We propose a scaling law for the onset of turbulence in pipe flow of neutrally buoyant suspensions. This scaling law, based on a large set of experimental data, relates the amplitude of the particle-induced perturbations ε to the critical suspension Reynolds number Res,c. Here ε is a function of the particle-to-pipe diameter ratio and the volume fraction of the suspended particles, ε=(d/D)1/2ϕ1/6. Res,c is found to scale as ε−1. Furthermore, the perturbation amplitude allows a distinction between classical, intermediate, and particle-induced transitions.@en

Particle-laden pipe flows exhibit a gradual laminar-turbulent transition, beyond a critical volume fraction (φ). While classical transition behavior is characterized by the presence of turbulent puffs, this intermittent nature is absent for particle-induced transition. For small pipe-to-particle diameter ratios (D/d) even dilute systems exhibit this particle-induced transition behavior. In this study we use neutrally buoyant particles with a D/d of 5.7, which represents a "sweet spot,"allowing the use of particle image velocimetry to study this particular phenomenon. The average velocity profile gradually changes from a parabola (laminar flow) to a blunted velocity profile for increasing Reynolds number. The instantaneous velocity profiles fluctuate around this profile. These velocity fluctuations, described by ux-rms and ur-rms, gradually increase for increasing Reynolds number, as do the Reynolds stresses. For low Res, the velocity fluctuations increase proportional to the bulk velocity, which can be explained by a simple model based on the finite size of the particles. The velocity fields show the presence of elongated streamwise structures. The largest length scales are found in the transition region, where average integral length scales up to 5D are found. The structures decrease in length when the flow has fully transitioned to a turbulent state.

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