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The effect of inflow turbulence level on the boundary layer transition on a Natural Laminar Flow (NLF) airfoil is investigated through detailed wind tunnel measurements. The free-stream turbulence level (\( Tu \)) is varied in the range \(0.01\%\le Tu \le 0.11\%\) by employing an active grid. Within the range of amplified TS-frequencies the spectral distribution of the \(u'\)-component could be matched to free flight measurements obtained for a glider at low to moderately turbulent conditions. Transition locations as function of turbulence level are determined for three airfoils with fundamentally different baseflows and the results are compared to the modified \(e^{9}\) method of Mack [6].

The present investigation is devoted to initial nonlinear stages of laminar–turbulent transition initiated by broadband disturbances in an essentially non-self-similar boundary layer, developing on a two-dimensional airfoil. The measurements are performed at fully controlled disturbance conditions with respect to the distribution of the initial spectra of excited 3D (in general) Tollmien–Schlichting (TS) waves. The main attention is devoted to the investigation of resonant (and non-resonant) interactions and amplification of broadband low-amplitude 3D instability waves in the presence (and in absence) of one or two primary harmonic 2D TS-waves. The broadband, “noise-like” TS-waves are composed of controlled perturbations, pseudo-random in time and space, with a continuous frequency–wavenumber spectrum. These perturbations simulate typical background disturbances usually observed at so-called “natural” disturbance conditions. The harmonic primary TS-wave simulates a primary instability mode, which has been formed by the linear instability mechanism. In fact, this paper represents the third step in a set of detailed investigations (Wurz et al., 2012 [1] ) and Wurz et al., 2012 [2] ) of weakly-nonlinear stages of transition performed in the same base flow (on an airfoil) but at increased complexity of initial disturbance conditions. In contrast to the studies of periodic resonant regimes described in refs. Wurz et al. (2012) [1] and Wurz et al. (2012) [2] , no specific (preinstalled) disturbance frequencies or/and spanwise wavenumbers were excited in the boundary layer (except for the primary wave). So, the flow was free to amplify almost any mode of the frequency–wavenumber spectrum by means of any available mechanisms of TS-wave interaction. Such disturbance conditions are the closest to the so-called “natural” ones, i.e. to those observed typically for uncontrolled external perturbations. Four main groups of regimes of disturbance excitation were studied: (i) two harmonic fundamental waves and a pair of frequency detuned subharmonics, (ii) the low-amplitude broadband disturbances only and (iii) the low-amplitude broadband disturbances together with harmonic 2D primary TS-waves, and (iv) the high-amplitude broadband disturbances only. It is found that in case (i) the superposition of the resonances takes place in a nonlinear way and joint efforts of the two fundamental waves are similar to a fundamental-mode amplitude enhancement, which always leads to the increase of the subharmonic amplification rates. In case (ii) the perturbations develop downstream in agreement with the linear stability mechanism. In case (iii) strong resonant interactions between the broadband perturbations and the harmonic primary TS-wave is observed in a wide frequency range. In case (iv) very similar strong resonant interactions are observed between 2D and 3D spectral modes starting already at significantly lower amplitudes of the 2D modes in the frequency range of the primary fundamental modes. In cases (i), (iii) and (iv) the amplification is double-exponential (exponent in exponent), similar to that found in isolated tuned and detuned resonances of deterministic modes in papers Wurz et al. (2012) [1] and Wurz et al. (2012) [2] . For all resonantly interacting disturbances the phase synchronism conditions are found to be satisfied. Based on the cumulative results obtained in the framework of this intensive investigation, the most important observation is the predominant role of resonant TS-wave interactions in the non-self-similar boundary layer developing on a natural laminar flow airfoil section.

The tonal self-noise emission of a vehicle side mirror and the associated flowfield are investigated experimentally. The relevant surface on the model includes a region of geometry-induced laminar ...

The tonal self-noise emission of a two-dimensional blunt-body side mirror model is investigated experimentally in order to characterize the underlying source mechanism. The two-dimensional side mirror design is closely related to an automotive side mirror model 1 which generates tonal self-noise. The examined flow field and tonal noise emission of the two-dimensional side mirror indicates the existence of an aeroacoustic feedback mechanism comprising convective boundary layer instability waves, their scattering to acoustic waves at the trailing edge and the acoustic receptivity at a dominant feedback point. Fundamental evidence of this concept is found in the typical variation of the discrete-frequency noise emission with the free-stream velocity as well as a laminar flow separation in the vicinity of the trailing edge featuring massively amplified discrete-frequency modes. The existence of an aeroacoustic feedback loop is finally confirmed by the systematic variation of the feedback loop resonance length, which is a crucial loop parameter.

