Evolution of the ring-like vortices and spike structure in transitional boundary layers

Abstract

At the late stage of transitional boundary layers, the nonlinear evolution of the ring-like vortices and spike structures and their effects on the surrounding flow were studied by means of direct numerical simulation with high order accuracy. A spatial transition of the flat-plate boundary layers in the compressible flow was conducted. Detailed numerical results with high resolution clearly represented the typical vortex structures, such as ring-like vortices and so on, and induced ejection and sweep events. It was verified that the formation of spike structures in transitional boundary layers had close relationship with ring-like vortices. Especially, compared to the newly observed positive spike structure in the experiments, the same structure was found in the present numerical simulations, and the mechanism was also studied and analyzed. boundary layer transition, ring-like vortices, spike structure, direct numerical simulation PACS: 47.27.Cn, 47.27.ekThe main stages of the boundary layer transition include receptivity, linear instability, weakly nonlinear instability, formation of complex vortex structures (late stage of the transition) and breakdown to turbulences. Experiments have proved that at the late-stage of the transition similar characteristic vortex structures can be found in the turbulence boundary layers. After more than a century of studies, the early stages of the transition process, such as linear theory, weakly nonlinear and secondary instability theory, are well understood. But the late-stage of the transition is still unclear and takes further investigation, such as the formation of ring-like vortices, and appearance of the spikes which are very intensive local streamwise velocity fluctuations.The formation of ring-like vortices is one of the important issues in the transition process. Kachnaov [1] suggested the existence of the chain of ring-like vortices based on hot-film measurement. Lee et al. [2] showed their clear pictures of real ring-like vortices. The appearance and development of high-frequency spike structures is an important stage of the boundary layer transition, yet the mechanism of production and the physical nature of spike structure remains unclear. Recent years have seen more progress on the investigation of the formation of ring-like vortices and spike structure. Bake et al. [3] studied the structures of turbulence development in periodic Klebanoff boundary layer transition, and found that ring-like vortices would induce highfrequency streamwise velocity fluctuations called spikes. Borodulin et al. [4] studied the late-stage transition mechanism in the boundary layers using numerical and experimental methods, and analyzed relative vortices and spike structure. They proposed that the formation of ring-like vortices was due to self-induction. Meyer et al. [5] by investigating the flow randomization process in a transitional boundary layer found that Λ-vortices and ring-like vortices

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

“…By this visualization method, the vortex structures shaped by the nonlinear evolution of T-S waves in the transition process are shown in Figure 5(A). The evolution details are studied in our previous papers [19][20][21][22][23], and the formation of ring-like vortices chains is consistent with the experimental work (see [13], Figure 5(B)) and previous numerical simulation by Bake et al [3].…”

Evolution of the vortex structures and turbulent spots at the late-stage of transitional boundary layers

“…It is revealed that high-speed flows of the out layer are drawn into the near wall region by the sweeping movement. According to our research of the positive spikes [4], it is believed that these "dark spots" structures are consistent with the formation of positive spikes in the previous work. Firstly, the quasistreamwise vortex structures at the outer part of the U-shaped vortex are produced by the accumulative positive spikes, and then are connected with the head part of the ring-like vortex to generate the U-shaped vortex, and finally develop into the barrel-shaped vortex.…”

“…Therefore, this is a matter of cardinal significance in exploring the mechanism of the boundary layer transition. At the late-stage of the transition, there are complex vortex structures [3,4], including the generation of the complex ring-like vortex, which are main features at this stage. With the evolution of the vortices in the flow field, more complex new vortex structures are produced [5], and turbulent spots have arisen in regions possessing some turbulent characteristics [6], and eventually evolve into a fully developed turbulent flow [7].…”

“…The 3D compressible Navier-Stokes equations in generalized curvilinear coordinates [4] are solved by the DNS method with a high-order accuracy. The inlet boundary condition is given by using the Blasius similar solution of 2-D flat-plate laminar boundary layer with enforced disturbances.…”

Numerical studies on evolution of secondary streamwise vortices in transitional boundary layers

“…Ring-like vortices play a vital role in the transition process of the wall boundary layer flow, and its formation mechanism is very complex [26][27] . Based on our numerical results, the relationship between the generation of ring-like vortices, the primary streamwise vortices, and secondary streamwise vortices is investigated.…”