<p>In computational fluid dynamic (CFD) and computational aeroacoustics (CAA) simulations, the wall surface is normally treated as a purely reflective wall. However, some surface treatments are usually applied in experiments. Thus, the results obtained by the simulation and experiment are sometimes not comparable. In the aeroacoustics community, impedance is a quantity to characterize the properties of an acoustically treated surface. i.e. reflectivity and absorption. One of the major numerical challenges in CAA simulations is to define acoustically well-posed boundary conditions. Basically, the impedance boundary condition is a frequency-domain boundary condition. For the broadband noise problem, the method based on frequency domain is computationally expensive and laborious. In addition, CFD and CAA simulations are time-domain computations, which means the frequency-domain impedance boundary condition cannot be applied in simulations. Therefore, several methods, including the three-parameter model, the z-transform method and the reflection coefficient model, were developed. The time-domain impedance boundary condition will allow the use of the newly developed computational aeroacoustics methods for the solution of duct acoustics and turbomachinery noise problems. In this paper, the modeling of the reflection coefficient is implemented, and is verified by the case with and without mean flow effect. It is indicated that the pressure distribution along the wall predicted by numerical simulation matches the analytical solution given by Fung and Ju (2001). Then, a coupling method that combines the time-domain impedance boundary condition and Large Eddy Simulations (LES) is proposed. A channel flow with wall-impedance is used as a test case and simulated at different flow velocities. The results of flow field are validated by the case with purely reflective wall-impedance. For the flow with wall-impedance, the flow field and near-wall turbulence structure are analyzed and compared to the structure obtained by the impermeable wall. In addition, the sound fields over a range of excitation frequency from 500Hz to 3,000Hz are computed and compared to experimental data shown in the previous study (Fung and Ju, 2001). The results indicate that the agreement between numerical and experimental results is generally good for most flow speed and excitation frequency. For the case of highly reflective impedance, the sound pressure is overestimated in simulations. In a summary, the time-domain impedance boundary condition used in the present study is valid for simple cases, i.e. channel flow, and is expected to be applied in other complicated cases in the future.</p>

Application and Verification of Time-Domain Impedance Boundary Conditions in CAA Simulations

Paper Proceedings: https://asmedigitalcollection.asme.org/FEDSM/FEDSM2021/volume/85284

ASME 2021 Fluids Engineering Division Summer Meeting (FEDSM2021)

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