Unsteadiness in shock-wave/boundary layer interactions

The need for better understanding of the low-frequency unsteadiness observed in shock<br/>wave/turbulent boundary layer interactions has been driving research in this area for<br/>several decades. This work investigates the interaction between an impinging oblique<br/>shock and a supersonic turbulent boundary layer via large-eddy simulations. Special<br/>care is taken at the inlet in order to avoid introducing artificial low-frequency modes<br/>that could affect the interaction. All simulations cover extensive integration times to<br/>allow for a spectral analysis at the low frequencies of interest. The simulations bring<br/>clear evidence of the existence of broadband and energetically-significant low-frequency<br/>oscillations in the vicinity of the reflected shock, thus confirming earlier experimental<br/>findings. Furthermore, these oscillations are found to persist even if the upstream<br/>boundary layer is deprived of long coherent structures.<br/><br/>Starting from an exact form of the momentum integral equation and guided by data<br/>from large-eddy simulations, a stochastic ordinary differential equation for the reflectedshock<br/>foot low-frequency motions is derived. This model is applied to a wide range<br/>of input parameters. It is found that while the mean boundary-layer properties are<br/>important in controlling the interaction size, they do not contribute significantly to<br/>the dynamics. Moreover, the frequency of the most energetic fluctuations is shown to<br/>be a robust feature, in agreement with earlier experimental observations. Under some<br/>assumptions, the coupling between the shock and the boundary layer is mathematically<br/>equivalent to a first-order low-pass filter. Therefore, it is argued that the observed lowfrequency<br/>unsteadiness is not necessarily a property of the forcing, either from upstream<br/>or downstream of the shock, but simply an intrinsic property of the coupled dynamical<br/>system.

Name dc:type.qualificationname

Ph.D.

Level dc:type.qualificationlevel

doctoral

Grantor dc:publisher.institution

University of Southampton

Year dc:date.issued

2010

Author dc:creator

• Touber, Emile

Advisors dc:contributor.advisor

• Sandham, N.D.
• Coleman, G.N.