Transition to Turbulence in Particulate Pipe Flow

Abstract

We investigate experimentally the influence of suspended particles on the transition to turbulence. The particles are monodisperse and neutrally-buoyant with the liquid. The role of the particles on the transition depends both upon the pipe to particle diameter ratios and the concentration. For large pipe-to-particle diameter ratios the transition is delayed while it is lowered for small ratios. A scaling is proposed to collapse the departure from the critical Reynolds number for pure fluid as a function of concentration into a single master curve.PACS numbers: 83.80.Hj, 83.50.Ha More than a century after Reynolds' work [1], understanding how turbulent regions grow in a pipe and bring the laminar Poiseuille flow to fully developed turbulence is still not completely achieved. Above a critical Reynolds number, the laminar flow is observed to be unstable, turbulent regions grow and are convected in the pipe. This flow regime is called intermittent. When the flow rate is further increased, the flow becomes fully turbulent [2]. In fact, the transition happens to be subcritical and the flow is linearly stable for all flow rates [3]. A finite amplitude perturbation is needed to trigger the transition and the critical Reynolds depends upon its amplitude. For small perturbations, laminar motion is observed as far as Re ≈ 10 5 but the transition in pure fluid can be reached for Re ≈ 2100 provided that the perturbation is strong enough to allow the growth of turbulent "puffs" [2]. Recent studies have investigated with different kinds of perturbations the nature of the unstable modes, either in the inlet region or in the fully developed flow [4,5].The objective of the present work is to examine how transition to turbulence is affected by the presence of suspended particles in the simplest case of neutral buoyancy. More specifically, we focus upon determining the transition threshold between the laminar and the intermittent regime as a function of the particle volume fraction φ of the suspension. Because the particles are neutrally buoyant and largely drag-free, the present study is related to recent work which has examined global subcritical stability behavior of plane Couette flow forced by the presence of a single spherical bead or a spanwise wire [6,7]. This work also has a practical aspect as it is related to pipeline flow of slurries.Experiments are performed with four sets of spherical polystyrene particles having density ρ = 1.0510 ± 0.001 g.cm −3 and diameters d presented in table I. To obtain neutral buoyancy, the densities of the fluid and of the particles are matched. We choose as a fluid a mixture of 22 % glycerol and 78 % water by mass. The temperature of the mixture is maintained at 25 ± 1 • C by using a thermostated bath as a fluid reservoir in the fluid circulating loop. At this temperature, the viscosity of the mixture is µ = 1.64 ± 0.03 cP. The experimental set-up consists of a straight and horizontal cylindrical glass tube of 2.6 m length mounted on a rigid support structure. Two different tubes havi...

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