Applied Mathematics Seminar
Friday (4/28/2006) at 4:00pm in 304 Pickard Hall
"Optimal Design for Geometry of Blade and Boundary Shape Control of Navier-Stokes 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 Eular-Lagrange equation for the blade's surface.
The main results are
(1) Rotationally Navier-Stokes 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(·) and Eular-Lagrenge equation;
(5) Numerical algorithms.