The Temperature-Sensitive Paint (TSP) method is used for surface-based flow visualizations on a swept-wing wind-tunnel model with a generic natural laminar-flow airfoil. Within the investigated parameter range the stationary crossflow instability is the dominating instability mechanism. Based on the TSP results the location of the laminar-turbulent transition and the most amplified wavenumber of the stationary crossflow instability are determined. The test is performed with three different conditions of the leading-edge surface: highly polished, unpolished, and highly polished with discrete roughness elements applied. The Temperature-Sensitive Paint method has proven to have sufficient spatial resolution and temperature sensitivity to resolve skin friction variations to detect the footprint of stationary crossflow vortices even inside of turbulent wedges. With the discrete roughness elements, i.e. cylindrical elements with micron-sized height, the transition could be delayed successfully for certain conditions. Local low-frequency movement of the beginning of turbulent wedges was detected for some data points with an unpolished leading edge.

Wind tunnel measurements have been performed to investigate the effect of large scale turbulence on the laminar to turbulent transition on a natural laminar flow airfoil through cyclic 2D variations of the inflow angle. The investigated range of reduced frequencies is \(k=\pi \cdot f\cdot c/U_{\infty }=0.22-1.67\) (corresponding to \(f=2{-}15\) Hz) and an equivalent angle of attack amplitude of \(\pm 0.5^{\circ }\). Transition locations are determined using the M-TERA intermittency method and time-dependent frequency spectra are calculated by a continuous wavelet transform. At high frequencies of inflow oscillation the downstream moving transition front is slower than the change in pressure gradient and the Tollmien-Schlichting peak is significantly reduced, indicating a “convective” transition mode. The downstream turning point of the transition location during the inflow angle cycle moves upstream for \(k>1.0\) while the upstream turning point is essentially unchanged for \(k\le 1.67\).

Within the Luftfahrtforschungsprogramm (LuFo), measurements on a laminar flow airfoil in flight as well as in a wind tunnel are combined with direct numerical simulations (DNS) to provide the base for future improvements of transition prediction under unsteady inflow conditions. Two regions of turbulent length scales of the inflow are of particular interest for investigating the effect on boundary layer transition on straight wings: large length scales leading to unsteady pressure distributions of the airfoil and small length scales corresponding to the streamwise wave lengths of Tollmien-Schlichting (TS) waves in the boundary layer. The current paper focuses on wind tunnel measurements of the effect of small scale turbulence. In the Laminar Wind Tunnel of the IAG, small scale turbulence is investigated using an active grid in the settling chamber, enabling measurements at turbulence levels (Tu) ranging from 0.01% (15-5000 Hz) without grid up to 0.11%. The turbulence spectra compare very well with flight measurements in the frequency range relevant for TS-instability. Hot-wire anemometry is used for detailed boundary layer measurement while modified piezoresistive pressure transducers are utilized to measure surface pressures fluctuations up to 8 kHz. In the range 0.01% = Tu = 0.11% the transition location on the pressure side of the MW-166-39-44-43 airfoil shifts upstream with increasing Tu, the frequency of the most amplified TS waves increases and the transition process change gradually from a quasi-uniform nature to a structure with isolated wave packets. Simultaneously the frequency wavenumber spectrum indicates an increased amount of energy at higher spanwise wave numbers. The Tu dependent n-factor of the MW-166-39-44-43 airfoil was found to match very well with the modified e^9 method of Mack, while the corresponding n-factor of a XIS40mod airfoil showed a much lower sensitivity, and a close to linear dependency on Tu. A variation in contribution of the receptivity coefficient in the modified e^9 method did not capture the difference in Tu-dependency observed for the two airfoils.

A semi-empirical model to determine the wall pressure frequency spectrum beneath a two-dimensional, pressure gradient turbulent boundary-layer is presented. The model is derived based on the experimental wall pressure data of various research groups. The experimental database includes both the equilibrium flat plate and non-equilibrium airfoil boundary-layer flow cases and covers a large range of Reynolds numbers, 1.0 times 103 < Reδ2 < 3.0 times 104. The enhanced model is a combination of the modified Chase-Howe, Goody and Rozenberg models, and is a simple function of the ratio of pressure and timescales of the outer to inner part of the boundary-layer. The key advantage of the present model is that it incorporates the Reynolds number, the boundary-layer loading as well as pressure gradient effects through an amplitude scaling function and timescale ratio, and compares well to the experimental data. Spectral features of the detailed measurement data and various scaling behavior of the wall pressure spectrum are elaborately investigated. A summary of the results on the applicability and limitation of the model for various test cases is discussed. The enhanced model is further applied to develop an airfoil turbulent boundary-layer trailing-edge interaction (TBL-TE) far-field noise prediction scheme. Prediction results are compared with the well established experimental database and encouraging results are found. The enhanced Wall Pressure Fluctuation (WPF) as well as trailing-edge noise spectra models accuracy for the maximum noise level is in ±2dB range for the test cases examined. The model can be applied further for acoustic airfoil design and optimization and in various aeroacoustic applications.

