Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence

Abstract

We present simultaneous experimental measurements of the dynamics of anisotropic particles transported by a turbulent flow and the velocity gradient tensor of the flow surrounding them. We track both rod-shaped particles and small spherical flow tracers using stereoscopic particle tracking. By using scanned illumination, we are able to obtain a high enough seeding density of tracers to measure the full velocity gradient tensor near the rod. The alignment of rods with the vorticity and the eigenvectors of the strain rate show agreement with numerical simulations. A full description of the tumbling of rods in turbulence requires specifying a seven-dimensional joint probability density function (PDF) of five scalars characterizing the velocity gradient tensor and two scalars describing the relative orientation of the rod. If these seven parameters are known, then Jeffery's equation specifies the rod tumbling rate and any statistic of rod rotations can be obtained as a weighted average over the joint PDF. To look for a lower-dimensional projection to simplify the problem, we explore conditional averages of the mean-squared tumbling rate. The conditional dependence of the mean-squared tumbling rate on the magnitude of both the vorticity and the strain rate is strong, as expected, and similar. There is also a strong dependence on the orientation between the rod and the vorticity, since a rod aligned with the vorticity vector tumbles due to strain but not vorticity. When conditioned on the alignment of the rod with the eigenvectors of the strain rate, the largest tumbling rate is obtained when the rod is oriented at a certain angle to the eigenvector that corresponds to the smallest eigenvalue, because this particular orientation maximizes the contribution from both the vorticity and strain.

Rotation of Nonspherical Particles in Turbulent Channel Flow

“…Spheroids' tendency to emphasize specific components of rotation can be explained by examining their orientation relative to fluid vorticity; the inner product between a particle's orientation vector and the local fluid vorticity vector yields an angle α, shown in Figure 2 for the nearly-isotropic channel center. For St=0 particles, results replicate previous observations [8][9][10][11][12][13][14] for discs and rods. Discs tend to align with their symmetry axis (z') orthogonal to the fluid vorticity, causing strong tumbling [8][9][10][11][12][13][14] and weak spinning [11,13].…”

“…For St=0 particles, results replicate previous observations [8][9][10][11][12][13][14] for discs and rods. Discs tend to align with their symmetry axis (z') orthogonal to the fluid vorticity, causing strong tumbling [8][9][10][11][12][13][14] and weak spinning [11,13]. Rods align parallel to local vorticity [8,[10][11][12][13][14] and thus spin along with it.…”

Shape effects on dynamics of inertia-free spheroids in wall turbulence

“…[7][8][9] It has been observed that disk-like particles tumble more than rod-like particles. 4,5,7,8 Rod-like particles preferentially align with the fluid vorticity vector and the vorticity component along the rod axis does not contribute to their tumbling.…”

“…2,3,6,7 In contrast to the rod-like particles, disks align perpendicular to the fluid vorticity vector and this preferential orientation results in higher tumbling rates. 5,9 The Lagrangian fluid stretching in turbulence aligns the major axis of an anisotropic particle with the fluid vorticity. 6 The variance of the total rotation rate of a spheroidal particle is almost independent of the particle shape.…”

Generalized Lagrangian coherent structures

“…Applications to three dimensions are less common because they are computationally expensive, rely on the accurate knowledge of the time-varying 3D velocity field that is challenging from both observational or modeling perspectives, and require advanced visualization of LCSs. As the LCS methods advance, in parallel with experimental ability to measure highly resolved 3D velocity fields [115], it is hoped that our ability to tackle three-dimensional unsteady flows will improve.…”