Abstract
This paper serves as a summary of new discoveries by DNS for late stages of flow transition in a boundary layer. The widely spread concept “vortex breakdown” is found theoretically impossible and never happened in practice. The ring‐like vortex is found the only form existing inside the flow field. The ring‐like vortex formation is the result of the interaction between two pairs of counter‐rotating primary and secondary streamwise vortices. Following the first Helmholtz vortex conservation law, the primary vortex tube rolls up and is stretched due to the velocity gradient. In order to maintain vorticity conservation, a bridge must be formed to link two Λ‐vortex legs. The bridge finally develops as a new ring. This process keeps going on to form a multiple ring structure. The U‐shaped vortices are not new but existing coherent vortex structure. Actually, the U‐shaped vortex, which is a third level vortex, serves as a second neck to supply vorticity to the multiple rings. The small vortices can be found on the bottom of the boundary layer near the wall surface. It is believed that the small vortices, and thus turbulence, are generated by the interaction of positive spikes and other higher level vortices with the solid wall. The mechanism of formation of secondary vortex, second sweep, positive spike, high shear distribution, downdraft and updraft motion, and multiple ring‐circle overlapping is also investigated.
Highlights
The transition process from laminar to turbulent flow in boundary layers is a basic scientific problem in modern fluid mechanics and has been the subject of study for over a century
The secondary vortex can be developed only through flow separation which is caused by the adverse pressure gradient
(2) A vortex tube inside the flow field cannot have ends, and vortex ring is the only form existing inside the flow field because the ring has no ends, head, or tail
Summary
The transition process from laminar to turbulent flow in boundary layers is a basic scientific problem in modern fluid mechanics and has been the subject of study for over a century. The ring-like vortex formation and development are a key topic for late flow transition in boundary layer. It appears that there is no turbulence without ring-like vortices. Crow theory [8] has been considered as the mechanism of multiple ring formation [2] They pointed out that “the formation of a set of vortex rings from two counter-rotating vortices is usually called “Crow instability.”. The paper is organized in the following way: Section 2 presents the governing Navier-Stokes equations and numerical approaches; Section 3 shows the code verification and validation to make sure that the DNS code is correct; Section 4 provides the new DNS results and summarizes the new discoveries and new mechanism of formation and further development of ring-like vortices.
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