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Flow control of weakly non-parallel flows: application to trailing vortices. (English) Zbl 1383.76072
Summary: A general formulation is proposed to control the integral amplification factor of harmonic disturbances in weakly non-parallel amplifier flows. The sensitivity of the local spatial stability spectrum to a base-flow modification is first determined, generalizing the results of A. Bottaro et al. [ibid. 476, 293–302 (2003; Zbl 1041.76029)]. This result is then used to evaluate the sensitivity of the overall spatial growth to a modification of the inlet flow condition. This formalism is applied to a non-parallel Batchelor vortex, which is a well-known model for trailing vortices generated by a lifting wing. The resulting sensitivity map indicates the optimal modification of the inlet flow condition enabling the stabilization of the helical modes. It is shown that the control, formulated using a single linearization of the flow dynamics carried out on the uncontrolled configuration, successfully reduces the total spatial amplification of all convectively unstable disturbances.
MSC:
76B47 Vortex flows for incompressible inviscid fluids
76B75 Flow control and optimization for incompressible inviscid fluids
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