Stability of Hypersonic Boundary Layers over a Compression Corner

Balakumar, Ponnampalam; Zhao, Hui; Atkins, Harold L.

doi:10.2514/1.3479

Cited by 75 publications

(46 citation statements)

References 12 publications

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“…as was seen in the study of compression corner flow by Balakumar et al 9 Figure 16 shows the growth of the n-factors for the second mode at frequencies = 0.3 and = 0.4 for M 1 = 4.5. The high frequency case is most unstable at locations approximately halfway between the separation point ͑Re x Ϸ 2.0ϫ 10 5 ͒ and the bubble apex and halfway between the bubble apex and reattachment ͑Re x Ϸ 3.3ϫ 10 5 ͒.…”

Section: -11supporting

confidence: 62%

“…As the Mach number increases, additional "Mack" modes ͑second mode, third mode, etc.͒ of instability appear, and at high Mach numbers these are the most unstable disturbances. Flow stability results in SBLI at M 1 = 4.8, focusing on the second-mode instabilities, are reported in Pagella et al 8 for a flat plate boundary layer and at M 1 = 5.373 in Balakumar et al 9 for a compression corner flow.…”

Section: Introductionmentioning

confidence: 87%

“…This latter work also demonstrated that the response to small-amplitude disturbances was practically identical. Compression corner flows at M 1 = 5.373 were also considered by Balakumar et al, 9 who showed that the second-mode disturbances were not significantly amplified over the separation bubble. In a later study of the same compression corner flow, Zhao and Balakumar 17 showed that a ͑0,2͒ mode arising from nonlinear interactions led to an oblique type of breakdown.…”

Section: Introductionmentioning

confidence: 92%

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The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

et al. 2007

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The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory ͑LST͒. To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number ͑based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow͒ and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations ͑PSE͒. At Mach 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At Mach 4.5 and Mach 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear layer. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher Mach number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wavenumbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at Mach 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes.

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Section: -11supporting

confidence: 62%

Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 92%

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The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

et al. 2007

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“…Atkins [21] gives the application of the essentiallynon-ossillatory (ENO) method to the N-S equations. Balakumar et al [22] describe in detail the solution method implemented in this computation.…”

Section: Solution Algorithmmentioning

confidence: 99%

Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability over Cones

2011

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The receptivity to freestream acoustic disturbances and the stability properties of hypersonic boundary layers are numerically investigated for boundary-layer flows over a 5 straight cone at a freestream Mach number of 6.0. To compute the shock and the interaction of the shock with the instability waves, the Navier-Stokes equations in axisymmetric coordinates were solved. In the governing equations, inviscid and viscous flux vectors are discretized using a fifth-order accurate weighted-essentially-non-oscillatory scheme. A third-order accurate total-variationdiminishing Runge-Kutta scheme is employed for time integration. After the mean flow field is computed, disturbances are introduced at the upstream end of the computational domain. The appearance of instability waves near the nose region and the receptivity of the boundary layer with respect to slow mode acoustic waves are investigated. Computations confirm the stabilizing effect of nose bluntness and the role of the entropy layer in the delay of boundary-layer transition. The current solutions, compared with experimental observations and other computational results, exhibit good agreement. Nomenclature = streamwise wave number C recpt = receptivity coefficient c p = specific heat at constant pressure c v = specific heat at constant volume E = total energy e = molecular internal energy F, G = inviscid flux vector in the axial and radial directions

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“…20 The solution method implemented in the present computations is described in Balakumar. 21 Schematic diagrams of the computational setup for each model case are shown in Figs. 2-4.…”

Section: A Solution Algorithmmentioning

confidence: 99%

Receptivity of Hypersonic Boundary Layers over Straight and Flared Cones

Balakumar

Kegerise

2015

AIAA Journal

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The effects of adverse pressure gradients on the receptivity and stability of hypersonic boundary layers were numerically investigated. Simulations were performed for boundary layer flows over a straight cone and two flared cones. The steady and the unsteady flow fields were obtained by solving the twodimensional Navier-Stokes equations in axi-symmetric coordinates using the 5 th -order accurate weighted essentially non-oscillatory (WENO) scheme for space discretization and using third-order total-variation-diminishing (TVD) Runge-Kutta scheme for time integration. The mean boundary layer profiles were analyzed using local stability and non-local parabolized stability equations (PSE) methods. After the most amplified disturbances were identified, two-dimensional plane acoustic waves were introduced at the outer boundary of the computational domain and time accurate simulations were performed. The adverse pressure gradient was found to affect the boundary layer stability in two important ways. Firstly, the frequency of the most amplified second-mode disturbance was increased relative to the zero pressure gradient case. Secondly, the amplification of first-and second-mode disturbances was increased. Although an adverse pressure gradient enhances instability wave growth rates, small nose-tip bluntness was found to delay transition due to the low receptivity coefficient and the resulting weak initial amplitude of the instability waves. The computed and measured amplitudefrequency spectrums in all three cases agree very well in terms of frequency and the shape except for the amplitude.

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Stability of Hypersonic Boundary Layers over a Compression Corner

Cited by 75 publications

References 12 publications

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

Effects of Nose Bluntness on Hypersonic Boundary-Layer Receptivity and Stability over Cones

Receptivity of Hypersonic Boundary Layers over Straight and Flared Cones

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