Team 07

Team Members: Jiyuan (Jackie) Ding, Michael Kolakowski, Ankita Sharma, Justin Stobart, Calvin Tran

Project Sponsors: Brandon Lee & TJ Flynn, University of Michigan

Originally, our project was to complete the design for (and then construct) a permanent-display-ready Bubble Board to commemorate the ME department's 150th anniversary. The Bubble Board must demonstrate fluid dynamics concepts in an aesthetically interesting manner while interactively responding to input from viewers.

With our project shifted to online-only work, we have performed Finite Element Analysis on the structural integrity of the welded tank, developed code for image processing, analyzed bubble velocity, and prepared experimental procedures for the next team to continue this project. From this work, we have produced realistic animations of rising bubbles in a Bubble Board simulation.

Bubble Velocity Analysis

The bubble velocity inside an open tank and a tank with thin tubes was analyzed to determine the effects thin tubes would have on rising speeds. Open tank bubble velocity was analyzed by looking at a study done by Baz-Rodríguez et al. It was found that open tank bubble velocity is dependent on a multitude of factors, such as: pressure difference, surface tension, gravity, bubble radius, etc. The bubble velocity within thin tubes, known as plug-flow velocity, was found using a study done by Searby et al. Their study found that velocity within thin tubes was proportional to the tube radius and liquid viscosity.

Below is a series of graphs that were created to model bubble velocity within an open tank and within thin tubes. The main takeaways from these models is that bubble velocities in thin tubes for small bubble radii (R < 3 cm) is about one-third of the speed in an open tank. The hope is that the next group can use this knowledge to choose an appropriate bubble radius to achieve the desired rising speed and thus create a more accurate model.

Experimental Procedures

Unfortunately, due to the effects of COVID-19, our team was unable to fulfill our goal of finishing the Bubble Board. However, we have created a set of three experimental procedures to assist the next team in getting started. All three procedures share the same layout: objective, hypothesis, materials, procedure, and results. Each experimental procedure was created to provide a starting point for the next group to analyze. The three experimental procedures are set out to validate one key element of the design and thus will help to inform them when producing the final product.

The first experimental procedure was created to validate the plug-flow equation from a study done by Searby et al and to also investigate the potential effects bubble length has on bubble velocity. As soon as the next group is able to validate this equation and determine the potential effects of bubble length, more accurate modeling can be done. The second experimental procedures aims to find the bond strength between two acrylic sheets. The most prolific problem with the previous design is the cracked tank that resulted in a mess. Thus, this procedure was designed to find the bond strength which will help in structural analysis. Lastly, the third experimental procedure looks to verify the appropriate bubble interactions are occurring once the bubbles leave the tubes. Our design was created such that the bubbles leave the tubes approximately halfway up to three-quarters of the way up into an open tank. Once the bubbles enter the open tank, the bubbles will begin to have side-to-side interactions which will help to showcase elements of bubble fluid dynamics.

Simulation

Building off of Image Processing, a simulation was written in MATLAB to create a virtual Bubble Board. The simulation allows the user to define design aspects of the Bubble Board at will, allowing modification of board dimensions, number of solenoids used, time delay between consecutive bubble initiation from a solenoid, and tube dimension. The simulation uses the Image Processing code described above to create a binary matrix from an image. Then, the simulation "prints" this image as bubbles, using the plug flow velocity equations to realistically depict bubble movement within respective tubes. A bit of random error/variation was considered in the initialization of bubbles, creating rows that are not perfectly uniform. The more solenoids used, and the less time delay between rows, the higher the resolution of the bubble image. An example of the simulation is shown on the title page.