Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation

Bonfigli, Giuseppe; Kloker, Markus J.

doi:10.1017/s0022112007006179

Cited by 105 publications

(139 citation statements)

References 26 publications

(95 reference statements)

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“…Fischer & Dallmann (1991); Malik et al (1999); Haynes & Reed (2000); Janke & Balakumar (2000); Koch et al (2000); Koch (2002); Bonfigli & Kloker (2007)) and on numerical investigations (e.g. Högberg & Henningson (1998); Wassermann & Kloker (2002; Bonfigli & Kloker (2007)) have been performed.…”

Section: Background and Present Workmentioning

confidence: 99%

“…Another relevant investigation on the secondary instability of stationary and travelling primary CF vortices was reported by Bonfigli & Kloker (2007). In this study the authors used spatial DNS and secondary linear stability theory (SLST), the latter previously applied by Fischer & Dallmann (1991); Malik et al (1994Malik et al ( , 1999; Janke & Balakumar (2000) and Koch (2002)).…”

Section: Secondary Instabilitymentioning

confidence: 99%

“…This is expected given that this mode is generated by the spanwise modulation of the primary travelling waves (see also Fischer & Dallmann (1991); Högberg & Henningson (1998); Janke & Balakumar (2000)) caused by the stationary CF vortices. One more important outcome from the work of Bonfigli & Kloker (2007) relates to the nature of type-I and type-II modes. The behaviour and location of these modes associates them to instabilities of the Kelvin-Helmholtz type.…”

Section: Secondary Instabilitymentioning

confidence: 99%

“…For more complete reviews the reader is instead referred to Bippes (1999); Arnal & Casalis (2000); Saric et al (2003) and to some more recent studies such as Wassermann & Kloker (2002; White & Saric (2005); Bonfigli & Kloker (2007); Downs & White (2013) and Hosseini et al (2013).…”

Section: Introductionmentioning

confidence: 99%

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Three-dimensional organisation of primary and secondary crossflow instability

2016

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An experimental investigation of primary and secondary crossflow instability developing in the boundary layer of a 45 • swept wing, at a chord Reynolds number of 2.17·10 6 is presented. Linear stability theory is applied for preliminary estimation of the flow stability while surface flow visualisation using fluorescent oil is employed to inspect the topological features of the transition region. Hot-wire anemometry is extensively used for the investigation of the developing boundary layer and identification of the statistical and spectral characteristics of the instability modes. Primary stationary as well as unsteady type-I (z-mode), type-II (y-mode) and type-III modes are detected and quantified. Finally, three-component, three-dimensional measurements of the transitional boundary layer are performed using tomographic particle image velocimetry. This research presents the first application of an optical experimental technique for this type of flow. Among the optical techniques tomographic velocimetry represents, to date, the most advanced approach allowing the investigation of spatially correlated flow structures in threedimensional fields. Proper orthogonal decomposition (POD) analysis of the captured flow fields is applied to this goal. The first POD mode features a newly reported structure related to low-frequency oscillatory motion of the stationary vortices along the spanwise direction. The cause of this phenomenon is only conjectured. Its effect on transition is considered negligible but, given the related high energy level, it needs to be accounted for in experimental investigations. Secondary instability mechanisms are captured as well. The type-III mode corresponds to low frequency primary travelling crossflow waves interacting with the stationary ones. It appears in the inner upwelling region of the stationary crossflow vortices and is characterised by elongated structures approximately aligned with the axis of the stationary waves. The type-I secondary instability consists instead of significantly inclined structures located at the outer upwelling region of the stationary vortices. The much narrower wavelength and higher advection velocity of these structures correlate with the higher-frequency content of this mode. The results of the investigation of both primary and secondary instability from the exploited techniques agree with and complement each other and are in line with existing literature. Finally, they present the first experimental observation of the secondary instability structures under natural flow conditions.

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Section: Background and Present Workmentioning

confidence: 99%

Section: Secondary Instabilitymentioning

confidence: 99%

Section: Secondary Instabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Three-dimensional organisation of primary and secondary crossflow instability

2016

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“…In some of the previous investigations (e.g. [16]), the flow within the cross-plane has, nonetheless, been found to have a large influence on the growth rates of high frequency secondary instability supported by the finite amplitude primary crossflow modes. To assess the importance of the cross-plane flow, the secondary instability characteristics were computed both with and without the cross-plane velocity components associated with the distorted mean flow.…”

Section: Linear Secondary Instability and Effect Of Controlmentioning

confidence: 89%

Roughness Based Crossflow Transition Control: A Computational Assessment

Choudhari

Chang

et al. 2009

27th AIAA Applied Aerodynamics Conference

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A combination of parabolized stability equations and secondary instability theory has been applied to a low-speed swept airfoil model with a chord Reynolds number of 7.15 million, with the goals of (i) evaluating this methodology in the context of transition prediction for a known configuration for which roughness based crossflow transition control has been demonstrated under flight conditions and (ii) of analyzing the mechanism of transition delay via the introduction of discrete roughness elements (DRE). Roughness based transition control involves controlled seeding of suitable, subdominant crossflow modes, so as to weaken the growth of naturally occurring, linearly more unstable crossflow modes. Therefore, a synthesis of receptivity, linear and nonlinear growth of stationary crossflow disturbances, and the ensuing development of high frequency secondary instabilities is desirable to understand the experimentally observed transition behavior. With further validation, such higher fidelity prediction methodology could be utilized to assess the potential for crossflow transition control at even higher Reynolds numbers, where experimental data is currently unavailable.

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Combined compact difference method for solving the incompressible Navier–Stokes equations

Chen

2011

Numerical Methods in Fluids

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SUMMARYThis paper presents a numerical method for solving the two-dimensional unsteady incompressible NavierStokes equations in a vorticity-velocity formulation. The method is applicable for simulating the nonlinear wave interaction in a two-dimensional boundary layer flow. It is based on combined compact difference schemes of up to 12th order for discretization of the spatial derivatives on equidistant grids and a fourthorder five-to six-alternating-stage Runge-Kutta method for temporal integration. The spatial and temporal schemes are optimized together for the first derivative in a downstream direction to achieve a better spectral resolution. In this method, the dispersion and dissipation errors have been minimized to simulate physical waves accurately. At the same time, the schemes can efficiently suppress numerical grid-mesh oscillations. The results of test calculations on coarse grids are in good agreement with the linear stability theory and comparable with other works. The accuracy and the efficiency of the current code indicate its potential to be extended to three-dimensional cases in which full boundary layer transition happens.

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Secondary instability of crossflow vortices: validation of the stability theory by direct numerical simulation

Cited by 105 publications

References 26 publications

Three-dimensional organisation of primary and secondary crossflow instability

Three-dimensional organisation of primary and secondary crossflow instability

Roughness Based Crossflow Transition Control: A Computational Assessment

Combined compact difference method for solving the incompressible Navier–Stokes equations

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