Theory and Computation of Hydrodynamic Stability

Criminale, W. O.; Jackson, T. L.; Joslin, Ronald D.

doi:10.1017/cbo9780511550317

Cited by 133 publications

(95 citation statements)

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“…The system with less viscous fluid near to the wall (dashed curve in Fig. 3(a) for β = 0) is inviscidly stable by Rayleigh's theorem 21 (R f = −3.1, R s = 3.0, R f + R s < 0), since the base velocity profile has no point of inflection. Now, for a configuration with R f + R s > 0 (R f = −2.9, R s = 3.0), U B ′′ ( y) = 0 at two points (solid curve in Fig.…”

Section: B Base Statementioning

confidence: 99%

“…Their results show the existence of an unstable DD mode in a classically stable system in the context of SC flows, i.e., when the less viscous fluid is placed in the annular region and the highly viscous fluid in the core region of the channel. The DD system is observed to exhibit stability characteristics that are fundamentally different from the SC system, in the sense that the DD instability occurs when the flow is inviscidly stable based on Rayleigh's theorem 21 or stably stratified with respect to viscosity as described by Sahu and Govindarajan. 18 Their investigation clearly demonstrates the significance of viscosity stratification in a double-diffusive two-fluid flow system and is motivated by the extensive studies (Turner, 14 Huppert, 15 and May and Kelley 16 ) on the stability of miscible flows where the viscosity is constant but density is dependent on the concentration of the species.…”

Section: Introductionmentioning

confidence: 99%

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Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

2014

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The effect of velocity slip at the walls on the linear stability characteristics of two-fluid three-layer channel flow (the equivalent core-annular configuration in case of pipe) is investigated in the presence of double diffusive (DD) phenomenon. The fluids are miscible and consist of two solute species having different rates of diffusion. The fluids are assumed to be of the same density, but varying viscosity, which depends on the concentration of the solute species. It is found that the flow stabilizes when the less viscous fluid is present in the region adjacent to the slippery channel walls in the single-component (SC) system but becomes unstable at low Reynolds numbers in the presence of DD effect. As the mixed region of the fluids moves towards the channel walls, a new unstable mode (DD mode), distinct from the Tollman Schlichting (TS) mode, arises at Reynolds numbers smaller than the critical Reynolds number for the TS mode. We also found that this mode becomes more prominent when the mixed layer overlaps with the critical layer. It is shown that the slip parameter has nonmonotonic effect on the stability characteristics in this system. Through energy budget analysis, the dual role of slip is explained. The effect of slip is influenced by the location of mixed layer, the log-mobility ratio of the faster diffusing scalar, diffusivity, and the ratio of diffusion coefficients of the two species. Increasing the value of the slip parameter delays the first occurrence of the DD-mode. It is possible to achieve stabilization or destabilization by controlling the various physical parameters in the flow system. In the present study, we suggest an effective and realistic way to control three-layer miscible channel flow with viscosity stratification.

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Section: B Base Statementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

2014

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“…9. The convective Mach number M c is here defined based on the frozen speed of sound, A f , at the inlet plane,…”

Section: B Convective Mach Number and Flow Modelmentioning

confidence: 99%

“…14 reveals that for all three flow models the most unstable of the two supersonic eigenvalues corresponds to a fast mode. 9 The ordinate of Fig. 14 shows c ‫ء‬ = ͑c r − V min ͒ / ͑V max − V min ͒ against / N for two values of the convective Mach number.…”

Section: Spatial Growth Rate Eigenvaluementioning

confidence: 99%

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Spatial linear stability of a hypersonic shear layer with nonequilibrium thermochemistry

Massa

Austin

2008

Physics of Fluids

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We examine the spatial linear stability of a shear layer in a hypervelocity flow where high temperature effects such as chemical dissociation and vibrational excitation are present. A shock triple point is used to generate a free shear layer in a model problem which also occurs in several aerodynamic applications such as shock-boundary layer interaction. Calculations were performed using a state-resolved, three-dimensional forced harmonic oscillator thermochemical model. An extension of an existing molecular-molecular energy transfer rate model to higher collisional energies is presented and verified. Nonequilibrium model results are compared with calculations assuming equilibrium and frozen flows over a range of (frozen) convective Mach numbers from 0.341 to 1.707. A substantial difference in two- and three-dimensional perturbation growth rates is observed among the three models. Thermochemical nonequilibrium has a destabilizing effect on shear-layer perturbations for all convective Mach numbers considered. The analysis considers the evolution of the molecular vibrational quantum distribution during the instability growth by examining the perturbation eigenfunctions. Oxygen and nitrogen preserve a Boltzmann distribution of vibrational energy, while nitric oxide shows a significant deviation from equilibrium. The difference between translational and vibrational temperature eigenfunctions increases with the convective Mach number. Dissociation and vibration transfer effects on the perturbation evolution remain closely correlated at all convective Mach numbers.

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Flow Instabilities and Transition

Tumin

2010

Encyclopedia of Aerospace Engineering

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This paper introduces the flow instability concept and the problem of transition prediction. The discussion is aimed at the Tollmien–Schlichting type of instability in low‐speed two‐dimensional boundary layers. The discussion includes an outline of the linear stability theory, paths to turbulence in wall layers, and the e N method for transition prediction.

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Theory and Computation of Hydrodynamic Stability

Cited by 133 publications

References 0 publications

Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

Double-diffusive two-fluid flow in a slippery channel: A linear stability analysis

Spatial linear stability of a hypersonic shear layer with nonequilibrium thermochemistry

Flow Instabilities and Transition

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