A modified FxLMS fluid flow control model for convectively unstable disturbance

Abstract

In this article, we propose a modified FxLMS (Filtered least mean square algorithm) fluid flow control model of a linear convectively unstable disturbance over a flat plate in one dimensional sense. In many flow situations, we need to suppress the flow instabilities as it causes unnecessary drag and noise due to enhancement of perturbation amplitude, whereas in few other flow situations, we deliberately need the flow perturbations in an enhanced desired permissible set level to obtain a desired mixing or controlled enhancement of heat transfer through the fluids. We propose a one dimensional modified FxLMS flow control model through which we can achieve controlled attenuation as well as enhancement in the amplitude of fluid perturbation with single additional gain in the control model. This method is widely used in noise control and signal processing areas. We adopt the similar modeling approach to confront the problem. One dimensional linearized Kuramoto–Sivashinsky equation model (KS equation) is used to model the fluid flow. We make use of model-free adaptive method to further apply it for fluids flows. A structurally modified adaptive algorithm incorporating FxLMS is designed and tested to get the desired set level of fluctuations in the fluid flow. In this control model, with a set value of additional gain, we achieve cancellation, attenuation, enhancement, and neutralization of perturbation amplitude downstream of the fluid flow in one dimensional sense. With the fast Fourier transformation (FFT) analysis, we have also observed that, the modified FxLMS fluid flow adaptive control model attenuates/enhances the set of troubling frequencies accordingly.