Douglas L. Sondak - Scientfic Computing and Visualization, Boston University
Sound can be produced by the interaction of fluid flow with a solid body in a diverse range of configurations, from jet-engine nozzles to woodwind instruments. One sound-producing geometry that has been studied extensively is that of the edgetone, which consists of a jet of air impinging on the point of a wedge. In the present study a simulation has been performed to examine the detailed unsteady fluid mechanics of the edgetone. The initial two-dimensional simulation, presented here, was based on one of the configurations from the experimental study of Brown .
The case chosen for the present simulation had a jet Mach number of 0.0514 and a jet-to-wedge spacing of 4.0 normalized by the jet width. The simulation was performed using Overflow , a 3-D, unsteady, compressible, finite-difference CFD code developed by NASA. The domain was discretized using three grids: an 87x31 grid modeling the jet nozzle, a 337x81 near-body grid , and a 111x81 far-field grid. Figure 1 shows the grid for the entire domain, and Figure 2 shows a close-up of the wedge impingement region.
The simulation was performed using central differences with matrix dissipation on the right-hand-side, a diagonalized scalar pentadiagonal scheme on the left, and low Mach number preconditioning. There were 120 dual-time-step subiterations performed for each global time step to achieve a level of convergence of the L2 norms of approximately three orders of magnitude on the inner iterations. The time step was chosen such that there were approximately 100 global steps per cycle, where a “cycle” is one up-and-down flapping motion of the jet.
The simulation was initialized to a quiescent condition, and a fixed total pressure and total temperature were impulsively imposed at the nozzle inlet. It was advanced until start-up transients settled down, which was deduced by monitoring four numerical pressure taps on the wedge surface and in the free field. An FFT of a pressure trace from a numerical tap on the wedge surface near the leading edge is shown in Figure 3. The experimental frequency of 1936 Hz is shown by the red line, and the predominant frequency in the simulation is 2099 Hz, about 8.4% higher than the experiment.
The video sequence shows a series of contour plots of vorticity over approximately one complete cycle, with clockwise vorticity shown in red and counterclockwise vorticity shown in blue.
Each frame shows a pair of vortex streets that are generated by the interaction of the vorticity in the jet with the wedge. As the vortices traverse the boundary layers on the wedge they pull away the boundary layers, which is of opposite-direction vorticity, causing a series of separations and re-attachments. (862 KB QuickTime)
Conclusions and Future Work
A 2-D simulation has been performed to examine the unsteady fluid mechanics of an edgetone. The simulated frequency was within 8.4% of the experimental value. A complex interaction has been shown to exist between the vorticity in the jet and that in the boundary layers on the surface of the wedge. Although it has been reported in the literature that the edgetone flow is truly 2-dimensional, a simulation is underway to see if there are indeed any 3-dimensional effects.
 Brown, G. B., “The Vortex Motion Causing Edge Tones,“ Proceedings of the Physical Society of London, 49, pp. 493-507, 1937.
 Buning, P. G., Gomez, R. J., and Scallion, W. I., “CFD Approaches for Simulation of Wing-Body Stage Separation,” AIAA-2004-4838, Aug., 2004.