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Numerical Analysis Seminar: Pejman Sanaei, Georgia State University, On mathematical modeling and simulation of flight stability of objects, tissue engineering and droplets
April 4 | 3:00 pm - 4:00 pm EDT
In this talk, I will present 3 problems on fluid structure interaction:
1) Flight stability of wedges: Recent experiments have shown that cones of intermediate apex angles display orientational stability with apex leading in flight. Here we show in experiments and simulations that analogous results hold in the two-dimensional context of solid wedges or triangular prisms in planar flows at Reynolds numbers 100 to 1000. Slender wedges are statically unstable with apex leading and tend to flip over or tumble, and broad wedges oscillate or flutter due to dynamical instabilities, but those of apex half angles between about 40◦ and 55◦ maintain stable posture during flight. The existence of ‘‘Goldilocks’’ shapes that possess the ‘‘just right’’ angularity for flight stability is thus robust to dimensionality.
2) Tissue engineering: In a tissue-engineering scaffold pore lined with cells, nutrient-rich culture medium flows through the scaffold and cells proliferate. In this process, both environmental factors such as flow rate, shear stress, as well as cell properties have significant effects on tissue growth. Recent studies focused on effects of scaffold pore geometry on tissue growth, while in this work, we focus on the nutrient depletion and consumption rate by the cells, which cause a change in nutrient concentration of the feed and influence the growth of cells lined downstream.
3) Moving droplets on a filter surface: Catalysts are an integral part of many chemical processes. They are usually made of a dense but porous material such as activated carbon or zeolites, which provides a large surface area. Liquids that are produced as a byproduct of a gas reaction at the catalyst site are transported to the surface of the porous material, slowing down transport of the gaseous reactants to the catalyst active site. One example of this is in a sulphur dioxide filter, which converts gaseous sulphur dioxide to liquid sulphuric acid. Such filters are used in power plants to remove the harmful sulphur dioxide that would otherwise contribute to acid rain. Understanding the dynamics of the liquid droplets in the gas channel in a device is critical in order to maintain performance and durability of the catalyst assembly. Our goal is to develop a mathematical model using the Immersed Boundary Method to quantify the droplet movement on the filter surface.