First Principles Based PID Control of Mixing Layer: Role of Inflow Perturbation Spectrum

The most amplified (fundamental) wave and its subharmonics trigger the instabilities of a mixing layer and its subsequent development. In the present work, an approach for controlling mixing layers is extended to assess the role of amplitude, phase and number of subharmonics of the most amplified wave. In the earlier study, a Proportional-Integral-Derivative (PID) control technique applied to a spectral solution was shown to be capable of rapidly driving the time-developing mixing layer to a target layer thickness, using the phase shift between the fundamental and its subharmonics as the control parameter. The present study uses the PID control technique with amplitude of the fundamental as the control variable to control the thickness of the mixing layer. The PID control demonstrates control of such layers by selectively picking and modulating the amplitude or relative phases of various modes. The previous study demonstrated that an assessment of the control regime in the temporally developing mixing layer is sufficient for defining the perturbation envelope for controlling the spatially developing layer. This affords us an efficient way of defining the spectrum of perturbations that can lead to varying degree of instability of the spatially growing layer. Hence a variety of different perturbations have been studied in the temporal domain to assess their effect on the development of the layer. Simulations of spatially growing layer are also performed to support the conclusions. Additionally, a collective interaction study of spatially growing layer where various modes yield not just pairing of structures but a collective interaction of more than two structures at a time, has been carried out that results in an appreciable change in the growth rate of the layer.