Simple cases of the streamline-curvature instability in three-dimensional boundary layers

Itoh, Nobutake

doi:10.1017/s0022112096000699

Cited by 58 publications

(39 citation statements)

References 8 publications

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“…4−8 In the flow on a rotating disk, the S-C instability has a very low critical Reynolds number and is amplified upstream of the critical point of C-F mode. 6 On the other hand, Takagi et al 9 and Takagi and Itoh 10 have observed that amplified S-C disturbances directly influence spatial growth rate of C-F mode. It is also observed that strongly amplified S-C mode leads to another route of transition that is different from the usual process governed by C-F streamwise vortices.…”

Section: Nomenclaturementioning

confidence: 99%

Experiments on Streamline-Curvature Instability in Boundary Layers on a Yawed Cylinder

2005

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Instability of the three-dimensional boundary layer on a yawed circular cylinder placed in a uniform flow is investigated experimentally by introducing acoustic disturbances from a point near the attachment line. To exemplify the flow dominated by streamline-curvature instability rather than crossflow instability, which has been often observed in many swept-wing flows, is the aim here. In upstream regions of the disturbance wedge originating from the point source, both streamline-curvature and crossflow disturbances are superposed on each other and yield complicated amplitude distributions. A newly proposed method enables the decomposition of the distorted amplitude distribution into contributions from the two instability modes. Detailed observations, however, show that the crossflow mode decays with the distance from the source much faster than the streamline-curvature mode and allows the latter to be dominant in a region further downstream. A fundamental characteristic of the streamlinecurvature instability wave is confirmed by examining its phase distribution in the spanwise and normal directions. Wave numbers and spatial growth rates are in good agreement with theoretical predictions. NomenclatureA = spanwise amplitude distribution A = spanwise total amplitude distribution a = total wave function C = inclination of phase D = cylinder diameter f = dimensional frequency L = streamwise length l s = surface length m = Falkner-Skan parameter N = spatial growth rate of disturbance Q = streamwise (parallel to the local external streamline) local velocity q = fluctuation of streamwise local velocity Re Q = uniform-flow Reynolds number Re δ = local Reynolds number t = time U = chordwise local velocity u = fluctuation of chordwise local velocity V = spanwise local velocity X = nondimensional chordwise (normal to the attachment line) distance from the attachment line along the surface x = dimensional chordwise distance Y = nondimensional spanwise (parallel to the attachment line) distance from the disturbance source Y 0 = nondimensional spanwise location where amplitude becomes maximum Z = nondimensional radial (normal to the surface) distance from the surface α r = chordwise wave number of disturbance β r = spanwise wave number of disturbance Presented as Paper 99-0814 at Science and Engineering, Utsunomiya. ϕ = phase difference between crossflow and streamline-curvature modes δ = boundary-layer thickness δ 99 = boundary-layer thickness where streamwise local mean velocity Q is 99% of edge velocity Q e = sweep angle λ = wave length ν = kinematic viscosity σ = standard deviation of amplitude distribution ϕ = spanwise phase of disturbance ϕ 0 = offset of phasē ϕ = spanwise total phase distribution = phase modulation ω = angular frequencŷ ω = nondimensional frequency Subscripts CF = crossflow mode e = local edge SC = streamline-curvature mode ω = component with angular frequency ω ∞ = uniform flow

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Section: Nomenclaturementioning

confidence: 99%

Experiments on Streamline-Curvature Instability in Boundary Layers on a Yawed Cylinder

2005

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“…It is also deduced that the cross-flow instability of three-dimensional boundary layers is not greatly affected by the nonparallelism of order R −1 , because this instability is of an inviscid inflection-point type. However the streamline-curvature instability, recently found to occur in three-dimensional boundary layers, [3][4][5] is of centrifugal type due to the curvature of external streamlines; therefore it cannot be described by the O-S equation, which ignores curvature effects of the nonparallel terms.…”

Section: Introductionmentioning

confidence: 99%

Multi-Instability Analysis of Swept-Wing Boundary Layers Part 1. A Nonparallel Model of Stability Equations

Itoh

Atobe

2002

Trans. Japan Soc. Aero. S Sci.

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Small disturbances superimposed on the growing boundary-layer flow along a long swept wing are governed by partial differential equations with respect to the local chordwise Reynolds number and the nondimensional vertical coordinate. For a simple and widely applicable method of stability estimation, however, it is desirable to reduce the exact disturbance equations to an eigenvalue problem of the corresponding ordinary differential equations, as in the stability analysis of two-dimensional parallel flows. This paper proposes such a simple model of the ordinary differential system that includes the most important terms of boundary-layer nonparallelism and wall curvature. Numerical computations show that the eigensolutions can properly describe multi-instability characteristics of the three-dimensional boundary layers near the attachment line of a long swept wing.

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“…This equation consists of the parallel-flow approximation plus some additional terms associated with the modified vertical velocityŴ of the basic flow; that is, a neglect of theŴ terms yields the Orr-Sommerfeld equation, and the additional terms given here may be considered to represent the most important nonparallel effects on stability characteristics of boundary-layer flows, as previously pointed out by the author. 8) The boundary conditions to be imposed on the disturbance velocity w are given by…”

Section: Basic Flow and Linear Stability Equationsmentioning

confidence: 99%

Development of Localized Disturbances in Flat Plate Boundary Layer

Itoh

2001

Trans. Japan Soc. Aero. S Sci.

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The method of complex characteristics is used to describe four kinds of localized disturbances in the boundary layer on a flat plate. The disturbances are those introduced by vibrating ribbon, two-dimensional pulse through a slit parallel to the leading edge, continuous excitement through a small hole on the plate, and an instantaneous jet from the same hole. The corresponding four equation systems are numerically solved to show fundamental properties of these disturbances. It is also intended to estimate quantitative effects of the leading-edge sweep angle and of the boundary-layer nonparallelism on the development of a three-dimensional wave packet.

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Simple cases of the streamline-curvature instability in three-dimensional boundary layers

Cited by 58 publications

References 8 publications

Experiments on Streamline-Curvature Instability in Boundary Layers on a Yawed Cylinder

Experiments on Streamline-Curvature Instability in Boundary Layers on a Yawed Cylinder

Multi-Instability Analysis of Swept-Wing Boundary Layers Part 1. A Nonparallel Model of Stability Equations

Development of Localized Disturbances in Flat Plate Boundary Layer

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