Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence
Summary
We use 3D printing to fabricate anisotropic particles in the shapes of jacks, crosses, tetrads, and triads, whose alignments and rotations in turbulent fluid flow can be measured from multiple simultaneous video images.
Abstract
Experimental methods are presented for measuring the rotational and translational motion of anisotropic particles in turbulent fluid flows. 3D printing technology is used to fabricate particles with slender arms connected at a common center. Shapes explored are crosses (two perpendicular rods), jacks (three perpendicular rods), triads (three rods in triangular planar symmetry), and tetrads (four arms in tetrahedral symmetry). Methods for producing on the order of 10,000 fluorescently dyed particles are described. Time-resolved measurements of their orientation and solid-body rotation rate are obtained from four synchronized videos of their motion in a turbulent flow between oscillating grids with Rλ = 91. In this relatively low-Reynolds number flow, the advected particles are small enough that they approximate ellipsoidal tracer particles. We present results of time-resolved 3D trajectories of position and orientation of the particles as well as measurements of their rotation rates.
Introduction
In a recent publication, we introduced the use of particles made from multiple slender arms for measuring rotational motion of particles in turbulence1. These particles can be fabricated using 3D printers, and it is possible to accurately measure their position, orientation, and rotation rate using multiple cameras. Using tools from slender body theory, it can be shown that these particles have corresponding effective ellipsoids2, and the rotational motions of these particles are identical to those of their respective effective ellipsoids. Particles with symmetric arms of equal length rotate like spheres. One such particle is a jack, which has three mutually perpendicular arms attached at its center. Adjusting the relative lengths of the arms of a jack can form a particle equivalent to any tri-axial ellipsoid. If the length of one arm is set equal to zero, this creates a cross, whose equivalent ellipsoid is a disk. Particles made of slender arms take up a small fraction of the solid volume of their solid ellipsoidal counterparts. As a result, they sediment more slowly, making them easier to density match. This allows the study of much larger particles than is convenient with solid ellipsoidal particles. Additionally, imaging can be performed at much higher particle concentrations because the particles block a smaller fraction of the light from other particles.
In this paper, methods for fabrication and tracking of 3D-printed particles are documented. Tools for tracking the translational motion of spherical particles from particle positions as seen by multiple cameras have been developed by several groups3,4. Parsa et al.5 extended this approach to track rods using the position and orientation of the rods seen by multiple cameras. Here, we present methods for fabricating particles of a wide variety of shapes and reconstructing their 3D orientations. This offers the possibility to extend 3D tracking of particles with complex shapes to a wide range of new applications.
This technique has great potential for further development because of the wide range of particle shapes that can be designed. Many of these shapes have direct applications in environmental flows, where plankton, seeds, and ice crystals come in a vast array of shapes. Connections between particle rotations and fundamental small-scale properties of turbulent flows6 suggest that study of rotations of these particles provides new ways to look at the turbulent cascade process.
Protocol
Representative Results
Discussion
Measurements of the vorticity and rotation of particles in turbulent fluid flow have long been recognized as important goals in experimental fluid mechanics. The solid-body rotation of small spheres in turbulence is equal to half the fluid vorticity, but the rotational symmetry of spheres has made direct measurement of their solid-body rotation difficult. Traditionally, the fluid vorticity has been measured using complex, multi-sensor, hot-wire probes14. But these sensors only get single-point vorticity measur…
Divulgations
The authors have nothing to disclose.
Acknowledgements
We thank Susantha Wijesinghe who designed and constructed the image compression system we use. We acknowledge support from the NSF grant DMR-1208990.
Materials
| Condor Nd:YAG 50W laser | Quantronics | 532-30-M | |
| High speed camera | Basler | A504k | |
| High speed camera | Mikrotron | EoSens Mc1362 | |
| Rhodamine-B | ScienceLab.com | SLR1465 | |
| Sodium Hydroxide | Macron | 7708 | Pellets. |
| 500 Connex 3D printer | Objet | Used to make smaller particles. Particles ordered from RP+M (rapid prototyping plus manufacturing). | |
| VeroClear | Stratasys | RGD810 | Objet build material. |
| Form 1+ 3D printer | Formlabs | Used to make larger particles. | |
| Clear Form 1 Photopolymer Resin | Formlabs | ||
| Cylindrical and spherical lenses | |||
| 200, 100, 50 mm macro camera lenses | F-mount. | ||
| Ultrasonic bath | Sonicator | ||
| Calcium Chloride | Spectrum Chemical Mfg. Corp. | CAS 10043-52-2 | Pellets. |
| LabVIEW System Design Software | National Instruments | Used to trigger cameras, control grid, and trigger laser. | |
| XCAP Software | EPIX | Used with LabVIEW to trigger cameras. | |
| MATLAB | Mathworks | Used for all image and data analysis. Programs for extracting 3D orientations from multiple images are included with this publication. | |
| OpenPTV: Open Source Particle Tracking Velocimetry | OpenPTV Consortium | ||
| ParaView | Kitware | ||
| AutoCAD | AutoDesk | Used to design all particles. Screenshots of particle designs are all of AutoCAD. | |
| Mesh with 0.040 x 0.053 inch holes | Industrial Netting | XN5170–43.5 | |
| Camera filters | Schneider Optics | B+W 040M |
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