# Linear transient growth of particulate pipe flows

## TL;DR

This study investigates how particles in pipe flow influence linear transient growth, revealing that particles can enhance flow instability especially when localized at specific radial positions, with optimal effects near the Segre-Silberberg radius.

## Contribution

It introduces a simple two-fluid model to numerically analyze the impact of particles on transient growth in pipe flows, highlighting the significance of particle size and location.

## Key findings

- Particles enhance transient growth, especially at specific radial locations.
- Optimal enhancement occurs with particles of intermediate size.
- Clustering at the Segre-Silberberg radius maximizes transient growth.

## Abstract

We tackle the question of whether the presence of particles in a pipe flow can influence the linear transient growth of infinitesimal perturbations, in view of better understanding the behaviour of particulate pipe flows in regimes of transition to turbulence. The problem is tackled numerically by means of a simple model where particles are modelled as a second fluid, that interacts with the fluid phase through a two-way Stokes drag only. The transient growth is found to be enhanced by the presence of particles, especially so if the particles are localised at a specific radial location of the pipe. At the same time, the mechanisms of transient growth themselves remain those of non-particulate flows. The effect is maximised for particles of intermediate size (somewhere between the ballistic limit of very light particles and the point where they are too heavy to be influenced by the flow). Most remarkably, the Segre-Silberberg radius (around 2/3 of the pipe radius), where particles naturally cluster in laminar flows, turns out to be close to the optimal location to enhance the transient growth.