Linear and non-linear stability analysis of incompressible boundary layer over a two-dimensional hump

Park, Donghun; Park, Seung O

doi:10.1016/j.compfluid.2012.12.007

Cited by 32 publications

(24 citation statements)

References 25 publications

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“…A similar trend was found by Worner et al (2003) and Park & Park (2013) based on their DNS and PSE calculations.…”

Section: Comparison With the Local Linear Stability Analysissupporting

confidence: 72%

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A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue

Dong

2016

J. Fluid Mech.

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This paper is concerned with the rather broad issue of the impact of abrupt changes (such as isolated roughness, gaps and local suctions) on boundary-layer transition. To fix the idea, we consider the influence of a two-dimensional localized hump (or indentation) on an oncoming Tollmien-Schlichting (T-S) wave. We show that when the length scale of the former is comparable with the characteristic wavelength of the latter, the key physical mechanism to affect transition is through scattering of T-S waves by the roughness-induced mean-flow distortion. An appropriate mathematical theory, consisting of the boundary-value problem governing the local scattering, is formulated based on triple deck formalism. The transmission coefficient, defined as the ratio of the amplitude of the T-S wave downstream the roughness to that upstream, serves to characterize the impact on transition. The transmission coefficient appears as the eigenvalue of the discretized boundary-value problem. The latter is solved numerically, and the dependence of the eigenvalue on the height and width of the roughness and the frequency of the T-S wave is investigated. For a roughness element without causing separation, the transmission coefficient is found to be about 1.5 for typical frequencies, indicating a moderate but appreciable destabilizing effect. For a roughness causing incipient separation, the transmission coefficient can be as large as O(10), suggesting that immediate transition may take place at the roughness site. A roughness element with a fixed height produces the strongest impact when its width is comparable with the T-S wavelength, in which case the traditional linear stability theory is invalid. The latter however holds approximately when the roughness width is sufficiently large. By studying the two-hump case, a criterion when two roughness elements can be regarded as being isolated is suggested. The transmission coefficient can be converted to an equivalent N-factor increment, by making use of which the e N -method can be extended to predict transition in the presence of multiple roughness elements.

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“…A similar trend was found by Worner et al (2003) and Park & Park (2013) based on their DNS and PSE calculations.…”

Section: Comparison With the Local Linear Stability Analysissupporting

confidence: 72%

“…The quadratic scaling with respect to h * is in contrast to linear one for steps and other forms of roughness. Park & Park (2013) used nonlinear PSE to study the nonlinear development of instability waves in a boundary layer over a wavy wall.…”

Section: Transmitted T-s Wavementioning

confidence: 99%

A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue

Dong

2016

J. Fluid Mech.

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“…It was suggested that expression (3) could be used to estimate the effect on stability and transition for a limited range of surface dimensions, provided that surface waviness did not enhance receptivity or excite nonlinear interaction with centrifugal instabilities that may develop as a result of the surface waviness [22]. PSE methods were also employed by Park and collaborators [23,24] to investigate the effects of a hump on both the linear and nonlinear development of the TS wave instability. Both the height and length scales of the hump were again critical to the amplification rate of the disturbances.…”

Section: Introductionmentioning

confidence: 99%

“…Fage [2] Experimental Flat Plate/Aerofoil Bulges/Hollows/Ridges Carmichael Group [3][4][5] Experimental Aerofoil Waviness Holmes Group [6,7] Experimental Aerofoil Steps/Gaps Wang & Gaster [8] Experimental Flat Plate Steps Lessen & Gangwani [9] Theoretical Flat Plate Waviness Nayfeh et al [13] Theoretical Flat Plate Humps Cebeci & Egan [14] Theoretical Flat Plate Humps Masad & Iyer [15] Theoretical Flat Plate Humps Wie & Malik [20] Theoretical Flat Plate Waviness Park Group [23,24] Theoretical Flat Plate Humps Brehm et al [25] Theoretical Flat Plate Ridges/Roughness Gaster [26] Experimental Flat Plate Ridges/Roughness where the parameter n defines the number of waves before the onset of transition x tr (given for the non-deformed model). Comparing their expression for the allowable measure of surface waviness with that formulated by Fage and Carmichael [2,4], Wie and Malik concluded that Fage's criteria (1) was quite restrictive and allows significantly smaller waviness than the relationship conceived by Carmichael (2).…”

Section: Introductionmentioning

confidence: 99%

Development of Tollmien-Schlichting disturbances in the presence of laminar separation bubbles on an unswept infinite wavy wing

2017

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The effect of long wavelength sinusoidal surface waviness on the development of TollmienSchlichting (TS) wave instabilities is investigated. The analysis is based on the compressible flow that forms over an unswept infinite wavy wing with surface variations of variable amplitude, wavelength and phase. Boundary layer profiles are extracted directly from the solutions of a Navier-Stokes solver, which allows a thorough parametric analysis to be undertaken. Many wavy surface configurations are examined that can be sufficient to establish localised pockets of separated flow. Linear stability analysis is undertaken using parabolised stability equations (PSE) and linearised NavierStokes (LNS) methods, and surface waviness is generally found to enhance unstable behaviour. Results of the two schemes are compared and criteria for PSE to establish accurate solutions in separated flows are determined, which are based on the number of TS waves per wavelength of the surface deformation. Relationships are formulated, relating the stability variations and the surface parameters, which are consistent with previous observations regarding the growth of TS waves on a flat plate. Additionally, some long wavelength surface deformations are found to stabilise TS disturbances. * c.thomas@imperial.ac.uk 2

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“…Various wave configurations and compressible flow conditions were considered and it was determined that the height and length of the surface wave were critical to the stability and transition calculations, providing agreement with the earlier experimental observations. PSE methods were further utilized in the analysis of humps on a two-dimensional flat plate [19,20]. The height and length scales of the hump were again critical to the amplification rates of the established disturbances, with significant increases in the N -factor observed when the hump width was reduced.…”

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confidence: 99%

Stability of an Infinite Swept Wing Boundary Layer with Surface Waviness

et al. 2016

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A scheme for generating boundary layers is described and applied to an infinite swept wing model with wavy surface deformations. Steady laminar mean flow is extracted directly from solutions of the Navier-Stokes system of equations, which is validated against computations of a compressible boundary layer method. Furthermore, the routines capture separated boundary layer profiles, overcoming the constraints of the conventional methods. The stability of crossflow disturbances is investigated using both PSE and LNS methods and the effect of chordwise waviness of variable wavelength, amplitude and phase is considered. Wavy surfaces are found to influence the growth of crossflow disturbances, suggesting that the onset of transition may also be affected by the variations in the surface geometry.

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Linear and non-linear stability analysis of incompressible boundary layer over a two-dimensional hump

Cited by 32 publications

References 25 publications

A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue

A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue

Development of Tollmien-Schlichting disturbances in the presence of laminar separation bubbles on an unswept infinite wavy wing

Stability of an Infinite Swept Wing Boundary Layer with Surface Waviness

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