Instability of the attachment line boundary layer in a supersonic swept flow

Theoretical analysis of attachment-line instabilities is performed for supersonic swept flows using the compressible Hiemenz approximation for the mean flow and the successive approximation procedures for disturbances. The theoretical model captures the dominant attachment-line modes in wide ranges of the sweep Mach number ${M_e}$ and the wall temperature ratio. It is shown that these modes behave similar to the first and second Mack modes in the boundary layer flow. This similarity allows us to extrapolate the knowledge gained for Mack modes to the attachment-line instabilities. In particular, we find that at sufficiently large ${M_e}$ , the dominant attachment-line instability is associated with the synchronisation of slow and fast modes of acoustic nature. Point-by-point comparisons of the theoretical predictions with the experiments of Gaillard et al. (Exp. Fluids, vol. 26, 1999, pp. 169–176) demonstrate that at ${M_e} > 4$ , the theory captures a significant drop of the transition onset Reynolds number, which is below the contamination criterion of Poll $({R_\mathrm{\ast }} = 250)$ at ${M_e} > 6$ . This contradicts the generally accepted assumption that the attachment-line flow is stable for ${R_\mathrm{\ast }} \le 250$ . The theoretical critical Reynolds numbers lie well below the experimental transition-onset Reynolds numbers. Stability computations using the Navier–Stokes mean flow and accounting for the leading-edge curvature effect do not eliminate this discrepancy. Most likely, in the experiments of Gaillard et al., we face with an unknown effect that does not fit to the concept of transition arising from linear instability.

Structures of Skin Friction, Surface Pressure, and Boundary Enstrophy Flux in Attachment-Line Flow

The on-wall structures in an attachment-line flow are discussed based on an exact solution of the Navier–Stokes (NS) equations, focusing on distinct features of skin friction, surface pressure, and boundary enstrophy flux (BEF) and intrinsic connections between them.

Measurement and modelling of the turbulent boundary layer near the attachment line of a swept wing

ABSTRACTThis work is motivated by the need for low-order aerodynamic models to predict accurately the effect on profile drag of controlling attachment line transition. Head's entrainment method(1), a rapid integral boundary layer technique used for design studies on swept wings, suffers from the governing swept-tapered turbulent integral boundary layer equations being ill-posed in the vicinity of the attachment line. This singularity has been treated using crude extrapolations of the attachment-line similarity solution for over half a century, but this approach is unlikely to deliver accurate predictions of the effect of changes in the attachment line flow on profile drag. An experimental study has been carried out to explore the nature of the turbulent flow in the vicinity of a highly swept swept attachment line and has revealed a quite complex, non-monotonic development of the momentum thickness in this region. It has also revealed lower levels of twist in the boundary layer velocity profiles than anticipated from the highly curved character of the inviscid flow streamlines. These observations have prompted an alternative approach to the modelling of the flow in this region which not only successfully eliminates the lack of robustness in the swept-tapered equations but which also matches the experimental results to within ±5%.

Linear modal instabilities of hypersonic flow over an elliptic cone

Steady laminar flow over a rounded-tip $2\,:\,1$ elliptic cone of 0.86 m length at zero angle of attack and yaw has been computed at Mach number $7.45$ and unit Reynolds number $Re^{\prime }=1.015\times 10^{7}~\text{m}^{-1}$. The flow conditions are selected to match the planned flight of the Hypersonic Flight Research Experimentation HIFiRE-5 test geometry at an altitude of 21.8 km. Spatial linear BiGlobal modal instability analysis of this flow has been performed at selected streamwise locations on planes normal to the cone symmetry axis, resolving the entire flow domain in a coupled manner while exploiting flow symmetries. Four amplified classes of linear eigenmodes have been unravelled. The shear layer formed near the cone minor-axis centreline gives rise to amplified symmetric and antisymmetric centreline instability modes, classified as shear-layer instabilities. At the attachment line formed along the major axis of the cone, both symmetric and antisymmetric instabilities are also discovered and identified as boundary-layer second Mack modes. In both cases of centreline and attachment-line modes, symmetric instabilities are found to be more unstable than their antisymmetric counterparts. Furthermore, spatial BiGlobal analysis is used for the first time to resolve oblique second modes and cross-flow instabilities in the boundary layer between the major- and minor-axis meridians. Contrary to predictions for the incompressible regime for swept infinite wing flow, the cross-flow instabilities are not found to be linked to the attachment-line instabilities. In fact, cross-flow modes peak along most of the surface of the cone, but vanish towards the attachment line. On the other hand, the leading oblique second modes peak near the leading edge and their associated frequencies are in the range of the attachment-line instability frequencies. Consequently, the attachment-line instabilities are observed to be related to oblique second modes at the major-axis meridian. The linear amplification of centreline and attachment-line instability modes is found to be strong enough to lead to laminar–turbulent flow transition within the length of the test object. The predictions of global linear theory are compared with those of local instability analysis, also performed here under the assumption of locally parallel flow, where use of this assumption is permissible. Fair agreement is obtained for symmetric centreline and symmetric attachment-line modes, while for all other classes of linear disturbances use of the proposed global analysis methodology is warranted for accurate linear instability predictions.

Experimental Study Of Effects Of Couple Weak Waves On Laminar-Turbulent Transition On Attachment Line Of Swept Cylinder

Experimental data of investigation of the influence of outer couple weak shock waves on the laminar-turbulent transition on attachment line of swept cylinder in supersonic flow are presented. The couple of waves were generated by a two-dimensional roughness on the wall of the test section of supersonic tunnel. It was found that the laminar-turbulent transition on the attachment line of sliding cylinder followed by abrupt perturbation growth. In case of the great distance between falling of the waves on attachment line and the point of measurement the impact on transition was not observed. In case of the short distance between falling of the waves on attachment line and the point of measurement the laminar-turbulent transition was observed at lower unit Reynolds numbers