### 6.6.1. Introduction to the Particle Collision Model

Highly loaded gas-particle flows are commonly simulated by the two-fluid model where interactions between particles are computed using the Kinetic Theory of Dense Gases. In classical Euler-Lagrange modeling, the equations of motion of individual particles are solved without considering collisions between particles because the presence of other particles is not taken into account.

The particle-particle collision model ( PPCM) in ANSYS CFX takes inter-particle collisions and their effects on the particle and gas phase into consideration. The model implemented into ANSYS CFX is the stochastic particle-particle collision model by Oesterlé & Petitjean [151] that has been extended by Frank, Th. [149], Hussmann, B. et al. [150] and Sommerfeld [152].

#### 6.6.1.1. Background Information

Standard Lagrange simulations are constrained to dilute gas-particle flows because particles are treated as being independent of their neighbors. Activating the particle collision model facilitates the application of the Lagrange model to dense gas-solid flows with a high mass-loading while the particle volume fraction is still low. Hence, dense multiphase flows in which contact forces between particles preponderate over aerodynamic forces exerted by the fluid, such as in fluidized beds or hoppers, are excluded. This is because the model is limited to binary collisions that dominate, if the average distance between two particles is much greater than their diameters.

Both the Euler-Euler multiphase model and the “classical” Euler-Lagrange model can approximate dense gas-solid flows only roughly. The LPTM-PPCM model implemented in ANSYS CFX expands the Euler-Lagrange model by a stochastic inter-particle collision model by enabling the so-called four-way coupling. Hereby, the mutual influence of gas and particles is accounted for as well as the mutual interaction of (spherical) particles by means of binary collisions.

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