The heterogeneous to homogeneous transition for slurry flow in pipes

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Models for modeling slurry flow present difficulties on long lines with large pipe diameters and with broad graded sands or gravels. In order to get more insight into the slurry flow process, the Delft Head Loss & Limit Deposit Velocity Framework has been developed that integrates the 5 main flow regimes of slurry transport: fixed or stationary bed transport, sliding bed transport, heterogeneous transport, homogeneous transport and sliding flow transport. Additional models for; the limit deposit velocity, the holdup function, the bed height, the concentration distribution and graded sands and gravels, complement the Framework. The Framework is based on constant spatial volumetric concentration curves for uniform sands and gravels. The models for the flow regimes and the limit deposit velocity are based on energy considerations. At line speeds near the transition of the heterogeneous and homogeneous flow regimes however, there is no sharp transition between the two flow regimes for medium sized particles. The limits of medium sized particles depend on the solid and liquid properties and on the pipe diameter. It is often observed that the hydraulic gradient lies in between the Equivalent Liquid Model (ELM) and the pure liquid Darcy Weisbach model at higher line speeds, resulting in the conclusion that at higher line speeds the pure liquid hydraulic gradient is approached. Based on energy considerations however, it is shown that the heterogeneous hydraulic gradient collapses due to turbulent near wall lift neutralizing the particle submerged weight and collisions with the pipe wall, while at higher line speeds the turbulent eddies integrate particles, resulting in a hydraulic gradient approaching a reduced ELM (RELM). For medium sized particles in large diameter pipes there is a gap between the moment the heterogeneous hydraulic gradient collapses and the homogeneous hydraulic gradient builds up, resulting in a hydraulic gradient approaching the RELM hydraulic gradient. The model for this transition is described and derived and experimental evidence is given.
Original languageEnglish
Pages (from-to)422-431
JournalOcean Engineering
Publication statusPublished - 2016

Bibliographical note

Accepted Author Manuscript


  • slurry transport
  • hydraulic gradient
  • limit deposit velocity


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