We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorovâ s two-equation model of turbulence. The governing system of equations is completed by initial and boundary conditions; concerning the velocity we consider generalized stickâ slip boundary conditions. The fact that the admissible class of boundary conditions includes various types of slipping mechanisms on the boundary makes the result robust from the point of view of possible applications.