Continuous adjoint-based shape optimization of a turbomachinery stage using a 3D volumetric parameterization

This work presents a novel volumetric parameterization technique along with the continuous adjoint method to support gradient-based CFD shape optimization of turbomachinery stages. The proposed parameterization retains axisymmetry and periodicity by acting on a transformed coordinate system. The same volumetric model controls the shape and the computational volume mesh in a seamless manner, avoiding the additional use of a mesh deformation tool. Moreover, it is differentiated to compute mesh sensitivities (i.e., derivatives of nodal coordinates with respect to the design variables) and is combined with the flow and continuous adjoint, multi-row solvers of the in-house PUMA software. Flow field solutions in successive rows communicate based on the mixing plane approach; the development of continuous adjoint to the latter is also presented in this article. The adjoint to the turbulence model and distance-from-the-wall (Hamilton-Jacobi) equations are solved, increasing the accuracy of the computed sensitivity derivatives. All these tools run on modern GPUs, accelerating both flow/adjoint solutions and shape/mesh manipulations. The capabilities of these tools are demonstrated in the shape optimization of the rotor blades of the MT1 high-pressure, transonic, turbine stage, aiming at maximum stage isentropic efficiency with constraints on stage reaction and inlet capacity.