Burns turbulent dispersion considers the dispersed phase as a passive scalar

TL;DR

This paper demonstrates that the Burns turbulent dispersion force can be interpreted as modeling bubbles as passive scalars in turbulent pipe flow, validating its use in low-void fraction PWR conditions.

Contribution

It shows that the Burns turbulent dispersion force is equivalent to treating bubbles as passive scalars, clarifying its theoretical basis and applicability.

Findings

Burns force aligns with passive scalar behavior in low-void fraction flows.

Bubbles in PWR conditions have low Stokes number, justifying turbulence-based dispersion modeling.

Burns force is suitable for representing bubble dispersion in industrial pipe flows.

Abstract

The Burns turbulent dispersion force is the most commonly used turbulent dispersion in the twofluid RANS bubbly-flow literature. However, its derivation is based on a series of hypothesis that are difficult to justify in industrial flows. It is shown that in low-void fraction vertical pipe flow, the Burns turbulent dispersion formulation is equivalent to considering the radial movement of the gas phase like a passive scalar that follows turbulent eddies. This is not apparent in the derivation of the force. As bubbles in pressurized water reactor (PWR) conditions have a low Stokes number ($\sim$ 10--1), considering bubbles are transported by turbulence is a good approximation for bubble dispersion in pipe flow. Therefore, the Burns turbulent dispersion force is appropriate to represent bubble dispersion in low-void fraction PWR flows.