Spatial development of particle laden turbulent pipe flow

The inhomogeneity of turbulence in wall bounded flows induces the phenomenology called turbophoresis whereby inertial particles of suitable mass accumulate at the solid wall. Particles injected near the axis of a fully turbulent pipe flow, after an initial spreading phase, undergo a segregation process which eventually leads to a pseudoequilibrium distribution sufficiently downstream. Wall densities up to thousand times the reference value can be easily achieved. The process is discussed here by analyzing the direct numerical simulation (DNS) data of a spatially developing particle laden pipe flow under the assumption of dilute suspension. Development phase and asymptotic state are addressed in quantitative terms. A Shannon-like entropy is introduced to quantify the level of spreading/segregation achieved by the particle distributions along the pipe. This allows to define on a physically sound basis the length of the developing region and to summarize in a single indicator the accumulation level as a function of the particle response time. By conditional statistics, it is unequivocally shown that particles approach the wall dragged by relatively fast yet comparatively rare events where highly accumulating particles follow the fluid in-rush toward the wall. On the contrary, the outward particle flux takes place in the form of much more frequent and gentle motions away from the wall. The analysis of DNS data and a simple argument highlight the role of the elongated clusters of particles at the wall as essential features responsible for the eventual asymptotic equilibrium.