An Acoustic Foundation for a Fully-Coupled Aeroelastic and Aeroacoustic Phonation Model Using OpenFOAM

Open Access
Irwin, Jeffrey Clark
Graduate Program:
Master of Science
Document Type:
Master Thesis
Date of Defense:
June 22, 2015
Committee Members:
  • Michael H Krane, Thesis Advisor
  • Brent A Craven, Thesis Advisor
  • Amanda D Hanford, Thesis Advisor
  • acoustics
  • resonance
  • wave propagation
  • time domain
  • computational fluid dynamics
  • computational acoustics
  • OpenFOAM
  • phonation
OpenFOAM, an open-source computational fluid dynamics package with unstructured meshing and fluid-structure interaction capabilities, was evaluated to determine its ability to accurately compute direct time-domain simulations of acoustic wave propagation and resonance. OpenFOAM's "sonicFoam" solver and second-order numerical schemes were tested to determine the accuracy of their predictions with respect to theoretically- and experimentally-determined results. The acoustic behavior of an open-ended cylindrical resonator and an axisymmetric expansion chamber (muffler) were simulated, and the predicted results from each of the two cases were analyzed following their arrival at states of periodic acoustic excitation. The results from the resonator case were compared against theoretically-determined time- and frequency-domain predictions, and the results from the expansion chamber case were used to compare simulated transmission loss curves against those previously determined in an experimental study on a muffler of identical internal geometry. In both cases, the effects of the time step and computational grid resolution on the accuracy of the numerically-predicted solutions were studied in detail. It was found that the resonator simulations produced results that compared favorably to theory, and which converged toward analytical predictions as both the computational grid resolution and the time step were continually refined. In a grid refinement study, four uniform "wedge" grids of the axisymmetric resonator were examined: a coarsened grid (3.400mm by 4.205mm cells), an original grid (1.133mm by 1.402mm cells), a refined grid (0.378mm by 0.467mm cells), and a further refined grid (0.126mm by 0.156mm cells). Frequencies between 20Hz and 5000Hz were simulated (corresponding to approximately 20, 61, 184, and 551 cells per acoustic wavelength at the highest simulated frequency), and the acoustic Courant number was kept constant at 0.68 (resulting in approximately 30, 90, 270, and 810 time steps per acoustic period at the highest simulated frequency). It was found that the coarsened grid was insufficient for predicting pressure amplitudes, acoustic impedances, or the reflection coefficient at the open end of the resonator; while the remaining three cases predicted these quantities with varying degrees of accuracy. The original case predicted all values fairly accurately, the first refined case noticeably improved upon the original, and the second refined case showed only very slight improvements over the first. The spatial and temporal resolution of the second refined case was found to be unnecessary, and the optimal resolution in this study was found to be the that of the first refined case. The first refined resonator grid was then run under a total of three different time steps; with acoustic Courant numbers of 0.68, 0.34, and 0.17 (resulting in approximately 270, 540, and 1080 time steps per acoustic period at the highest simulated frequency of 5000Hz). While improvements in accuracy were found with each time step refinement, they were extremely small, and thus the standard time step (with acoustic Courant number of 0.68) was found to be sufficient. Similarly accurate results were observed in the expansion chamber simulations, where computed transmission loss curves were found to converge toward experimental results with continual refinement of the computational grid and time step. Three uniform "wedge" grids were created for the axisymmetric expansion chamber: a coarsened grid (3.333mm by 3.571mm cells), an original grid (1.111mm by 1.190mm cells), and a refined grid (0.370mm by 0.397mm cells). Frequencies between 20Hz and 2000Hz were simulated (resulting in approximately 52, 156, and 469 cells per acoustic wavelength at the highest simulated frequency), and the acoustic Courant number was held constant at 0.70 (resulting in approximately 75, 225, and 675 time steps per acoustic period at the highest simulated frequency). The coarsened grid was found to be insufficient, and the refined grid was found to best recreate the experimental transmission loss curve of the muffler (both in magnitude and overall contour). However, its accuracy was still lacking at certain critical frequencies, due to an incompletely-resolved acoustic boundary layer that resulted in insufficient acoustical damping within the computational model. The results of the expansion chamber case reinforced the importance of the acoustic boundary layer in determining grid resolution requirements. Boundary layer requirements are distinct from those in the direction of propagation (which are driven simply by the need to accurately preserve a traveling wave), though resolution of the boundary layer is absolutely necessary to properly simulate acoustical damping within in a computational domain. In this study, only uniform grids were used, and it was found that the acoustic boundary layer was not adequately resolved, even in the finest grids. It was therefore concluded that graded meshes (possessing finer grid resolutions along solid boundaries) will be necessary in future work, if acoustical damping effects are to be accurately modeled. Ultimately, it was determined that OpenFOAM is capable of accurately computing solutions to problems involving time-domain acoustical propagation and resonance. However, it was also discovered that small time steps and fine computational grids are required in order to attain sufficient accuracy.