Study On Instability Of Stationary Crossflow Vortices In Hypersonic Swept Blunt Plate Boundary Layers

Whether the flow over the surface of an aircraft is laminar or turbulent makes a significant difference in the drag and the heat flux.Therefore,the transition onset plays an important role in the drag design of an aircraft and in the heat protection design of a supersonic aircraft.What is more,transition prediction relies on the comprehensive knowledge of instability mechanisms.Crossflow instability which includes both stationary crossflow vortex and travelling wave is a typical instability mechanism in the swept flow.Because of the lower turbulence level,the stationary crossflow vortex dominates the transition process in flight condition.In this thesis,the instability of stationary crossflow vortex in supersonic boundary layers on a swept blunt plate are studied.The focus is on the nonlinear evolution of stationary crossflow disturbances and the secondary instability of saturated crossflow vortices.The main work and conclusions are as follow.The corresponding research methods are improved:1.The algorithm for solving the nonlinear parabolized stability equations(NPSE)is improved.The mean flow distortion is included into the linear operator.Additionally,an under relaxation factor is introduced when the nonlinear terms are calculated iteratively.The proposed algorithm dramatically improved the convergence of NPSE method.2.In order to investigate the secondary instability of stationary crossflow vortices,we proposed a strategy,which can be referred as Bi-coordinate strategy,built on two coordinate systems.Based on this strategy,the Bi-Global method and the 3DPLE method marching along a plane are established.The Bi-coordinate strategy not only covers the shortage of the orthogonal coordinate strategy,but also avoid the complexity of the non-orthogonal one.More comprehensive knowledge of crossflow instability mechanism is also acquired.1.The characteristic of crossflow instability in the conditions with different cruising altitudes and different flight Mach number is studied.It is explained theoretically that a small angle must exist between the wave vector direction and the perpendicular direction of potential flow.2.The nonlinear evolution of stationary crossflow disturbance,the interaction between waves with different spanwise wavenumbers and the development of the stationary crossflow vortices are studied in hypersonic flow.Then the conclusions come as follow.Although the nonlinearity leads to the saturation of stationary crossflow vortex,the linear growth rate,to some extent,determines the saturation characteristic.The stationary crossflow vortex does not sustain the saturation unless the disturbances possess long amplification zone and large grow rate.The wave with limited amplitude and big spanwise wavenumber can dramatically suppress the amplification of the most unstable wave.Although the velocity component in wall-normal and spanwise directions are significantly less than the one in the vortex axes direction,they play a key role in the development of the vortex structures.3.The secondary instability characteristic of saturated stationary crossflow vortices in a (6 =6 flow is analyzed by Bi-Global method.Accompanying with the amplification of the disturbance and the development of the vortex,the strong velocity shear appears on the top of the vortex,which leads to the secondary instability.As the vortex becomes stronger,the secondary instability is enhanced and more unstable modes are observed.The secondary instability is most unstable when the mean flow distortion reaches its saturation.Although the amplitude of disturbance sustains saturation for the downstream,the secondary instability becomes weaker.The reason is that the low momentum fluid near the wall is not rolled up enough to the top of the vortex and then the velocity shear becomes weaker.4.DNS and 3DLPSE are applied in studying the spatial evolution of secondary dominant modes.It is found that Bi-Global method can be used for showing the characteristics of secondary modes.However,non-parallelism influences the secondary instability of steady crossflow vortices obviously and leads to a larger growth rate.We focus on the dominant modes and find that dominant modes grow or decay independently and a non-dominant mode or a simplified disturbance may grow to be a dominant one.5.For the case (6 =10,the excitation of steady crossflow vortices is studied by DNS with the compensation of boundary conditions.We conclude that the steady crossflow vortices can be excited by a micrometer scale roughness element and there is a linear relationship between the amplitude of the crossflow vortices and the height of the roughness elements.Based on the linear stability theory,the influence of streamwise length on receptivity of crossflow vortices can be estimated by a Fourier analyses.