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On the controllability of saturating crossflow vortices

Backer Dirks, T. (2018). On the controllability of saturating crossflow vortices. (Unpublished Doctoral thesis, City, University of London)


This thesis examines the suitability of the crossflow generated by rotating boundary layers for investigating crossflow amplification control thresholds at scales suitable for university wind tunnels. Using rotating disk flow as a starting point, it was postulated that the addition of a concentric annulus, rotating at a different angular velocity to the inner disk, would allow controlled changes in crossflow growth just prior to non-linear saturation. A novel formulation for the boundary layer a rotating disk with radially variable angular velocity was derived for application on the disk-annulus system, though ultimately it was determined that the resultant equations were elliptical in character and therefore no longer representative of the physics of the swept-wing boundary layer.

In order to ensure parabolicity, a configuration involving a rotating body in an axial flow was proposed. It was speculated that local variations in edge velocity, induced by the body geometry, would provide an appropriate analogue to the variable pressure gradients found in the vicinity of swept-wing leading edge. A novel formulation for the boundary layer equations for a generalised rotating body of revolution, both with and without an incompressible axial flow, was subsequently derived, implemented within the QinetiQ BL2D boundary layer method and validated against other shape-specific formulations. The formulation employs a velocity switch, u*, which allows for a seamless transition between quiescent and axial flow investigations and provides a valuable alternative to other shape and flow specific formulations.

The perturbation and stability equations in a general orthogonal curvilinear coordinate system were derived to include Coriolis accelerations terms, as well as retaining viscous curvature. The existing QinetiQ e^N method, CoDS, was modified and extended to enable the analysis of rotating boundary layers and provided qualitatively good agreement with results published by Garrett (2002), with quantitative differences attributed mainly to scaling.

The methods were combined in order to answer the original research question, whether the boundary layer due to a rotating body could be used as a viable analogue for swept-wing flow in the context of crossflow growth control. Velocity profiles for rotating axi-symmetric bodies were shown to provide a good match to those of swept-wing flow, with differences only in the second wall-normal derivatives. Results showed that geometries could be selected which demonstrated non-monotonic N-factor growth, of the type encountered during HYLTEC and AFLoNext. An axi-symmetric body derived from the upper surface of the RAE2822 demonstrated N-factor amplification followed by sudden stabilisation.

Publication Type: Thesis (Doctoral)
Subjects: T Technology > TL Motor vehicles. Aeronautics. Astronautics
Departments: Doctoral Theses
School of Science & Technology > School of Science & Technology Doctoral Theses
School of Science & Technology
School of Science & Technology > Engineering > Mechanical Engineering & Aeronautics
Text - Accepted Version
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