The present study is devoted to nonlinear (resonant) mode interactions in the wake of a medium height, cylindrical roughness element, which is placed in a laminar, airfoil boundary layer. The roughness element causes a considerable mean flow distortion in the near wake centerline region and two counter-rotating vortex pairs arise in the outer spanwise domain. In the streamwise evolution the mean flow stabilizes and a spanwise uniform flow is recovered in the far wake. Upstream of the roughness controlled, low-amplitude Tollmien-Schlichting (TS) wave modes are excited in the upper branch unstable region. The interference of the excited, 2D fundamental modes with the roughness results in the excitation of oblique modes in a broad spanwise wave number range. Nonlinear interactions in-between the (oblique) fundamental modes in the destabilized near wake lead to the generation of primary, low-frequency modes at the difference frequencies of the fundamental modes, before the fundamental modes can recover linear stability characteristics in the far wake. In contrast, the primary, subharmonic-type modes experience a nonlinear growth, which is a result of frequency and spanwise wave number detuned resonant mode interactions with the 2D fundamental modes. The resonant growth of the primary interaction modes initiates a symmetrization of the spectrum in the low-frequency, subharmonic range. That is, symmetric subharmonic-type (secondary) modes are resonantly amplified in the far wake. Therefore, although the fundamental modes recover linear stability characteristics with the stabilization of the mean flow, resonant mode interactions in the low-frequency, subharmonic range initiate the onset of boundary layer transition in the far wake of the medium height roughness element.

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 $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}n$-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.

In the current study, we investigate a route to reduction of the turbulent boundary layer–trailing edge interaction noise. The trailing edge noise is generated by surface pressure fluctuations beneath a turbulent boundary and scattered at the trailing edge of wind turbine blades. Trailing edge noise is considered to be the dominant noise source of modern wind turbines. Therefore, efforts are constantly made to attenuate the noise. Today, noise emission can be reduced by proper airfoil design or passive devices, such as trailing edge serrations. A further improved candidate technology for trailing edge noise attenuation is active flow control in the form of wall-normal suction. With active flow control, the boundary layer features responsible for trailing edge noise generation can be manipulated, and correspondingly the trailing edge noise can be reduced. Detailed experimental investigations were performed at the Universities of Tel-Aviv and Stuttgart. The tests showed that steady wall-normal suction has a positive effect on the trailing edge noise by reducing the boundary layer thickness, and with it the integral length scales of the eddies within the boundary layer.

In this paper an effective approach to estimate airfoil Turbulent Boundary-Layer Trailing-Edge (TBL-TE) far-field noise from measured surface pressure fluctuations (SPF) is evaluated. Measurements of both SPF and TE noise were performed on a NACA 0012 airfoil of 0.4 m chord at Reynolds numbers of 1.0–1.9 millions for various angles of attack. A non-homogeneously spaced array of five Kulite-sensors near the TE at x/ c = 0.989 is employed to measure point spectra and spanwise two-point correlations of surface pressure fluctuations. Finally spanwise SPF length-scales are derived as function of frequency. Comparisons to measured TE noise and semi-empirical predictions of surface pressures and far-field noise show very good agreement. It is found, that the proposed method can cover a larger frequency range than standard acoustic measurement techniques. Therefore it can provide valuable assistance in extending spectra obtained conventionally, mainly to low frequencies. Furthermore, pressure and suction side contributions to far-field noise can be obtained separately.

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 two-dimensional fundamental waves tend to generate additional modes at modulation frequency. These low-frequency disturbances are found to be produced by a non-resonant 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.

Experimental investigations on an isolated vehicle side mirror model are performed in a low turbulence wind tunnel aiming at the identification of the acoustic source mechanism leading to tonal noise emission. A combination of acoustic measurements and Particle Image Velocimetry shows that the discrete frequency noise can be related to the presence of a laminar boundary layer separation extending up to the trailing edge on the mirror’s side surface and upper side. In the vicinity of the trailing edge, the shear layer develops into a vortical structure, which impinges on the trailing edge. By utilization of Proper Orthogonal Decomposition on the ensembles of instantaneous velocity fields and application of a phase sorting method, the length scales of the vortical structures could be extracted and related to the acoustic radiation. Order of magnitude analyses show parallels to the acoustic feedback mechanism known from the NACA 0012 airfoil.

