Brief Communication Threshold for sediment erosion in pipe flow Y. Peysson a, * , M. Ouriemi b,c , M. Medale c , P. Aussillous c , É. Guazzelli c a IFP, 1 et 4 Avenue de Bois-Préau, 92852 Rueil-Malmaison Cedex, France b IFP-Lyon, Rond-Point de l’échangeur de Solaize, BP 3, 69360 Solaize, France c IUSTI CNRS UMR 6595 – Polytech’ Marseille – Aix-Marseille Université (U1), 5 rue Enrico Fermi, 13453 Marseille Cedex 13, France article info Article history: Received 22 December 2008 Received in revised form 28 January 2009 Accepted 10 February 2009 Available online 26 February 2009 Keywords: Shields number Sediment transport Pipe flow abstract Ó 2009 Elsevier Ltd. All rights reserved. 1. Introduction The response of a sedimented bed of particles to shearing flows is an issue which has been widely studied and discussed for over a century. This problem is indeed at the center of the understanding of a variety of natural phenomena such as sediment transport in rivers and estuaries, erosion and deposition leading to the evolu- tion of mountains and landscapes, and dune formation in the des- ert (aeolian dunes) or underwater. It is also of fundamental importance in numerous industrial processes such as slurry trans- port or cutting discharge by hydraulic transport in the mining industry. In practice, slurries which consist of mixtures of solid and fluid are conveyed through pipelines, see e.g. Matoušek (2005). Understanding the flow of settling slurries in pipelines is also of great interest in the oil and gas industry especially in the context of hydrate (solid crystal of clathrate) formation that are encountered in offshore oil production. One of the essential issue in slurry transport is to predict the on- set of solid flow. The usual way of representing the incipient motion of the particles is to use a dimensionless number called the Shields number, h ¼ s b =ðq p  q f Þgd, which measures the relative impor- tance of the destabilizing hydrodynamic force, i.e. s b d 2 where s b is the shear stress at the bed surface, and the stabilizing gravity force, i.e. the apparent weight of a grain ðq p  q f Þd 3 g, where d is the grain diameter, q p and q f the density of the solid and the fluid respectively, and g the acceleration due to gravity. The data, which are mostly col- lected in the turbulent flow regime as shown in e.g. White (1970), Mantz (1977), Yalin and Karahan (1979) and Dancey and Diplas (2002), are conventionally represented using the Shields curve by plotting h against the boundary Reynolds number defined with the friction velocity ¼ ffiffiffiffiffiffiffiffiffiffiffiffi s b =q f q as a velocity scale and d as length scale. This representation, which seems somehow circular, stems from Shields assumption that his measured shear stress attains a constant value for large Reynolds numbers which is based on analogy with Nikuradse (1933) finding that the friction factor (or drag coefficient) also reaches a constant value, see e.g. Buffington (1999) discussion of the Shields curve (his Fig. 4). The main issue comes from unambiguously defining the shear stress s b . In the low-Reynolds-number viscous regime, it is defined as s b ¼ g _ c where g is the fluid viscosity and _ c the shear rate. In vis- cous pipe flow, Ouriemi et al. (2007) precisely computed this shear rate and, through measurement for the onset of grain motion, in- ferred a critical Shields number h c ¼ 0:12 independent of the Reynolds number for a large range of small particle Reynolds num- bers. The objective of the present brief communication is to extend this approach up to the turbulent regime. In Section 2, the thresh- old for motion is characterized in a precise way through the cessa- tion of granular motion. In Section 3, we propose a simple model in which the basic assumption is that the critical Shields number found in the laminar regime holds up to the turbulent regime. The shear stress is defined using the friction factor in the two limits of laminar and turbulent flows. In Section 4, this model is tested against the experiments. 2. Experiments Four different batches of spheres and four mixtures of UCON oil 75H-90000 and water at different temperatures were used in the experiments, see their characteristics in Tables 1 and 2. The 0301-9322/$ - see front matter Ó 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijmultiphaseflow.2009.02.007 * Corresponding author. Tel.: +33 147526960; fax: +33 147527002. E-mail address: yannick.peysson@ifp.fr (Y. Peysson). International Journal of Multiphase Flow 35 (2009) 597–600 Contents lists available at ScienceDirect International Journal of Multiphase Flow journal homepage: www.elsevier.com/locate/ijmulflow