期刊名称：Proceedings of the National Academy of Sciences
印刷版ISSN：0027-8424
电子版ISSN：1091-6490
出版年度：2015
卷号：112
期号：26
页码：7920-7924
DOI：10.1073/pnas.1509451112
语种：English
出版社：The National Academy of Sciences of the United States of America
摘要：SignificanceThe precise dynamics of disturbance energy growth and breakdown in pipe transition is a century-old unresolved problem in fluid mechanics. In this paper, we demonstrate that the mystery attributed to the breakdown process of the Osborne Reynolds pipe transition can be partially resolved with a direct, spatially evolving simulation that carries weakly but finitely perturbed laminar inflow through gradual rather than abrupt transition arriving at the fully developed turbulent state. Some of the previously attributed abruptness and mysteriousness was perhaps due to the inability to study the process accurately with very fine spatial and temporal resolution. The energy norm was found to grow exponentially rather than algebraically. The sensitivity of the transition process to pipe entrance conditions is demonstrated. The precise dynamics of breakdown in pipe transition is a century-old unresolved problem in fluid mechanics. We demonstrate that the abruptness and mysteriousness attributed to the Osborne Reynolds pipe transition can be partially resolved with a spatially developing direct simulation that carries weakly but finitely perturbed laminar inflow through gradual rather than abrupt transition arriving at the fully developed turbulent state. Our results with this approach show during transition the energy norms of such inlet perturbations grow exponentially rather than algebraically with axial distance. When inlet disturbance is located in the core region, helical vortex filaments evolve into large-scale reverse hairpin vortices. The interaction of these reverse hairpins among themselves or with the near-wall flow when they descend to the surface from the core produces small-scale hairpin packets, which leads to breakdown. When inlet disturbance is near the wall, certain quasi-spanwise structure is stretched into a Lambda vortex, and develops into a large-scale hairpin vortex. Small-scale hairpin packets emerge near the tip region of the large-scale hairpin vortex, and subsequently grow into a turbulent spot, which is itself a local concentration of small-scale hairpin vortices. This vortex dynamics is broadly analogous to that in the boundary layer bypass transition and in the secondary instability and breakdown stage of natural transition, suggesting the possibility of a partial unification. Under parabolic base flow the friction factor overshoots Moody's correlation. Plug base flow requires stronger inlet disturbance for transition. Accuracy of the results is demonstrated by comparing with analytical solutions before breakdown, and with fully developed turbulence measurements after the completion of transition.
