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Lagrangian-based investigation of multiphase flows by finite-timelyapunov exponents

Acta Mechanica Sinica 2012年第3期28卷 612-624页

作者： Jia-Ning Tang Chien-Chou Tseng Ning-FeiWang School of Aerospace Engineering Beijing Institute of Technology100081 Beijing China Department of Mechanical and Electro-Mechanical Engineering National Taiwan Sun Yat-Sen UniversityKaohsiung Taiwan China Department of Aerospace Engineering University of Michigan Ann ArborM148109 USA

Multiphase flows are ubiquitous in our daily life and engineering applications. It is important to investigate the flow structures to predict their dynamical behaviors ef- fectively. Lagrangian coherent structures （LCS） defined by the ridges of the finite-time lyapunov exponent （FTLE） is utilized in this study to elucidate the multiphase interactions in gaseous jets injected into water and time-dependent turbu- lent cavitation under the framework of Navier-Stokes flow computations. For the gaseous jets injected into water, the highlighted phenomena of the jet transportation can be observed by the LCS method, including expansion, bulge, necking/breaking, and back-attack. Besides, the observation of the LCS reveals that the back-attack phenomenon arises from the fact that the injected gas has difficulties to move toward downstream re- gion after the necking/breaking. For the turbulent cavitating flow, the ridge of the FTLE field can form a LCS to capture the front and boundary of the re-entraint jet when the ad- verse pressure gradient is strong enough. It represents a bar- rier between particles trapped inside the circulation region and those moving downstream. The results indicate that the FFLE field has the potential to identify the structures of mul- tiphase flows, and the LCS can capture the interface/barrier or the vortex/circulation region.

关键词： finite-time lyapunov exponents Lagrangiancoherent structures Multiphase flow Gaseous jets injectedinto water Cavitation

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Identification of Lagrangian coherent structures in the turbulent boundary layer

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Science China(Physics,Mechanics & Astronomy) 2009年第2期52卷 248-257页

作者： PAN Chong WANG JinJun ZHANG Cao Institute of Fluid Mechanics Beijing University of Aeronautics and AstronauticsBeijing 100083China

Using finite-time lyapunov exponents (FTLE) method, Lagrangian coherent structures (LCSs) in a fully developed flat-plate turbulent boundary layer are successfully identified from a two-dimensional (2D) velocity field obtained by time-resolved 2D PIV measurement. The typical LCSs in the turbulent boundary layer are hairpin-like structures, which are characterized as legs of quasi-streamwise vor- tices extending deep into the near wall region with an inclination angle θ to the wall, and heads of the transverse vortex tube located in the outer region. Statistical analysis on the characteristic shape of typical LCS reveals that the probability density distribution of θ accords well with t-distribution in the near wall region, but presents a bimodal distribution with two peaks in the outer region, corresponding to the hairpin head and the hairpin neck, respectively. Spatial correlation analysis of FTLE field is im- plemented to get the ensemble-averaged inclination angle θ R of typical LCS. θ R first increases and then decreases along the wall-normal direction, similar to that of the mean value of θ. Moreover, the most probable value of θ saturates at y+=100 with the maximum value of about 24°, suggesting that the most likely position where hairpins transit from the neck to the head is located around y+=100. The ensem- ble-averaged convection velocity Uc of typical LCS is finally calculated from temporal-spatial correla- tion analysis of FTLE field. It is found that the wall-normal profile of the convection velocity Uc(y) ac- cords well with the local mean velocity profile U(y) beyond the buffer layer, evidencing that the down- stream convection of hairpins determines the transportation properties of the turbulent boundary layer in the log-region and beyond.

关键词： turbulent boundary layer coherent structures vortex identification scheme finite-time lyapunov exponents hairpin-like

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