The simulation calculates the minimum fluidization velocity by equating the pressure drop from the Ergun equation to the buoyant weight of the bed, then estimates the porosity at minimum fluidization with the Wen and Yu approximation.
Symbols
- \(\rho_p\) — particle density
- \(\rho_f\) — fluid density
- \(\mu\) — fluid viscosity
- \(g\) — gravitational acceleration
- \(D_p\) — effective particle diameter
- \(\phi_s\) — particle sphericity
- \(u_0\) — superficial velocity
- \(\epsilon\) — bed porosity
- \(\epsilon_{mf}\) — porosity at minimum fluidization
- \(u_{mf}\) — minimum fluidization velocity
- \(Re_p\) — particle Reynolds number
Ergun equation (equated to weight)
\( (\rho_p - \rho_f)g = \dfrac{150\mu u_0(1-\epsilon)}{\phi_s^2 D_p^2 \epsilon^3} + \dfrac{1.75\rho_f u_0^2}{\phi_s D_p \epsilon^3} \)
Wen and Yu approximation
\( \dfrac{1}{\phi_s \epsilon_{mf}^3} \approx 14 \implies \epsilon_{mf} = (14\phi_s)^{-1/3} \)
Particle Reynolds number
\( Re_p = \dfrac{\rho_f u_0 D_p}{\mu} \)