Reduced-Order Modeling of Cavity Flow Oscillations across Multi-Mach Numbers Using Deep Learning

The reduced-order model can accurately and efficiently predict unsteady problems in many aerospace engineering applications. The traditional reduced-order model based on proper orthogonal decomposition (POD) and Galerkin projection has poor robustness and large error in predicting complex problems. In this paper, a reduced-order model combining POD and deep learning is proposed to predict cavity flow oscillations under different flow conditions. Firstly, POD modes and corresponding coefficients are obtained by POD. Then, two deep learning frameworks, including multilayer perceptron (MLP) and long short-term memory (LSTM) neural networks, are used to predict the future POD coefficients, respectively. Finally, the cavity flow oscillations across multi-Mach numbers are predicted by the POD modes and the future coefficients. The results show that both of these frameworks can accurately predict cavity flow oscillations when the flow conditions change, and the time cost is reduced by order of magnitude. In addition, due to the performance of LSTM is better than that of MLP, its calculation speed is faster.

Energy harvesting from cavity flow oscillations

This study investigates the energy harvesting prospects of self-sustained flow oscillations emanating from grazing flow over a rectangular cavity by employing experimental and computational methods. Two cavity geometries with length-to-depth ratios of 2 and 3, exposed to an incoming flow of 30 m/s, were selected for the purpose. The power spectral density of the baseline cavity flows showed the presence of high-amplitude peaks whose frequencies agreed to those estimated from Rossiter’s feedback model. For energy harvesting, a piezoelectric beam was placed perpendicular to the aft wall and its natural frequency tuned to match closely with the dominant frequencies of the cavity flow oscillations. From the experiments, an average and maximum instantaneous power of 21.11 and 284.18 µW was recorded for the cavity with L/ D = 2 whereas for the cavity with L/ D = 3 the corresponding values were 32.16 and 403.46 µW respectively. Time-frequency analysis showed the forcing of the beam at the cavity oscillation frequency and the substantial increase in the amplitude of beam vibrations when this frequency was close to the natural frequency of the beam.

Review of Flow-Excited Resonance of Acoustic Trapped Modes in Ducted Shallow Cavities

Flow-excited resonances of acoustic trapped modes in ducted shallow cavities are reviewed in this paper. The main components of the feedback mechanism which sustains the acoustic resonance are discussed with particular emphasis on the complexity of the trapped mode shapes and the strong three-dimensionality of the cavity flow oscillations during the resonance. Due to these complexities of the flow and sound fields, it is still difficult to theoretically or numerically model the interaction mechanism which sustains the acoustic resonance. Strouhal number and resonance amplitude charts are therefore included to help designers avoid the occurrence of resonance in new installations, and effective countermeasures are provided which can be implemented to suppress trapped mode resonances in operating plants.

Feedback control of cavity flow oscillations using simple linear models

Using data from direct numerical simulations, linear models of the compressible flow past a rectangular cavity are found. The emphasis is on forming simple models which capture the input–output behaviour of the system, and which are useful for feedback controller design. Two different approaches for finding a linear model are investigated. The first involves using input–output data of the linearized cavity flow to form a balanced, reduced-order model directly. The second approach is conceptual, and involves modelling each element of the flow physics separately using simple analytical expressions, the parameters of which are chosen based on simulation data at salient points in the cavity’s computational domain. Both models are validated: first in the time domain by comparing their impulse responses to that of the full system in direct numerical simulations; and second in the frequency domain by comparing their frequency responses. Finally, the validity of both linear models is shown most clearly by using them for feedback controller design, and then applying each controller in direct numerical simulations. Both controllers completely eliminate oscillations, and demonstrate the advantages of model-based feedback controllers, even when the models upon which they are based are very simple.

Control of Cavity Flow Oscillations by High Frequency Forcing

Time resolved two-dimensional particle image velocimetry (2DPIV) experiments have been conducted to contribute to the understanding of the physics governing the suppression mechanism of cavity flow self-sustained oscillations by means of high frequency excitation of the cavity shear layer. High frequency excitation was introduced by the spanwise coherent vortex shedding in the wake of a cylindrical rod positioned just upstream the cavity entrance, at the edge of the incoming boundary layer. The effectiveness of this suppression was demonstrated for a cavity having the length-to-depth ratio equal to three, in incompressible flow. The spatial and time resolved PIV measurements of the whole flow field in the plane normal to the cavity floor, linear stability analysis of the measured shear layer mean velocity profiles, and preliminary PIV measurements in a plane parallel to the cavity allowed us to offer a better insight into the involved physical mechanisms in suppressing cavity self-sustained oscillations.