Interactions between second mode and low-frequency waves in a hypersonic boundary layer

2017 ◽  
Vol 820 ◽  
pp. 693-735 ◽  
Author(s):  
Xi Chen ◽  
Yiding Zhu ◽  
Cunbiao Lee
Keyword(s):  
Boundary Layer ◽  
Parametric Resonance ◽  
Low Frequency ◽  
Frequency Mode ◽  
Linear Stability Theory ◽  
Hypersonic Boundary Layer ◽  
Reynolds Stresses ◽  
Second Mode ◽  
Low Frequency Mode ◽  
Low Frequency Waves

The stability of a hypersonic boundary layer on a flared cone was analysed for the same flow conditions as in earlier experiments (Zhang et al., Acta Mech. Sinica, vol. 29, 2013, pp. 48–53; Zhu et al., AIAA J., vol. 54, 2016, pp. 3039–3049). Three instabilities in the flared region, i.e. the first mode, the second mode and the Görtler mode, were identified using linear stability theory (LST). The nonlinear-parabolized stability equations (NPSE) were used in an extensive parametric study of the interactions between the second mode and the single low-frequency mode (the Görtler mode or the first mode). The analysis shows that waves with frequencies below 30 kHz are heavily amplified. These low-frequency disturbances evolve linearly at first and then abruptly transition to parametric resonance. The parametric resonance, which is well described by Floquet theory, can be either a combination resonance (for non-zero frequencies) or a fundamental resonance (for steady waves) of the secondary instability. Moreover, the resonance depends only on the saturated state of the second mode and is insensitive to the initial low-frequency mode profiles and the streamwise curvature, so this resonance is probably observable in boundary layers over straight cones. Analysis of the kinetic energy transfer further shows that the rapid growth of the low-frequency mode is due to the action of the Reynolds stresses. The same mechanism also describes the interactions between a second-mode wave and a pair of low-frequency waves. The only difference is that the fundamental and combination resonances can coexist. Qualitative agreement with the experimental results is achieved.

Low-frequency unsteadiness in shock wave–turbulent boundary layer interaction

2012 ◽  
Vol 699 ◽  
pp. 1-49 ◽  
Author(s):  
Stephan Priebe ◽  
M. Pino Martín
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Turbulent Boundary Layer ◽  
Low Frequency ◽  
Separated Flow ◽  
Frequency Mode ◽  
Statistical Relation ◽  
Boundary Layer Interaction ◽  
Shock Motion ◽  
Low Frequency Mode

AbstractThe low-frequency unsteadiness is characterized in the direct numerical simulation of a shock wave–turbulent boundary layer interaction generated by a $2{4}^{\ensuremath{\circ} } $ compression ramp in Mach 2.9 flow. Consistent with experimental observations, the shock wave in the simulation undergoes a broadband streamwise oscillation at frequencies approximately two orders of magnitude lower than the characteristic frequency of the energetic turbulent scales in the incoming boundary layer. The statistical relation between the low-frequency shock motion and the upstream and downstream flow is investigated. The shock motion is found to be related to a breathing of the separation bubble and an associated flapping of the separated shear layer. A much weaker statistical relation is found with the incoming boundary layer. In order to further characterize the low-frequency mode in the downstream separated flow, the temporal evolution of the low-pass filtered flow field is investigated. The nature of the velocity and vorticity profiles in the initial part of the interaction is found to change considerably depending on the phase of the low-frequency motion. It is conjectured that these changes are due to an inherent instability in the downstream separated flow, and that this instability is the physical origin of the low-frequency unsteadiness. The low-frequency mode observed here is, in certain aspects, reminiscent of an unstable global mode obtained by linear stability analysis of the mean flow in a reflected shock interaction (Touber & Sandham, Theor. Comput. Fluid Dyn., vol. 23, 2009, pp. 79–107).

scholarly journals Stability Analysis of Hypersonic Boundary Layer over a Cone at Small Angle of Attack

2014 ◽  
Vol 6 ◽  
pp. 217976
Author(s):  
Feng Ji ◽  
Xunhua Liu ◽  
Qiang Wang ◽  
Xiangjiang Yuan ◽  
Qing Shen
Keyword(s):  
Boundary Layer ◽  
Small Angle ◽  
Growth Rates ◽  
Angle Of Attack ◽  
Maximum Growth ◽  
Base Flow ◽  
Linear Stability Theory ◽  
Unstable Wave ◽  
Hypersonic Boundary Layer ◽  
Second Mode

An investigation on the stability of hypersonic boundary layer over a cone at small angle of attack has been performed. After obtaining the steady base flow, linear stability theory (LST) analysis has been made with local parallel assumption. The growth rates of the first mode and second mode waves at different streamwise locations and different azimuthal angles are obtained. The results show that the boundary layer stability was greatly influenced by small angles of attack. The maximum growth rate of the most unstable wave on the leeward is larger than that on the windward. Moreover, dominating second mode wave starts earlier on the leeward than that on the windward. The LST result also shows that there is a “valley” region around 120°~150° meridian in the maximum growth rates curve.

