Particle-wall drag

The solids contribution to the pressure drop, APls, is a consequence of both the particle-wall and particle-particle interactions. The latter is reflected in the dependence of the friction factor fs on the particle diameter, drag coefficient, density, and relative (slip) velocity by (Hinkel, 1953) ... 

The incipient gas velocity for a particle rolling along the wall can be determined by the torques exerted on the particle. Assuming that the drag force, gravitational force, and lift force are exerted through the central point of the sphere, the balance of the torques about the uppermost point of the particle-wall contact plane (see Fig. 11.8) can be given by... 

There are two main approaches for the numerical simulation of the gas-solid flow 1) Eulerian framework for the gas phase and Lagrangian framework for the dispersed phase (E-L) and 2) Eulerian framework for all phases (E-E). In the E-L approach, trajectories of dispersed phase particles are calculated by solving Newton s second law of motion for each dispersed particle, and the motion of the continuous phase (gas phase) is modeled using an Eulerian framework with the coupling of the particle-gas interaction force. This approach is also referred to as the distinct element method or discrete particle method when applied to a granular system. The fluid forces acting upon particles would include the drag force, lift force, virtual mass force, and Basset history force.Moreover, particle-wall and particle-particle collision models (such as hard sphere model, soft sphere model, or Monte Carlo techniques) are commonly employed for this approach. In the E-E approach, the particle cloud is treated as a continuum. Local mean... 

Fig. 5 Predictions of various models for drag coefficient for a spherical particle Wall Effects on Drag Coefficient...

Some empirical equations to predict cyclone pressure drop have been proposed (165,166). One (166) rehably predicts pressure drop under clean air flow for a cyclone having the API model dimensions. Somewhat surprisingly, pressure drop decreases with increasing dust loading. One reasonable explanation for this phenomenon is that dust particles approaching the cyclone wall break up the boundary layer film (much like spoiler knobs on an airplane wing) and reduce drag forces. 

Transport Disengaging Height. When the drag and buoyancy forces exerted by the gas on a particle exceed the gravitational and interparticle forces at the surface of the bed, particles ate thrown into the freeboard. The ejected particles can be coarser and more numerous than the saturation carrying capacity of the gas, and some coarse particles and clusters of fines particles fall back into the bed. Some particles also coUect near the wall and fall back into the fluidized bed. 

Drag reduction has been reported for low loadings of small diameter particles (<60 [Lm diameter), ascribed to damping of turbulence near the wall (Rossettia and Pfefl er, AIChE J., 18, 31-39 [1972]). 

The particles are subject to centrifugal, inertial, and drag forces as they are carried in the spriraling flow, and it is assumed that the particles that strike the outer wall before the fluid reaches the vortex finder will be collected. It is assumed that the tangential velocity of the particle is the same as that of the fluid (Vp0 = Ve) but that the radial velocity is not (Fpr Vr), because the particles move radially toward the wall relative to the fluid. The centrifugal force acting on the particle is... 

---