The present study is devoted to nonlinear mode interactions in the wake of a medium height, isolated roughness placed in a laminar, airfoil boundary layer. Upstream of the roughness low-amplitude, fundamental TS-wave bands are excited. Nonlinear interactions in-between the fundamental modes in the near wake lead to the formation of low-frequency, subharmonic-type modes before the fundamental modes can recover linear stability characteristics with the stabilization of the mean flow. For lower roughness heights the low-frequency modes are only weakly distinct and the disturbance evolution is dominated by the fundamental modes in the roughness wake. With increasing mean flow distortion, that is roughness height, the subharmonic-type modes experience a resonant growth stage in the far wake, which provokes the onset of turbulence. For further increased roughness heights, the fundamental and the subsequent interactions modes reach nonlinear amplitudes in the near wake and, thereby, initiate the laminar flow breakdown before the boundary layer can stabilize.

This paper describes an extensive assessment and a step by step validation of different turbulent boundary-layer trailingedge noise prediction schemes developed within the European Union funded wind energy project UpWind. To validate prediction models, measurements of turbulent boundary-layer properties such as two-point turbulent velocity correlations, the spectra of the associated wall pressure fluctuations and the emitted trailing-edge far-field noise were performed in the laminar wind tunnel of the Institute of Aerodynamics and Gas Dynamics, University of Stuttgart. The measurements were carried out for a NACA 643-418 airfoil, at Re D 2:5 106, angle of attack of 6i to 6i. Numerical results of different prediction schemes are extensively validated and discussed elaborately. The investigations on the TNO-Blake noise prediction model show that the numerical wall pressure fluctuation and far-field radiated noise models capture well the measured peak amplitude level as well as the peak position if the turbulence noise source parameters are estimated properly including turbulence anisotropy effects. Large eddy simulation based computational aeroacoustic computations show good agreements with measurements in the frequency region higher than 1 kHz, whereas they over-predict the sound pressure level in the low-frequency region. Copyright © 2011 John Wiley & Sons, Ltd.

A method for the prediction of the airfoil trailing-edge far-field noise is presented. The model employs the airfoil analysis code XFOIL to determine the initial and boundary conditions for a subsequent boundary-layer analysis using the finite-difference code EDDYBL featuring a Reynolds stress turbulence model that finally provides the input data for the noise prediction by a modified TNO Institute of Applied Physics model. The prediction scheme was applied in the European silent rotors by acoustic optimization project to design new, quieter airfoils for the outer blade region of three different wind turbines in the megawatt class. The objective was to reduce the airfoil self-noise without loss in aerodynamic performance

The effect of an isolated, cylindrical roughness on the stability of an airfoil boundary layer has been studied based on particle image velocimetry and hot-wire anemometry. The investigated roughness elements range from a sub-critical to a super-critical behavior with regard to the critical roughness Reynolds number. For the sub-critical case, the nonlinear disturbance growth in the near wake is governed by oblique Tollmien–Schlichting (TS) type modes. Further downstream, these disturbance modes are, however, damped with the mean flow stabilization and no dominant modes persist in the far wake. By contrast, in the transitional configuration the disturbance growth is increased, but still associated with a TS-type instability in the near-wake centerline region of the low-aspect (height-to-diameter) ratio element. That is, the disturbances in the centerline region show a similar behavior as known for 2D elements, whereas in the outer spanwise domain a Kelvin–Helmholtz (KH) type, shear-layer instability is found, as previously reported for larger aspect ratio isolated elements. With increasing height and, thereby, aspect ratio of the roughness, the KH-type instability domain extends toward the centerline and, accordingly, the TS-type instability domain decreases. For high super-critical cases, transition is already triggered in the wall-normal and spanwise shear layers upstream and around the roughness. In the immediate wake, periodic shear-layer disturbances roll up into a—for isolated elements characteristic—shedding of vortices, which was not present at the lower roughness Reynolds number cases due to the decreased aspect ratio and, thereby, different instability mechanism.

