With steel pipes, just as with any pipes, it is important to be able to predict the behaviour of the fluids that pass through the system.

But in steel pipes with a rough inner surface, it is particularly important to be aware of how the interaction between the contents and that surface can create turbulent flow.

The picture is further complicated when the fluid contained within the system is a gas containing solid particles in suspension – with the flow of the two materials needing to be modelled separately, but understood together.

Researchers at the University of Saskatchewan have now devised a two-fluid model, described in the Journal of Fluids Engineering, to simplify this understanding.

Professor Donald John Bergstrom and corresponding author Ashraf Uz Zaman write that a two-fluid formulation allowed them “to model both the gas and solid phases for turbulent gas-particle flow in a vertical tube”.

Their paper focuses specifically on how surface roughness alters the turbulent kinetic energy and granular temperature, whether the surface is particularly smooth or rough, potentially making the method a useful means of predicting the performance of installations of steel pipes, for reliable long-term operation.