Abstract
In Lagrangian stochastic collision models, a fictitious particle is generated to act as a collision partner, with a velocity correlated to the velocity of the real colliding particle. However, most often, the fluid velocity seen by this fictitious particles is not accounted for in the generation of the fictitious particle velocity, leading to a de-correlation between the fictitious particle velocity and the local fluid velocity, which, after collision, leads to an unrealistic de-correlation of the real particle velocity and the fluid velocity as seen by the particle. This de-correlation, in turn, causes a spurious decrease of the particle kinetic energy, even though the collisions are assumed perfectly elastic. In this paper, we propose a new model in which the generated fictitious particle velocity is correctly correlated to both the real particle velocity and the local fluid velocity at the particle, hence preventing the spurious loss of the total particle kinetic energy. The model is suitable for small inertial particles. Two algorithms for integrating the collision frequency are also compared to each other. The models are validated using large eddy simulation (LES) of mono-dispersed particle-laden stationary homogeneous isotropic turbulence. Simulations are conducted with spherical particles with different turbulent Stokes number, St_t = [0.75 - 5.8], and volume fractions, alpha _p = [0.014 - 0.044], and are compared to the results of the LES using a deterministic discrete particle simulation model.
Highlights
Turbulent two-phase flows are found in various environmental, biological and industrial processes
The algorithm to predict gas-solid flow consists of three steps: (1) the Eulerian turbulent flow dynamics are resolved using direct numerical simulation (DNS) or a model for turbulence; (2) the particle dynamics are evaluated via a particle-transport step; (3) the inter-particle collisions are treated and the particle post-collisional velocities computed
To validate the working of the newly proposed model for the stochastic inter-particle collision model, Large Eddy Simulation (LES) of stationary homogeneous isotropic turbulence are performed in a periodic cubic box of length Lbox = 0.128 m with 643 grid cells, laden with particles
Summary
Turbulent two-phase flows are found in various environmental, biological and industrial processes. The particle solver is coupled with either Direct Numerical Simulation (DNS) or Large Eddy Simulation (LES), which are numerical tools to solve the dynamics of turbulent flows. The former may be more accurate, as it captures all the scales of the turbulence, but it is computationally very expensive for flows with a high Reynolds number. The level of coupling between the particles and the turbulent flow depends mainly on the volume fraction and mass loading (Balachandar and Eaton 2010). If the volume fraction is higher than about 10−3 , the interaction between particles, i.e. collisions, must be taken into account, and simulations are described as four-way coupled
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