Geometry of discrete and continuous bounded surfaces

We work on reconstructing discrete and continuous surfaces with boundaries using length constraints. First, for a bounded discrete surface, we discuss the rigidity and number of embeddings in three-dimensional space, modulo rigid transformations, for given real edge lengths. Our work mainly considers the maximal number of embeddings of rigid graphs in three-dimensional space for specific geometries (annulus, strip). We modify a commonly used semi-algebraic, geometrical formulation using Bézout\u27s theorem, from Euclidean distances corresponding to edge lengths. We suggest a simple way to construct a rigid graph having a finite upper bound. We also implement a generalization of counting embeddings for graphs by segmenting multiple rigid graphs in d-dimensional space. Our computational methodology uses vector and matrix operations and can work best with a relatively small number of points

Scalable and Controllable Fabrication Process for Membrane Mirrors

With the future need of larger telescopes, membrane mirrors are an option to create large-scale reflectors needed for space base observation at a lower cost than conventionally made mirrors. Proposed methods of how membrane mirrors have been put into place with ideas such as Dr. Chris Walker’s inflatable spherical telescope and the L’Garde Inflatable Antenna Experiment (IAE). With data from L’Garde, Dr. Aden Meinel presented the curvature of a membrane mirror does not produce a spherical curvature. From there a look into what sort of aberrations that curvature produces and attempts to correcting it or processing it to other benefits by altering the material. Procedures will be done on a small-scale in a process that can be applied to larger-scale systems

Computational Performance Assessment of Buoyant Shrouded Turbines in UAE

With the increase in the economic impact of fossil fuel consumption over the past few decades, the demand for alternative sources of fuel for consumer consumption led to the initiation of scientific research related to renewable resources. The present research aims at analyzing the wind energy capability at low and high altitudes in low wind regions like the UAE (United Arab Emirates) by studying the different wind speed-altitude models and studying the potential of augmenting wind turbines performance using diffuser augmented-floating turbine systems incorporating the horizontal axis wind turbine (HAWT). The study was conducted computationally using Ansys Fluent and MATLAB software. The k-ω SST (Shear Stress Transport) turbulent model was used to carry out the simulation and the power was determined from the computational result. The computational simulation for both the bare turbine and the shrouded turbine was run at a base wind velocity of 8m/s. The determination of the airfoil profile for the design of the annular shroud was carried out in MATLAB with the computational results as the input parameter. The buoyant calculations for the study were carried out entirely theoretically utilizing the literature as a reference and a prototype representation of the buoyant turbine system is presented. The presented results are determined through a comprehensive comparison study between a buoyant shrouded turbine system and a bare turbine at altitudes of 18 m and 200 m respectively at a design wind velocity of 8m/s. The study concluded that the 13m chord length variant of the KT (Karman-Trefftz) profile provided a maximum of 270% increase in the available wind power ratio and a maximum of 61% increase in the airflow rate within the annular shroud. The NACA (National Advisory Committee for Aeronautics) symmetric airfoil having a thickness of 25% was selected based on annular shroud volume as the performance in symmetric airfoil did not converge and presented a consistent increase in its shroud performance with thickness increase. The power ratio for 0 and -2 degree AOA (Angle of Attack) of 13m KT profile variants presented better results in comparison to the others. In analyzing the turbine with the inclusion of the shroud, the CFD (Computational Fluid Dynamics) performance results indicated a 201% increase in the generated turbine power when compared with the manufacturer\u27s bare turbine power. The conceptual design of the shroud presented a net buoyant lift of 17.01% higher than the weight of the system while the lift is also 24.7% higher than the net drag of the system. The conceptual representation of the system design is also presented for better visualization of the system design