4 results
Swept wing boundary-layer receptivity to localized surface roughness
- David Tempelmann, Lars-Uve Schrader, Ardeshir Hanifi, Luca Brandt, Dan S. Henningson
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- Journal:
- Journal of Fluid Mechanics / Volume 711 / 25 November 2012
- Published online by Cambridge University Press:
- 20 September 2012, pp. 516-544
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The receptivity to localized surface roughness of a swept-wing boundary layer is studied by direct numerical simulation (DNS) and computations using the parabolized stability equations (PSEs). The DNS is laid out to reproduce wind tunnel experiments performed by Saric and coworkers, where micron-sized cylinders were used to trigger steady crossflow modes. The amplitudes of the roughness-induced fundamental crossflow wave and its superharmonics obtained from nonlinear PSE solutions agree excellently with the DNS results. A receptivity model using the direct and adjoint PSEs is shown to provide reliable predictions of the receptivity to roughness cylinders of different heights and chordwise locations. Being robust and computationally efficient, the model is well suited as a predictive tool of receptivity in flows of practical interest. The crossflow mode amplitudes obtained based on both DNS and PSE methods are 40 % of those measured in the experiments. Additional comparisons between experimental and PSE data for various disturbance wavelengths reveal that the measured disturbance amplitudes are consistently larger than those predicted by the PSE-based receptivity model by a nearly constant factor. Supplementary DNS and PSE computations suggest that possible natural leading-edge roughness and free-stream turbulence in the experiments are unlikely to account for this discrepancy. It is more likely that experimental uncertainties in the streamwise location of the roughness array and cylinder height are responsible for the additional receptivity observed in the experiments.
Receptivity, instability and breakdown of Görtler flow
- LARS-UVE SCHRADER, LUCA BRANDT, TAMER A. ZAKI
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- Journal:
- Journal of Fluid Mechanics / Volume 682 / 10 September 2011
- Published online by Cambridge University Press:
- 11 July 2011, pp. 362-396
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Receptivity, disturbance growth and breakdown to turbulence in Görtler flow are studied by spatial direct numerical simulation (DNS). The boundary layer is exposed to free-stream vortical modes and localized wall roughness. We propose a normalization of the roughness-induced receptivity coefficient by the square root of the Görtler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Görtler vortices than localized roughness. The boundary layer is most receptive to zero- and low-frequency free-stream vortices, exciting steady and slowly travelling Görtler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Görtler vortices. This connection between transient and exponential amplification is absent on flat plates and promotes transition to turbulence on curved walls. We demonstrate that the Görtler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Görtler rolls via a nonlinear receptivity mechanism. In addition to the receptivity study, we have carried out DNS of boundary-layer transition due to broadband free-stream turbulence with different intensities and frequency spectra. It is found that nonlinear receptivity dominates over the linear mechanism unless the free-stream fluctuations are concentrated in the low-frequency range. In the latter case, transition is accelerated due to the presence of travelling Görtler modes.
Transition to turbulence in the boundary layer over a smooth and rough swept plate exposed to free-stream turbulence
- LARS-UVE SCHRADER, SUBIR AMIN, LUCA BRANDT
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- Journal:
- Journal of Fluid Mechanics / Volume 646 / 10 March 2010
- Published online by Cambridge University Press:
- 08 March 2010, pp. 297-325
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Receptivity, disturbance growth and transition to turbulence of the three-dimensional boundary layer developing on a swept flat plate are studied by means of numerical simulations. The flow is subject to a favourable pressure gradient and represents a model for swept-wing flow downstream of the leading edge and upstream of the pressure minimum of the wing. The boundary layer is perturbed by free-stream turbulence and localized surface roughness with random distribution in the spanwise direction. The intensity of the turbulent free-stream fluctuations ranges from conditions typical for free flight to higher levels usually encountered in turbo-machinery applications. The free-stream turbulence initially excites non-modal streak-like disturbances as in two-dimensional boundary layers, soon evolving into modal instabilities in the form of unsteady crossflow modes. The crossflow modes grow faster than the streaks and dominate the downstream disturbance environment in the layer. The results show that the receptivity mechanism is linear for the disturbance amplitudes under consideration, while the subsequent growth of the primary disturbances rapidly becomes affected by nonlinear saturation in particular for free-stream fluctuations with high intensity. Transition to turbulence occurs in the form of localized turbulent spots randomly appearing in the flow. The main features of the breakdown are presented for the case of travelling crossflow vortices induced by free-stream turbulence. The flow is also receptive to localized roughness strips, exciting stationary crossflow modes. The mode with most efficient receptivity dominates the downstream disturbance environment. When both free-stream fluctuations and wall roughness act on the boundary layer at the same time, transition is dominated by steady crossflow waves unless the incoming turbulence intensity is larger than about 0.5% for roughness amplitudes of about one tenth of the boundary-layer displacement thickness. The results show that a correct prediction of the disturbance behaviour can be obtained considering the receptivity and evolution of individual modes. In addition, we provide an estimate for the amplitudes of the external disturbance sources above which a fully nonlinear receptivity analysis is necessary.
Receptivity mechanisms in three-dimensional boundary-layer flows
- LARS-UVE SCHRADER, LUCA BRANDT, DAN S. HENNINGSON
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- Journal:
- Journal of Fluid Mechanics / Volume 618 / 10 January 2009
- Published online by Cambridge University Press:
- 10 January 2009, pp. 209-241
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Receptivity in three-dimensional boundary-layer flow to localized surface roughness and free-stream vorticity is studied. A boundary layer of Falkner–Skan–Cooke type with favourable pressure gradient is considered to model the flow slightly downstream of a swept-wing leading edge. In this region, stationary and travelling crossflow instability dominates over other instability types. Three scenarios are investigated: the presence of low-amplitude chordwise localized, spanwise periodic roughness elements on the plate, the impingement of a weak vortical free-stream mode on the boundary layer and the combination of both disturbance sources. Three receptivity mechanisms are identified: steady receptivity to roughness, unsteady receptivity to free-stream vorticity and unsteady receptivity to vortical modes scattered at the roughness. Both roughness and vortical modes provide efficient direct receptivity mechanisms for stationary and travelling crossflow instabilities. We find that stationary crossflow modes dominate for free-stream turbulence below a level of about 0.5%, whereas higher turbulence levels will promote the unsteady receptivity mechanism. Under the assumption of small amplitudes of the roughness and the free-stream disturbance, the unsteady receptivity process due to scattering of free-stream vorticity at the roughness has been found to give small initial disturbance amplitudes in comparison to the direct mechanism for free-stream modes. However, in many environments free-stream vorticity and roughness may excite interacting unstable stationary and travelling crossflow waves. This nonlinear process may rapidly lead to large disturbance amplitudes and promote transition to turbulence.
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