The three-dimensional acoustic receptivity of laminar boundary layers in presence of microscopic surface vibrations (the vibro-acoustic receptivity) is examined. The flow under investigation is the boundary layer on an airfoil at relatively high Reynolds numbers close to realistic ones for gliders. This flow has favourable and adverse pressure gradients and develops on a curved wall. The goal of the present study is to obtain quantitative information about the receptivity characteristics of this flow for excitation of the 3D Tollmien–Schlichting (TS) waves in cases when the frequencies of surface vibrations ( f v ) have the same order of magnitudes as those of the acoustic waves ( f ac ) . The experiments were performed at controlled disturbance conditions. The 2D acoustic field was produced by loudspeakers, while the localised non-stationary surface non-uniformities were simulated by a controlled circular surface vibrator. The TS-wave generation was investigated for several values of the parameter of non-stationarity of the surface non-uniformity K = f v / f ac . The receptivity was investigated in two general cases: in ‘plus-regimes’ when the TS-waves were excited at combination frequencies f TS + = f ac + f v and in ‘minus-regimes’ when the excitation occurred at frequencies f TS − = f ac − f v . The complex (amplitude and phase) receptivity coefficients are obtained experimentally as functions of the spanwise wavenumber (and the wave propagation angle) for three different frequency ratios K and also for several TS-wave frequencies at fixed values of K. The obtained vibro-acoustic receptivity coefficients are compared with the acoustic-roughness receptivity coefficients (i.e. for K = 0 ) found in previous experiments and DNS.

The paper is devoted to an experimental and numerical investigation of the problem of excitation of three-dimensional Tollmien–Schlichting (TS) waves in a boundary layer on an airfoil owing to scattering of an acoustic wave on localized microscopic surface non-uniformities. The experiments were performed at controlled disturbance conditions on a symmetric airfoil section at zero angle of attack. In each set of measurements, the acoustic wave had a fixed frequency fac, in the range of unstable TS-waves. The three-dimensional surface non-uniformity was positioned close to the neutral stability point at branch I for the two-dimensional perturbations. To avoid experimental difficulties in the distinction of the hot-wire signals measured at the same (acoustic) frequency but having a different physical nature, the surface roughness was simulated by a quasi-stationary surface non-uniformity (a vibrator) oscillating with a low frequency fv. This led to the generation of TS-wavetrains at combination frequencies f1,2=fac ∓ fv. The spatial behaviour of these wavetrains has been studied in detail for three different values of the acoustic frequency. The disturbances were decomposed into normal oblique TS-modes. The initial amplitudes and phases of these modes (i.e. at the position of the vibrator) were determined by means of an upstream extrapolation of the experimental data. The shape of the vibrator oscillations was measured by means of a laser triangulation device and mapped onto the Fourier space.

Roughness induced transition in the leading edge region of airfoils is one of the challenges in the design of highly efficient wind turbine blades especially with respect to various inflow turbulence levels. The present experimental investigation discusses, therefore, the interaction of a laminar boundary layer perturbed by a single, 2D disturbance mode with a cylindrical roughness element at medium height. High and low speed streaks in the roughness wake suggest the presence of a counter-rotating vortex pair. A significantly increased amplification of the disturbance mode downstream of the roughness in comparison to the zero roughness height case leads to the formation of 3D structures with a dominant spanwise length scale corresponding to the roughness diameter. However, these 3D structures are only very weakly distinctive far downstream.

The flow field around sharp leading edges in subsonic, low Reynolds number flow is investigated experimentally. Separation occurs already at small angles of attack. Under certain conditions reattachment takes place and a separation bubble develops. As this influences the lift and drag of an airfoil decisively, the conditions leading to reattachment and the formation of a laminar boundary layer are of special interest. The influences of the Reynolds number, angle of attack and leading edge apex angle on the boundary layer properties are studied by means of hot-wire anemometry, flow visualisation techniques and measurements of the pressure distribution over the leading edge. For a small parameter range, laminar separation followed by laminar reattachment is observed.

Aeroacoustic measurements on two NACA 0012 airfoil sections with different chord length and sharp trailing edge were conducted at the Laminar Wind Tunnel (LWT) of the University of Stuttgart. The LWT is a closed test section wind tunnel with a very low turbulence level and an acoustically optimized diffusor section allowing for high-quality aerodynamic as well as aeroacoustic measurements. Trailing edge noise measurements were performed using the Coherent Particle Velocity (CPV) method, which is based on a cross-spectral analysis of two hot-wire sensor signals placed on the suction and the pressure side of the airfoil trailing edge, respectively. At high angles of attack, the cross-spectral analysis of the two sensor signals used for the measurement of the trailing edge noise can be prone to a disturbing influence of hydrodynamic fluctuations. Hence, continuous shifts in the phasing of the cross-correlation are observed mainly for low sensor distances to the trailing edge. The quantitative evaluation of the trailing edge noise predominately in the low frequency range is, therefore, considerably disturbed. A new approach is proposed, which allows for the correction of the cross-correlation function based on the averaged single wire auto-spectrum. The results are compared to measurements with increased sensor distance and show good agreement. In the following, trailing edge noise measurements were performed on a NACA 0012 airfoil in a wide range of angles of attack (α = 0°–8°) and free-stream velocities ( $$u_{\infty} = 30{-}70\,{\hbox{m/s}}$$ ). The tripped flow cases exhibit a very good consistency for the scaling of the 1/3 octave spectra based on outer variables. Moreover, a common intersection point of the sound pressure level was observed for trailing edge noise spectra measured at constant free-stream velocity and different angles of attack. In cases without boundary layer tripping, the presence of an acoustic feedback loop was observed and linked to the presence of a laminar separation bubble on the pressure side in the vicinity of the trailing edge. Finally, a comparison of the aeroacoustic measurements based on the CPV method showed reasonably good agreement with published data obtained with both a microphone array and the Coherent Output Power method in open-test section facilities.

