The application of Buckingham π theorem to Lattice-Boltzmann modelling of sewage sludge digestion

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Colleges, School and Institutes

External organisations

  • Karlsruhe Institute of Technology, IMK-IFU
  • Dept. of Civil Engineering
  • University of Bradford
  • Karlsruhe Institute of Technology, IMK-IFU, Garmisch-Partenkirchen, Germany


For the first time, a set of Lattice-Boltzmann two-way coupling pointwise Euler-Lagrange models is applied to gas mixing of sludge for anaerobic digestion. The set comprises a local model, a “first-neighbour” (viz., back-coupling occurs to the voxel where a particle sits, plus its first neighbours) and a “smoothing-kernel” (forward- and back-coupling occur through a smoothed-kernel averaging procedure). Laboratory-scale tests display grid-independence problems due to bubble diameter being larger than voxel size, thereby breaking the pointwise Euler-Lagrange assumption of negligible particle size. To tackle this problem and thereby have grid-independent results, a novel data-scaling approach to pointwise Euler-Lagrange grid independence evaluation, based on an application of the Buckingham π theorem, is proposed. Evaluation of laboratory-scale flow patterns and comparison to experimental data show only marginal differences in between the models, and between numerical modelling and experimental data. Pilot-scale simulations show that all the models produce grid-independent, coherent data if the Euler-Lagrange assumption of negligible (or at least, small) particle size is recovered. In both cases, a second-order convergence was achieved. A discussion follows on the opportunity of applying the proposed data-scaling approach rather than the smoothing-kernel model.


Original languageEnglish
Article number104632
JournalComputers and Fluids
Publication statusPublished - 15 Sep 2020


  • Anaerobic digestion, Euler-Lagrange, Grid independence, Lattice-Boltzmann, Non-Newtonian, OpenLB

ASJC Scopus subject areas