SENSITIVITY ANALYSIS AND OPTIMIZATION OF COUPLED THERMAL AND FLOW PROBLEMS WITH APPLICATIONS TO CONTRACTION DESIGN

The finite element method and the Newton-Raphson solution algorithm ar e combined to solve the momentum, mass and energy conservation equatio ns for coupled flow problems. Design sensitivities for a generalised r esponse function with respect to design parameters which describe shap e, material property and load data are evaluated via the direct differ entiation method. The efficiently computed sensitivities are verified by comparison with computationally intensive, finite difference sensit ivity approximations. The design sensitivities are then used in a nume rical optimization algorithm to minimize the pressure drop in flow thr ough contractions. Both laminar and turbulent flows are considered. In the turbulent flow problems the time-averaged momentum and mass conse rvation equations are solved using a mixing length turbulence model.