Aerodynamic optimization of internal and external flows using the adjoint-equation method

Aerodynamic shape optimization for internal and external flows is studied. A cost function is defined based on the design objective of a particular application. Gradient-based method is used to minimize the cost function, and the adjoint equation method is applied to obtain the gradient information. Both inviscid and viscous design cases are considered, and the adjoint equations and boundary conditions are derived for the Euler equations and the Navier-Stokes equations for cases in which the cost function can be expressed as a sum of boundary integrals. The finite-volume method with time marching iterations is applied to obtain the numerical solutions of the flow governing equations and the adjoint equations. Most of the numerical methods for the flow solver are applicable to the adjoint-equation solver.; The gradient information is obtained by perturbing the geometry and calculating the corresponding cost-function variation. Only one solution of the flow field and one solution of the adjoint equations are needed to determine the gradient of the cost function, and the computational cost is essentially independent of the number of design parameters. Compared to the finite-difference method, the adjoint-equation method is much more efficient when the number of design parameters is large.; Several design cases are tested in this study, including wing design, turbomachinery blade design, and intake diffuser design. For the wing design cases, inverse design and drag minimization are tested; for the turbomachinery blade design cases, inverse design, entropy production minimization, and exit flow angle distribution control are tested; for the intake diffuser design case, non-axial momentum minimization is tested. The results show that the cost-function values are reduced significantly after the design process, which means the design method is able to improve the aerodynamic performances effectively for these design cases.