Discrete frequency tones in the trailing edge noise spectra of NACA 0012 airfoils are investigated with the Coherent Particle Velocity method. The Reynolds number and angle of attack range, in which these discrete frequency tones are present, are consistent with published results. The discrete tones are composed of a main tone and a set of regularly spaced side peaks resulting in a ladder-type structure for the dependency on the free stream velocity. The occurrence of this discrete frequency noise could be attributed to the presence of a laminar boundary layer on the pressure side opening up into a separation bubble near the trailing edge, which was visualized using oil flow. Wall pressure measurements close to the trailing edge revealed a strong spanwise and streamwise coherence of the flow structures inside this laminar separation bubble. The laminar vortex shedding frequencies inferred from the streamwise velocity fluctuations, which were evaluated from hot-wire measurements at the trailing edge, were seen to coincide with the discrete tone frequencies observed in the trailing edge noise spectra. Previous findings on discrete frequency tones for airfoils with laminar boundary layers up to the trailing edge hint at the existence of a global feedback loop. Hence, sound waves generated at the trailing edge feed back into the laminar boundary layer upstream by receptivity and are, then, convectively amplified downstream. The most dominant amplification of these disturbance modes is observed inside the laminar separation bubble. Therefore, the frequencies of the most pronounced tones in the trailing edge noise spectra are in the frequency range of the convectively most amplified disturbance modes. Modifying the receptivity behavior of the laminar boundary layer on the pressure side by means of very thin, two-dimensional roughness elements considerably changes the discrete tone frequencies. For roughness elements placed closer to the trailing edge, the main tone frequency was seen to decrease, while the frequency spacing in-between two successive tones increased. Based on the stability characteristics of the laminar boundary layer and the characteristics of the upstream traveling sound wave, a method for predicting the discrete tone frequencies was developed showing good agreement with the measured results. Hence, with a controlled modification of the laminar boundary layer receptivity behavior, the existence of the proposed feedback loop could be confirmed. At the same time, no significant influence of a second feedback loop previously proposed for the suction side of the NACA 0012 airfoil was observed neither by influencing the boundary layer with a receptivity–roughness element nor by tripping the boundary layer at the leading edge.

The work is devoted to the study of weakly non-linear interactions of Tollmien-Schlichting waves in an incompressible 2D airfoil boundary layer. Selected resonant regimes are investigated with emphasis to the regimes where more than one fundamental T-S wave is present in the flow. The results show that amplification rates of the effective sub-harmonic modes are not affected by modulations in time of the fundamental wave. In addition, modulations of the fundamental wave tend to generate additional modes at the modulation frequency via nonlinear wave interaction. These low frequency modes can act as self generated seeds for subharmonic resonance. The nature of these modes and their downstream evolution is investigated in detail. The observations are in agreement with results obtained for much more complicated case of wave bands. The observed mechanism seems to be a possible route for transition in the case of Natural Laminar Flow airfoils under ‘natural’ environment disturbance conditions.

The flow field around sharp leading edges in subsonic, low Reynolds number flow is investigated experimentally. Separation occurs already at small angles of attack. Under certain conditions reattachment takes place and a separation bubble develops. As this influences the lift and drag of an airfoil decisively, the conditions leading to reattachment and the formation of a laminar boundary layer are of special interest. The influences of the Reynolds number, angle of attack and leading edge apex angle on the boundary layer properties are studied by means of hot-wire anemometry, flow visualisation techniques and measurements of the pressure distribution over the leading edge. For a small parameter range, laminar separation followed by laminar reattachment is observed.

Most studies of TS wave evolution consider a perfectly smooth surface, whereas studies of roughness induced transition consider a perfectly quiet flow. It appears that a combination of these scenarios could better represent a practical situation. This work investigates the effect of a small and medium sized $$ (h/\partial^* < 0.2) $$ roughness on the evolution of a pre-existing T-S wave. A cylindrical element was used as a localized roughness. Several roughness heights were tested experimentally under different sets of flow parameters. The results indicated that under various circumstances the fundamental resonance was the dominant mechanism in the wake of the roughness. A physical model for the prediction of the effect the roughness on a non quiet environement was then proposed and verified.

