Recent studies have shown that roughness element can suppress mode S when it is placed at the right location. In particular, our previous DNS research has shown that when the 2-D roughness element is placed downstream of the synchronization location, mode S is suppressed. On the other hand, if the roughness element is located upstream of the synchronization point, mode S is amplified and destabilized. Recently, an experiment has confirmed the roughness stabilization effects on mode S by judiciously placing roughness elements downstream of the most dangerous frequency's synchronization point on a flared cone. In the present paper, we extend our study on the roughness effect by using DNS and a theoretical approach of PSE analysis. The goals here are to investigate the mechanism of roughness effects observed in DNS simulations, and to study the role of neutral stability point and synchronization point. Different roughness heights and widths are considered similar to our previous studies. It is found that PSE can indeed predict the roughness effects observed in DNS, and the PSE results confirm the trends of roughness height and width effects as seen in simulations. Our PSE results also suggest that the effect of roughness on Mack mode is the result of alteration of meanflow, and no new instability mode is found. Lastly, our DNS results overwhelmingly show that the synchronization location is an important parameter in determining the roughness effect comparing with the location of the neutral stability point.
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