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A robust two-node, 13 moment quadrature method of moments for dilute particle flows including wall bouncing

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journal contribution
posted on 09.12.2016, 13:39 by Dan Sun, Andrew Garmory, Gary Page
For flows where the particle number density is low and the Stokes number is relatively high, as found when sand or ice is ingested into aircraft gas turbine engines, streams of particles can cross each other’s path or bounce from a solid surface without being influenced by inter-particle collisions. The aim of this work is to develop an Eulerian method to simulate these types of flow. To this end, a two-node quadrature-based moment method using 13 moments is proposed. In the proposed algorithm thirteen moments of particle velocity, including cross-moments of second order, are used to determine the weights and abscissas of the two nodes and to set up the association between the velocity components in each node. Previous Quadrature Method of Moments (QMOM) algorithms either use more than two nodes, leading to increased computational expense, or are shown here to give incorrect results under some circumstances. This method gives the computational efficiency advantages of only needing two particle phase velocity fields whilst ensuring that a correct combination of weights and abscissas are returned for any arbitrary combination of particle trajectories without the need for any further assumptions. Particle crossing and wall bouncing with arbitrary combinations of angles are demonstrated using the method in a two-dimensional scheme. The ability of the scheme to include the presence of drag from a carrier phase is also demonstrated, as is bouncing off surfaces with inelastic collisions. The method is also applied to the Taylor-Green vortex flow test case and is found to give results superior to the existing two-node QMOM method and in good agreement with results from Lagrangian modelling of this case.


This work has been funded by the Innovate UK (formerly the United Kingdom Technology Strategy Board, TSB) under SILOETII, in conjunction with Rolls-Royce PLC.



  • Aeronautical, Automotive, Chemical and Materials Engineering


  • Aeronautical and Automotive Engineering

Published in

Journal of Computational Physics




493 - 509


SUN, D., GARMORY, A. and PAGE, G.J., 2017. A robust two-node, 13 moment quadrature method of moments for dilute particle flows including wall bouncing. Journal of Computational Physics, 330, pp. 493-509.


© Elsevier


AM (Accepted Manuscript)

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This paper was accepted for publication in the journal Journal of Computational Physics and the definitive published version is available at






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