| 1. |
- Schrader, Lars-Uve, et al.
(författare)
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Excitation of cross-ow vortices by surface roughness on a sweptwing
- 2011
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Konferensbidrag (refereegranskat)abstract
- We have carried out direct numerical simulations (DNS) of the flow over a wing with 45° sweep and -4° angle-of-attack. On the upper wing side, a substantial cross flow creates ideal conditions for the study of cross-flow instability. Our simulation models a wind-tunnel experiment carried out at the Arizona State University (ASU), where 6μm high roughness cylinders were used to excite steady cross-flow vortices. We have successfully reproduced the linear growth rate of these vortices, whereas the receptivity amplitude obtained from our DNS is 40% of that measured in the experiment. Possible reasons for this discrepancy have been investigated by refining the roughness model of the DNS on the one hand, and, on the other hand, by carefully comparing the results from the DNS and the experiment with solutions to the parabolized stability equations (PSE). Good agreement between all approaches could be obtained when assuming a roughness height of 15μm. This suggests that the roughness cylinders in the experiment might have been slightly higher than 6μm, or that natural roughness might have contributed to the receptivity. Moreover, small differences in the pressure distribution or the presence of weak free-stream fluctuations in the wind tunnel may explain the larger modal amplitude measured in the ASU experiment.
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| 2. |
- Schrader, Lars-Uve, et al.
(författare)
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Flow past a plate with elliptic leading edge : layer response to free-stream vorticity
- 2010
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Ingår i: SEVENTH IUTAM SYMPOSIUM ON LAMINAR-TURBULENT TRANSITION. - Dordrecht : Springer Netherlands. - 9789048137220 ; , s. 565-568
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Konferensbidrag (refereegranskat)abstract
- We show the response of the boundary-layer flow past a wing to free-stream disturbances with axial, vertical and spanwise vorticity and explain the associated receptivity mechanisms. A flat plate with elliptic leading edge serves as wing model. and the vortical free-stream disturbances are modeled by space and time periodic Fourier modes. The results are extracted from solutions to the incompressible Navier-Stokes equations computed with the Spectral Element Method.
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| 3. |
- Schrader, Lars-Uve
(författare)
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Nonlinear receptivity of leading-edge ow to oblique free-stream vortical modes
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Boundary-layer receptivity to pairs of unsteady oblique free-stream vortical modes is studied for flat-plate flow using direct numerical simulation (DNS). This kind of forcing gives rise to steady boundary-layer streaks and the associated receptivity mechanism is nonlinear in the forcing amplitude. The flat plates considered feature elliptic leading edges with two different aspect ratios, allowing for the study of leading-edge bluntness effects on the receptivity. The free stream is perturbed by three types of unsteady oblique Fourier modes upstream of the leading edge. These modes differ in the magnitude of the three vorticity components. It is found that the bluntness of the leading edge hardly affects the streak amplitudes obtained. This observation also holds for oblique waves with vertical vorticity alone and is in contrast to the linear receptivity to this kind of modes, which is known to depend strongly on the leading-edge shape. While being irrelevant at low frequencies the nonlinear receptivity mechanism becomes important for high-frequency free-stream vortices to which the boundary layer is linearly non-receptive. Although the linear receptivity mechanism for zero- or low-frequency forcing is more efficient in producing disturbance streaks than the nonlinear receptivity to high-frequency disturbances, the nonlinear mechanism is expected to contribute significantly to the boundary-layer receptivity to free-stream turbulence.
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| 4. |
- Schrader, Lars-Uve, et al.
