Direct Numerical Simulation And Statistical Analysis Of Compressible Turbulent Boundary Layer

Investigation of compressible turbulent boundary layer is of great importance forthe development of high-speed vehicles and turbulence modeling. In this dissertation,statistical properties of compressible turbulent boundary layer are studied using directnumerical simulation. The results and conclusions are brie?y given as follows:(1) Characteristics of coherent vortical structures in a compressible turbulentboundary layer are statistically analyzed for Mach number M∞= 2 andReynolds number Reθ≈1350. It is found that a large variety of hairpin-like andcane-like vortical structures exist in the boundary layer and the most popularstructure is the cane-like one. The ejection and sweep events contribute a majorproportion of the total Reynolds stress. This study indicates structural simi-larities with the incompressible case. Moreover, the length scales of coherentstructures in the streamwise and spanwise directions increase with the distancefrom the wall. The inclination angle of coherent vortical structures with respectto the streamwise direction increases from the sublayer to the bu?er layer andthen decreases from the bu?er layer to the wake region.(2) The ?ow topology of compressible turbulent boundary layer at Mach 2 has beenstudied systematically based on the analysis of the velocity gradient tensor in-variants. It is found that the inner layer is mainly comprised of the unstablefocus/compressing (UFC) topology, and the outer layer is dominated by the un-stable node/saddle/saddle (UN/S/S) topology. The dissipation and dissipationproduction mainly come from UN/S/S. The enstrophy is related to the unsta-ble focus/stretching (UFS) topology, and the enstrophy production depends onUN/S/S in the inner layer and on UFS in the outer layer. It is also revealed thatthe compressed region is favorable to the stable topologies, and the expandingone to the unstable topologies. Moreover, in the compressed region, the oc-currence possibility and enstrophy of UFC are decreased, while the dissipation,dissipation production and enstrophy production of UFC are increased. In theexpanding region, the occurrence possibility and enstrophy of SFS are decreased,while the dissipation, dissipation production and enstrophy production in theinner layer of SFS are increased. Then, the ?ow topologies associated with theinvariants of the rotation-rate tensor and strain-rate tensor are analyzed. It isfound that the e?ect of compressibility is to enhance the dissipation and theexpanding turbulent structures are more dissipative than the compressed ones.(3) Statistical properties of the interaction between strain and vorticity in com-pressible turbulent boundary layer at Mach 2 are investigated. The enstrophyproduction in the invariants plane is investigated by observation of the statisticaltendency of the vorticity vector to align with the eigenvectors of the strain-ratetensor. It is identified that, in the inner layer, the vorticity vector tends to beperpendicular to the extensive strain-rate eigenvector for all the topologies, andthe enstrophy production mainly comes from the unstable node/saddle/saddle (UN/S/S); in the outer layer, the vorticity vector prefers to align with the exten-sive strain-rate eigenvector for stable focus/stretching (SFS) topology, and theenstrophy production is dominated by this topology. Then, the joint probabilitydensity functions of the enstrophy production rate and the relevant quantitiesare analyzed for the enstrophy producing and enstrophy destroying regions. Itis found that higher enstrophy production is associated with higher dissipationproduction and higher enstrophy destruction with higher dissipation destruc-tion in the inner layer. Moreover, the enstrophy producing region has a distincttendency to form'sheet-like'structures and high enstrophy production tends tocoincide with large swirling strength in the boundary layer. It is also found thatthe enstrophy destroying region tends to be'tube-like'in the inner layer.(4) E?ects of Mach number on statistical properties of turbulence are investigatedwith free-stream Mach numbers 2, 4 and 6. Some typical turbulent quantitiesare studied. It is found that the turbulence intensities are significantly de-creased, and the magnitudes of the turbulent kinetic energy budget terms areincreased with the increasing Mach number. The onset of the intrinsic inter-mittency occurs nearer the wall for higher Mach number. Then, the statisticalproperties of the velocity gradient tensor invariants are analyzed. It is revealedthat the dissipation, enstrophy, dissipation production and enstrophy produc-tion are increased with the increase of Mach number. The mean dilatation andthe magnitude of the dilatation are also increased. With the Mach numbervarying from 2 to 6, the contributions of the stable focus/stretching topologyto the dissipation, enstrophy, dissipation production and enstrophy productionare decreased and the contributions of the unstable focus/stretching topologyare increased.(5) Impinging shock wave/turbulent boundary layer interaction at Mach number 2is studied. The e?ects of the inclined shock wave on the statistical propertiesof turbulence in the interaction zone are investigated. It is found that thedissipation and enstrophy are weakened in the inner layer and enhanced inthe outer layer. The dissipation production and enstrophy production are alsoincreased in the outer layer. Moreover, the magnitudes of the dissipation andenstrophy budget terms are increased. As the e?ect of shock wave, the mean?ow is compressed and the dilatation term tends to enhance the dissipation andenstrophy.