Fluidisation models and their drag formulations

Fluidisation models

1. Drag Factor Schiller Naumann (1933) Reasonably good for gas-liquid system for Reynold number less than 800

2. Putnam (1961)

3. Morsi & Alexnder (1972) a 1 , a 2 and a 3 are function of Re

4. Schuh et al.

5. Where U sf = superficial velocity Pressure loss due to viscous drag due to inertial drag Where u = phase velocity For packed bed ε f =0.4 Ergun Equation (1959) This equation is valid till minimum fluidization velocity

6. Ergun Equation in terms of Velocity Difference of the Phases Two Fluid Equation

7. Wen & Yu Drag Correlation

8. Gidaspow Drag Correlation

9. Virtual Mass Force When a body is accelerated through a fluid, there is a corresponding acceleration of the fluid which is at the expense of work done by the body. This additional works relates to the virtual mass effect. If fluid is in rest then the virtual mass force on the particle should be in the direction opposite to the particle acceleration Virtual mass force accounts for form drag due to acceleration.

10. Basset Force Basset term accounts for viscous effects The term address the temporal delay in boundary layer development as the relative velocity changes with the time The value of Basset force depends on the acceleration history up to the present time Basset term has to be modify to include the case when there is an initial velocity

11. The Basset term and virtual mass term becomes insignificant for : Where ω is frequency of oscillation

12. Basset- Boussinesq - Oseen (BBO) Equation Equation of motion of a single particle

13. Lift Force

14. Coupling between Phases One-way coupling: Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer. No influence of particulate phase on the gas phase. Two-way coupling: Fluid phase influences particulate phase via aerodynamic drag and turbulence transfer. Particulate phase reduces mean momentum and turbulent kinetic energy in fluid phase. Four-way coupling: Includes all two-way coupling. Particle-particle collisions create particle pressure and viscous stresses.

15. iitg uwahati Gas Mean Motion Gas Fluctuating Motion Particle Mean Motion Particle Fluctuating Motion Turbulence Kinetic Theory of Granular Flow (KTGF) Drag Flux of kinetic energy Types of Interactions in Gas Solid Dispersed Flow Closure Problem