Lattice Boltzmann schemes for convection-diffusion phenomena : application to packages of agricultural products

R.G.M. van der Sman

    Research output: Thesisexternal PhD, WU


    <p>Packaging is crucial for the control of quality of fresh agricultural products. How to optimise the packaging design for a particular product and distribution chain, is still not fully understood. Various empirical studies have shown that existing packaging designs can still be improved significantly. The packaging design process can be greatly enhanced by the use of computer models, describing the physical and physiological processes.</p><p>In transport packaging systems with vent holes, the dominant physical processes are convection-diffusion of heat and water vapour. The numerical solution of convection-diffusion problems is a complex matter. Traditionally, solutions are obtained with specific Finite Element or Finite Difference schemes, which require a highly-specialised knowledge of numerical mathematics. /P><p>In this thesis, the Lattice Boltzmann method is investigated as an alternative numerical method to solve the convection-diffusion problems in packaging systems. It simulates physical transport phenomena with quasi-particles, which move and collide on a lattice. Space, time and particle speed are discrete.</p><p>The dynamics of the quasi-particles are governed by a discretised Boltzmann equation. Since the Lattice Boltzmann method has shown to be able to model Navier-Stokes flow, it has recieved a rapidly growing interest from the scientific community. This interest can be attributed to the simplicity and the appeal to physical intuition of the Lattice Boltzmann method.</p><p>In the first part of this thesis several test case problems, taken from the practice of packing agricultural products, are solved with the Lattice Boltzmann method. Accurate and efficient schemes have been developed for the following applications: the cooling of cut flowers, the natural convection in a potato container, and the water vapour transfer in a potato container with vent holes.</p><p>In order to solve these test case problems, the Lattice Boltzmann method has been extended with:</p><OL><LI>a scheme for convection-diffusion on an orthorhombic lattice,<LI>a scheme for porous media flow as described by Darcy's law,<LI>interactions modelling heat and mass transfer between solid and fluid phase of a porous medium,<LI>boundary conditions for heat conducting and water permeating packaging material, and<LI>boundary conditions for vent holes.</OL><p>Despite the successful solution of the test case problems, the Lattice Boltzmann schemes have up to now have had drawbacks, which make them difficult to compete with Finite Element and Finite Difference schemes.</p><p>Because the lack of a clear theoretical foundation, and the inability to Support grid refinements, it is difficult for the Lattice Boltzmann method to compete with the Finite Element and Finite Difference method in solving convection-diffusion problems. Hence, in the latter part of the thesis we investigate whether these drawbacks of the Lattice Boltzmann scheme can be resolved.</p><p>Theoretical analysis shows that the diffusion Lattice Boltzmann scheme can be derived from the basic principle that the hydrodynamic moments of the equilibrium particle distribution must equal those of the Maxwell-Boltzmann distribution up to second order.</p><p>By extending this theoretical framework to convection-diffusion, LB schemes are developed for orthorhombic lattices and irregular grids. These new Lattice Boltzmann schemes are compared to several Finite Difference and Finite Element schemes by solving benchmark problems. Analysis of the numerical solutions shows that the accuracy of the Lattice Boltzmann schemes is comparable to high-order Finite Element schemes, but can be achieved with much less computer resources, i.e., memory and computing time. Its good performance, the existence of a theoretical framework clearly linked with physics, and the algorithmic simplicity, make the Lattice Boltzmann method a strong competitor for conventional numerical schemes.</p><p>From the results of this thesis it can be concluded that the Lattice Boltzmann method is a very suitable framework for modelling convection-diffusion phenomena and can be applied to packaging systems. It has attractive properties in simplicity, efficiency, and accuracy. Thereby, it can greatly contribute to better quality management of packed, fresh agricultural products.</p>
    Original languageEnglish
    QualificationDoctor of Philosophy
    Awarding Institution
    • Bot, G.P.A., Promotor, External person
    • Ernst, M.H.J.J., Promotor, External person
    • van Opheusden, J.H.J., Promotor, External person
    Award date7 May 1999
    Place of PublicationS.l.
    Print ISBNs9789058080486
    Publication statusPublished - 1999


    • agricultural products
    • packaging
    • transport

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