Data assimilation of flow-acoustic resonance.

A data assimilation (DA) strategy was developed for accurate prediction of the flow-acoustic resonant fields within a channel-branch system. The challenges of numerical simulation of such internal aeroacoustic systems are primarily associated with determination of the transfer loss between the acoustic waves and the shear layer vortices. Thus, a data-assimilated momentum loss model that comprises a viscous loss item and an inertial loss item was established and embedded into the Navier-Stokes equations. During the DA, the acoustic pressure pulsations measured from a dynamic pressure array served as the observational data, the ensemble Kalman filter served as the optimization algorithm, and a three-dimensional transient computational fluid dynamics method comprising an explicit algebraic Reynolds stress model (EARSM) served as the predictive model system. EARSM was used because its ability to predict internal flow-acoustic resonances was superior to that of other eddy viscosity models and Reynolds stress models. The data-assimilated flow-acoustic resonant fields were then comprehensively validated in terms of their acoustic fields, time-averaged flow fields, and phase-dependent flow fields. The time-averaged flow fields were obtained from planar particle-image velocimetry (PIV) measurements, and the phase-dependent flow fields were obtained from field programmable gate array-based phase-locking PIV measurements. The results demonstrate that the use of DA afforded an optimal simulation that efficiently decreased the numerical errors in the frequencies and amplitudes of the acoustic pressure pulsations, thereby achieving better agreement between time-averaged flow distributions and fluctuations. In addition, the data-assimilated numerical simulation completely reproduced the spatiotemporal evolution of the shear layer vortices, that is, their formation, developing, transport, and collapsing regions.