Observations of a low-frequency mode in a linear multiple mirror

1985 ◽  
Vol 28 (7) ◽  
pp. 2302
Author(s):  
M. A. Makowski ◽  
G. A. Emmert
Keyword(s):  
Low Frequency ◽  
Frequency Mode ◽  
Low Frequency Mode

Light Scattering from Pulsed Laser Deposited BaBi4Ti4O15 Thin Films

2000 ◽  
Vol 623 ◽  
Author(s):  
R.K. Soni ◽  
Anju Dixit ◽  
R. S. Katiyar ◽  
A. Pignolet ◽  
K.M. Satyalakshmi ◽  
...  
Keyword(s):  
Thin Films ◽  
Light Scattering ◽  
Room Temperature ◽  
Layer Structure ◽  
Low Frequency ◽  
Pulsed Laser ◽  
Buffer Layers ◽  
Frequency Mode ◽  
High Frequency Vibrations ◽  
Low Frequency Mode

AbstractLight scattering investigations are carried out on BaBi4Ti4O15 (BBiT) which is a member of the Bi-layer structure ferroelectric oxide with n = 4. The BBiT thin films, thickness ∼ 300 nm, were grown on epitaxial conducting LaNiO3 electrodes on epitaxial buffer layers on (100) silicon by pulsed laser deposition. Micro-Raman measurements performed on these films reveal a sharp low-frequency mode at 51 cm−1 along with broad highfrequeficy modes corresponding to other lattice vibrations including TiO6 octahedra. No temperature dependence of the low frequency mode is seen while a weak dependence of the broad high frequency vibrations are observed in the mixed oriented regions. Raman polarization carried out at room temperature indicates that the prominent modes have Alg and Eg symmetries in the BaBi4Ti4O15 thin films.

Growth and breakdown of low-speed streaks leading to wall turbulence

2007 ◽  
Vol 586 ◽  
pp. 371-396 ◽  
Author(s):  
MASAHITO ASAI ◽  
YASUFUMI KONISHI ◽  
YUKI OIZUMI ◽  
MICHIO NISHIOKA
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Low Frequency ◽  
Wall Turbulence ◽  
Linear Stability Theory ◽  
Transition Flow ◽  
Wall Suction ◽  
Low Speed ◽  
Low Speed Streaks ◽  
Near Wall

Two-dimensional local wall suction is applied to a fully developed turbulent boundary layer such that near-wall turbulence structures are completely sucked out, but most of the turbulent vortices in the original outer layer can survive the suction and cause the resulting laminar flow to undergo re-transition. This enables us to observe and clarify the whole process by which the suction-surviving strong vortical motions give rise to near-wall low-speed streaks and eventually generate wall turbulence. Hot-wire and particle image velocimetry (PIV) measurements show that low-frequency velocity fluctuations, which are markedly suppressed near the wall by the local wall suction, soon start to grow downstream of the suction. The growth of low-frequency fluctuations is algebraic. This characterizes the streak growth caused by the suction-surviving turbulent vortices. The low-speed streaks obtain almost the same spanwise spacing as that of the original turbulent boundary layer without the suction even in the initial stage of the streak development. This indicates that the suction-surviving turbulent vortices are efficient in exciting the necessary ingredients for the wall turbulence, namely, low-speed streaks of the correct scale. After attaining near-saturation, the low-speed streaks soon undergo sinuous instability to lead to re-transition. Flow visualization shows that the streak instability and its subsequent breakdown occur at random in space and time in spite of the spanwise arrangement of streaks being almost periodic. Even under the high-intensity turbulence conditions, the sinuous instability amplifies disturbances of almost the same wavelength as predicted from the linear stability theory, though the actual growth is in the form of a wave packet with not more than two waves. It should be emphasized that the mean velocity develops the log-law profile as the streak breakdown proceeds. The transient growth and eventual breakdown of low-speed streaks are also discussed in connection with the critical condition for the wall-turbulence generation.

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