The Numerical Simulation Of Transition For Spanwise Wavepacket Disturbances In Boundary Layers And The Prediction By The PSE Method

In this paper, the evolutions of disturbances in incompressible boundary layers onflat plates and curved surfaces were investigated based on the spatial model. Firstly,the evolutions of two types of disturbances were studied. The two types were identicalamplitude and wavepacket along the spanwise in flat plate boundary layers. Thetransition mechanisms of two types of disturances were studied too. Secondly, withthe improved PSE method, the evolution of disturbances and prediction of thetransition position were studied in flat plate boundary layers. The results werecompared with the numerical simulation. Lastly, the disturbances evolution and theapplication of PSE in curved boundary layers were researched. We obtained thefollowing conclusions:(1) The evolution characteristics of identical amplitude disturbances alongspanwise were showed. In the upstream, the two-dimensional basic wavedominated. With the disturbance evolution, the amplitude of the2-D basicwave increased firstly and then decreased. The decrease was induced by therapid growth of3-D basic waves. Then3-D basic waves would dominantwhen the amplitudes exceeded2-D wave. Because of the rapid growth of3-D waves, the high harmonic waves were stimulated and the spanwise sizebecame smaller, then the transition occurred.(2) The evolution characteristics of spanwise wavepacket disturbances wereshowed. With the evolution of disturbances, one peak splited to two peaks.Between peaks, the high wavenumber3-D waves appeared and then thepeaks would gradually vanish. The spanwise of wavepacket would expand.The large scale structures broken into small scale structures. The higherwavenumber3-D waves were simulated by low wavenumber waves. Theflow structures would be crescent,-vortex, streamwise streak andunordered turbulence structure successively.(3) For identical amplitude and wavepacket disturbances, the stabilities of localmean flow were analysed. The transition mechanism was obtained. In initialstage of evolution, the stable zone was small and only a few waves couldgrow. With the evolution, the mean flow velocity profile changed quickly due to the nonlinear effect. The instability zone enlarged and more andmore high harmonic waves were simulated rapidly and the transitionhappened. The analysis of different spanwise positions indicated that thetransiton was triggered by definite amplitude of spanwise wavepacketdisturbance. In different spanwise positions, the transition positions weredifferent, but the transition processes and characteristics were similar.(4) For all kinds of boundary layers that were discussed, the evolution ofdisturbances was consistent by PSE and numerical simulation beforetransition. The position of the PSE invalid and the beginning of transitionby numerical simulation were the same basically. Therefore, the PSEinvalid position could predict the transition position.(5) With PSE method, the influence of spanwise wavenumber and amplitude onthe transition position was studied for identical amplitude disturbances. Thespanwise wavenumber which made the transition position forefront existed.When the wavenumbers were larger than critical wavenumber, thetransition position would delay with the wavenumber increase. The largerwere the initial amplitudes, the fronter were the transition positions.(6) For the identical curvature circle pipeline, the transitions were restrainedbecause of the curvature. The transition positions would be delay with thelarger curvature. For the NACA0012wing boundary layer, the relations ofthe transition position and the amplitude and frequency of2-D wave weredisscussed. Besides, the transition positions were predicted.