Similarity properties of the laminar or turbulent separation phenomena in a non-uniform supersonic flow

Carrière, Pierre; Sirieix, M.; Solignac, J. L.

doi:10.1007/978-3-642-85640-2_11

Cited by 8 publications

(12 citation statements)

References 2 publications

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“…Carrière et al (1969) report a generalised correlation functionF independent of Mach and Reynolds number. It accounts for non-uniformities in the incoming outer flow as well as for wall curvature effects and is especially suited for SWBLI featuring strong streamline curvature in the free interaction zone (Matheis & Hickel 2015).…”

Section: Grid-and Domain-sensitivity Studymentioning

confidence: 99%

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

2017

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We analyse the low-frequency dynamics of a high-Reynolds-number impinging shockwave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by 19.6○ . The Reynolds number based on the incoming boundary layer thickness of Re δ0 ≈ 203 ⋅ 10 3 is considerably higher than in previous LES studies. The very long integration time of 3805 δ 0 U 0 allows for an accurate analysis of low-frequency unsteady effects. Experimental wallpressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separationbubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identify streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the lowfrequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.

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Section: Grid-and Domain-sensitivity Studymentioning

confidence: 99%

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

2017

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“…In the following we give a brief introduction to the Zone of free interaction Isentropic compression waves FIGURE 18. Schematic of the free interaction, after Carrière et al (1969) and Charwat (1970).…”

Section: Transition Criteriamentioning

confidence: 99%

“…We emphasise that more comprehensive reviews on the free interaction theory can be found, for example, in Erdos & Pallone (1963), Carrière et al (1969), Charwat (1970), Delery & Marvin (1986), and Babinsky & Harvey (2011). Consider figure 18, which schematically depicts the zone of free interaction.…”

Section: Transition Criteriamentioning

confidence: 99%

“…For our purposes, equation (4.9) can be used to approximate the wall-pressure evolution for a given Mach number and friction coefficient, once F (s) has been determined by experiments or numerical simulations. Carrière et al (1969) proposed a generalisation of Chapman's theory to account for non-uniformities in the incoming outer flow, in particular, the adverse pressure gradient caused by wall curvature. They showed that the universal function has in the most general case the form…”

Section: Transition Criteriamentioning

confidence: 99%

“…We will demonstrate that turbulent fluctuations play a crucial role in triggering the transition between RSWBLI and ISWBLI and that classical gas-dynamics methods are suitable for the analysis of the transient data. In § 4 we apply the free interaction theory (Chapman, Kuehn & Larson 1958;Carrière, Sirieix & Solignac 1969) for the approximation of the deflection across the separation shock (the reflected shock) and classical two-and three-shock theory for the determination of a critical deflection across the incident shock for which an ISWBLI can occur. Though the derived transition criteria should be seen as an engineering approach in the sense of a conservative worst-case estimate, the subsequent validation for the highly asymmetric SWBLI at Ma 0 = 3 yields very promising results, see § 5.…”

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confidence: 99%

See 2 more Smart Citations

On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions

Matheis

Hickel

2015

J. Fluid Mech.

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The reflection of strong oblique shock waves at turbulent boundary layers is studied numerically and analytically. A particular emphasis is put on the transition between regular shock-wave/boundary-layer interaction (SWBLI) and Mach reflection (irregular SWBLI). The classical two-and three-shock theory and a generalised form of the free interaction theory are used for the analysis of well-resolved large-eddy simulations (LES) and for the derivation of stability criteria. We found that at a critical deflection angle across the incident shock wave, the perturbations related to the turbulent boundary layer cause bi-directional transition processes between regular and irregular shock patterns for a free-stream Mach number of Ma 0 = 2. Computational results show that the mean deflection angle across the separation shock is decoupled from the incident shock wave and can be accurately modelled by the generalised free interaction theory. On the basis of these observations, and the von Neumann and detachment criteria for the asymmetric intersection of shock waves, we derive the critical incident shock deflection angles at which the shock pattern may/must become irregular. Numerical data for a free-stream Mach number of Ma 0 = 3 confirm the existence of the dual-solution domain predicted by theory.

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Experimental analysis of unsteady separated flows in a supersonic planar nozzle

Bourgoing

Reijasse

2005

Shock Waves

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Similarity properties of the laminar or turbulent separation phenomena in a non-uniform supersonic flow

Cited by 8 publications

References 2 publications

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

On the transition between regular and irregular shock patterns of shock-wave/boundary-layer interactions

Experimental analysis of unsteady separated flows in a supersonic planar nozzle

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