Late Boundary Layer Transition Research Articles

DNS study on bursting and intermittency in late boundary layer transition

Experimental and numerical investigations have suggested the existence of a strong correlation between the passage of coherent structures and events of bursting and intermittency. However, a detailed cause-and-effect study on the subject is rarely found in the literature due to the complexity and the nonlinear multiscale nature of turbulent flows. The primary goal of this research is to explore the motion and evolution of coherent structures during late transition, whose structure is much more ordered than that of fully developed turbulence, and their relationship with events of bursting and intermittency based on a verified high-order direct numerical simulation (DNS). The computation was carried out on a flat plate at Reynolds number 1000 (based on the inflow displacement thickness) with an inflow Mach number 0.5. It is concluded that bursting and intermittency detected by stationary sensors in a transitional boundary layer actually result from the passage and development of vortical structures, and it would be more rational to design transitional turbulence models based on modelling the moving vortical structures rather than the statistical features and experimental experiences.

DNS Study on Vortex and Vorticity in Late Boundary Layer Transition

AbstractVortex and vorticity are two correlated but fundamentally different concepts which have been the central issues in fluid mechanics research. Vorticity has rigorous mathematical definition (curl of velocity), but no clear physical meaning. Vortex has clear physical meaning (rotation) but no rigorous mathematical definition. For a long time, many people treat them as a same thing. However, based on our high-order direct numerical simulation (DNS), we found that first, “vortex” is not “vorticity tube” or “vortex tube” which is widely defined as a bundle of vorticity lines without any vorticity line leak. Actually, vortex is an open area for vorticity line penetration. Second, vortex is not necessarily congregation of vorticity lines, but dispersion in many 3-dimensional cases. Some textbooks say that vortex cannot end inside the flow field but must end on the solid wall (and/or boundaries). Our DNS observation and many other numerical results show almost all vortices are ended inside the flow field. Finally, a more theoretical study shows that neither vortex nor vorticity line can attach to the solid wall and they must be detached from the wall.

Physics of turbulence generation and sustenance in a boundary layer

In this paper, a systematic report of our recent DNS study on physics of late boundary layer transition is presented. This includes mechanism of the large coherent vortex structure formation, small length scale generation and flow chaos. First, it is not appropriate to call the turbulent flow as a “random” motion since the conservation law of mass, momentum and energy must be satisfied. Turbulence is built up by organized “vortex packets” which can be accepted by Navier–Stokes equations. Second, the linearly unstable modes are important, but the role of these modes is only to trigger the vorticity rollup. They cannot form the vortex by themselves and cannot cause the flow transition directly. The flow transition is mainly an inherent property of fluid flow, which shows that fluids cannot tolerate shear and shear must transfer to rotation when Reynolds number is large. The commonly accepted concept that “Lambda vortex self-deforms to hairpin vortex” does not exist. Finally, the widely spread concept “vortex breakdown to turbulence”, which was considered as the last stage of flow transition, is not observed.We proposed a new mechanism about turbulence generation and sustenance, that all small length scales (turbulence) are generated by shear layer instability produced by large vortex structure with multiple level vortex rings, multiple level sweeps and ejections, and multiple level negative and positive spikes near the laminar sub-layers. Therefore, “turbulence” is not generated by “vortex breakdown” but rather positive and negative spikes and consequent high-shear layers. “Shear layer instability” is considered as the “mother of turbulence”. This new mechanism may give a universal mechanism for turbulence generation and sustenance – the energy is brought by large vortex structure through multiple level sweeps not by “vortex breakdown”. Fluid shear, which is dominant in laminar boundary layer, is conditionally unstable but fluid rotation, which is dominant in turbulent boundary layer, is stable. In other words, the laminar boundary layer is an unstable state, but the turbulent is a stable state, and thus transition from laminar to turbulent is doomed when the Reynolds number is large enough. We prefer to present new stages to describe the boundary layer transition with five steps, i.e. perturbation (may include receptivity and linear instability), vorticity rollup, large vortex formation, small length scale generation, loss of symmetry and becoming chaotic to turbulence.

DNS study on Λ-vortex and vortex ring formation in flow transition at Mach number 0.5

Large vortex structure in late boundary layer transition with an inflow Mach number of 0.5 is studied by DNS (Direct Numerical Simulation) in this paper. First, we found that there are no Λ-vortex tubes, contradicting to what the existing literatures and textbooks addressed. The so-called Λ-vortex is always open on head, which has a different shape from Λ. Λ-vortex is really a pair of open rotation cores with a lower half of the Λ shape. It is also found that the Λ-vortex and ring-like vortex are formed separately and independently. There is no such a process that the Λ-vortex self-deforms to a hairpin vortex at the tip as many literatures indicated. Λ-vortex and ring-like vortex can be visualised by the iso-surface of λ2. However, the iso-surfaces of λ2 only represent rotation cores but not necessarily vortex tubes. In fact, many spanwise vortex filaments can easily penetrate the so-called Λ-vortex (iso-surface of λ2), change the direction toward the streamwise direction, and then leave the iso-surface of λ2. The vortex ring is not part of the original Λ-vortex but is formed separately. The Λ-vortex cores were originated from the 2D and 3D T-S waves, amplified and became strong by attracting neighbouring spanwise vortex filaments from the boundary shear layer. As the Λ-vortex becomes strong, a strong shear layer is formed above the Λ-vortex roots, which is caused by ejection of the Λ-vortex rotation to bring low speed flow from the bottom of the boundary layer to form an olive-like low speed zone. As a result, the instability of the shear layer leads to the formation of new ring-like vortex tubes one by one.

