Hydrodynamic shape optimization of propulsor configurations using a continuous adjoint approach

The use of high-fidelity computational fluid dynamic simulations in propulsor and pump detailed design is currently limited to the analysis of candidate geometries. This work explores the viability of extending the use of high-fidelity flow modeling to the realm of hydrodynamic shape optimization of turbomachinery operating in the incompressible flow regime.; A methodology for affordable gradient-based shape optimization is presented. The approach is based on a continuous adjoint formulation. Complete derivations of the adjoint governing equations and boundary conditions are carried out for rotating flows governed by both the pseudo-compressible Euler and Reynolds-averaged Navier-Stokes equations. Also derived are the associated expressions for the cost function gradient in each case. These derivations are carried out using the inverse design cost function—a cost function chosen primarily for its verifiability. This property is essential for unambiguously establishing the viability of the approach. The numerical solution of the flow and adjoint systems is described. Both the flow and adjoint solution procedures are parallelized using the Message-Passing Interface standard. The design variables used to describe the blade geometry are the normal-direction displacement of the surface-coincident computational mesh points. A simple and robust algebraic domain re-meshing procedure is also presented. Steepest descent is employed as the optimization algorithm.; The inverse design of an inlet guide vane and a rotor blade are successfully carried out for both inviscid and viscous flows. The coarse mesh Euler inverse designs using 1,625 design variables require less than 12 seconds per design cycle. The fine mesh turbulent inverse designs using 11,025 design variables require less than 4.5 minutes per design cycle. These results clearly establish the efficiency and accuracy of the overall approach and lay the foundation for future propulsor design tool development.