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Second-mode attenuation and cancellation by porous coatings in a high-speed boundary layer

Published online by Cambridge University Press:  31 May 2013

Guillaume A. Brès ,
Matthew Inkman ,
Tim Colonius  and
Alexander V. Fedorov
Guillaume A. Brès
Affiliation:
Department of Mechanical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
Matthew Inkman
Affiliation:
Department of Mechanical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
Tim Colonius
Affiliation:
Department of Mechanical Engineering, California Institute of Technology, 1200 E. California Blvd., Pasadena, CA 91125, USA
Alexander V. Fedorov
Affiliation:
Department of Aeromechanics and Flight Engineering, Moscow Institute of Physics and Technology, Zhukovsky, 140180, Russia
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Abstract

Numerical simulations of the linear and nonlinear two-dimensional Navier–Stokes equations, and linear stability theory are used to parametrically investigate hypersonic boundary layers over ultrasonic absorptive coatings. The porous coatings consist of a uniform array of rectangular pores (slots) with a range of porosities and pore aspect ratios. For the numerical simulations, temporally (rather than spatially) evolving boundary layers are considered and we provide evidence that this approximation is appropriate for slowly growing second-mode instabilities. We consider coatings operating in the typical regime where the pores are relatively deep and acoustic waves and second-mode instabilities are attenuated by viscous effects inside the pores, as well as regimes with phase cancellation or reinforcement associated with reflection of acoustic waves from the bottom of the pores. These conditions are defined as attenuative and cancellation/reinforcement regimes, respectively. The focus of the present study is on the cases which have not been systematically studied in the past, namely the reinforcement regime (which represents a worst-case scenario, i.e. minimal second-mode damping) and the cancellation regime (which corresponds to the configuration with the most potential improvement). For all but one of the cases considered, the linear simulations show good agreement with the results of linear instability theory that employs an approximate porous-wall boundary condition, and confirm that the porous coating stabilizing performance is directly related to their acoustic scattering performance. A particular case with relatively shallow pores and very high porosity showed the existence of a shorter-wavelength instability that was not initially predicted by theory. Our analysis shows that this new mode is associated with acoustic resonances in the pores and can be more unstable than the second mode. Modifications to the theoretical model are suggested to account for the new mode and to provide estimates of the porous coating parameters that avoid this detrimental instability. Finally, nonlinear simulations confirm the conclusions of the linear analysis; in particular, we did not observe any tripping of the boundary layer by small-scale disturbances associated with individual pores.

JFM classification

Boundary Layers: Boundary layer stability Aerodynamics: High-speed flow Flow Control: Instability control
Type
Papers
Information
Journal of Fluid Mechanics , Volume 726 , 10 July 2013 , pp. 312 - 337
Copyright
©2013 Cambridge University Press 

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