Shape Optimization Analysis of Flow Field : Growth-Strain Method Approach

Abstract

A new analytical approach for optimizing shapes of the flow field is presented. The reshaping is accomplished by the growth-strain method which was first developed using the finite-element calculation of the deformation of shapes by generating bulk strain for solid problems. The generation law of the bulk strain is given as a function of a distributed parameter to be made uniform. For solid problems, the validity of the use of the shear strain energy density to maximize the strength based on the Mises criterion or the strain energy density to maximize the stiffness for the distributed parameter has been confirmed. In the present paper, we propose the use of the dissipation energy density for the distributed parameter to minimize the total energy dissipated due to the viscosity of the fluid. Numerical results for abruptly enlarged channel problems in steady state assuming low Reynolds number and incompressible viscous fluid shows the validity of the present approach.