Nonlinear instabilities of a non-self-similar boundary layer on an airfoil: Experiments, DNS, and theory

Würz, W.; Sartorius, D.; Kloker, Markus J.; Бородулин, В. И.; Kachanov, Y. S.; Smorodsky, B. V.

doi:10.1016/j.euromechflu.2011.07.006

Cited by 14 publications

(20 citation statements)

References 37 publications

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“…Upstream of the source the disturbance amplitude decays rapidly, that is the amplitude 20 mm upstream of the disturbance source is only 4 % of the amplitude measured 20 mm downstream for a frequency of f = 549 Hz (compare figure 3). This is in good agreement with previous theoretical (Terentev 1981) and experimental (Würz et al 2012) findings.…”

Section: Airfoil Design and Modelsupporting

confidence: 94%

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On the disturbance evolution downstream of a cylindrical roughness element

2014

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Roughness-induced transition is one of the main parameters contributing to performance loss of airfoils. Within this paper, the disturbance evolution downstream of a single, cylindrical roughness element, which is placed in a laminar boundary layer in an airfoil leading edge region, is investigated. The experiments focus on medium height roughness elements with respect to the local boundary layer displacement thickness. Hence, transition is not directly tripped at the roughness element. The roughness diameter is comparable to the streamwise wavelength of the most amplified (linear) disturbance eigenmodes. The vortical structures observed downstream of the roughness are in agreement with previous findings in the literature. In the near roughness wake, a distinct growth of high-frequency (fundamental) modes, that is modes with a high n-factor at the roughness location, is observed. In the far roughness wake, these fundamental modes recover linear stability characteristics due to a possible relaxation of the mean flow. However, an interaction of particularly two-dimensional fundamental modes and by the roughness interference excited oblique fundamental modes results in an excitation of subharmonic type, low-frequency combination modes, which are associated with a phase-locked interaction mechanism. Depending on the initial growth of the fundamental modes in the near wake, the low-frequency modes can experience a nonlinear growth in the far roughness wake and, thereby, trip turbulence. The fundamental mode growth rate in the near wake in turn is a weak function of the disturbance frequency and of the pressure gradient, whereas it is decisively increasing with the roughness height, that is with the mean flow distortion caused by the roughness.

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Section: Airfoil Design and Modelsupporting

confidence: 94%

“…Würz et al 2012). A very thin slit (length = 320 mm, width = 0.2 mm) is integrated surface flush into the model at a streamwise position of x/c = 0.1 and via tubes (length = 2 m, spanwise spacing dz = 2.5 mm) connected to 128 individually controllable micro-loudspeakers (Sennheiser CX300).…”

Section: Airfoil Design and Modelmentioning

confidence: 99%

On the disturbance evolution downstream of a cylindrical roughness element

2014

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“…They were able to amplify even quasi-subharmonic waves with frequency detunings greater than one half of the subharmonic frequency. This result was corroborated by subsequent experimental and theoretical studies; for a review see Würz et al (2012a) and Wu, Stewart & Cowley (2007). A very detailed systematic experimental investigation of frequency-detuned subharmonic-type resonances was performed by Borodulin et al (2002d) for an adverse-pressure-gradient (APG) selfsimilar boundary layer (with Hartree parameter β H = −0.115).…”

Section: Introductionsupporting

confidence: 57%

“…General descriptions of transition scenarios in the boundary-layer flows under study can be found in Herbert (1988) and Kachanov (1994). A detailed review of the state of the art in the field of experimental, theoretical, and numerical investigations of weakly nonlinear stages of boundary-layer transition has recently been given in Würz et al (2012a). Therefore, in the present introduction we only outline briefly the main studies on this topic and then concentrate on the motivation of the present work.…”

Section: Introductionmentioning

confidence: 98%

Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves

et al. 2013

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Weakly nonlinear interactions involving amplitude-modulated Tollmien-Schlichting waves in an incompressible, two-dimensional aerofoil boundary layer are investigated experimentally. Selected resonant regimes are examined with emphasis on the regimes where more than one fundamental Tollmien-Schlichting (TS) wave is present in the flow. The experiments were performed on an NLF-type aerofoil section for glider applications. Disturbances with controlled frequency-spanwise-wavenumber spectra were excited in the boundary layer and studied by phase-locked hot-wire measurements. The results show that nonlinear mechanisms connected with the steepening of the primary TS wave modulation do not play any significant role in the transition scenarios studied. It is also shown that modulations of the twodimensional fundamental waves tend to generate additional modes at modulation frequency. These low-frequency disturbances are found to be produced by a nonresonant quadratic combination of spectral components of the primary, modulated TS wave. The investigations show that the efficiency of the process is higher for three-dimensional low-frequency modes in comparison with two-dimensional modes. Thus, the emergence of three-dimensionality for the low-frequency waves does not require any resonant interactions. In a subsequent nonlinear stage, the self-generated detuned subharmonics are found to be strongly amplified due to resonant interactions with the primary TS waves. The sequence of weakly nonlinear mechanisms found and investigated here seems to be the most likely route to the laminar-turbulent transition, at least for two-dimensional boundary layers of aerofoils with a long extent of laminar flow and in a 'natural' disturbance environment.

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“…The set of loudspeakers is placed outside the test section and 1.2 m long tubes are led into the test section from below the flat plate. The tubes are arranged along a line in the spanwise direction beneath a 0.2 mm wide slot in the surface of the flat plate, while the construction principle is similar to that of Borodulin, Kachanov & Koptsev (2002) and Würz et al (2012). Five tubes with an outer diameter of 3 mm are connected to every loudspeaker, giving a total width of the disturbance source of 240 mm.…”

Section: Experimental Set-upmentioning

confidence: 99%

On the role of adaptivity for robust laminar flow control

et al. 2015

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In boundary-layer flows, one may reduce skin-friction drag by delaying the onset of laminar-to-turbulent transition via the attenuation of small-amplitude Tollmien-Schlichting (TS) waves. In this work, we use numerical simulations and experiments to compare the robustness of adaptive and model-based techniques for reducing the growth of two-dimensional TS disturbances. In numerical simulations, the optimal linear quadratic Gaussian (LQG) regulator shows the best performance under the conditions it was designed for. However, it is found that the performance deteriorates linearly with the drift of the Reynolds number from its nominal value. As a result, an order-of-magnitude loss of performance is observed when applying the computation-based LQG controller in wind-tunnel experiments. In contrast, it is shown that the adaptive filtered-X least-mean-squares (FXLMS) algorithm is able to maintain an essentially constant performance for significant deviations of the nominal values of the disturbance amplitude and Reynolds number.

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Nonlinear instabilities of a non-self-similar boundary layer on an airfoil: Experiments, DNS, and theory

Cited by 14 publications

References 37 publications

On the disturbance evolution downstream of a cylindrical roughness element

On the disturbance evolution downstream of a cylindrical roughness element

Weakly nonlinear stages of boundary-layer transition initiated by modulated Tollmien–Schlichting waves

On the role of adaptivity for robust laminar flow control

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