New Findings by High‐Order DNS for Late Flow Transition in a Boundary Layer

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 counterrotating 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.

DNS Study on Physics of Late Boundary Layer Transition

“…Qualitative vortex structure comparison with experiment All these verifications and validations above show that our code is correct and our DNS results are reliable.III. Observation and Analysis by Our DNSFollowing observations have been made and reported by our previous publications(Chen et al, 2009Liu et al, 2010aLiu et al, , 2010bLiu et al, , 2010cLiu et al, , 2011aLiu et al, , 2011b Liu et al, 2011c Liu et al, , 2011dLu et al, , 2011b.…”

“…In our DNS work(Chen et al, 2009Liu et al, 2010aLiu et al, , 2010bLiu et al, , 2010cLiu et al, , 2011a, 2011b 2011c, 2011d; Lu et al, 2011a, 2011b, 2011c), we have made a number of new findings on late flow transition in a boundary layer including the mechanism of large vortex structure formation, small-length scale generation and flow randomization (loss of symmetry), which can be summarized as follows (some of conclusions have been published in our previous papers):…”

New Theories on Boundary Layer Transition and Turbulence Formation

“…The classical theory, which considers "vortex breakdown" as the last stage of boundary layer transition on a flat plate, is challenged and the phenomenon of "hairpin vortex breakdown to smaller structures" is not observed by our new DNS [24,27,28]. The so-called "spikes" are actually a process of multibridge or multiring formation, which is a rather stable large vortex structure and can travel for a long distance.…”

“…In the new DNS [27,28], it has been observed that the multiple vortex structure is a quite stable structure and never breaks down. Previously reported "vortex breakdown" is either based on 2-D visualization or made by using low pressure center as the vortex center (Figure 21(a)).…”

Numerical Study on Randomization in Late Boundary Layer Transition

“…They concluded that the U-shaped vortex is a barrel-shaped head wave, secondary vortex, and is induced by second sweeps and positive spikes. In order to get deep understanding the mechanism of the late flow transition in a boundary layer and physics of turbulence, we recently conducted a high order direct numerical simulation (DNS) with 1920×128x241 gird points and about 600,000 time steps to study the mechanism of the late stages of flow transition in a boundary layer at a free stream Mach number 0.5 (Chen et al, 2009(Chen et al, , 2010a(Chen et al, , 2010b(Chen et al, , 2011a(Chen et al, , 2011bLiu et al, 2010aLiu et al, , 2010bLiu et al, , 2010cLiu et al, , 2011aLiu et al, , 2011bLiu et al, 2011cLiu et al, , 2011dLu et al, 2011aLu et al, , 2011b. The work was supported by AFOSR, UTA, TACC and NSF Teragrid.…”