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

Davide Dapelo, Robin Trunk, Mathias J. Krause, Nigel Cassidy, John Bridgeman

Research output: Contribution to journalArticlepeer-review


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 Sept 2020


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

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)


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