The Myth of URANS

TL;DR

This paper provides a theoretical analysis of unsteady RANS (URANS), revealing its limitations in accurately predicting turbulence decay and explaining why it tends to revert to steady RANS over time.

Contribution

It extends fixed point analysis to develop a theoretical model for URANS dynamics, highlighting its inaccuracies and potential for hybrid model improvements.

Findings

URANS can predict incorrect decay rates.

Solutions tend to stabilize to steady RANS.

Forced turbulence shows a fixed energy level of about 30%.

Abstract

Since the 1990s, RANS practitioners have observed spontaneous unsteadiness in RANS simulations. Some have suggested deliberately using this as a method of resolving large turbulent structures. However, to date, no one has produced a theoretical justification for this unsteady RANS (URANS) approach. Here, we extend the dynamical systems fixed point analysis of Speziale and Mhuiris (1989), Girimaji et al. (2006) to create a theoretical model for URANS dynamics. The results are compared to URANS simulations for homogeneous isotropic decaying turbulence. The model shows that URANS can predict incorrect decay rates and that the solution tends towards steady RANS over time. Similar analysis for forced turbulence shows a fixed modeled energy of about 30% of total energy, regardless of the model parameters. The same analysis can be used to show how hybrid type models can begin to address these issues.