Detection and isolation of Tollmien-Schlichting waves in shear flows using blind source separation

Abstract

Abstract A blind source separation (BSS) method for the detection and isolation of Tollmien-Schlichting (TS) waves in sub-critical transitional shear flows is presented. The method is based on an adaptation of the celebrated independent component analysis (ICA) technique to the problem at hand, using appropriate modeling of the flow field and the disturbances acting on it. This modeling is founded on the representation of the acquired flow measurements as mixtures (generated by an a priori unknown mixing process) of disturbance sources. Only the disturbance mixtures, as measured by the sensors embedded in the flow field, are input to the new method. Linear stability theory (LST) is used to model the measured mixtures of sources acquired by sensors placed in the shear flow field. A physics-based design criterion, assuming prior knowledge of the TS wavelengths, is derived for proper sensor placement in order to successfully separate TS wave disturbances. The criterion is verified both numerically, for wall-bounded shear flows, and experimentally, via a wind-tunnel experimental study of flow over a flat plate. The new disturbance detection and isolation approach is expected to prove useful in various applications, including closed-loop flow control problems.