SHAPE OPTIMIZATION ANALYSIS OF FLOW-FIELD - (GROWTH-STRAIN METHOD APPROACH)

A new analytical approach for optimizing shapes of the flow field is p resented. The reshaping is accomplished by the growth-strain method wh ich was first developed using the finite-element calculation of the de formation of shapes by generating bulk strain for solid problems. The generation law of the bulk strain is given as a function of a distribu ted parameter to be made uniform. For solid problems, the validity of the use of the shear strain energy density to maximize the strength ba sed on the Mises criterion or the strain energy density to maximize th e stiffness for the distributed parameter has been confirmed. In the p resent 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 enlarge d channel problems in steady state assuming low Reynolds number and in compressible viscous fluid shows the validity of the present approach.