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Rapid prediction of the aeroacoustic response is a key component in thedesign of aircraft and turbomachinery. While it is possible to achieve accuratepredictions using direct solution of the compressible Navier-Stokes equations,applications of such solvers is not feasible in design optimization due to thehigh cost of resolving wave phenomena in an Eulerian setting. In this work, wepropose a technique for highly accelerated predictions of aeroacoustic responseusing a data-driven model reduction approach based on the eigensystemrealization algorithm (ERA), as a non-intrusive balanced truncation method.Specifically, we create and compare ERA ROMs based on the training datagenerated by solving the linearized and nonlinear Euler equations with Gaussianpulse inputs, and use them for prediction of the aeroacoustic response of anairfoil subject to different types of gust loading. The results show that bothROMs are in good agreement with the full-order model (FOM) solution in a purelypredictive setting, while achieving orders of magnitude reduction in the onlinecomputation time. Using ERA for prediction of the acoustic response requiresactivating each input channel separately in the FOM for training ROMs, andoperating on a large Hankel matrix, that can become computationally infeasible.We address this bottleneck in two steps: first, we propose a multi-fidelitygappy POD method to identify the most impactful input channels based on acoarser grid. Therefore, we reduce the computation cost on the FOM and ROMlevels as we build the Markov sequence by querying the high-resolution FOM onlyfor the input channels identified by gappy POD. Second, we use tangentialinterpolation at the ROM level to reduce the size of the Hankel matrix. Theproposed methods enable application of ERA for highly accurate online acousticresponse prediction and reduce the offline computation cost of ROMs.

Data-driven Balanced Truncation for Predictive Model Order Reduction of Aeroacoustic Response