A history and progress of second mode dominated boundary-layer transition on a Mach 6 flared cone

Chynoweth, Brandon C.; Hader, Christoph; Batista, Armani; Juliano, Thomas J.; Kuehl, Joseph; Wheaton, Bradley M.; Fasel, Hermann F.; Schneider, Steven P.

doi:10.2514/6.2018-0060

Cited by 9 publications

(6 citation statements)

References 37 publications

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“…Typical c h values in the streaks formed beneath the spot for T W = 3 are about −2 × 10 −3 , consistent with turbulent estimates in HBLs 58 . This increases to approximately −3 × 10 −3 and −4 × 10 −3 , for T W = 0.5 and T W = 0.1, respectively.…”

Section: V4 Wall Loadingsupporting

confidence: 84%

Instability characteristics of cooled hypersonic boundary layers

Unnikrishnan

Gaitonde

2020

AIAA Scitech 2020 Forum

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Wall cooling has substantial qualitative and quantitative effects on the development of instabilities and subsequent transition processes in hypersonic boundary layers (HBLs). A sequence of linear stability theory, two-dimensional and non-linear three-dimensional direct numerical simulations is used to analyze Mach 6 boundary layers, with wall temperatures ranging from near-adiabatic to highly cooled conditions, where the second-mode instability is accompanied by radiation of energy. Decomposition of linear stability modes into their fluid-thermodynamic (acoustic, vortical and thermal) components shows that this radiation comprises both acoustic as well as vortical waves. Furthermore, in these cases, 2D simulations show that the conventional "trapped" nature of second-mode instability is ruptured. A quantitative analysis indicates that although the energy efflux of both acoustic and vortical components increases with wall-cooling, the destabilization effect is much stronger and no significant abatement of pressure perturbations is realized. The direct impact of these mechanisms on the transition process itself is examined with high-fidelity simulations of three-dimensional second-mode wavepacket propagation. In the near-adiabatic HBL, the wavepacket remains trapped within the boundary layer and attenuates outside the region of linear instability. However, wavepackets in the cooled-wall HBLs amplify and display nonlinear distortion, and transition more rapidly. The structure of the wavepacket also displays different behavior; moderately-cooled walls show bifurcation into a leading turbulent head region and a trailing harmonic region, while highly-cooled wall cases display lower convection speeds and significant wavepacket elongation, with intermittent spurts of turbulence in the wake of the head region. This elongation effect is associated with a weakening of the lateral jet mechanism due to the breakdown of spanwise coherent structures. These features have a direct impact on wall loading, including skin friction and heat transfer. In moderately cooled-walls, the spatially-localized wall loading is similar to those in near-adiabatic walls, with dominant impact due to coherent structures in the leading turbulent head region. In highly-cooled walls, the elongated near-wall streaks in the wake region of the wavepacket result in more than twice as large levels of skin friction and heat transfer over a sustained period of time.

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Section: V4 Wall Loadingsupporting

confidence: 84%

Instability characteristics of cooled hypersonic boundary layers

Unnikrishnan

Gaitonde

2020

AIAA Scitech 2020 Forum

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“…Thus, it remains to determine whether or not the thermoacoustic Reynolds stress energy terms act as sources or sinks of energy for second modes. The Purdue flared cone is chosen to test this because it was specifically designed to unambiguously isolate second-mode instability [37].…”

Section: Confirmation Of Energy Sourcementioning

confidence: 99%

Thermoacoustic Interpretation of Second-Mode Instability

Kuehl

2018

AIAA Journal

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A thermoacoustic interpretation of Mack's second-mode instability is proposed. It is demonstrated that the fundamental mechanism of second-mode wave growth in hypersonic boundary layers is consistent with standingwave thermoacoustically driven instability. The resonant nature of such modes is sustained by an acoustic impedance well between the wall (infinite impedance) and near the sonic line (secondary peak in impedance). A Lagrangian approach is adopted to show that such resonant standing waves derive energy from the base flow through thermoacoustic Reynolds stress, which results from the divergence of acoustic power inside the impedance well, and thermodynamic work. This treatment does not represent a complete energy closure (due to the neglect of viscosity), but it does provide insight toward a fundamental energy source and the physical mechanisms governing Mack's acoustic second mode.

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“…1, specifically at the Mach 6 Purdue Quiet Tunnel conditions) is known to exhibit laminar flow breakdown that is dominated by Mack's second-mode instability. 16,17 Second modes are thought to be trapped acoustic waves, which resonate within a thermoacoustic impedance well formed between the vehicle wall and the maximum boundary layer density gradient, with thermoacoustic Reynolds stresses providing the fundamental energy source. [18][19][20] As secondmode waves behave as wave packets (finite-frequency-bandwidth disturbances) in the boundary layer, [21][22][23] they exhibit a nonlinear breakdown physics that is particularly relevant to our investigation: (1) The primary 300 kHz second-mode wave packet grows linearly.…”

Section: Example: Synthetic Data Of Hypersonic Boundary Layer Instmentioning

confidence: 99%

Toward a unified interpretation of the “proper”/“smooth” orthogonal decompositions and “state variable”/“dynamic mode” decompositions with application to fluid dynamics

2020

Self Cite

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A common interpretation is presented for four powerful modal decomposition techniques: “proper orthogonal decomposition,” “smooth orthogonal decomposition,” “state-variable decomposition,” and “dynamic mode decomposition.” It is shown that, in certain cases, each technique can be interpreted as an optimization problem and similarities between methods are highlighted. By interpreting each technique as an optimization problem, significant insight is gained toward the physical properties of the identified modes. This insight is strengthened by being consistent with cross-multiple decomposition techniques. To illustrate this, an inter-method comparison of synthetic hypersonic boundary layer stability data is presented.

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A history and progress of second mode dominated boundary-layer transition on a Mach 6 flared cone

Cited by 9 publications

References 37 publications

Instability characteristics of cooled hypersonic boundary layers

Instability characteristics of cooled hypersonic boundary layers

Thermoacoustic Interpretation of Second-Mode Instability

Toward a unified interpretation of the “proper”/“smooth” orthogonal decompositions and “state variable”/“dynamic mode” decompositions with application to fluid dynamics

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