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Braun, Stefan; Kluwick, Alfred

Blow-up and control of marginally separated boundary layers. (English) Zbl 1152.76371

Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 363, No. 1830, 1057-1067 (2005).
Summary: Interactive solutions for steady two-dimensional laminar marginally separated boundary layers are known to exist up to a critical value \(\Gamma _{c}\) of the controlling parameter (e.g. the angle of attack of a slender airfoil) \(\Gamma \) only. Here, we investigate three-dimensional unsteady perturbations of such boundary layers, assuming that the basic flow is almost critical, i.e. in the limit \(\Gamma _{c} - \Gamma \rightarrow 0\). It is then shown that the interactive equations governing such perturbations simplify significantly, allowing, among others, a systematic study of the blow-up phenomenon observed in earlier investigations and the optimization of devices used in boundary-layer control.

Cited in 7 Documents

MSC:

76D10 Boundary-layer theory, separation and reattachment, higher-order effects
76D55 Flow control and optimization for incompressible viscous fluids

Keywords:

separation bubble; laminar-turbulent transition; Fisher equation; finite time blow-up; moving singularities; flow control
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\textit{S. Braun} and \textit{A. Kluwick}, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 363, No. 1830, 1057--1067 (2005; Zbl 1152.76371)
Full Text: DOI

References:

[1] Alam, M. & Sandham, N.D. 2000 Direct numerical simulation of ’short’ laminar separation bubbles with turbulent reattachment. <i>J. Fluid Mech.</i>&nbsp;<b>410</b>, 1–28. · Zbl 0959.76035
[2] Borodulin, V.I., Gaponenko, V.R., Kachanov, Y.S., Meyer, D.G.W., Rist, U., Lian, Q.X. & Lee, C.B. 2002 Late-stage transitional boundary-layer structures. Direct numerical simulation and experiment. <i>Theor. Comput. Fluid Dyn.</i>&nbsp;<b>15</b>, 317–337. · Zbl 1057.76529
[3] Braun, S. & Kluwick, A. 2004 Unsteady three-dimensional marginal separation caused by surface-mounted obstacles and/or local suction. <i>J. Fluid Mech.</i>&nbsp;<b>514</b>, 121–152. · Zbl 1067.76028
[4] Braun, S., Kluwick, A. & Trenker, M. 2003 Leading edge separation: a comparison between interaction theory and Navier–Stokes computations. <i>Proceedings of the GAMM 2002 Conference, Augsburg 2002. Proc. Appl. Math. Mech.</i>&nbsp;<b>2</b>, 312–313. · Zbl 1201.76164
[5] Gerhold, T., Galle, M., Friedrich, O. & Evans, J. 1997 Calculation of complex three-dimensional configurations employing the DLR-TAU-code. AIAA Paper 1997-0167. Reston, VA: American Institute of Aeronautics and Astronautics.
[6] Hocking, L.M., Stewartson, K., Stuart, J.T. & Brown, S.N. 1972 A nonlinear instability burst in plane parallel flow. <i>J. Fluid Mech.</i>&nbsp;<b>51</b>, 705–735. · Zbl 0232.76053
[7] Mary, I. & Sagaut, P. 2002 Large eddy simulation of flow around an airfoil near stall. <i>AIAA J.</i>&nbsp;<b>40</b>, 1139–1145.
[8] Ruban, A.I. 1981 Asymptotic theory of short separation regions on the leading edge of a slender airfoil. <i>Izv. Akad. Nauk SSSR: Mekh. Zhidk. Gaza</i>&nbsp;<b>1</b>, 42–51. [English transl. <i>Fluid Dyn.</i>&nbsp;<b>17</b>, 33–41.].
[9] Stewartson, K., Smith, F.T. & Kaups, K. 1982 Marginal separation. <i>Stud. Appl. Math.</i>&nbsp;<b>67</b>, 45–61.
[10] Theofilis, V. 2003 Advances in global linear instability analysis of nonparallel and three dimensional flows. <i>Prog. Aerosp. Sci.</i>&nbsp;<b>39</b>, 249–315.
[11] Weideman, J.A.C. 2003 Computing the dynamics of complex singularities of nonlinear PDEs. <i>SIAM J. Appl. Dyn. Syst.</i>&nbsp;<b>2</b>, 171–186. · Zbl 1088.65582
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