(författare)
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Numerical study of boundary-layer receptivity on a swept wing
- 2010
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Direct numerical simulations (DNS) of the flow over a wing with 45◦ sweep and −4◦ angle-of-attack are presented. This flow configuration was investigated in a series of wind-tunnel experiments at the Arizona State University (ASU). On the upper wing side, the flow develops a substantial crossflow and is therefore ideally suited for a study of the receptivity mechanisms of crossflow vortices. Here, we examine the boundary-layer receptivity to surface roughness and to single vortical free-stream modes. The roughness is modeled by a shallow circular disk and is identical with one single element of the spanwise roughness array considered in the ASU experiments. The boundary layer develops a steady crossflow mode downstream of the roughness. The spatial evolution of the modal amplitude obtained by the DNS is in excellent agreement with a solution to the nonlinear parabolized stability equations (NPSE) while being lower than that measured in the experiments. The reasons for this discrepancy are yet to be determined. Possible explanations are the idealization of the roughness array by spanwise periodic boundary conditions in our simulations, or the presence of traveling crossflow waves due to background free-stream turbulence in the experiments. We demonstrate that the boundary-layer receptivity to roughness can be successfully predicted by a nonlocal, adjoint-based receptivity model. Stationary crossflow vortices can also be triggered by zero-frequency free-stream vortical modes. We consider two types of mode, carrying stream wise and chordwise vorticity. Both modes give rise to nonmodal disturbances near the leading edge, which soon evolve into a steady crossflow mode. The boundary layer is found to be somewhat more receptive to the streamwisevorticity mode than to the chordwise vorticity.
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| 5. |
- Schrader, Lars-Uve, et al.
(författare)
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Receptivity, instability and breakdown of Görtler flow
- 2011
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Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 682, s. 362-396
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Tidskriftsartikel (refereegranskat)abstract
- Receptivity, disturbance growth and breakdown to turbulence in Gortler 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 Gortler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Gortler vortices than localized roughness. The boundary layer is most receptive to zero- and low-frequency free-stream vortices, exciting steady and slowly travelling Gortler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Gortler 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 Gortler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Gortler 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 Gortler modes.
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| 6. |
- Schrader, Lars-Uve, et al.
(författare)
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Receptivity mechanisms in three-dimensional boundary-layer flows
- 2009
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Ingår i: Journal of Fluid Mechanics. - 0022-1120 .- 1469-7645. ; 618, s. 209-241
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Tidskriftsartikel (refereegranskat)abstract
- 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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| 7. |
- Schrader, Lars-Uve, 1978-
(författare)
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Receptivity of Boundary-Layer Flows over Flat and Curved Walls
- 2010
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Direct numerical simulations of the receptivity and instability of boundary layers on flat and curved surfaces are herein reported. Various flow models are considered with the aim to capture aspects of flows over straight and swept wings such as wall curvature, pressure variations, leading-edge effects, streamline curvature and crossflow. The first model problem presented, the flow over a swept flat plate, features a crossflow inside the boundary layer. The layer is unstable to steady and traveling crossflow vortices which are nearly aligned with the free stream. Wall roughness and free-stream vortical modes efficiently excite these crossflow modes, and the associated receptivity mechanisms are linear in an environment of low-amplitude perturbations. Receptivity coefficients for roughness elements with various length scales and for free-stream vortical modes with different wavenumbers and frequencies are reported. Key to the receptivity to free-stream vorticity is the upstream excitation of streamwise streaks evolving into crossflow modes. This mechanism is also active in the presence of free-stream turbulence. The second flow model is that of a Görtler boundary layer. This flow type forms on surfaces with concave curvature, e.g. the lower side of a turbine blade. The dominant instability, driven by a vertically varying centrifugal force, appears as pairs of steady, streamwise counter-rotating vortical rolls and streamwise streaks. The Görtler boundary layer is in particular receptive to free-stream vortical modes with zero and low frequencies. The associated mechanism builds on the excitation of upstream disturbance streaks from which the Görtler modes emerge, similar to the mechanism in swept-plate flows. The receptivity to free-stream vorticity can both be linear and nonlinear. In the presence of free-stream turbulence, nonlinear receptivity is more likely to trigger