Discretization and perturbations in the simulation of localized turbulence in a pipe with a sudden expansion

Abstract

At low Reynolds numbers, the flow through a pipe with a sudden expansion is characterized by the localized occurrence of flow instabilities, with the formation of a so-called turbulence puff. In the literature, physical experiments typically predict earlier occurrence of turbulence than computational fluid dynamics simulations. However, the behaviour of 'natural' transition to turbulence without perturbations, and the dependence of transition to turbulence on perturbations, are not yet fully understood, particularly for the simulations. The purpose of the present study is therefore to investigate this flow, including possible sources of perturbation in numerical simulations, and to evaluate their effect on transition to turbulence. Through the exploration of different flow rates, numerical settings and inlet perturbation amplitudes, and by evaluating coarse and refined simulations, insights into low-Reynolds-number transitional turbulent flows are obtained. The turbulence kinetic energy budget of the turbulence puff or slug characteristic of this flow is also evaluated. In conclusion, even when perturbations are not intentionally added, there can still be significant sources of numerical perturbation and error that trigger turbulence in simulations, but perturbations will need to be added in refined simulations in order to produce turbulence. Finally, the results agree with the notion that there may not be a scenario where the flow transitions naturally to turbulence without any perturbation.