Triangulating the Real Projective Plane

We consider the problem of computing a triangulation of the real projective plane P2, given a finite point set S={p1, p2,..., pn} as input. We prove that a triangulation of P2 always exists if at least six points in S are in general position, i.e., no three of them are collinear. We also design an algorithm for triangulating P2 if this necessary condition holds. As far as we know, this is the first computational result on the real projective plane

Facilitation of Homogeneous Combustion with Oxygen Enrichment for High-Temperature Industrial Furnaces

A substantial portion of literature discussing highly efficient and low pollutant emission combustion systems comprises of Homogeneous Combustion (HC) or its variants (MILD, FLOX, CDC etc.). The underlying theory among the aforementioned methods is the reduction of the Damköhler number (Da) to the order of unity. To attain high temperatures, industrial heating is often accomplished by using “enriched” oxidizer streams i.e. XO2 > 21%. Extending the concept of HC to applications of industrial heating (e.g. glass melting furnaces) is a desirable but a challenging task. Higher reactant concentrations increase reaction rates. Fast reactions lead to an increase in temperature which in-turn accelerates the reaction rates and the heat release rate. This self-accelerating cycle causes a shift to the conventional mode of combustion (higher Da) with high NOx emissions. The broad research goal in this work is to keep Da ~ 1 to facilitate HC with enriched oxidizers. The first strategy employed towards this was to enhance the heat removal from the reaction zone by enabling the presence of soot in the reaction zone. The conjecture was that presence of soot will augment heat radiation, reduce temperatures, and reduce NOx emissions; similar to what has been reported for highly luminous flames. Since natural gas (methane) does not soot except under high pressure environments, fuel blends containing small amounts of lightly sooting fuels like ethylene were investigated. It was found that while the presence of soot definitely improves radiation heat transfer and reduces specific NOx emissions, there is an optimal blend level. A multi-variate regression model was used to demarcate the radiation emanating from the wall and from the gaseous zone. The second strategy employed was to engineer the flow in the furnace to enhance mixing and reduce Da. Experimentally studying the confined turbulent jet(s) flow in the furnace with limited optical access was infeasible and hence computational simulations were utilized. A number of steps to reduce computational expenses were taken. These included utilization of furnace symmetry and writing external code to describe furnace recuperator operation. The 3-D flow within the furnace was described/understood by breaking it into a set of canonical flows. The utilization of a detailed mechanism (GRI Mech-3.0) enabled accurate capture of the NOx field to within a few ppm. It was discovered that optimizing geometry and flow is important to achieve HC with enriched oxidizers. The third strategy focused on further enhancing jet dilution by modifying nozzle design. It was found that altering the nozzle shape caused essentially no reduction in NOx emissions from the furnace. It was also found that NOx emissions were independent of the inlet temperature of the reactants. Another strategy was to have a localized swirling injection for the oxidizer jet. While swirl did help in reducing NOx, there existed an optimal swirl number beyond which NOx emissions were aggravated to levels even higher than configurations with no swirl. Swirl, even though localized, was seen to affect the in-furnace flow even in the far-field (~75 diameters). A mutual competition was seen between swirl assisted and entrainment driven dilution; and at higher swirl intensities, the reduction in the latter overwhelmed the gains accrued by the former (in terms of NOx emissions).PHDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/155272/1/kumaraa_1.pd