Uncertainty Quantification for Direct Aeroacoustic Simulations of Cavity Flows

Abstract

We investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows. The so-called Rossiter feedback requires a direct numerical computation of the acoustic noise, which solves hydrodynamics and acoustics simultaneously, in order to capture the interaction of acoustic waves and the hydrodynamics of the flow. Due to the large bandwidth of spatial and temporal scales, a high-order numerical scheme with low dissipation and dispersion error is necessary to preserve important small scale information. Therefore, the open-source CFD solver FLEXI, which is based on a high-order discontinuous Galerkin spectral element method, is used to perform the aforementioned direct simulations of an open cavity configuration with a laminar upstream boundary layer. To analyze the precision of the deterministic cavity simulation with respect to random input parameters, we establish a framework for uncertainty quantification (UQ). In particular, a nonintrusive spectral projection method with Legendre and Hermite polynomial basis functions is employed in order to treat uniform and normal probability distributions of the random input. The results indicate a strong, nonlinear dependency of the acoustic feedback mechanism on the investigated uncertain input parameters. An analysis of the stochastic results offers new insights into the noise generation process of open cavity flows and reveals the strength of the implemented UQ framework.

$hp$-Multilevel Monte Carlo Methods for Uncertainty Quantification of Compressible Flows

“…Finally we demonstrate the efficiency of the hp-MLMC method with the novel sample estimator for two different compressible flow problems, the lid-driven cavity problem and the open cavity flow problem. The latter is an important problem in computational acoustics that exhibits physical phenomena with high sensitivity with respect to the problem parameters [17]. Moreover, we show for the open cavity flow problem that the hp-MLMC method is more efficient than the MOMC method.…”

“…The dominant peaks, which correspond to the so-called Rossiter modes (cf. [11,17]) are clearly observable in the mean spectrum. The total work of both methods is again optimal, see Figure 6a.…”

“…In this numerical example we investigate the influence of uncertain input parameters on the aeroacoustic feedback of cavity flows as in [17]. The prediction of aeroacoustic noise is an important branch of research for example in the automotive industry, however due to the large bandwidth of spatial and temporal scales, a high order numerical scheme with low dissipation and dispersion error is necessary to preserve important small scale information and hence it poses a very challenging numerical problem for UQ.…”

“…The Mach number in this example is M a = 0.6 and the Reynolds number corresponds to Re = 1500. Detailed information about the open boundary condition can be found in [17].…”

Aeroacoustics research in Europe: The CEAS-ASC report on 2018 highlights

“…With the help of this framework, the system response of a cavity flow problem under the influence of uncertain parameters has been analyzed. Uncertainties in the upstream boundary layer as well as randomness in the cavity geometry have been investigated [71]. As an example, the acoustic response to an uncertain cavity depth revealed strong non-linearities.…”