Control of Tollmien–Schlichting waves using particle swarm optimization

The implementation of the Particle Swarm Optimization (PSO) algorithm is investigated to optimize the active attenuation of Tollmien–Schlichting (TS) waves developing in a two-dimensional zero pressure gradient boundary layer. This is done numerically, where the PSO algorithm optimizes the characteristics of harmonic suction and blowing jets, in a feedforward control framework. The PSO-based controller selects and modifies the phase and amplitude of the jets to minimize the pressure fluctuation amplitude downstream of the actuator. To allow for efficient simulation, the 2-dimensional incompressible Navier–Stokes equations are expanded in a harmonic perturbation form and solved in linear and nonlinear variants using harmonic balancing. This study explores the performance of control in both linear and nonlinear development regimes of TS waves through control of single and multi-frequency ensembles of instabilities. Respectively, linear and nonlinear controller design approaches are employed. The findings reveal that the integration of PSO into the control design produces an effective suppression of TS waves through opposition control. The linearly designed controller effectively attenuates single and multi-frequency disturbances. However, when applied in regions of strong nonlinear interactions among instability modes, performance degradation is observed. On the contrary, the nonlinearly designed controller proves effective in mitigating nonlinear multi-frequency instabilities dominating the later stages of growth. A near-complete elimination of TS waves is achieved by accounting for nonlinear interactions among harmonic modes detected by an input sensor. This highlights the benefit of integrating the PSO algorithm in control of TS waves, particularly in the nonlinear growth regime, where classical control methods are generally ineffective.