Application of the Partially-Averaged Navier-Stokes Equations to Propeller-Rudder Interaction

Other conference contribution, 2026

The Reynolds-Averaged Navier-Stokes (RANS) equations are still the most commonly used approach in the numerical simulation of flows from an industrial perspective, as flow quantities such as average forces and moments can be predicted with reasonable accuracy. However, scale-resolving simulations and approaches such as Detached Eddy Simulation (DES) and Large Eddy Simulation (LES) are becoming more prominent for research purposes, since they lead to a more detailed flow description and perform better when massive flow separation occurs. Regardless of numerical approach, numerical errors are always present. The discretization error, which is usually the dominant component of the numerical error, is linked to the refinement of the grid being used. In most scale-resolving methods, grid parameters are a part of the mathematical model being solved, making the discretization error entangled with the modelling error [1] and causing grid refinement studies to be inadequate to assess the discretization error. Some scale-resolving methods, such as the Partially-Averaged Navier-Stokes (PANS) equations [3], do not suffer from these limitations, as grid cell size is not a part of the governing equations being solved. Consequentely, discretization and modelling errors are separated and can be estimated independently [2]. In our work, we apply the Partially-Averaged Navier-Stokes equations to the flow of a model-scale propeller and rudder in a cavitation tunnel. Different loading conditions on the propeller and rudder angles are considered. Results are compared against available experimental data and with RANS simulations. The work is conducted with the commercial flow solver STAR-CCM+, which does not include PANS in its modelling capabilities. In order to assess that the implementation of PANS carried out by the authors is correct, simulations are also performed on a simpler test-case consisting of the flow around a circular cylinder.

[1] - Pereira, F., 2018. Towards predictive scale-resolving simulations of turbulent external flows. Instituto Superior Técnico, Lisbon, Portugal. Ph.d thesis.
[2] - Girimaji S., Jeong E., Srinivasan R., Partially Averaged Navier-Stokes Method for Turbulence: Fixed Point Analysis and Comparison with Unsteady Partially Averaged Navier-Stokes, Journal of Applied Mechanics, 73(3):422–429, 2005.