Recent advances in Lagrangian modelling of complex
particle-laden flows
M. Sommerfeld
Zentrum für Ingenieurwissenschaften
Martin-Luther-Universität Halle-Wittenberg
Halle (Saale), Germany
The Euler/Lagrange approach is a hybrid technique where the continuous phase is calculated
on a fixed grid in an Eulerian frame and the dispersed phase is simulated in a Lagrangian
fashion by tracking a large number of computational particles through the flow field. A
converged fully-coupled solution of the two-phase flow system is reached by sequentially
solving the Eulerian and Lagrangian part, accounting for the source- or coupling-terms in the
conversation equations of the fluid phase. Calculations of turbulent flow fields can be done by
applying direct numerical simulations (DNS), large eddy simulations (LES) or Reynoldsaveraged
methods (RANS) combined with an appropriate turbulence model. Based on that
and the considered flow configuration, the coupled Euler/Lagrange calculations are done
fully-unsteady, quasi-unsteady or steady. The Euler/Lagrange approach is only applicable to
multiphase flows with dispersed particles (i.e. solid particles, droplets or bubbles) which are
treated as point masses. The great advantage of the Lagrangian approach is that the discrete
nature of the particles is maintained, allowing a detailed modelling of all relevant elementary
processes (e.g. particle-wall collisions, inter-particle collisions, agglomeration or
coalescence), and in addition the particle size distribution can be easily resolved. It should be
emphasised that there is no limitation on the applicability of the Lagrangian approach with
respect to the particle volume fraction as it is quite often stated in the literature. The
limitations are only seen in the required computational time, the number of particles which
may be handled and the modelling requirements.
One may identify basically three methods in treating the particulate phase, namely, the
classical Lagrangian tracking without inter-particle collisions, the hard-sphere approach
(Lagrangian tracking with inter-particle collisions or often named discrete particle method
(DPM)) and the soft sphere approach which is often implemented by the discrete element
approach (DEM). In the DPM only binary instantaneous collisions between neighbouring
particles are considered describing the momentum exchange through the application of
Newton's second and third law. Depending on the type of flow calculation being used (e.g.DNS, LES or RANS) and the particle system (i.e. particle volume fraction) considered a  
deterministic or stochastic collision model may be applied.  
In the DEM multiple particle contacts or collisions are resolved, requiring a rather  
sophisticated modelling of the contact forces often accomplished through a spring, dashpot  
and friction slider system for each contact. In this approach all real particles have to be  
considered, limiting the computable size of the system.  
The Euler/Lagrange approach applied in the present study is based on a RANS approach for  
the continuous phase (i.e. k-e turbulence model or Reynolds-stress model) and the Lagrangian  
approach using the concept of parcels (i.e. each computational particle or parcel represents a  
number of real particles with identical properties). Recent advances in modelling particle  
dispersion in turbulence, particle-wall collisions accounting for wall roughness and inter- 
particle collisions on the basis of a stochastic approach are introduced and illustrated.  
Finally, the importance of these elementary processes for predicted particle-laden flows are  
highlighted based on some typical industrial confined flow configurations. Examples are a  
particle-laden free jet, pneumatic conveying in channels and pipes and unsteady swirling  
flow. The computational results are validated based on available experiments.