In this work the Topology Optimization Method is employed to generate designs with rotating compressible flows. The Navier Stokes and energy equations are solved for steady state cases. The perfect gas model is used. The Brinkman penalization is applied to represent the solid regions inside the domain. The physical model is represented in a rotating reference frame and, to account for turbulent flows, the Favre average is used with the Wray Agarwal turbulence model from 2018. The main objective

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... of the work is to optimize designs with compressible rotating flows, however incompressible and non-rotating cases have also been accounted. The objective functions considered for incompressible flows are the energy dissipation and the pump efficiency and, for compressible flow problems, the entropy variation and the impeller isentropic efficiency. The calculation of the sensitivities for the optimization problem is executed with the adjoint method in the continuous and the discrete approaches. The discrete approach developed is a novel methodology and is based on a finite differences scheme. The implementation is made with the use of the finite volume library OpenFOAM, the C++ library Eigen and the scientific library PETSc. Numerical examples are presented considering incompressible laminar flows with and without rotation, compressible laminar flows with and without rotation and compressible turbulent flows with and without rotation. Also, an assessment of the behavior of the turbulence model in an optimization context is performed. The numerical examples show that the sensitivity calculation is correctly implemented and the methodology developed is capable of generating designs to work with compressible rotating flows.