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Applied Mathematics Seminar
Date/Time/Room:
Friday (4/28/2006) at 4:00pm in 304 Pickard Hall "Optimal Design for Geometry of Blade and Boundary Shape Control of NavierStokes Equations"Abstract: Turbomachinery design is driven by the need for improved performance and reliability. Up to now we did not _nd a geometric design from mathematical view. Here we try to proposal a principle for full mathematical design of the surface of blade in the impeller, that is a mathematical modelling of general minimal surface by minimizing a functional proposed by us. A key point is how to realize our design process.By using tensor analysis technique we overcome this obstacle and obtain EularLagrange equation for the blade's surface.The main results are (1) Rotationally NavierStokes Equations In turbomachinery, (2) Goal Functional and Geometrical Design of blade's Surface, (3) Existence of solution of optimal control problem; (4) Gradient grad J(ยท) and EularLagrenge equation; (5) Numerical algorithms.

