The central objective of this thesis is to investigate the interaction of turbulent flow structures with low-inertia particles in a pipe flow. We have performed direct numerical simulations (DNS) of a turbulent pipe flow at Reynolds numbers Re = 5300 and 10300 based on bulk velocity and pipe diameter. We have also solved concentration transport equations for passive scalars and low- inertia particles with Stokes numbers up to St+ = 1 in a vertical pipe with no-gravity, upward or downward flow, with Froude numbers Fr_z = ±0.4, ±4. The particle velocities were obtained from the equilibrium Eulerian model of Ferry and Balachandar [2001]. Extended proper orthogonal decomposition (EPOD) was employed to find the flow structures most correlated with the particle concentration. A novel Fukagata-Iwamoto-Kasagi (FIK) identity was derived that has allowed us to quantify for the first time the role of individual turbulent structures on the time-averaged depo- sition. This approach made it possible to identify which structures contributed most to deposition, relative to their turbulent kinetic energy, and how this changes depending on Reynolds, Stokes and Froude numbers. The pre-multiplied concentration spectra were analysed as well and it was found that inertia shifts the peak to smaller wavelengths and away from the wall.
To further probe the effect of inertia, a new resolvent operator for low-inertia particles was derived. This allows us to analyse the effect of the different fluid and particle parameters directly from the governing equations. Using this resolvent formulation it was possible to reproduce the shape of the particle concentration spectra and capture all the relevant physical phenomena of inertial particles such as turbophoresis, near-wall accumulation and inertial clustering. Inspection of the blocks that constitute the resolvent operator also revealed the existence of a separate critical layer for the particle concentration. The distance between the critical layers of velocity and particle concentration was related to the combined effect of gravity and inertia. The new critical layer can be used to explain why particles move towards the centre in a downward flow, and near the wall in an upward flow.
Finally, the resolvent analysis tool was extended to account for the two-way coupling between the turbulent flow and the particles. This made it possible to analyse how the turbulent kinetic energy changes depending on the Stokes number, Froude number and mass fraction of the particle phase. This resolvent formulation could also predict the observations made in previous experiments and simulations, namely that the streamwise velocity and concentration fluctuations reduce in amplitude near the wall, that the radial fluctuations reduce in the entire domain, and that the smallest wavelengths of the turbulent kinetic spectra are amplified in a two-way coupled flow.