Hostname: page-component-cd9895bd7-jn8rn Total loading time: 0 Render date: 2024-12-30T20:36:12.987Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bountin, D. A., Shiplyuk, A. N., Maslov, A. A. & Chokani, N. 2004 Nonlinear aspects of hypersonic boundary-layer stability on a porous surface. AIAA Paper 2004–0255.CrossRefGoogle Scholar
Brès, G. A. & Colonius, T. 2008 Three-dimensional instabilities in compressible flow over open cavities. J. Fluid Mech. 599, 309–339.Google Scholar
Brès, G. A., Colonius, T. & Fedorov, A. V. 2008a Interaction of acoustic disturbances with micro-cavities for ultrasonic absorptive coatings. AIAA Paper 2008–3903.CrossRefGoogle Scholar
Brès, G. A., Colonius, T. & Fedorov, A. V. 2008b Stability of temporally evolving supersonic boundary layers over micro-cavities for ultrasonic absorptive coatings. AIAA Paper 2008–4337.Google Scholar
Brès, G. A., Colonius, T. & Fedorov, A. V. 2010 Acoustic properties of porous coatings for hypersonic boundary-layer control. AIAA J. 48 (2), 267–274.CrossRefGoogle Scholar
Brès, G. A., Inkman, M., Colonius, T. & Fedorov, A. V. 2009 Alternate designs of ultrasonic absorptive coatings for hypersonic boundary layer control. AIAA Paper 2009–4217.Google Scholar
Colonius, T., Lele, S. K. & Moin, P. 1993 Boundary conditions for direct computation of aerodynamic sound. AIAA J. 31 (9), 1574–1582.CrossRefGoogle Scholar
De Tullio, N. & Sandham, N. D. 2010 Direct numerical simulation of breakdown to turbulence in a Mach 6 boundary layer over a porous surface. Phys. Fluids 22, 094105.Google Scholar
Fedorov, A. V. 2010 Temporal stability of hypersonic boundary layer on porous wall: comparison of theory with DNS. AIAA Paper 2010–1242.Google Scholar
Fedorov, A. V. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 79–95.Google Scholar
Fedorov, A. V. & Khokhlov, A. P. 2001 Prehistory of instability in hypersonic boundary layer. Theor. Comput. Fluid Dyn. 14, 359–375.Google Scholar
Fedorov, A. V., Kozlov, V. F., Shiplyuk, A. N., Maslov, A. A., Sidorenko, A. A., Burov, E. V. & Malmuth, N. D. 2003a Stability of hypersonic boundary layer on porous wall with regular microstructure. AIAA Paper 2003–4147.Google Scholar
Fedorov, A. V., Malmuth, N. D., Rasheed, A. & Hornung, H. G. 2001 Stabilization of hypersonic boundary layers by porous coatings. AIAA J. 39 (4), 605–610.Google Scholar
Fedorov, A. V., Shiplyuk, A. N., Maslov, A. A., Burov, E. V. & Malmuth, N. D. 2003b Stabilization of a hypersonic boundary layer using an ultrasonically absorptive coating. J. Fluid Mech. 479, 99–124.Google Scholar
Fedorov, A. V. & Tumin, A. 2011 High-speed boundary-layer instability: old terminology and a new framework. AIAA J. 49 (8), 1647–1657.Google Scholar
Freund, J. B. 1997 Proposed inflow/outflow boundary condition for direct computation of aerodynamic sound. AIAA J. 35 (4), 740–742.Google Scholar
Gaster, M. 1962 A note on the relation between temporally-increasing and spatially-increasing disturbances in hydrodynamic stability. J. Fluid Mech. 14, 222–224.Google Scholar
Hader, C. & Fasel, H. F. 2011 Numerical investigation of porous walls for a Mach 6.0 boundary layer using an immersed boundary method. AIAA Paper 2011–3081.Google Scholar
Kendall, J. M. 1975 Wind tunnel experiments relating to supersonic and hypersonic boundary layer transition. AIAA J. 13 (3), 290–299.Google Scholar
Kimmel, R. 2003 Aspects of hypersonic boundary layer transition control. AIAA Paper 2003–0772.Google Scholar
Kozlov, V. F., Fedorov, A. V. & Malmuth, N. D. 2005 Acoustic properties of rarefied gases insides pores of simple geometries. J. Acoust. Soc. Am. 117 (6), 3402–3412.Google Scholar
Lele, S. K. 1992 Compact finite difference scheme with spectral-like resolution. J. Comput. Phys. 103, 16–42.Google Scholar
Mack, L. M. 1969 Boundary-layer stability theory. In Part B. Doc. 900-277. Jet Propulsion Lab, CA.Google Scholar
Mack, L. M. 1984 Boundary layer linear stability theory. In AGARD–R–709 Special Course on Stability and Transition of Laminar Flow, pp. 3.1–3.81.Google Scholar
Malmuth, N. D., Fedorov, A. V., Shalaev, V., Cole, J., Khokhlov, A., Hites, M. & Williams, D. 1998 Problems in high speed flow prediction relevant to control. AIAA Paper 98–2695.CrossRefGoogle Scholar
Maslov, A. A., Shiplyuk, A. N., Sidorenko, A. A., Polivanov, P., Fedorov, A. V., Kozlov, V. F. & Malmuth, N. D. 2006 Hypersonic laminar flow control using a porous coating of random microstructure. AIAA Paper 2006–1112.Google Scholar
Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104–129.CrossRefGoogle Scholar
Rasheed, A., Hornung, H. G., Fedorov, A. V. & Malmuth, N. D. 2002 Experiments on passive hypervelocity boundary layer control using an ultrasonically absorptive surface. AIAA J. 40 (3), 481–489.Google Scholar
Sandham, N. D. & Lüdeke, H. 2009 A numerical study of Mach 6 boundary layer stabilization by means of a porous surface. AIAA J. 47 (9), 2243–2252.Google Scholar
Schlichting, H. & Gersten, K. 2000 Boundary Layer Theory, 8th edn. Springer.Google Scholar
Stetson, K. F. & Kimmel, R. G. 1992 Example of second-mode instability dominance at a Mach number of 5.2. AIAA J. 30 (12), 2974–2976.Google Scholar
Stetson, K. F., Thomson, E. R., Donaldson, J. C. & Siler, L. G. 1983 Laminar boundary-layer stability experiments on a cone at Mach 8, Part 1: sharp cone. AIAA Paper 83–1761.Google Scholar
Thompson, K. W. 1990 Time-dependent boundary conditions for hyperbolic systems, II. J. Comput. Phys. 89, 439–461.CrossRefGoogle Scholar
Wartemann, V., Lüdeke, H. & Sandham, N. D. 2009 Stability analysis of hypersonic boundary layer flow over microporous surfaces. AIAA Paper 2009–7202.Google Scholar