Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

The overall goal of this experiment is to use the 3D printer to fabricate particles of a wide variety of shapes and measure their motion in a turbulent flow. This method can help to answer key questions in fluid dynamics such as how particles rotate and align in turbulent fluid flows. It's main advantage is it allows for precision time resolved measurements of the orientations of particles with complex shapes that could not be achieved with previous methods.

This method has provided insight into the motion of discs and spheres in turbulence, and can be used to measure dynamics of particles with complex shapes in many other situations. Generally, individuals new to this method will struggle with 3D camera calibration and adapting the orientation finding algorithm to specific specific particles being used. Helping to demonstrate the procedure will be Guy Marcus, who performed the original experiments with crosses and jacks.

Begin by using computer aided design software to create particle models for printing. To create a triad using AutoCAD, first use the circle command to draw a circle with the diameter of 0.3 millimeters. Then, use the extrude command to make a cylinder three millimeters long.

Cylinders of this size are the building blocks of the particles. Now use the rotate command and select the axis of rotation to be along the X axis, and the rotation angle to be 90 degrees. Adjust the view to allow room to work with other cylinders.

Next, make a copy of the cylinder that will be the second arm of the triad. At the end of this cylinder, apply the rotate 3D command with the axis of rotation along the Z axis. Rotate the cylinder 120 degrees for the triad.

Move the rotated cylinder into position to form an arm of the triad. The centers of the cylinder ends should coincide. Make and position the third arm in the same way.

Then, rotate the object so that no cylinder points along the vertical or horizontal access. When all arms are in place, select them all and use the union command to join them into a single object. Save the file to a format for 3D printing.

Create the other particles to be used in the experiment by following similar steps. In addition to the triad, there is the cross made of two orthogonal cylinders with a common center, the jack made of three mutually orthogonal cylinders with a common center, and the tetrad in which the cylinders share a common end, and are at 109.5 degree angles with respect to one another. Have about 10, 000 of each particle type printed in high resolution mode.

Prepare to store the printed particles in a solution in which they are neutrally buoyant. For this, use a solution of calcium chloride, and approximately 1, 600 liters of water at the neutral buoyancy density. Remove about one liter of the solution to store each type of particle.

Take the liter of solution to the bench and begin work with the particles. The particles used in this experiment have been commercially printed. They arrive encased in resin used as a support material.

Free the particles by gently breaking the large pieces into small sections. Work with each section to manually massage it until much of the excess resin comes off. This will make later steps easier.

To further clean the particles, prepare a 10%by mass solution of sodium hydroxide in a beaker. Next place some particles and what remains of their resin encasing into the beaker to remove the resin. Move the beaker with the solution into an ultrasonic bath.

Keep the particles in the ultrasonic bath for one hour initially, then an additional half hour after rinsing. To recover the particles, prepare a second beaker to receive the sodium hydroxide solution from the bath and a filter. After the ultrasonic cleaning steps are complete, use gloves to remove the beaker from the bath, and pour the contents through the filter into the second beaker.

Rinse the particles before moving them to the density matched solution where they will be immersed to prevent deformation. These are particles that have been freed from their resin, cleaned in the ultrasonic bath, and are now ready for dyeing to fluoresce under green laser light. To dye the particles, use a one liter solution of Rhodamine-B dye in water and place it on a hot plate.

Heat the dye to 80 degrees Celsius for the material of this particle. Loosely fill a small container with particles from storage. This will be about 2, 500 particles.

Add the particles to the dye solution, and maintain the temperature while they are immersed. After about two or three hours, remove the solution and particles from the heat. Use a mesh and separate container to filter the particles from the solution.

Be careful not to damage them while they are soft from the heat. Next, rinse the particles carefully to remove excess dye. When done, store them in the neutral buoyancy solution until they are needed for the experiment.

The experiment will take place in a tank with cameras placed to record the particles in the center of the flow. This schematic provides an overview of the tank's set up, which has an octagonal cross section, oscillating grids used to create turbulent flow, the measurement volume, and the camera positions. Use a minimum of four cameras for orientation measurement accuracy.

Each camera should have at least one megapixel resolution at 450 frames per second, and be connected to a dedicated computer. Position the cameras with large angles between any two of them, and ensure that they are all focused on the desired measurement volume. To minimize optical distortion, viewing ports are built into the tank that are perpendicular to the camera viewing direction.

