One of the current challenges in fluid topology optimization is to address these turbulent flows such that industrial or more realistic fluid flow devices can be designed. Therefore, there is a need for considering turbulence models in more efficient ways into the topology optimization framework. From the three possible approaches (DNS, LES, and RANS), the RANS approach is less computationally expensive. However, when considering the RANS models that have already been considered in fluid topology optimization (Spalart–Allmaras, k–ε, and k–ω models), they all include the additional complexity of having at least two more topology optimization coefficients (normally chosen in a “trial and error” approach). Thus, in this work, the topology optimization method is formulated based on the Wray–Agarwal model (“WA2018”), which combines modeling advantages of the k–ε model (“freestream” modeling) and the k–ω model (“near-wall” modeling), and relies on the solution of a single equation, also not requiring the computation of the wall distance. Therefore, this model requires the selection of less topology optimization parameters, while also being less computationally demanding in a topology optimization iterative framework than previously considered turbulence models. A discrete design variable configuration from the TOBS approach is adopted, which enforces a binary variables solution through a linearization, making it possible to achieve clearly defined topologies (solid–fluid) (i.e., with clearly defined boundaries during the topology optimization iterations), while also lessening the dependency of the material model penalization in the optimization process (Souza et?al. 2021) and possibly reducing the number of topology optimization iterations until convergence. The traditional pseudo-density material model for topology optimization is adopted with a nodal (instead of element-wise) design variable, which enables the use of a PDE-based (Helmholtz) pseudo-density filter alongside the TOBS approach. The formulation is presented for axisymmetric flows with rotation around an axis (“2D swirl flow model”). Numerical examples are presented for some turbulent 2D swirl flow configurations in order to illustrate the approach.