Instabilities in supersonic compression ramp flow

Fletcher, A. J. P.; Ruban, Anatoly I.; Walker, James D.

doi:10.1017/s0022112004000916

Cited by 16 publications

(37 citation statements)

References 18 publications

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“…Our observations are qualitatively similar to [7] but not [6]. The same equations with a slight change in boundary conditions for the moving wall problem show no instabilities.…”

Section: Resultssupporting

confidence: 74%

“…Of course, this does not preclude other types of instability modes or global instability at much larger ramp angles. The numerical results of Cassel et al [6] and Fletcher et al [7] suggest that there are instabilities present for all the angles studied in figures 2 and 3. …”

Section: (B) Global Stability Resultsmentioning

confidence: 77%

“…It was suggested that this instability is associated with the formation of inflection points of the velocity profile in the recirculation region. On the other hand, a related study by Fletcher et al [7] suggested that the compression ramp flow is convectively unstable for angles α in the range 3.2 ≤ α < 3.7. For larger angles, Fletcher et al [7] suggested that an absolute instability may be responsible for the abrupt local breakdown of the boundary layer.…”

Section: Introductionmentioning

confidence: 95%

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Instability of supersonic compression ramp flow

Logue

Gajjar

Ruban

2014

Phil. Trans. R. Soc. A.

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The instability of supersonic compression ramp flow is investigated. It is assumed that the Reynolds number is large and that the governing equations are the unsteady triple-deck equations. The mean flow is first calculated by solving the steady equations for various scaled ramp angles α , and the numerical results suggest that there is no singularity for increasing ramp angles. The stability of the flow is investigated using two approaches, first by solving the linearized unsteady equations and looking for global modes proportional to e λ t . In the second approach, the linearized unsteady equations are solved numerically with various initial conditions. Whereas no globally unsteady modes could be found for the range of ramp angles studied, the numerical simulations show the formation of wavepacket type disturbances which grow and convect and reach large amplitudes. However, the numerical results show large variations with grid size even on very fine grids.

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“…Our observations are qualitatively similar to [7] but not [6]. The same equations with a slight change in boundary conditions for the moving wall problem show no instabilities.…”

Section: Resultssupporting

confidence: 74%

Section: (B) Global Stability Resultsmentioning

confidence: 77%

Section: Introductionmentioning

confidence: 95%

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Instability of supersonic compression ramp flow

Logue

Gajjar

Ruban

2014

Phil. Trans. R. Soc. A.

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“…Previous computations of 2D flows near isolated compression corners have been reported in refs. [23][24][25]. Compared to the 2D grid, the 3D mesh has a substantially higher streamwise grid density in the vicinity of the trip array, in order to resolve the stronger mean-flow gradients in that region.…”

Section: Mean Flowmentioning

confidence: 99%

Stability Analysis of Roughness Array Wake in a High-Speed Boundary Layer

Choudhari

Edwards

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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Computations are performed to examine the effects of both an isolated and spanwise periodic array of trip elements on a high-speed laminar boundary layer, so as to identify the potential physical mechanisms underlying an earlier transition to turbulence as a result of the trip(s). In the context of a 0.333 scale model of the Hyper-X forebody configuration, the time accurate solution for an array of ramp shaped trips asymptotes to a stationary field at large times, indicating the likely absence of a strong absolute instability in the mildly separated flow due to the trips. A prominent feature of the wake flow behind the trip array corresponds to streamwise streaks that are further amplified in passing through the compression corner. Stability analysis of the streaks using a spatial, 2D eigenvalue approach reveals the potential for a strong convective instability that might explain the earlier onset of turbulence within the array wake. The dominant modes of streak instability are primarily sustained by the spanwise gradients associated with the streaks and lead to integrated logarithmic amplification factors (N factors) approaching 7 over the first ramp of the scaled Hyper-X forebody, and substantially higher over the second ramp. Additional computations are presented to shed further light on the effects of both trip geometry and the presence of a compression corner on the evolution of the streaks.

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“…In the context of supersonic boundary layers, an implicit first order accurate in time and second-order accurate in space finite difference numerical scheme that was originally developed by Ruban (1978), a similar scheme has also been used by Jenson, Burggraf & Rizzetta (1975), was employed by Cassel, Ruban & Walker (1995, 1996 and more recently by Fletcher, Ruban & Walker (2004) in order to study the onset of absolute and convective instabilities in compression ramp flows. The evolution of unstable wave packets leading to violent breakdown of the boundary layer was discussed in these studies and associated with inflection points in the streamwise velocity component, in the manner pointed out earlier by Tutty & Cowley (1986), while the stabilizing effect of wall cooling was quantified.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear interaction between a boundary layer and a liquid film

Vlachomitrou

Pelekasis

2009

J. Fluid Mech.

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The nonlinear stability of a laminar boundary layer that flows at high Reynolds number (Re) above a plane surface covered by a liquid film is investigated. The basic flow is considered to be nearly parallel and the simulations are based on triple deck theory. The overall interaction problem is solved using the finite element methodology with the two-dimensional B-cubic splines as basis functions for the unknowns in the boundary layer and the film and the one-dimensional B-cubic splines as basis functions for the location of the interface. The case of flow above an oscillating solid obstacle is studied and conditions for the onset of Tollmien–Schlichting (TS) waves are recovered in agreement with the literature. The convective and absolute nature of TS and interfacial waves is captured for gas-film interaction, and the results of linear theory are recovered. The evolution of nonlinear disturbances is also examined and the appearance of solitons, spikes and eddy formation is monitored on the interface, depending on the relative magnitude of Froude and Weber numbers (Fr, We), and the gas to film density and viscosity ratios (ρ/ρw, μ/μw). For viscous films TS waves grow on a much faster time scale than interfacial waves and their effect is essentially decoupled. The influence of interfacial disturbances on short-wave growth in the bulk of the boundary layer bypassing classical TS wave development is captured. For highly viscous films for which inertia effects can be neglected, e.g. aircraft anti-icing fluids, soliton formation is obtained with their height remaining bounded below a certain height. When water films are considered interfacial waves exhibit unlimited local growth that is associated with intense eddy formation and the appearance of finite time singularities in the pressure gradient.

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Instabilities in supersonic compression ramp flow

Cited by 16 publications

References 18 publications

Instability of supersonic compression ramp flow

Instability of supersonic compression ramp flow

Stability Analysis of Roughness Array Wake in a High-Speed Boundary Layer

Nonlinear interaction between a boundary layer and a liquid film

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