Abstract
Swirling strength is an effective vortex indicator in wall turbulence, and it can be determined based on either two-dimensional (2D) or three-dimensional (3D) velocity fields, written as λci2D and λci3D, respectively. A comparison between λci2D and λci3D has been made in this paper in sliced XY, YZ, and XZ planes by using 3D DNS data of channel flow. The magnitude of λci2D in three orthogonal planes differs in the inner region, but the difference tends to diminish in the outer flow. The magnitude of λci3D exceeds each λci2D, and the square of λci3D is greater than the summation of squares of three λci2D. Extraction with λci2D in XY, YZ, and XZ planes yields different population densities and vortex sizes, i.e., in XZ plane, the vortices display the largest population density and the smallest size, and in XY and YZ planes the vortices are similar in size but fewer vortices are extracted in the XY plane in the inner layer. Vortex size increases inversely with the threshold used for growing the vortex region from background turbulence. When identical thresholds are used, the λci3D approach leads to a slightly smaller population density and a greater vortex radius than the λci2D approach. A threshold of 0.8 for the λci3D approach is approximately equivalent to a threshold of 1.5 for the λci2D approach.
Highlights
Wall-bounded turbulent flows have been found to be dominated by spatially organized, temporally evolving vortices which play an important role in shaping the wall turbulence.[1,2,3] From the perspective of vortex, many phenomena of interest to scientists and engineers can be explained, such as entrainment, mixing, transport and combustion
Among various methods for vortex extraction, the swirling strength criterion has been proven to be effective and efficient in wall turbulence.[4,5,6,7,8,9,10]. This method was first proposed by Zhou et al.[11] and has been refined by Tomkins and Adrian,[12] Wu and Christensen,[7] and Chen et al[13] The swirling strength, λci, is the imaginary part of complex eigenvalues for the velocity gradient tensor, and it offers an excellent vortex indicator in wall turbulence where strong mean shear exists
While the general trends are in consistence, the present study reports smaller vortex size than Herpin et al.[4]
Summary
Wall-bounded turbulent flows have been found to be dominated by spatially organized, temporally evolving vortices which play an important role in shaping the wall turbulence.[1,2,3] From the perspective of vortex, many phenomena of interest to scientists and engineers can be explained, such as entrainment, mixing, transport and combustion. The difference for vortex properties between planar PIV and DNS (or volumetric PIV) is related with the selection of swirling strengths (either 2D or 3D) for vortex extraction. The influence of the selection of swirling strength on vortex properties is lack of investigation. Another important issue in vortex extraction concerns the selection of threshold. The influence of the selection of swirling strengths (either 2D or 3D) on vortex properties (such as, population density and size) was quantitatively evaluated; the selection of threshold on vortex size was investigated.
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