Design of Low Residue Packs by Smoothed Particle Hydrodynamics

  • Aaron English

Student thesis: Phd


Many Unilever products, principally gels and sauces, leave a residue in the container when ‘empty’ due to the interaction of the product with the interior packaging surface. This is a free surface and boundary problem. Smoothed particle hydrodynamics (SPH) is well suited for free surface flows in complex geometries but accurate representation of solid surfaces requires fundamental development. A robust but approximate boundary condition for general complex shapes, known as the dynamic boundary condition, is widely used but has underlying physical and theoretical weaknesses, limiting accuracy. This has been improved in this project by extrapolating properties from the flow domain, to fixed boundary particles to maintain the robustness of the dynamic boundary condition while removing its physical and theoretical limitations; this has become known as the modified dynamic boundary condition. However conventional boundary conditions are no slip but many flow problems in the process industries incur partial slip, with a small flow velocity on the solid surface. Formulations in SPH have been developed for the first time which has been possible with the `modified' dynamic boundary condition. This has been progressed with application to parallel flows, Couette and Poiseuille, for which new analytical solutions have been developed to enable validation. The important rheometer case, used for quantifying particularly non-Newtonian fluid properties, has also been studied, comparing with limited available experimental data. The groundwork for generalisation to complex shapes, including no slip and partial slip, has thus been laid. The aim of a versatile simulation tool with free surfaces has been demonstrated for diverse applications, the standard dam break with violent impact on a column and the new fish pass problem comprising a complex channel flow with transverse weirs and gates. New experimental data for pouring from a beaker has been simulated but have shown that limitations for small flow depths of the order of particle size need to be addressed when the beaker is almost empty. The modified dynamic boundary condition with density extrapolation and zero velocity solid boundary particles (or with velocity of the body if moving) is now available in the open source DualSPHysics code which can run efficiently on CPUs and GPUs.
Date of Award1 Aug 2021
Original languageEnglish
Awarding Institution
  • The University of Manchester
SupervisorPeter Stansby (Supervisor) & Steven Lind (Supervisor)


  • SPH
  • CFD
  • Computational Fluid Dynamics
  • Free Surface Flows
  • Packaging
  • Boundary Conditions
  • Smoothed Particle Hydrodynamics
  • Partial Slip

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