Abstract:Effects of circulation on the evolution of vortex tubes and the associated response of near-wall flows in the shear of laminar boundary-layer flows are investigated using a model proposed by Hon and Walker (Hon, T.L. & Walker, J.D.A, Computers & Fluids, 20(3), pp. 343-358, 1991). Direct numerical simulations with freestream Mach number of 0.5 are conducted. Firstly, the dynamics of single hairpin vortex is investigated. Numerous secondary hairpin vortices, much more than previously reported, which are regular… Show more
The effects of free-stream turbulence (FST) on the evolution of hairpin vortices during the process of laminar-turbulent transition are investigated by direct numerical simulation. The simulations are conducted for FST intensities of 0-6% and a free-stream Mach number of 0.5. FST changes the symmetry of the hairpin vortex, the arrangement of vortices inside the boundary layer, the location of high friction at the wall, and the scales of the vortices. The relationship between high-friction regions at the wall and hairpin vortices convected downstream is investigated by analyzing the computed flow fields. When FST is introduced along with inlet sinuous disturbances, asymmetric hairpin vortices and numerous secondary hairpin vortices, which are different from the case of no FST, are generated. The boundary-layer transition is characterized by an increase in skin-friction. As a result of vortex creation very close to the wall, high-friction regions are generated. To detect the vortex parts responsible for generating the high-friction regions, a new judgement algorithm for interior points is derived based on the Euler angle. The interior points of the near-wall vortices responsible for generating such highfriction regions are successfully visualized as a group of points in R 3. The high-friction regions are the tips of hairpin legs and the regions of near-wall vortices induced beneath a hairpin packet. These regions often correspond to the periphery of the hairpin packets.
The effects of free-stream turbulence (FST) on the evolution of hairpin vortices during the process of laminar-turbulent transition are investigated by direct numerical simulation. The simulations are conducted for FST intensities of 0-6% and a free-stream Mach number of 0.5. FST changes the symmetry of the hairpin vortex, the arrangement of vortices inside the boundary layer, the location of high friction at the wall, and the scales of the vortices. The relationship between high-friction regions at the wall and hairpin vortices convected downstream is investigated by analyzing the computed flow fields. When FST is introduced along with inlet sinuous disturbances, asymmetric hairpin vortices and numerous secondary hairpin vortices, which are different from the case of no FST, are generated. The boundary-layer transition is characterized by an increase in skin-friction. As a result of vortex creation very close to the wall, high-friction regions are generated. To detect the vortex parts responsible for generating the high-friction regions, a new judgement algorithm for interior points is derived based on the Euler angle. The interior points of the near-wall vortices responsible for generating such highfriction regions are successfully visualized as a group of points in R 3. The high-friction regions are the tips of hairpin legs and the regions of near-wall vortices induced beneath a hairpin packet. These regions often correspond to the periphery of the hairpin packets.
“…Figure 29( a ) shows that strongly entwining time-lines deform around the streamwise vortex, creating a time-line pattern and isosurfaces that are quite different from the time-line visualization of figure 28, and the visualizations shown in §§ 3.2 and 3.3. Figure 29.( a ) Time-lines reconstructed from a DNS dataset for a laminar boundary layer with a straight vortex tube (Matsuura 2016). Time-lines were initiated at ).…”
Section: Figure 26mentioning
confidence: 99%
“…The time-line pattern created by a nearly straight vortex tube in a laminar boundary layer is simulated in figure 29. The DNS data were provided by Professor K. Matsuura, in accordance with Matsuura (2016). The vortex tube is inclined to the wall at an angle of , with circulation .…”
Section: Figure 26mentioning
confidence: 99%
“…( a ) Time-lines reconstructed from a DNS dataset for a laminar boundary layer with a straight vortex tube (Matsuura 2016). Time-lines were initiated at ).…”
“…APPENDIX A Here, NFD terms are derived for the continuity equation, the compressible Navier-Stokes equations, the energy equation, and the vorticity equations [32]. These equations are nondimensional, and the method of non-dimensionalization is same as Matsuura [33].…”
A new method that evaluates dominant local dynamics by skeletonization, mathematical term decomposition and the re-combination of a reduced number of dominant terms around the skeleton points is proposed to clarify the dynamics of hairpin vortices generated during the boundary-layer transition under free-stream turbulence (FST). The development of the method is based on the results of direct numerical simulations conducted for the laminar-turbulent transition on a flat plate with FST intensities of 0-6% and a free-stream Mach number of 0.5. Regarding the skeletonization, a new algorithm for extracting the interior points of vortex structures represented by enclosed iso-surfaces is developed. To identify the dominant terms, governing equations are decomposed into non-further-decomposable (NFD) terms. The proposed method is also extended to time series flow field data to reveal the variation of the combination set of dominant NFD terms during the evolution of vortex structures. The present method enables the automatic finding and categorization of the variations of the sets of dominant terms that govern local dynamics during the evolution of hairpin vortices.
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