Experimental studies of stability and transition in high-speed wakes

Abstract

The investigation undertaken deals with the development of disturbances in a supersonic wake (free viscous layer and regular wake) behind a flat plate both in its linear and nonlinear stages. The influence of a number of factors (Mach and Reynolds numbers, temperature factor, thickness of the plate, length of its stern) on the wake stability and transition was studied. The development of the artificial disturbances in a wake at Mach number M∞ = 2 was investigated also.It was found that compressibility of the flow (increasing Mach number) stabilizes the wake disturbances – their amplification rates decrease, and the transition point moves away from the model plate. Cooling of the model surface at M∞ ≈ 7 has a destabilizing influence on the development of disturbances in the wake. With increase of unit Reynolds number the beginning of transition in the wake moves forward to a rear critical point. It was confirmed that a distinctive maximum in the spectral distribution of fluctuations appears, corresponding to Strouhal number (based on frequency of this maximum) of 0.3. With the growth of the model thickness the disturbance amplification rates in the wake increase, which results in earlier transition of a laminar wake into turbulent one. With the growth of length of the plate stern, the position of the wake transition moves back accordingly, while the wake stability increases a little (though very unsignificantly). In the nonlinear stage of development of disturbances, the occurrence of a triad of waves, satisfying the resonant correlation of frequencies, and the growth of harmonics are observed. A monochromatic packet of waves of Tollmien–Schlichting type, rather narrow (in the transversal coordinate) in the boundary layers on a flat plate with an opposite wedge at the stern, was found to extend in the wake. The wake disturbances have a complex wave structure. At the Mach number of free flow 2.0, the three-dimensional disturbances are the most unstable in the wake.

Three-dimensional evolution of structure and acoustic wave generation in a compressible plane wake

“…In the compressible turbulent wake behind the turbulent boundary layers, Gai et al (2002) visualized weak periodical large-scale inclined structures. Lysenko (1999) showed the development of three-dimensional disturbances in the supersonic wake of a at plate with a stern. A complete quantitative description of the underlying mechanism of a compressible wake that links to three-dimensional behavior in incompressible wakes and the resultant structures awaits DNS studies.…”

Compressibility effects on the structural evolution of transitional high-speed planar wakes

“…It is unclear why the observed oblique perturbation undergoes the largest growth. It could be related to one of the following reasons: (i) the growth of the most unstable oblique mode, as found by Papageorgiou (1990); (ii) as hypothesized by Lysenko (1999), a receptivity of an inclined symmetric mode which emerges for Ma r > 1.2 (Watanabe & Maekawa 2004); (iii) a secondary acoustic mode which resonates between the sonic lines of the wake as in the boundary layer (Mack 1990); or (iv) a triadic nonlinear interaction as observed in the H-type transition in the boundary layer (Hebert 1988). The debate surrounding the origin of the three-dimensional modes remains open and central to the understanding of the transitional mechanism of the planar wake.…”

“…This result was nuanced by Papageorgiou (1990) who questioned the validity of the parallel flow assumption inherent in the temporal stability calculations and showed that a three-dimensional wave inclined at 60 • has the highest growth rate for spatially evolving wakes with a Gaussian velocity profile at Ma ∞ = 3.0. The obliquity of the transitional mode was experimentally observed by Lysenko (1999) by artificially forcing a splitter-plate wake at Ma ∞ = 2.0. It is unclear why the observed oblique perturbation undergoes the largest growth.…”

Анализ Развития Возмущений В Гиперзвуковом Пограничном Слое За Волнистой Поверхностью

“…Известно, что увеличение числа Маха оказывает стабилизирующий эффект на течение в свободных слоях смешения и спутных следах (например, [1]). Естественно предположить, что относительно длин-ный свободный слой смешения, сформированный около обтекаемой поверхности, может уменьшить темпы роста и подавить возмущения второй моды, имеющие короткую длину волны (порядка двух толщин пограничного слоя).…”