On the application of linear stability theory to the problem of supersonic boundary-layer transition

Mack, Leslie M.

doi:10.2514/6.1974-134

Cited by 67 publications

(102 citation statements)

References 15 publications

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“…19,20 These investigations at hypersonic Mach numbers between 6 and 8, have shown the dominance of the so-called second mode of instabilities on conical geometries. This confirms the earlier Linear Stability Theory results of Mack 21,22 who predicted the amplification of an inviscid mode distinct from the one responsible for transition at lower speeds. However, only few studies have extended these investigations to larger Mach numbers while keeping low enthalpy levels.…”

Section: Nomenclaturesupporting

confidence: 81%

Hypersonic Boundary Layer Transition on a 7 Degree Half-Angle Cone at Mach 10

Grossir

Regert

Pinna

et al. 2014

7th AIAA Theoretical Fluid Mechanics Conference

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Hypersonic boundary layer transition experiments are performed in the low-enthalpy Longshot wind tunnel with a free-stream Mach number ranging between 12 ≥ M∞ ≥ 9.5 and Reynolds number between 12 × 10 6 /m ≥ Reunit,∞ ≥ 3.3 × 10 6 /m. The model is an 800 mm long 7• half-angle cone with nosetip radii between 0.2 and 10 mm. Instrumentation includes flushmounted fast-response thermocouples and pressure sensors. Boundary layer transition onset location is determined from the wall heat flux distribution. Nose bluntness has a strong stabilizing effect. No transition reversal could be observed at RB = 10RN for a Reynolds number based on the nosetip radius of ReR N ,∞ = 123, 000. Increasing freestream unit Reynolds number results in larger Rex B ,e. Wavelet analysis of the boundary layer fluctuations shows that numerous wave packets are present during the transition process. Comparison with Linear Stability Theory results for second mode waves shows an excellent agreement for the most amplified frequencies. The N -factor of the wind-tunnel is 5 based on these computations and on the transition location measured experimentally. The convection velocity of the disturbances is closely approximated by the local boundary layer edge velocity for all conditions investigated. Schlieren flow visualization of the instabilities exhibits the typical rope shape of second mode disturbances for the sharpest nosetips. For nose bluntness larger than 4.75 mm, disturbances are mainly present at the edge of the boundary layer and within the inviscid shock layer. Their shape no longer presents the second mode typical structure although a frequency analysis of the disturbances is still compatible with second mode instabilities. Present results confirm the dominance of second mode waves in the transition process along a conical geometry for Mach numbers larger than 10.

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Section: Nomenclaturesupporting

confidence: 81%

Hypersonic Boundary Layer Transition on a 7 Degree Half-Angle Cone at Mach 10

Grossir

Regert

Pinna

et al. 2014

7th AIAA Theoretical Fluid Mechanics Conference

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“…5), typical of conventional wind tunnels. From M ∞ = 4 to 5, the main destabilizing process for the §at plate is changed from oblique 1st mode (TS-like waves) to acoustic straight 2nd mode in Mack£s classi¦cation [8]. This explains the nonmonotonic behavior of N factors observed in Fig.…”

Section: N Factor Computationsupporting

confidence: 50%

Hypersonic laminar/turbulent transition: computations and experiments

Orlik

Kornilov

Ferrier

et al. 2012

Progress in Flight Physics

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In order to predict the laminar/turbulent transition on a hypersonic vehicle forebody at Mach numbers 4 and 6, the three-dimensional (3D) modal linear stability analysis is applied, coupled with the e N method. Nevertheless, N factors are unknown for wind tunnel conditions. Experimental investigations have been carried out on a §at plate in the blowdown wind tunnel T-313 of ITAM RAS (Novosibirsk). At M ∞ = 2 to 6, the position of laminar/turbulent transition was measured by both Pitot tube and thermocouples. Then, stability analysis allows computing N factors at transition on the §at plate: they are about 3 ∼ 4, typical of conventional wind tunnels. These §at plate correlations can then be used to predict the transition on the forebody in the same wind tunnel. Experiments for the forebody are currently in progress and will allow checking the predicted transition location.

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“…One reasonable explanation, as pointed in ref. [19], is that the strong wall cooling can be seen as a perturbation source or sink that projects or absorbs the energy and impacts the perturbation of the velocity component that is normal to the wall. These will lead to large flow flux, such as heat flux.…”

Section: Turbulent Intensitymentioning

confidence: 99%

DNS of a spatially evolving hypersonic turbulent boundary layer at Mach 8

Liang

2013

Sci. China Phys. Mech. Astron.

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This paper reports the direct numerical simulation (DNS) for hypersonic turbulent boundary layer over a flat-plate at Ma ∞ =8 with the ratio of wall-to-freestream temperature equal to 1.9, which indicates an extremely cold wall condition. It is primarily used to assess the wall temperature effects on the mean velocity profile, Walz equation, turbulent intensity, strong Reynolds analogy (SRA), and compressibility. The present high Mach number with cold wall condition induces strong compressibility effects. As a result, the Morkovin's hypothesis is not fully valid and so the classical SRA is also not fully consistent. However, some modified SRA is still valid at the far-wall region. It is also verified that the semi-local wall coordinate y * is better than conventional y + in analysis of statistics features in turbulent boundary layer (TBL) in hypersonic flow. DNS, compressibility effects, turbulent boundary layer PACS number(s): 47

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On the application of linear stability theory to the problem of supersonic boundary-layer transition

Cited by 67 publications

References 15 publications

Hypersonic Boundary Layer Transition on a 7 Degree Half-Angle Cone at Mach 10

Hypersonic Boundary Layer Transition on a 7 Degree Half-Angle Cone at Mach 10

Hypersonic laminar/turbulent transition: computations and experiments

DNS of a spatially evolving hypersonic turbulent boundary layer at Mach 8

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