sources along the critical layer and near-wall regions provide a unified understanding of the local energy amplification mechanisms of the inviscid modes in hypersonic boundary layers.
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