Fluid dynamics of coarse dispersions

Extension of a model for the distribution of voidage around bubbles in a fluidized bed

“…As a result the gradient of particle stresses can be written as −∇p 1 , where p 1 represents the pressure in the dispersed phase. This approximation resembles the ideal-fluid approximation given by Euler [3]. The total conservation of momentum can thus be expressed as…”

“…In some special cases the dispersed phase in a gas-solid fluidized bed may be modeled as a dense gas [3]. The model extended in the present study is based on the closure of the conservation equation for the dispersed phase in a fluidized bed based on this dense gas assumption.…”

“…This force will be ignored in the total interphase interaction force and is an acceptable assumption when working with gas as the ambient fluid [3]. Moreover this force will be much less significant compared to the influence of the drag and buoyancy forces.…”

“…with ρ 1 the particle phase density, φ the solid fraction, w the particle velocity, P the tensor of the particulate stresses and f the interphase interaction force per particle [3]. The number concentration of particles are represented by n and g is gravitational acceleration.…”

“…The number concentration of particles are represented by n and g is gravitational acceleration. The averaged values in equation (1), namely the total volume flux, φw , and the random forces experienced by the particles, f , can be approximated by φw and f respectfully, given that the fluctuations of these quantities are relatively small [3]. For simplicity of the model these random forces and the total volume flux was assumed as non-fluctuating quantities.…”