The present paper is devoted to the detailed experimental study of weakly nonli- near resonant interactions of Tollmien-Schlichting waves in a specially designed 2D non self-similar boundary layer on an airfoil. The influence of the funda- mental frequency on the efficiency of the tuned subharmonic resonance is in- vestigated as well as the influence of frequency and spanwise wavenumber de- tunings. The results are compared with Direct Numerical Simulations based on a vorticity-velocity formulation of the complete Navier-Stokes equations. Good overall agreement is achieved.

In the present paper, the linear 3D acoustic-roughness receptivity of the 2D boundary layer of an airfoil is investigated systematically with respect to main influence parameters by means of wind tunnel experiments and Direct Numerical Simulations (DNS). A plane acoustic wave with frequency f ac scatters at a specially designed localized roughness element, that is capable to vibrate with frequency f v . The resulting Tollmien-Schlichting (TS) waves appear at combination frequencies (f 1,2 = f ac ∓ f v ) and develop as a wave train downstream of the surface roughness. The complex receptivity function is evaluated by normalization of the initial TS-spectra with the related amplitudes and phases of the surface vibrator and the acoustics. The main influence parameters investigated are the frequency (of the acoustic and the TS wave), the pressure gradient (given by the streamwise position of the surface roughness) and the influence of surface vibrations on the acoustic receptivity. Additionaly pure vibrational receptivity is studied. The main goal of this investigation is to study and compare systematically different types of receptivity in the same base flow developing on an airfoil at a Reynolds number typical for glider applications.

In the present paper, the linear local vortex-roughness receptivity of the 2D boundary layer of an airfoil is investigated. The vortex is modeled by the convected wake of a vibrating wire that is oriented perpendicular to the free stream speed vector and parallel to the airfoil surface. Hot-wire measurements were taken down­stream of local 2D and 3D roughness elements, phase-locked with the wire vibra­tions to study the Tollmien-Schlichting (TS) waves developing inside the boundary layer. Experiments with a circular 3D roughness element were performed in order to evaluate the complex 3D vortex-roughness receptivity function. The wave train developing downstream of the roughness was measured in spanwise scans at a con­stant wall distance. After Fourier decomposition of these scans the development of single wave numbers were compared to linear stability theory which then was used to find the initial Tollmien-Schlichting amplitudes at the position of the roughness. The receptivity function was found by normalizing them to the vortex amplitude measured at the boundary layer edge and the roughness height. The 3D roughness shape was Fourier decomposed so that the results are independent from the actual physical shape.

In the present paper, the influence of a pressure gradient on the acoustic roughness receptivity is investigated by means of wind tunnel experiments and Direct Numerical Simulations (DNS). The receptivity function for three different locations of a 3-D surface non-uniformity on an airfoil is calculated from the experimental and numerical data and compared to each other. The combined effects of the roughness acoustic receptivity and the amplification of the generated disturbances are taken into account in order to evaluate the position on the airfoil at which a surface non-uniformity is most dangerous in provoking an early transition.

Hot-wire measurements are perfomed on linear 3D acoustic receptivity in a two-dimensional laminar boundary layer. A localized quasi steady surface roughness serves as the receptivity element. A plane acoustic wave with frequency f ac scatters at this vibrating source and the generated TS-wave train is measured downstream in spanwise cuts and at combination frequencies (f 1,2 = f ac ∓ f v ). After Fourier decomposition linear stabiltity theory is used for upstream extrapolation to the initial amplitudes at the roughness element. The dispersion characteristic is determined and the complex receptivity function is calculated by normalization of the initial TS-spectra with the related amplitudes and phases of the surface vibrator and the acoustics. The results are compared with Direct Numerical Simulations based on a vorticity-velocity formulation of the complete Navier-Stokes equations and a new embeded wall model. Good overall agreement is achieved.

Hot-wire measurements were performed under controlled conditions in the Laminar Wind Tunnel on an airfoil with pressure gradient. A quantitatively known acoustic field was established in the test section. The receptivity of the 2-dimensional laminar boundary layer in the presence of a localized 3D surface roughness was studied. The development of the generated Tollmien-Schlichting-waves was measured at different streamwise stations as cuts in spanwise direction. The quasi steady 3D roughness was modeled by a vibrating source driven at a frequency two orders below the acoustic one. The amplitude of the TS-waves was measured at combination frequencies. Fourier decomposition in time and space leads to wave number spectra which can be compared to linear stability theory. The receptivity function was evaluated by upstream extrapolation to the initial distributions at the source position.

