A novel computationally efficient approach for numerical simulation of helical vortex ropes in axially symmetric diffusers is presented and investigated. It is based on the assumption that the vortex is stationary in the frame of reference, rotating with the vortex core. Steady-state Reynolds-Averaged Navier-Stokes equations, written in rotating frame of reference are solved iteratively in pseudo-time using artificial compressibility method. An algorithm for automatic adjustment of angular velocity of reference frame rotation is developed and implemented. The proposed approach, called RSS (rotating steady state), is compared with true unsteady computations in the same computational domain. Several two-equation eddy viscosity models, k-e Kim-Chen, SST, SST-CC, as well as hybrid SST-DES model were used for turbulence closure. Both approaches, RSS and unsteady, were verified against available numerical and experimental data for a single axially symmetric diffuser and a Francis turbine with conical draft tube. It was established that in case there is a periodic vortex rope in unsteady simulation, then it can be captured in frames of our rotating steady state statement. The frequency of vortex rope rotation and the amplitude of pressure pulsations on the wall are in good agreement for both approaches. At that RSS approach offers one to two orders of magnitude reduction in computational time compared to unsteady computation. Shortcomings of the proposed RSS approach are also discussed.