PhD Studentship ‘Multiple-Scales and Adjoint Analysis of Boundary Layer Instability’

Industrial CASE co-supported by Airbus Operations Ltd

This project concerns the development of an industrially-applicable methodology for the design of laminar flow wings. The current state-of-the-art methodology for the analysis of laminar-turbulent transition for swept, transonic aircraft wings is the Parabolised Stability Equation (PSE) approach. For design studies the adjoint form of the PSE are derived and used to calculate the sensitivity of boundary layer disturbances to changes in surface and free stream boundary conditions, such as surface suction and pressure gradients which are typically employed by the wing designer to delay laminar-turbulent transition and thus reduce aircraft drag.

The popularity of the PSE approach belies the numerical awkwardness of the parabolic system of equations which require the establishment of an initial condition prior to the numerical solution of the instability problem. The initial condition is usually taken to be branch 1 of the neutral stability curve, but this is a priori unknown, and an inelegant iterative procedure is therefore required to converge on an appropriate initial condition for the stability analysis. A more versatile approach than the PSE is the method of multiple scales which is able to match the accuracy of PSE predictions with a number of advantages, not least a more straightforward extension to three-dimensional flows and an ability to incorporate rapid eigenvalue approximation techniques into the analysis of non-parallel stability, thus opening up the prospect of industrial exploitation of the technique.

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The objectives of the project are the development of a multiple-scales method for calculating the stability of non-parallel, compressible, three-dimensional flows, incorporating options for both rapid eigenvalue estimation and adjoint analysis, followed by the deployment of such a tool within an industrial environment such as that of the project sponsor, Airbus UK. There is also scope to validate the method by means of a wind-tunnel test. The work would aim to deliver to industry an advanced, yet easily-integrated, methodology for analysis of laminar-turbulent transition mechanisms and for the design of Laminar Flow Control wings.

The work will provide a competitive alternative to the favoured adjoint PSE method while for the first time demonstrating design analysis for truly three-dimensional flows. Experimental validation of instability modes in a three-dimensional boundary layer would also be a first for the community.


The PhD candidate will be responsible for developing a computational method along the lines described above, followed by appropriate validation, evaluation and application of the method. The candiate will be also repsonsible for reporting his results in agreement with the standards set by the University and submit papers for peer review journals or relevant international conferences.

Person Specification

A good first degree in Engineering or Mathematics is required.

Additional Information

If you require further information please contact Professor Chris Atkin, School of Engineering and Mathematical Sciences, City University London, Loncon, EC1V 0HB, or via email: Applicants should send their CV to Professor Atkin by email.

Closing date: 8 July 2013

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