### 6.6.3. Range of Applicability of Particle-Particle Collision Model

The aim of the LPTM-PPCM is to raise one of the restrictions for a Lagrangian particle tracking model, namely to extend the range of applicability to higher concentrations of the dispersed particulate phase. A fluid particle flow can either be characterized by the ratio of the mean time between particle-particle collisions and the particle relaxation time:

| (6–181)

or by the inter-particle spacing defined as the ratio of the distance between two particles in the flow and the particle diameter:

| (6–182)

A fluid-particle flow is particle-particle collision dominated, if the ratio < 1, it means that the time between adjacent particle-particle collisions is too small in order to enable the particle to get accelerated by aerodynamic forces to its normal slip velocity with the carrier fluid until the next particle-particle collision occurs. This fairly well corresponds to an inter-particle spacing of less than 10 and the fluid-particle flow is called a dense flow.

In the case of dense fluid-particle flow, it is necessary to additionally account for the direct particle-to-particle momentum transfer. The PPCM model, in accordance with Oesterlé & Petitjean and Sommerfeld, accounts for this inter-particle momentum transfer by making the assumption that only binary particle collisions occur in the intermediate regime between dilute fluid-particle flows and flow regimes in packed and fluidized beds. For the latter conditions it is not sufficient to assume binary particle collisions and therefore the PPCM model is not applicable to flow regimes, where multiple particles collide at the same time or stay in direct frictional contact.

Also see Requirements for the Applicability of Particle-Particle Collision Model in the CFX-Solver Modeling Guide.

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