Next, place an image calibration mask in the measurement volume of the tank. This will allow the analysis of the experimental data collected by the cameras. To simulate the experimental conditions, begin filling the tank with the bulk neutral buoyancy solution.

When the tank is filled, set up lights to illuminate the mask. Next, return to work with the cameras. Focus each camera on the same point on the mask, then acquire and store images for calibration.

After draining the tank, continue setting up the experiment by placing a neodymium yttrium aluminium garnet laser. Arrange for a beam splitter to direct part of the laser beam to a mirror. The light goes from the mirror through lenses that form a cylindrical beam and into the tank.

At the opposite side of the tank, place a mirror to reflect exiting laser light back along its path. Use the other output of the beam splitter and a similar arrangement of mirrors and lenses to create a cylindrical beam perpendicular to the first as in this top view schematic. The mirrors where the beams exit help create more uniform illumination.

Then, inspect the tank that is filled with de-gassed neutral buoyancy calcium chloride solution. Before proceeding, ensure that the cameras and data acquisition software are ready. Prepare to add the approximately 10, 000 tetrads that have been readied for this experiment to the tank.

Move them into position near the port at the top of the tank. When ready, open the port, and add the particles to the water in the tank. Close the port once all the particles have been added.

Next, move to the laser. There, turn it on, and open the laser aperture. Then use the grid controls to start the grid oscillating at three hertz.

In the tank, let the grid oscillate for about one minute to allow turbulence to fully develop. At that point, begin data acquisition and record about one million frames. At the conclusion of the run, stop data collection and close the laser aperture.

After all experiments have been run, move to the tank outlet. There, place a filter to remove the particles from the solution, and empty the tank. Save the collected particles in the neutral buoyancy solution for later use.

Perform data analysis on the recorded images using software to find the particle position and orientation. The following steps are implemented in software. Starting with four synchronous images of a particle captured by the four cameras, use two dimensional information to determine its three dimensional position.

Project a three dimensional numerical model of the illuminated particle onto each camera using the camera calibration parameters. This creates a two dimensional model of light intensity from the particle on all four cameras. Next, run a non-linear least squares fitting routine to find the model orientation that best fits what is seen on all four cameras.

Combine information from all four cameras to minimize the difference between the model projected onto each camera, and the observed particle. These steps will be done for all frames that have particles in view of all cameras. This is the evolution of a tetrad in position and orientation.

Notice the discontinuous change in the orientation of the tetrad arms, which is possible to have without safeguards. This second version of the tetrad evolution shows that the software ensures the oiler angles for each frame are the smallest rotation with respect to the previous frame. The position and orientation information are saved for later use.

This is one camera image of a tetrad in the experiment. In the second image, the superimposed model indicates the orientation as found by the algorithm. Despite the simplicity of the two dimensional intensity model, the method produces accurate measurements of particle orientation.

In the experiment, the orientation finding algorithm is used to obtain the evolution of the oiler angles along the entire trajectory of every particle. This is a reconstruction of the complete trajectory of a tetrad across the viewing volume. This is achieved by combining the orientation and three dimensional coordinates of the particle for each frame in which it is in view by all four cameras.

The length of the track is 229 frames. Note that the particle is not drawn to scale. The data also allow for the determination of the probability density function of the measured tumbling rate.

The red squares are data for crosses. Blue circles are data for jacks. The solid line represents the result of numerical simulation of spheres, which matches the experimental data very well.

Once mastered, this technique can be done in three days if performed properly. While attempting this procedure, it is important to allow the particles a couple of hours in the solutions of different densities. It is also essential to ensure that the cameras are properly aligned, fixed, and synchronized throughout the duration of the experiment.

Following this procedure, other methods like tracking of tracer particles can be used to measure how 3D printed particles respond to the full velocity gradient tenser in the surrounding flow. After watching this video, you should have a good understanding of how to use anisotropic particles to extract information about the velocity gradient tenser from turbulent flow using four stereoscopic video images. Don't forget that working with Rhodamine-B dye and sodium hydroxide can be hazardous, and precautions such as gloves and goggles should always be taken while performing this procedure.