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 R_λ = 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 th....

Protocol

1. Fabrication of Particles

1. Use a 3D Computer Aided Drafting program to create particle models. Export one file per model in a file format that can be processed by the 3D printer used.
   1. Use the Circle command to draw a circle with a diameter of 0.3 mm. Use the Extrude function to make a cylinder with a length of 3 mm.
   2. Make a cross with two orthogonal cylinders with a common center; make a jack with three mutually orthogonal cylinders with a common center; make a tetrad with four cylinders sharing a common end at 109.5° angles to one another; make a triad with three cylinders in a plane sharing a common end at 120° angles to one anothe....

Results

Figure 3a shows an image of a tetrad from one of our cameras above a plot of the Euler angles obtained from a section of its trajectory (Figure 3c). In Figure 3b, the results of the orientation-finding algorithm, described in Protocol 5 - 5.3, are superimposed on the tetrad image. The arms of the tetrad in Figure 3a do not follow the simple intensity distributions that are used to create the model (Protocol 5.1.3.1). This.......

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.......

Materials

List of materials used in this article

Name	Company	Catalog Number	Comments
Condor Nd:YAG 50 W 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.
Clear Form 1 Photopolymer Resin	Formlabs
Cylindrical and spherical lenses
200 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