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The suspended particles are considered as rigid spheres of same diameter d, and density {latex}{\large$\rho_p$}{latex}. Newton's second law written for the particle i stipulates: {latex}{\large$mlarge $m_p \frac{d \mathbf{u}_p^i}{dt}=\mathbf{f}_{ex}^i$}{latex} where {latex}{\large$\mathbf{u}_p^i$}{latex} is the velocity of particle i, {latex}{\large$large $\mathbf{f}_{ex}^i$}{latex} the forces exerted on it, and {latex}{\large$mlarge $m_p$}{latex} its mass. In order to know accurately the hydrodynamic forces exerted on a particle one needs to resolve the flow to a scale significantly smaller than the particle diameter. This is computationally prohibitive. Instead, the hydrodynamic forces can be approximated roughly to be proportional to the drift velocity: {latex}{\large$large $\frac{d \mathbf{u}_p^i}{dt}=\frac{\mathbf{u}_f-\mathbf{u}_p^i}{\tau_p}$}{latex} where {latex}{\large$large $\tau_p$}{latex} is known as the particle response time. This equation needs to be solved for all particles present in the domain. This is done in Fluent via the module: Discrete Phase Model(DPM). |
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