Implicit CFD methods for transitional shock wave – boundary layer interaction

George Zografakis (Department of Engineering, University of Liverpool, Liverpool, UK)
George Barakos (Department of Engineering, University of Liverpool, Liverpool, UK)

Aircraft Engineering and Aerospace Technology

ISSN: 0002-2667

Publication date: 5 September 2016



This paper aims to explore the potential of transition prediction methods for modelling transitional shock wave/boundary layer interactions. The study is fuelled by the strong interest of researchers and airframe manufacturers in reducing the drag of vehicles flying at transonic speeds. The principle of drag reduction via flow laminarity is valid, provided there is no need for the flow to sustain large pressure gradients or shocks. This is true, as laminar boundary layers are less resistant to flow separation.


It is, therefore, worthwhile to assess the performance of CFD methods in modelling laminar boundary layers that can be tripped to turbulent just before an interaction with a shock. In this work, the CFD solver of Liverpool University is used. The method is strongly implicit, and, for this reason, the implementation of intermittency-based models requires special attention. The Navier–Stokes equations, the transport equations of the kinetic energy of turbulence and the turbulent frequency are inverted at the same time as the transport equations for the flow intermittency and the momentum thickness Reynolds number.


The result is stable and robust convergence even for complex three-dimensional flow cases. The method is demonstrated for the flow around the V2C section of the TFAST EU, F7 project. The results suggest that the intermittency-based model captures the fundamental physics of the interaction, but verification and validation are needed to ensure that accurate results can be obtained. For this reason, comparisons with the TFAST experiments is put forward as a means of establishing confidence in the transition prediction tools used for shock/boundary layer interaction simulation.

Research limitations/implications

At the moment, experimental data for transonic transitional buffet are not yet available, although this will change in the near future.

Practical implications

The required CPU time is neither insignificant not prohibitive for routine computations.

Social implications

Reducing aircraft drag without compromising on stall characteristics will result in lower fuel consumption and contribute to a greener and more economic flight for passengers.


To the authors’ knowledge, this is the first time that transitional buffet has been addressed.



This work is supported by the EU Collaborative Project TFAST, FP7-AAT-2010-RDT-1, under Grant Agreement N°265455. Present address: School of Engineering, University of Glasgow, Glasgow G12 8QQ, Scotland UK. Correspondence to:


Zografakis, G. and Barakos, G. (2016), "Implicit CFD methods for transitional shock wave – boundary layer interaction", Aircraft Engineering and Aerospace Technology, Vol. 88 No. 5, pp. 636-648.

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