| Turbulence is always a complex issue in research of flow dynamics,and the discussion on the turbulence mechanism is controversial.The vortex structure has been widely recognized in turbulent flow field,and plays a critical role in turbulence generation,evolution and the sustenance.However,there is no doubt that the mathematical definition of vortex and its identification is the starting point to be studied in the first place,which is particularly important for the further study on vortex generation and development,and on the correlational mechanism.The study is based on the contribution of the vortex mathematical definition and identification.On the one hand,a systematic analysis on the vorticity structures,vortex structures as well as their generation mechanism by direct numerical simulation(DNS)is given.The corresponding discussion is combined with the vorticity flux conservation law,vorticity transport equation,correlation between the volume vorticity and rotation and the mode decomposition.On the other hand,the vortex rings/shock interaction in supersonic turbulent boundary layer is simulated by implicit large eddy simulation(ILES).The mechanism of the vortex rings/shock interaction is studied based on their structure and frequency characteristics.(1)A new fl method based on the determination of ε function is proposed as a superior method over other vortex identification methods,such as △,λci,Q,λ2 and Ω criteria.The new fl vortex identification method is non-dimensional,functional,case-and time-independent and robust,and has capability to capture the strong and weak vortices simultaneously,which naturally becomes the basic tool for the further research on vortex structures.In addition,an accurate vortex vector named as Rortex,giving the local rotation strength as well as the rotation axis,is co-proposed as a participant.The vortex structures in any flow can be accurately illustrated and displayed by using Rotex lines,Rortex vector field or Rortex iso-surface.(2)The generation of vorticity structures in a transition flow on a flat plate and its comparison with the vortex structures are discussed.Meanwhile,a snapshot proper orthogonal decomposition(Snapshot POD)on various vortex structures in late transitional flow is performed to decompose the typical modes with typical energy,and to do the flow field reconstruction.For the vorticity structures,except for the vorticity lines which come from and end at periodic side boundaries,another type of vorticity structure,self-closed vorticity lines,which can be called vorticity rings,are numerously generated inside the domain during the transition process.The basic mechanism of vorticity generation can be described that the new vorticity can be changed by the flow diffusion,and the stretching,tilting and twisting of the vorticity tubes;all newly generated vorticity can only have a unique form without exception—vorticity rings.For the vortex structures,the streamwise vortex always plays the most dominant role in transitional flow since it takes up 99.5%of the total energy of the vortex structures.(3)Volume vorticity and volume fl are introduced to describe the turbulence generation and increase in the late flow transition.The results show the flow transition is a process with significant volume vorticity increase,which is attributed by two crucial factors:the elongation of the vorticity tubes from side boundary due to the vorticity line stretching,distortion and tangling and the generation of numerous self-closed vorticity rings within the domain.On the other hand,the volume Ω equals zero in the laminar flow but quickly increases during the flow transition process.The increase of volume Ω reflects the buildup of vortex in flow transition.There is a close correlation between the volume vorticity and the volume Ω.(4)The process of the shock wave and the vortex ring interaction in a supersonic ramp flow is simulated to analyze the frequency characteristics of both vortex ring motion and the shock oscillation.The shock produced by a compression ramp flow has a non-dimensional,dominant low frequency around Stshock=0.002.Meanwhile,the vortex rings generated by the MVG in a supersonic ramp flow has a dominant high frequency around Stvortex=0.038.The dominant low frequency of the shock can be weakened or even removed by the vortex rings through the shock and vortex ring interaction due to the higher frequency of the vortex ring motion behind MVG.However,the vortex rings are strong and stiff enough to break or weaken the shock but keep its high frequency and their structures. |
