Direct numerical simulation of the stability of zero-pressure-gradient boundary layer over corrugated wall using the immersed interface method

Abstract

The influences of surface corrugations on zero-pressure-gradient boundary-layer instability were examined numerically by solving the two-dimensional compressible Navier-Stokes equations. The immersed interface method with compact filter and Navier-Stokes characteristic boundary condition (NSCBC) was newly proposed and applied. Two kinds of computation were made: a channel flow to validate the numerical scheme used and a zero-pressure-gradient boundary layer over a corrugated surface whose amplitude was less than 10% of the boundary layer thickness and wavelength was ranged from half to double the T-S wavelength. Linear stability analyses based on the parabolized stability equations (PSE) were also made to see how critically the corrugation modified the neutral stability curves. The results showed that the characteristics of the T-S waves in the channel with the corrugated wall were in excellent agreement with the linear stability theory, thus verifying the numerical accuracy of the present scheme. The surface corrugation destabilized the boundary layer significantly due to positive energy production occurring just behind the corrugation crest. The PSE analyses well described the development of T-S waves over the corrugated surface. When the corrugation height was 3%, 5% and 7% of the boundary-layer thickness, the critical Reynolds number based on the displacement thickness was about 4%, 14% and 19% lower than that for the smooth surface, respectively, while destabilization effect was weakly dependent of the corrugation wavelength. It was also found that the transient distance of change in surface geometry was much shorter for boundary-layer flows than for channel flow; for corrugation whose height was 4% the boundary layer thickness and wavelength was the same order as that of TS wave, the instability nature became the same as that for the case of corrugation over entire surface at the distance of about 4 times the corrugation wavelength from the beginning of corrugation, which was about 1/5 of that for the channel.

Keywords

• boundary-layer instability
• corrugated wall
• immersed interface method
• direct numerical simulation (dns)
• parabolized stability equations