Abstract
The possibility of controlling the laminar-turbulent transition in hypersonic shock layers by means of porous coatings is considered. The linear stability of the shock layer to acoustic disturbances is analyzed. A dispersion relation is derived in an analytical form and analyzed for different characteristic values of porosity of the wall, which allows one to study the spectrum of acoustic disturbances in the shock layer. Analytical expressions for the growth rate of instability of acoustic disturbances are presented as functions of the reflection factor. Their structure indicates that the porous coating effectively decreases acoustic instability of the shock layer.
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REFERENCES
M. R. Malik, T. A. Zang, and D. M. Bushnell, “Boundary layer transition in hypersonic ows,” AIAA Paper No. 90-5232 (1990).
V. I. Lysenko A. A. Maslov (1984) ArticleTitleThe effect of cooling on supersonic boundary-layer stability J. Fluid Mech. 147 38–52
N. D. Malmuth, A. V. Fedorov, V. I. Shalaev, et al., “Problems in high speed ow prediction relevant to control,” AIAA Paper No. 98-2695 (1998).
A. V. Fedorov N. D. Malmuth (2001) ArticleTitleStabilization of hypersonic boundary layers by porous coatings AIAA J. 39 IssueID4 605–610
A. Rasheed H. G. Hornung A. V. Fedorov N. D. Malmuth (2002) ArticleTitleExperiments on passive hypervelocity boundary layer control using a ultrasonically absorptive surface AIAA J. 40 IssueID3 481–489
A. Fedorov A. Shiplyuk A. Maslov et al. (2003) ArticleTitleStabilization of a hypersonic boundary layer using an ultrasonically absorptive coating J. Fluid Mech. 479 99–124
V. M. Fomin A. V. Federov A. N. Shiplyuk et al. (2002) ArticleTitleStabilization of a hypersonic boundary layer by coatings absorbing ultrasound Dokl. Akad. Nauk SSSR 384 IssueID2 1–5
A. Fedorov, V. Kozlov, A. Shiplyuk, et al., “Stability of hypersonic boundary layer on porous wall with regular microstructure,” AIAA Paper No. 2003-4147 (2003).
G. V. Petrov, “Effect of the shock wave bounding a hypersonic shock layer on boundary-layer stability,” in: Instability of Subsonic and Supersonic Flows (collected scientific papers) [in Russian], Inst. Theor. Appl. Mech., Sib. Div., Acad. of Sci. of the USSR (1982), pp. 25–34.
G. V. Petrov, “Stability of thin viscous shock layer on wedge in hypersonic ow of a perfect gas,” in: Laminar-Turbulent Transition, Proc. IUTAM Symp., Novosibirsk (1984), pp. 487–493.
V. R. Gushchin A. V. Fedorov (1988) ArticleTitleAsymptotic structure of wave disturbances in a thin shock layer Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 6 72–79
V. R. Gushchin A. V. Fedorov (1989) ArticleTitleShort-wave instability in a shock layer of a perfect gas Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza 1 10–14
M. V. Fedoryuk (1983) Asymptotic Methods for Linear Ordinary Differential Equations Nauka Moscow
M. Abramowitz I. A. Stegun (1972) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables John Wiley and Sons New York
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 44–54, January–February, 2005
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Fedorov, A.V., Yumashev, D.V. Theoritical analysis of acoustic instability of a hypersonic shock layer on a porous wall. J Appl Mech Tech Phys 46, 33–41 (2005). https://doi.org/10.1007/s10808-005-0005-9
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DOI: https://doi.org/10.1007/s10808-005-0005-9