Effect Of Distributed Surface Roughness On Crossflow Instability Through Generalized Resonance Mechanism

The prediction of transition location under wing surface is an important element for designing energy-efficient wing,and depends on the physical understanding of flow instability and transition.Experiments have shown that micron-sized distributed surface roughness can promote transition on the swept wing significantly.The corresponding mechanism behind this is not fully understood.The present thesis will try to give a theoretical explanation by studying the effect of distributed surface roughness on crossflow instability of Falkner-Skan-Cooke boundary layer.Unlike previous theoretical studies,the effect of distributed roughness on crossflow instability is studied in this thesis based on the resonant interaction between the disturbance induced by distributed roughness and crossflow eigenmodes.The traditional triad resonance and Bragg scattering are generalized to govern the resonant interaction.Based on finite Reynolds-number theory,the amplitude equations of crossflow eigenmodes are derived.By solving the amplitude equations,two parameters,which are growth-rate correction coefficient and amplitude ratio,are introduced in order to describe the effect of distributed surface roughness on crossflow eigenmodes quantitatively.Growth-rate correction coefficient reveals the correction to original growth rate which is the product of it and roughness height.Amplitude ratio reveals that the eigenmodes involved in resonance are fully coupled,and the ratio of their amplitudes must be definite.The numerical results show that growth-rate correction coefficient can be relatively large,even be of O(1),with roughness wavenumbers sufficiently close to the wavenumbers of the right-branch stationary neutral eigenmode,where micron-sized roughness(1% of the local boundary-layer thickness)can have a great influence on growth rate.For multiple-wavenumber roughness there exists the most dangerous scales that effect the growth rates of crossflow eigenmodes.The larger growth-rate correction coefficient for larger m means that crossflow instability is much more sensible to roughness around the leading edge.When roughness wavenumbers are equal to the wavenumbers of the right-branch stationary neutral eigenmode,with nonparallelism considered the corresponding boundary-layer response and growth-rate correction coefficient are finite values.