Study On Liutex/vortex Identification Method And Flow Transition Of Airfoil

The vortex structure is usually called the turbulent coherent structure in turbulent flow.It is considered to be one of the most significant characteristics in the process of turbulence generation and maintenance,and plays an important role in the generation(transition),maintenance and evolution of turbulence.Therefore,the study of turbulence can be carried out from the following two aspects.The first is to give a clear and generally accepted definition of vortex and coherent structure,and form a clear understanding of the turbulent structure according to the clear vortex definition.Then further study the dynamic characteristics of vortex and its relationship with turbulence,the main work and research results of this paper are as follows:(1)Based on the definition of the Liutex vortex structure proposed by Liu Chaoqun et al.and a special(transposed)Schur form of the velocity gradient tensor,the explicit expression for the Liutex definition is presented from a purely mathematical perspective.According to the explicit expression,a new implementation is proposed without any explicit calculation of the coordinate rotation,which indicates further improvement of the computational efficiency.It contributes to the application of Liutex concept in turbulence research(2)Analyze the dynamic characteristics of Liutex.When the results of the direct numerical simulation of the plate boundary layer reach a stable state,record the values of Liutex,Q,Vorticity and velocity pulsation at different positions in the boundary layer with time step,and perform spectral analysis and turbulent kinetic energy spectrum analysis of each variable,the conclusions are as follows:Both the frequency and wavenumber spectrums follow the-5/3 law almost exactly in a moderate Reynolds number turbulent boundary layer.On the other hand,the spectrum of vorticity and other vortex identification methods,for example,Q,deviate from power law spectrum of any order.In addition,the energy spectrum of the same flow only marginally matches the-5/3 law in a much smaller frequency range.This astonishing Liutex similarity attributes to that Liutex represents the rigid rotation motion part which are free from viscous effect while vorticity and other vortex identification methods are contaminated by stretching and shearing,the energy spectrum can only be asymptotic obtained given sufficient high Reynolds number.Therefore,the Liutex similarity of-5/3 law independent of the assumption of high Reynolds number and applies more generally.It may become an important similarity law in turbulence and could be served as a better method to study turbulence.(3)The large eddy numerical simulation of the flow around the airfoil with different Reynolds number and different swept angle is carried out,and the experimental verification is given.The pressure and velocity component pulsation in each region of the boundary layer is detected,and the pulsation characteristics of each variable in each region are obtained.The evolution process of the vortex structure on the airfoil surface is obtained by using the Liutex characterization method,the conclusions are as follows:The flow in the separation region on the airfoil surface is divided into two stages.The streamlines in the first stage are relatively regular,and the streamlines in the second stage are very chaotic,the flow state of the fluid changes,and a transition occurs during this process.In the viscous bottom layer of fully developed turbulent region,the relative values of pressure and velocity components are much larger than those in the laminar region,the Liutex line is chaotic,and the state of fluid motion in the viscous bottom layer is not like laminar flow.With the increase of Reynolds number,the earlier the flow separation occurs,but the smaller the bubble size is,the earlier the transition occurs.With the increase of the sweep angle,the maximum velocity on the upper surface of the airfoil,especially on the leading edge of the airfoil,will decreases;The starting position of separation is further away from the leading edge of the airfoil,but the amplitude of the cross-flow velocity component increases faster,and the proportion of the influence of the cross-flow velocity component on the flow transition increases,which promotes the transition,also makes the reattachment position advance.So,the size of separation bubble decreases.Streamline and vorticity are not good methods to characterize the transient vortex structure.Streamline is easily affected by the time average velocity,while vorticity is easily contaminated by shearing.In the latter part of the flow separation zone,the spanwise vortex falls off.The spanwise vortices move to the downstream and become larger gradually,and become irregular ? vortices which with head and legs.In the process of moving downstream,the ? vortex deforms and the flow becomes more disordered.There are many irregular small vortices(irregular flow vortices)under the spanwise vortices.During the movement of the spanwise vortex,the small vortex in the bottom layer will be brought to the high layer,and the vortex will mix with the spanwise vortices to form a vortex leg,which will promote the formation of ? vortex,and the spanwise vortices will continue to rise in the process of deformation.The larger the sweepback angle is,the easier the spanwise vortices will deform rapidly,and the vortex inclines,which makes the ? vortex more asymmetric.