A continuous adjoint approach to design optimization in cavitating flow using a barotropic model

• A continuous adjoint method is developed for design optimization in cavitating flow.
• A homogeneous multiphase mixture model is used with a barotropic equation of state.
• Standard explicit methods are used to solve both the primary and adjoint systems.
• Results are presented for both surface- and volume-based vapor minimization.
• Cost function gradients compare well with the complex-step method.

A continuous adjoint method is developed for design optimization in multiphase flow based on a homogeneous multiphase mixture model. The mixture model consists of variable-density mass and momentum equations and uses a barotropic equation of state for the density that depends on only the local static pressure and the vapor pressure of the liquid. In that case, the primary equations are homogeneous, and a conventional hybrid multistage explicit method based on central differencing and second- and fourth-order scalar artificial dissipation can be applied to solve both the primary and adjoint systems. Results are presented for both surface- and volume-based vapor minimization cost functions for a two-dimensional cavitating hydrofoil in which the geometry is parameterized using B-splines. The cost function gradients computed using the adjoint method are shown to compare well with gradients computed using the complex-step method.