Mathematical formulation for the analysis of the periodic convergence during co-processing routines in long-run, scale-resolving simulations of turbomachinery

Abstract

Scale-resolving simulations, like LES modelling, are recent CFD techniques to analyse numerically unsteady flows and turbulence in turbomachinery. Despite their high computational costs, they provide an unsteady, time-resolved solution of the flow with embedded turbulent scales that requires an additional statistical description. This paper provides the mathematical formulation required to compute and assure its periodic convergence, updating the phase-averaged values and the residual on the run, so the amount of data to be stored is extremely reduced. The formulation, applied over a numerical database of a wall-modelled LES simulation of the rotor-stator interaction in a low-speed axial fan using a 3D linear cascade model, reveals that primary flow variables converge faster than turbulent structures due to inherent instabilities of the coherent flow vortices. This work forms part of the concept of co-processing, where some post-processing routines are resolved during the iterative process of CFD simulations to save computational costs.