Research On Nonlinear Mode Interactions Relating To Supersonic Boundary Layer Transition

Nonlinear interaction between instability waves is one of the most important processes in boundary layer(BL)transition,research on which could contribute to the transition mechanisms.A combined numerical and theoretical research was performed in this thesis to study two types of most common nonlinear interaction processes: one is oblique breakdown initiated by oblique first modes in supersonic BL with medium or low Mach number,the other is selective enhancement of oblique modes by finite amplitude second mode in supersonic BL with high Mach number.As for supersonic BL with medium or low Mach number,oblique breakdown initiated by the most unstable oblique first mode is the most relevant transition mechanism.PSE was applied in this thesis to simulate process of oblique breakdown in Ma=2.0,3.0,4.5 flat-plate BL,focusing on the amplification characteristics of the stationary streamwise vortex mode and its influence on other modes.As for hypersonic BL,the most unstable two-dimensional(2D)second mode waves are likely to be amplified to finite amplitude first and bring nonlinear effects to other oblique modes.A transformed PSE method(tPSE)was derived in this thesis by applying a spectral transformation to the original PSE method,which enabled the method to simulate nonlinear interactions between modes with arbitrary frequencies efficiently.Using this method,evolution of different oblique modes under the influence of finite amplitude second mode were studied in a Ma 6.0 flat-plate BL.Nonlinear evolution characteristics of oblique modes in the whole relevant frequency band were drawn in the present thesis.The secondary instability analysis method were also applied in this thesis focusing on its applicability problem in supersonic BL.The main conclusions of this research are listed below:1.In the process of oblique breakdown,the stationary streamwise vortex(SSV)mode plays an active role in promoting the transition process by two ways.When the amplitude of the SSV mode overtakes the fundamental oblique mode,it could enhance the amplification of other quadratic harmonic modes and higher order harmonic modes through nonlinear interactions;when the SSV mode is amplified to a certain larger amplitude it could enhance the amplification of both the fundamental oblique mode and the non-harmonic mode by distorting the mean flow,which will promote the transition process.2.The relationship between amplitude evolution of the SSV mode and the fundamental mode were studied by a simplified theoretical model and numerical method.The theoretical analysis show that,as a result of the characteristic of its linear operator,the amplitude of SSV tends to be very large.The numerical results also confirms that the amplitude of the SSV mode is larger than other quadratic modes by an order.3.When the 2D second mode reaches a certain amplitude,it could enhance the amplification of oblique modes in a broad frequency band.The enhancement effect is accomplished by nonlinear interactions between the oblique mode,the 2D second mode and their difference mode.Two types of oblique modes are most likely to be amplified through the nonlinear interaction with 2D second mode: 1)Oblique modes with frequency around the fundamental frequency.The combining forced difference modes are the nearly stationary streamwise vortex mode.2)General oblique modes with frequency covering most of the unstable first mode frequency band.The combining forced difference mode are also general oblique modes.4.The amplitude of the 2D second mode is of critical importance: when amplitude of the 2D second mode is not very large,general oblique modes in a broad frequency band are more likely to be amplified;when the amplitude of the second mode reaches a certain value,say 0.06,the oblique modes with frequency around the fundamental frequency exhibit significantly larger nonlinear growth rates.5.Secondary instability analysis provides excellent prediction for the amplification of oblique modes with fundamental frequency,while the prediction for general oblique modes is also satisfactory.The analysis shows that the amplification of general oblique modes is caused by instability of the shear layer near the BL edge,which belongs to subharmonic secondary instability mode with a broad frequency detuning.The growth rate of this type is comparable with that of the second mode instability mode.While the amplification of the oblique modes with fundamental frequency are caused by instability of the shear layer near the wall,which belongs to fundamental secondary instability mode,with a much larger growth rate but smaller frequency band.