Hot-wire measurements of transitional boundary layer quantities were performed in the Laminar Windtunnel of the IAG under „natural“ conditions on a 2-d airfoil section at a Reynolds number of Re=1.2*106. The measured amplification of Tollmien-Schlichting waves is compared to linear stability theory. A careful experimental setup allows the measurement of very small velocity fluctuations resulting in a large measurable amplitude ratio of Amax/Amin≅1800. The determined „onset“ of transition is compared to the transition prediction with en-methods. Some remarks are made on the accuracy of simplified envelope-methods.

Transition prediction in two-dimensional laminar boundary layers developing on airfoil sections at subsonic speeds and very low turbulence levels is still a challenge. The commonly used semi-empirical prediction tools are mainly based on linear stability theory and do not account for nonlinear effects present unavoidably starting with certain stages of transition. One reason is the lack of systematic investigations of the weakly nonlinear stages of transition, especially of the strongest interactions of the instability modes predominant in non-self-similar boundary layers. The present paper is devoted to the detailed experimental, numerical, and theoretical study of weakly nonlinear subharmonic resonances of Tollmien-Schlichting waves in an airfoil boundary layer, representing main candidates for the strongest mechanism of these initial nonlinear stages. The experimental approach is based on phase-locked hot-wire measurements under controlled disturbance conditions using a new disturbance source being capable to produce well-defined, complex wave compositions in a wide range of streamwise and spanwise wave numbers. The tests were performed in a low-turbulence wind tunnel at a chord Reynolds number of Re = 0.7 × 106. Direct numerical simulations (DNS) were utilized to provide a detailed comparison for the test cases. The results of weakly nonlinear theory (WNT) enabled a profound understanding of the underlying physical mechanisms observed in the experiments and DNS. The data obtained in experiment, DNS and WNT agree basically and provide a high degree of reliability of the results. Interactions occurring between components of various initial frequency-wavenumber spectra of instability waves are investigated by systematic variation of parameters. It is shown that frequency-detuned and spanwise-wavenumber-detuned subharmonic-type resonant interactions have an extremely large spectral width. Similar to results obtained for self-similar base flows it is found that the amplification factors in the frequency-detuned resonances can be even higher than in tuned cases, in spite of the strong base-flow non-self-similarity. An explanation of this unusual phenomenon is found based on the theoretical analysis and comparison of experimental, theoretical, and DNS data.

An extensive assessment and step by step validation of turbulent boundary-layer trailing-edge interaction (TBL-TE) prediction was conducted based on the boundary layer properties calculated by three different aerodynamics methods, XFOIL, Wilcox EDDYBL and the RANS solver FLOWer. For this purpose detailed measurements of turbulent boundary-layer properties like two-point turbulent velocity correlations, the spectrum of the associated wall pressure fluctuations (WPFs) and the emitted trailing-edge noise have been performed in the Laminar Wind Tunnel (LWT). The measurements were performed for the NACA 0012 airfoil. Most of the investigated cases show that the numerical WPF and far-field radiated noise models capture the measured peak amplitude level as well as the peak position remarkably well, if the turbulence noise source parameters are estimated properly including turbulence anisotropy effects.

Laminar separation bubbles play an important role in the flow about airfoils at Reynolds numbers below 3 millions in incompressible flows. Drag as well as stall behaviour can be deteriorated considerably. Designing or analysing airfoils in this flight regime, with some success, requires understanding of the flow phenomena envolved in the formation of these regions with locally separated flow. Detailed experimental studies were carried out on laminar separation bubbles that formed near the midchord of different airfoils at Reynolds numbers from 0.7 to 3 millions. Static pressure, hot wire anemometry, and flow visualisation data were acquired. The data were used to evaluate the applicability of existing separation bubble models. Some details of the materials gathered are presented in the following context.

Weakly non-linear interactions of Tollmien-Schlichting (T-S) waves are investigated experimentally for an incompressible 2D boundary layer. The number of waves introduced in the boundary layer is varied, covering regimes composed of few waves or bands of T-S waves (frequency and wavenumber). The experiments are carried out on the pressure side of an airfoil designed to achieve a long region of laminar flow. The results show that modulations of fundamental wave tend to generate disturbances in a range of low frequencies, via nonlinear wave interaction, which can act as self-generated seeds for subharmonic resonance. This sequence of weakly non-linear events were recently described 2 for regimes composed of few waves. The results shown here, for wave bands, are in qualitative agreement with previous findings. The mechanism seems to be a possible route for transition in the case of Natural Laminar Flow airfoils under ‘natural’ environment disturbance conditions.