Keywords: shape optimization, optimal control theory, acoustic velocity, finite element method, Lagrange multiplier method, weighted gradient method, fluid force.

The purpose of this paper is to find an optimal shape of a body located in the viscous flow using the acoustic velocity. The optimal shape is defined so as to minimize the fluid forces acting on the body. In this paper, the formulation is based on an optimal control theory, in which a performance function is expressed in terms of the fluid force. The performance function should be minimized satisfying state equations. Therefore, the optimal control problem results in the minimization problem with constraint conditions. The problem can be transformed into a minimization problem without a constraint condition using the Lagrange multiplier method. The minimization technique used is the gradient based method. For the discretization, the finite element method is used for the state and adjoint equations. The shape determination of the minimum drag and lift forces is carried out.

In this study, the shape optimization in the viscous flow using the acoustic velocity is presented. The formulation based on the optimal control theory is applied to the viscous flow using the acoustic velocity. The volume of the target body is kept constant. The gradient which is obtained by the variation of the extended performance function for the surface coordinates is used to obtain the final shape. The method of this study has been applied to a shape optimization problem for flows of the Reynolds number of 1, 40, 100 and 250.

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £140 +P&P)