Adjoint-based optimization of steady suction for disturbance control in incompressible flows

• Published in: Journal of fluid mechanics Vol. 467; pp. 129 - 161
• Main Authors: PRALITS, JAN O., HANIFI, A., HENNINGSON, D. S.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.09.2002
• Subjects: blasius boundary-layer; Boundary layer; Boundary layers; Exact sciences and technology; Flow alteration; Flow velocity; Fluid dynamics; Fluid mechanics; Fundamental areas of phenomenology (including applications); Optimization techniques; parabolized stability equations; Physics; transition; Transition to turbulence; Turbulence control; Turbulent flows, convection, and heat transfer; Aspiration; Tollmien Schlichting wave; Digital simulation; Disturbances; Control systems; Transition flow; Incompressible fluid; Boundary layers; Optimization; Turbulent laminar transition; Flat plate
• ISSN: 0022-1120; 1469-7645; 1469-7645
• DOI: 10.1017/S0022112002001301

The optimal distribution of steady suction needed to control the growth of single or multiple disturbances in quasi-three-dimensional incompressible boundary layers on a flat plate is investigated. The evolution of disturbances is analysed in the framework of the parabolized stability equations (PSE). A gradient-based optimization procedure is used and the gradients are evaluated using the adjoint of the parabolized stability equations (APSE) and the adjoint of the boundary layer equations (ABLE). The accuracy of the gradient is increased by introducing a stabilization procedure for the PSE. Results show that a suction peak appears in the upstream part of the suction region for optimal control of Tollmien–Schlichting (T–S) waves, steady streamwise streaks in a two-dimensional boundary layer and oblique waves in a quasi-three-dimensional boundary layer subject to an adverse pressure gradient. The mean flow modifications due to suction are shown to have a stabilizing effect similar to that of a favourable pressure gradient. It is also shown that the optimal suction distribution for the disturbance of interest reduces the growth rate of other perturbations. Results for control of a steady cross-flow mode in a three-dimensional boundary layer subject to a favourable pressure gradient show that not even large amounts of suction can completely stabilize the disturbance.