Stability of thin Viscous Shock Layer on a Wedge in Hypersonic Flow of a Perfect Gas

Петров, Г. В.

doi:10.1007/978-3-642-82462-3_59

Cited by 14 publications

(9 citation statements)

References 1 publication

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“…A fairly restrictive (and somewhat ad hoc) model was presented by Petrov (1984), using inviscid linear stability equations, and somewhat heuristic conditions on the shock (which was also assumed to lie at the edge of the boundary layer). Cowley and Hall (1988) presented an asymptotic model, applicable to three-dimensional viscous modes of instability, with appropriately simplified conditions applied on the shock surface (derived from the Rankine-Hugoniot conditions), which was taken to lie just outside of the boundary layer.…”

Section: Introdactionmentioning

confidence: 99%

On the interaction between the shock wave attached to a wedge and freestream disturbances

Duck

Lasseigne

Hussaini

1995

Theoret. Comput. Fluid Dynamics

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Section: Introdactionmentioning

confidence: 99%

On the interaction between the shock wave attached to a wedge and freestream disturbances

Duck

Lasseigne

Hussaini

1995

Theoret. Comput. Fluid Dynamics

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“…In the hypersonic regime, a shock arises even in a flat-plat boundary layer because of the strong viscous-inviscid interaction near the leading edge. The presence of a shock could influence instability as perturbations may be reflected between the shock and boundary, and this effect can, as was first recognized by Petrov (1984), be accounted for by imposing the linearized Rankine-Hugoniot relations as boundary conditions on the linearized stability equations. Adopting these conditions and the high-Reynolds-number asymptotic framework of triple-deck formalism, Cowley & Hall (1990) analysed the stability of the boundary layer over a sharp wedge.…”

Section: Introductionmentioning

confidence: 99%

Response and receptivity of the hypersonic boundary layer past a wedge to free-stream acoustic, vortical and entropy disturbances

Qin

2016

J. Fluid Mech.

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This paper analyses the response and receptivity of the hypersonic boundary layer over a wedge to free-stream disturbances including acoustic, vortical and entropy fluctuations. Due to the presence of an attached oblique shock, the boundary layer is known to support viscous instability modes whose eigenfunctions are oscillatory in the far field. These modes acquire a triple-deck structure. Any of three elementary types of disturbances with frequency and wavelength on the triple-deck scales interacts with the shock to generate a slow acoustic perturbation, which is reflected between the shock and the wall. Through this induced acoustic perturbation, vortical and entropy free-stream disturbances drive significant velocity and temperature fluctuations within the boundary layer, which is impossible when the shock is absent. A quasi-resonance was identified, due to which the boundary layer exhibits a strong response to a continuum of high-frequency disturbances within a narrow band of streamwise wavenumbers. Most importantly, in the vicinity of the lower-branch neutral curve the slow acoustic perturbation induced by a disturbance of suitable frequency and wavenumbers is in exact resonance with a neutral eigen mode. As a result, the latter can be generated directly by each of three types of free-stream disturbances without involving any surface roughness element. The amplitude of the instability mode is determined by analysing the disturbance evolution through the resonant region. The fluctuation associated with the eigen mode turns out to be much stronger than free-stream disturbances due to the resonant nature of excitation and in the case of acoustic disturbances, to the well-known amplification effect of a strong shock. Moreover, excitation at the neutral position means that the instability mode grows immediately without undergoing any decay, or missing any portion of the unstable region. All these indicate that this new mechanism is particularly efficient. The boundary-layer response and coupling coefficients are calculated for typical values of parameters.

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“…Furthermore, it is well known that any kind of modes, for instance, acoustic, vorticity or entropy modes, which can generally be found in any real supersonic free stream, produces all three modes when passing the shock wave [3]. One of the first attempts to understand the effect of a shock wave on the boundary-layer stability was Petrov's work [4]. In his study the inviscid eigensolution outside the boundary layer was replaced by the linearized Rankine-Hugoniot jump conditions for the normal momentum equation.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of supersonic entropy layers including shock effects

Mählmann

2002

Proc. Appl. Math. Mech.

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The prediction of the laminar/turbulent transition location in supersonic boundary layers plays an important role to accurately compute aerodynamic forces and heating rates for the aerodynamic design and control of hypersonic vehicles. The stability characteristics of supersonic boundary layers depend e.g. on nose bluntness, transverse curvature, wall temperature, shock waves, etc. Most parameters can be theoretically investigated by performing conventional stability calculations with vanishing or asymptotic perturbation conditions at the far field. In this approach the formation of a shock in front of the leading edge of a blunt body is ignored. However, to improve the understanding of the interaction between instability waves originating inside supersonic boundary layer with those coming from the inviscid entropy layer, the presence of the shock has to be taken into account.This paper presents a method, how shock effects can be physically consistently included in stability calculations. The outer free-stream boundary conditions are replaced by appropriate shock conditions. The required perturbation equations can be derived from the linearized unsteady Rankine-Hugoniot equations, accounting for the effect of shock oscillations due to perturbated waves which originate from the flow field windward of the shock.

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Stability of thin Viscous Shock Layer on a Wedge in Hypersonic Flow of a Perfect Gas

Cited by 14 publications

References 1 publication

On the interaction between the shock wave attached to a wedge and freestream disturbances

On the interaction between the shock wave attached to a wedge and freestream disturbances

Response and receptivity of the hypersonic boundary layer past a wedge to free-stream acoustic, vortical and entropy disturbances

Stability analysis of supersonic entropy layers including shock effects

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