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.

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.

The receptivity of a swept-wing boundary layer to localised surface roughness is studied by means of direct numerical simulations (DNS). The flow case considered is meant to model wind tunnel experiments performed at the Arizona State University by Saric & coworkers. The receptivity amplitude of the crossflow disturbances predicted by the DNS is 40% of that measured in the experiments. The DNS results are then used to evaluate the performance of different receptivity models based on either the parabolised stability equations or the finite Reynolds number theory (FRNT). In general it is found that receptivity amplitudes are well predicted for micron sized roughness elements if non-parallel effects are accounted for. 

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). 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 presence of traveling crossflow waves due to background free-stream turbulence in the experiments or the slight difference between the numerical and experimental pressure gradients at the roughness site. Stationary crossflow vortices can also be triggered by zero-frequency free-stream vortical modes. We consider two types of mode, carrying streamwise and vertical 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 streamwise-vorticity mode than to the chordwise vorticity. Copyright

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.

The receptivity to localised surface roughness of a swept-wing boundary layer is studied by direct numerical simulation (DNS) and computations using the parabolised stability equations (PSE). The DNS is laid out to reproduce wind tunnel experiments performed by Saric & 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 PSE 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 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.

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.

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.

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.

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.