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

Authors: Jesús Manuel Fernández-Oro

Addresses: Fluid Mechanics Area of the Energy Department, Gijón Polytechnic School of Engineering, University of Oviedo, Department Building East Zone, Campus of Viesques, 33203, Gijón, Spain

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.

Keywords: statistical convergence; co-processing; phase-averaging; LES simulation; rotor-stator interaction; axial fan; CFD; turbomachinery; turbulence; BPF; periodicity.

DOI: 10.1504/PCFD.2021.10036934

Progress in Computational Fluid Dynamics, An International Journal, 2021 Vol.21 No.3, pp.141 - 151

Received: 26 Feb 2020
Accepted: 27 Aug 2020

Published online: 19 May 2021 *

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