Numerical investigation on chaos in late boundary layer transition to turbulence

The mechanism of chaos in late boundary layer transition is a key issue of the laminar-turbulent transition process in a flat plate boundary layer. A careful study on the characteristic of chaos is carried out by high order direct numerical simulation (DNS). The process of flow chaos was originally considered as a result of large background noise and non-periodic spanwise boundary conditions. It was addressed that the large ring structures are affected by background noises first, and then the change of large ring structures affect the small scale vortices quickly, which directly lead to chaos and formation of turbulent flow. However, according to our DNS observation, the loss of symmetry starts from the middle level vortex rings while the top and bottom rings are still symmetric. The non-symmetric structure of second level vortex rings will influence the small scale vortices at the boundary layer bottom quickly. The loss of symmetry at the bottom of the boundary layer quickly spreads to upper level through ejections. This will lead to chaos of the whole flow field. Therefore, the internal instability of multiple level ring structures, especially the middle ring cycles, is the main reason for the process of flow chaos, but not the large background noise.

Numerical investigation on mechanism of multiple vortex rings formation in late boundary-layer transition

Mechanism of multiple vortex ring formation is one of key issues of late flow transition in a boundary layer. In this paper, a new mechanism is presented that the multiple ring formation is a result of shear layer instability. According to our DNS observation, a momentum deficit zone is formed above the original hairpin vortex tube due to the ejection of the streamwise hairpin vortex tube, which brings the low speed flow from the lower level to the higher level of the boundary layer through vortex rotation. Then the momentum deficit zone generates a sharp olive-shaped shear layer surrounded by the high speed flow. As the shear layer moves up, inviscid instability is developed due to the existence of inflection points (inflection surface in 3-D). Consequently, the new vortex rings are formed one by one. During the new spanwise vortex ring formation process, the spanwise vorticity is increased; however, the original streamwise hairpin vortex tube is weakened with decreasing of the streamwise vorticity. This process follows the Helmoholtz vorticity conservation law.

New Theories on Boundary Layer Transition and Turbulence Formation

This paper is a short review of our recent DNS work on physics of late boundary layer transition and turbulence. Based on our DNS observation, we propose a new theory on boundary layer transition, which has five steps, that is, receptivity, linear instability, large vortex structure formation, small length scale generation, loss of symmetry and randomization to turbulence. For turbulence generation and sustenance, the classical theory, described with Richardson's energy cascade and Kolmogorov length scale, is not observed by our DNS. We proposed a new theory on turbulence generation that all small length scales are generated by “shear layer instability” through multiple level ejections and sweeps and consequent multiple level positive and negative spikes, but not by “vortex breakdown.” We believe “shear layer instability” is the “mother of turbulence.” The energy transferring from large vortices to small vortices is carried out by multiple level sweeps, but does not follow Kolmogorov's theory that large vortices pass energy to small ones through vortex stretch and breakdown. The loss of symmetry starts from the second level ring cycle in the middle of the flow field and spreads to the bottom of the boundary layer and then the whole flow field.

Numerical study on U-shaped vortex formation in late boundary layer transition

This paper illustrates the mechanism of the U-shaped vortex formation, which has been found by both experiments and DNS in boundary-layer transition. The main goal of this paper is to find how the U-shaped vortex is formed and further developed. According to the results obtained by our direct numerical simulation (DNS) with high order accuracy, the U-shaped vortex is part of the large coherent vortex structure. This new finding is quite different from existing theories which describe that the U-shaped vortex is a secondary vortex induced by second sweeps, and it is newly formed as the head of young turbulence spot and finally breaks down to small pieces. However, it is found that the U-shaped vortex is neither generated by the second sweeps nor the consequent positive spikes. Actually, the U-shaped vortex is induced by the secondary vortices and the solid wall. The new finding also shows the U-shaped vortex is a vortex tube but not the heading wave. In addition, it is found that the U-shaped vortex has the same vorticity sign as the original Λ-shaped vortex legs, which means the U-shaped vortex is not secondary but tertiary. It serves as an additional channel to provide vorticity to support the multiple ring-like vortices when the original vortex tube is stretched and multiple rings are generated.

DNS study on mechanism of small length scale generation in late boundary layer transition

It has been widely accepted that small length vortices, a key mechanism for late flow transition and turbulence generation, are generated by “large vortex breakdown”. However, according to our recent DNS results, the hairpin vortex structure remains very stable and never breaks down. We also recognize strong multiple level negative and positive spikes and consequent multiple level high shear (HS) layers near the bottom of the boundary layer. From our DNS results, we found a second sweep of the first level rings gathering energy from the inviscid region downdraft and generating positive spikes and consequent HS layers. With the instability of the HS layer, new vortex rings and consequent new sweeps are generated. Then, the second level negative and positive spikes and high shear layers are formed near the laminar sub-layer. According to our observation, all small length scales (turbulence) are found around high shear layers generated by multilevel positive spikes and the wall surface, especially near the bottom of the boundary layer, but no small length vortices are found generated by “large vortex breakdown”. This paper provides detailed description and analysis for the energy transfer paths and small length scale (turbulence) generation and sustenance observed by our DNS.