Transient Growth Of Perturbation In Shear Flows And Its Control

Transient growth of perturbation in shear ?ows plays an important role in theirtransition to turbulence involved in a wide range of engineering applications. The dis-sertation is devoted to the transient growth characteristics of shear ?ows, the in?uenceof transient growth of perturbations on the nonlinear evolution of swirling ?ow and thelinear feedback control of transient growth of perturbation energy in shear ?ows. Themain body contains three major parts:(1)The e?ects of channel curvature, wall suction/injection and surface tension ontransient growth of perturbation in shear ?ows are investigated based on the optimalperturbation analysis. The investigation of the optimal perturbation for CCPF showthat in the wide-gap case, channel curvature exhibits strong suppression of transientgrowth of perturbation energy; in the narrow-gap case, the transient growth charac-teristics of CCPF are qualitatively consistent with those of plane Poiseuille ?ow; inthe transition region, transient growth of perturbations, the magnitude of which isclosely related to the sensitivity of the eigenvalue spectrum to channel curvature, is notsensitive to the change of curvature. The study of the optimal perturbation for theTaylor-Couette ?ow with radial through-?ow implies that in the wide-gap case, radial?ow has a relatively large e?ect on transient growth. Strong radial ?ow is su?cientto destroy the lift-up mechanism responsible for transient growth of axisymmetric dis-turbances and always makes the axisymmetric mode the largest-growth one among allazimuthal modes. While in the narrow-gap case, radial ?ow has a relatively small e?ectand the lift-up mechanism, however, is a reasonable explanation for transient growthof axisymmetric modes. Radial ?ow does not alter the relative magnitudes of transientgrowth of di?erent azimuthal modes. The optimal perturbation analysis of CAF showsthat transient growth of the short-wavelength mode is suppressed to a greater extentby surface tension than that of the long-wavelength mode in axisymmetric cases, andthe increase of azimuthal wavenumber has a more signi?cant e?ect on transient growthof the long-wavelength perturbation.(2)The nonlinear evolution of swirling ?ow is analyzed by means of the ?nite di?er-ence scheme in cylindrical coordinate. It is found that the temporally evolving processof the optimal perturbation of the Oseen vortex can be divided into three stages: thelinear growth of perturbation energy, the interaction between the vortex ring and thevortex core and secondary energy growth; in the nonlinear stage, some dynamic phe-nomena is observed, such as the outward radial motion of vortex ring pair, and the su?cient ampli?cation of perturbation energy in the linear stage is the key to the ap-pearance of such dynamic behaviors; moreover, the perturbation in the form of the leaststable eigenmode always decreases with time. For the Batchelor vortex, the increase ofswirl ratio q tends to favor the formation of vortex ring with negative azimuthal voricityin the time evolution of axisymmetric optimal perturbation; in non-axisymmetric cases,the rapid production of the small eddies can not be found.(3)The suppression of transient energy growth in the Taylor-Couette ?ow by wallsuction/injection is studied based on the analysis of linear feedback control. Resultsshow that for axisymmetric modes, wall suction/injection has a better suppression ef-fect on transient growth in the narrow-gap case than that in the wide-gap case. Incontrast to radial through-?ow, wall suction/injection, does not alter the fact that thelift-up mechanism causes transient growth. For the transition parameters found in ex-periments (non-axisymmetric), the suppression in the energy growth is more signi?cantthan that in the axisymmetric case. Di?erent from the case of plane channel ?ow,actuation using the axial or azimuthal velocity component at walls has minor in?u-ences on the development of the optimal perturbation, thus cannot suppress its energygrowth e?ectively. Further, the results of DNS con?rm the suppression e?ect of un-steady wall suction/injection on the perturbation energy in the nonlinear evolution ofTaylor-Couette ?ow.