steady Görtler vortices than linear receptivity unless the frequencies of the free-stream fluctuations are very low. The third set of simulations considers the boundary layer on a flat plate with an elliptic leading edge. This study aims to identify the effect of the leading edge on the boundary-layer receptivity to impinging free-stream vortical modes. Three types of modes with streamwise, vertical and spanwise vorticity are considered. The two former types trigger streamwise disturbance streaks while the latter type excites Tollmien-Schlichting wave packets in the shear layer. Simulations with two leading edges of different bluntness demonstrate that the leading-edge shape hardly influences the receptivity to streamwise vortices, whereas it significantly enhances the receptivity to vertical and spanwise vortices. It is shown that the receptivity mechanism to vertical free-stream vorticity involves vortex stretching and tilting - physical processes which are clearly enhanced by blunt leading edges. The last flow configuration studied models an infinite wing at 45 degrees sweep. This model is the least idealized with respect to applications in aerospace engineering. The set-up mimics the wind-tunnel experiments carried out by Saric and coworkers at the Arizona State University in the 1990s. The numerical method is verified by simulating the excitation of steady crossflow vortices through micron-sized roughness as realized in the experiments. Moreover, the receptivity to free-stream vortical disturbances is investigated and it is shown that the boundary layer is most receptive, if the free-stream modes are closely aligned with the most unstable crossflow mode
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| 8. |
- Schrader, Lars-Uve, 1978-
(författare)
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Receptivity of Boundary Layers under Pressure Gradient
- 2008
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Boundary-layer flow over bodies such as aircraft wings or turbine blades is characterized by a pressure gradient due to the curved surface of the body. The boundary layer may experience modal and non-modal instability, and the type of dominant instability depends on whether the body is swept with respect to the oncoming flow or not. The growth of these disturbances causes transition of the boundary-layer flow to turbulence. Provided that they are convective in nature, the instabilities will only arise and persist if the boundary layer is continuously exposed to a perturbation environment. This may for example consist of turbulent fluctuations or sound waves in the free stream or of non-uniformities on the surface of the body. In engineering, it is of relevance to understand how susceptive to such perturbations the boundary layer is, and this issue is subject of receptivity analysis. In this thesis, receptivity of simplified prototypes for flow past a wing is studied. In particular, the three-dimensional swept-plate boundary layer and the boundary layer forming on a flat plate with elliptic leading edge are considered. The response of the boundary layer to vortical free-stream disturbances and surface roughness is analyzed, receptivity mechanisms are identified and their efficiency is quantified.
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| 9. |
- Schrader, Lars-Uve, et al.
(författare)
-
Receptivity to free-stream vorticity of flow past a flat plate with elliptic leading edge
- 2010
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Ingår i: Journal of Fluid Mechanics. - 0022-1120 .- 1469-7645. ; 653, s. 245-271
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Tidskriftsartikel (refereegranskat)abstract
- Receptivity of the two-dimensional boundary layer on a flat plate with elliptic leading edge is studied by numerical simulation. Vortical perturbations in the oncoming free stream are considered, impinging on two leading edges with different aspect ratio to identify the effect of bluntness. The relevance of the three vorticity components of natural free-stream turbulence is illuminated by considering axial, vertical and spanwise vorticity separately at different angular frequencies. The boundary layer is most receptive to zero-frequency axial vorticity, triggering a streaky pattern of alternating positive and negative streamwise disturbance velocity. This is in line with earlier numerical studies on non-modal growth of elongated structures in the Blasius boundary layer. We find that the effect of leading-edge bluntness is insignificant for axial free-stream vortices alone. On the other hand, vertical free-stream vorticity is also able to excite non-modal instability in particular at zero and low frequencies. This mechanism relies on the generation of streamwise vorticity through stretching and tilting of the vertical vortex columns at the leading edge and is significantly stronger when the leading edge is blunt. It can thus be concluded that the non-modal boundary-layer response to a free-stream turbulence field with three-dimensional vorticity is enhanced in the presence of a blunt leading edge. At high frequencies of the disturbances the boundary layer becomes receptive to spanwise free-stream vorticity, triggering Tollmien-Schlichting (T-S) modes and receptivity increases with leading-edge bluntness. The receptivity coefficients to free-stream vortices are found to be about 15% of those to sound waves reported in the literature. For the boundary layers and free-stream perturbations considered, the amplitude of the T-S waves remains small compared with the low-frequency streak amplitudes.
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| 10. |
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