Non-equilibrium, nonlinear critical layers in laminar-turbulent transition

Wang, Xuesong

doi:10.1007/bf02489370

Cited by 7 publications

(5 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…7b and 7c. The theory of the phase-locked nonlinear interaction, also known as nonlinear critical-layer analysis, is well developed (see the review by Wu [62]). Our experimental results show how the energy of the second-mode wave is transferred from beneath the sonic line into the critical layer.…”

Section: A ω;ϑ In the Second Modementioning

confidence: 99%

Transition in Hypersonic Boundary Layers: Role of Dilatational Waves

et al. 2016

View full text Add to dashboard Cite

Transition and turbulence production in a hypersonic boundary layer is investigated in the Mach 6 wind tunnel at Peking University, using Rayleigh-scattering visualization, fast-response pressure measurements, and particle image velocimetry. Detailed analysis of the experimental observations is provided. It is found that, although the second mode is primarily an acoustic wave, it causes the formation of high-frequency vortical waves. Moreover, the second mode interacts strongly with low-frequency waves, which leads to immediate transition to turbulence.freestream velocity, m∕s u = velocity vector, m∕s u = x component of the velocity, m∕s v = y component of the velocity, m∕s w = z component of the velocity, m∕s x = streamwise coordinate along the cone's surface, mm y = coordinate normal to the cone's surface, mm z = transverse coordinate normal to the x-y plane, mm= viscous normal stress, Pa ρ = density, kg∕m 3 τ f = flow time scale, s τ p = particle relaxation time, s Φ = viscous dissipation function per unit volume, kg∕m · s 3 ω = vorticity, 1∕s

show abstract

Section: A ω;ϑ In the Second Modementioning

confidence: 99%

Transition in Hypersonic Boundary Layers: Role of Dilatational Waves

et al. 2016

View full text Add to dashboard Cite

show abstract

Section: Analysis and Discussionmentioning

confidence: 99%

“…Based on a nonlinear critical layer theory developed using a small parameter perturbation and the asymptotic matching method, Wu (2004) proposed a phase-locking mechanism to explain the rapid growth of 3-D disturbances, but their research focused on the fundamental resonance of the same frequency disturbance. Later, Li et al (2020) and extended the phase-locked mechanism to the interaction of different frequency disturbances, holding that the phase velocity locking mechanism can explain the interaction between the second mode and the first mode, and the second mode can transfer energy to the first mode through the phase velocity locking mechanism.…”

Section: Instability Interactionmentioning

confidence: 99%

Boundary layer transition of hypersonic flow over a delta wing

Qiu,

Shi,

Zhu

et al. 2024

J. Fluid Mech.

View full text Add to dashboard Cite

Cross-flow transition over a delta wing is systematically studied in a Mach 6.5 hypersonic wind tunnel, employing the Rayleigh scattering flow visualisation, high-speed schlieren and fast-response pressure sensors. Direct numerical simulations and analysis based on linear stability theory under the same flow conditions are applied to analyse the transition mechanism. Three unstable modes are identified: the travelling cross-flow instabilities, the second mode and the low-frequency waves. It is shown that the travelling cross-flow vortices first appear in the cross-flow region near the leading edge of the model. These vortices can modulate the mean profile of the flow, which benefits the growth of second mode. A phase-locked interaction mechanism transfers energy from the cross-flow instabilities to the high-frequency second mode, leading to amplification at the expense of the cross-flow instability. As the second mode grows to a critical amplitude, it triggers a $z$ -type secondary instability within a similar frequency range, which introduces secondary finger-like structures connecting to the cross-flow vortex. It is further found that the generation of these finger-like structures is related to the expansion and compression of the second mode. These finger vortices further evolve along the streamwise direction into low-frequency waves and corresponding hairpin-like structures that finally trigger turbulence. An interaction mechanism likely exists between the secondary instability and the low-frequency waves, since their phase speeds are approaching each other. These observations of the interaction mechanism are consistent with those of previous studies on hypersonic boundary layers (Zhang et al., Phys. Fluids, vol. 32 (7), 2020, 071702; Li et al., Phys. Fluids, vol. 32 (5), 2020, 051701).

show abstract

“…This scenario is referred to as the fundamental resonance (FR) and a schematic for the FR in the spectrum space is shown in figure 1(c). Based on the critical-layer theory (Wu 2004;Zhang & Wu 2022), Wu, Luo & Yu (2016) deduced the evolution equations for the oblique modes and claimed that the 2-D mode acts as a catalyst to promote the growth of the oblique modes. The 2-D dominant mode and the small-amplitude oblique modes are found to be phase-locked.…”

Section: Introductionmentioning

confidence: 99%

Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint

Song,

Dong,

Zhao

2024

J. Fluid Mech.

View full text Add to dashboard Cite

The fundamental resonance (FR) in the nonlinear phase of the boundary-layer transition to turbulence appears when a dominant planar instability mode reaches a finite amplitude and the low-amplitude oblique travelling modes with the same frequency as the dominant mode, together with the stationary streak modes, undergo the strongest amplification among all the Fourier components. This regime may be the most efficient means to trigger the natural transition in hypersonic boundary layers. In this paper, we aim to reveal the intrinsic mechanism of the FR in the weakly nonlinear framework based on the large-Reynolds-number asymptotic technique. It is found that the FR is, in principle, a triad resonance among a dominant planar fundamental mode, a streak mode and an oblique mode. In the major part of the boundary layer, the nonlinear interaction of the fundamental mode and the streak mode seeds the growth of the oblique mode, whereas the interaction of the oblique mode and the fundamental mode drives the roll components (transverse and lateral velocity) of the streak mode, which leads to a stronger amplification of the streamwise component of the streak mode due to the lift-up mechanism. This asymptotic analysis clearly shows that the dimensionless growth rates of the streak and oblique modes are the same order of magnitude as the dimensionless amplitude of the fundamental mode $(\bar {\epsilon }_{10})$ , and the amplitude of the streak mode is $O(\bar {\epsilon }_{10}^{-1})$ greater than that of the oblique mode. The main-layer solution of the streamwise velocity, spanwise velocity and temperature of both the streak and the oblique modes become singular as the wall is approached, and so a viscous wall layer appears underneath. The wall layer produces an outflux velocity to the main-layer solution, inclusion of which leads to an improved asymptotic theory whose accuracy is confirmed by comparing with the calculations of the nonlinear parabolised stability equations (NPSEs) at moderate Reynolds numbers and the secondary instability analysis (SIA) at sufficiently high Reynolds numbers.

show abstract

Non-equilibrium, nonlinear critical layers in laminar-turbulent transition

Cited by 7 publications

References 33 publications

Transition in Hypersonic Boundary Layers: Role of Dilatational Waves

Transition in Hypersonic Boundary Layers: Role of Dilatational Waves

Boundary layer transition of hypersonic flow over a delta wing

Principle of fundamental resonance in hypersonic boundary layers: an asymptotic viewpoint

Contact Info

Product

Resources

About