FLOW IN FLUIDIZED BEDS Fluidization refers to those gas-solids and liquid-solids system in which the solid phase is subjected to behave more or less like a fluid by the upwelling current of gas or liquid stream moving through the bed of solid particles. When a fluid flows upward thro a packed bed of particles at low velocities, the particles remain stationary. As the fluid velocity is increased, ∆P increases according to Ergun equation.ppt

Fluidization starts at a point when the bed pressure drop exactly balances the net downward forces (gravity minus buoyancy forces) on the bed packing. Then the particles just begin to move, and this is the onset of fluidization or minimum fluidization. The fluid velocity at which fluidization begins is the min. fluidization velocity (v’mf) based on empty cross section of the tower. The porosity of the bed when true fludization occurs is the min. porosity for fluidiztoin and is εmf The bed expands to this voidage or porosity before particle motion appears.

As stated earlier, the ∆P increases as the gas velocity is increased until the onset of min. fluidization. Then as the velocity is further increased, ∆P decreases very slightly and then remains practically unchanged as the bed continues to expand or increase in porosity with increase in velocity

Relationship bet. Bed height & porosity Since the volume LA(1- ε) is equal to the total volume of solids……..

Min. fluidization velocity Fluidization starts at a point when the force obtained from the pressure drop times the cross sectional area must equal the gravitational force exerted by the mass of the particles minus the buoyant force of the displaced fluid. 1

From Ergun eqn…..and at min. fluidization… By comparing (1) & (2) 2 3

For very small particles, only the laminar-flow (NRe,mf < 20) term of the Ergun eqn is significant For large particles, only the turbulent-flow (NRe,mf >1000) term of the Ergun eqn is significant

3 Dimensionless form

If the terms v’mf and/or Φs are not known, Wen and Yu found for a variety of systems that This eqn. holds good for a Reynolds number range of 0.001 to 4000

Prob. Minimum velocity for fluidization Solid particles having a size of 0.12mm, a shape factor of 0.88 and a density of 1000kg/m3 are to be fluidized using air at 2 atm abs and 25ºC. The voidage at min. fluidizing is 0.42 a). If the cross section of the empty bed is 0.3m2 and the bed contains 300kg of solid, calculate the min.height of the fluidized bed. b). Calculate the pressure drop at min. fluidizing condns. c). Calculate the min. velocity for fluidization Air properties at 2 atm abs and 25ºC are Viscosity=1.845x10-5 Pa.s ; density = 2.374 kg/m3

a). vol. of solids (300kg / 1000 kg/m3) = 0.3 m3 Initial bed ht…(ht of solids if ε1 = 0), L1=0.3m3/0.3m2 We know By sub. values…Lmf=1.724m b).we know == ∆P=9786 N/m2

c). sub. the values in the eqn……. NRe,mf = 0.07764 === v’mf =0.004618 m/s

Prob…….. A tower having a diameter of 0.1524m is being fluidized with water at 20.2ºC. The uniform spherical beads in the tower bed have a dia of 4.42mm and a density of 1603 kg/m3. Estimate the min. fluidization velocity and compare with the experimental value of 0.02307 m/s of Wilhelm and Kwauk

which is app. equal to the expt. value 0.02307 m/s sub. the values in the eqn… ==NRe,mf = 114.5445 v’mf = 0.02592 m/s. which is app. equal to the expt. value 0.02307 m/s

Motion of particle through fluid Whenever a particle is moving thro a fluid, a number of forces will be acting on the particle. For a rigid particle moving in a fluid, there are 3 forces acting on the body. Gravity force acting downward (Fg) Buoyant force acting upward (Fb) Resistance or Drag force acting in opposite direction to the particle motion (FD)

The gravity force , Fg = mg Buoyant force, Fb = Vpρg = mρg / ρp The drag force FD = CD (v2/2) ρ Ap where CD is the drag coefficient which is similar to friction factor in flow of fluids in pipes

The resultant force on the body is then Fg-Fb-FD. This resultant force must equal the force due to acceleration. If we start from the moment the body is released from its position of rest, the falling of the body consists of two periods: The period of accelerated fall (very short) The period of constant velocity fall which is MAX (which is called as free settling velocity or terminal settling velocity ‘vt’ )

To solve for terminal velocity by sub To solve for terminal velocity by sub. dv/dt = 0 in the eqn (1) and re-arranging

Stokes’ law vt α Dp2 Newton’s law vt α Dp0.5

Types of settling When the particle is at sufficient distance from the boundaries of the container and from other particles, so that its fall is not affected by them, the process is called free settling. If the motion of the particle is impeded by other particles, which will happen when the particles are near each other even though they may not actually be colliding, the process is called hindered settling.

Hindered settling In hindered settling, for a uniform suspension, the settling velocity ‘us’ can be estimated from the terminal velocity for an isolated particle using the empirical equation of Maude and Whitmore: ‘n’ is known as Richardson zaki index which varies from 4.6 in the Stokes’ law to 2.5 in the Newton’s law region

Terminal settling velocity of dust particles Calculate the terminal settling velocity of dust particles having a dia of 60μm in air at 294K and 101.32kPa. The dust particles can be considered spherical with a density of 1280 kg/m3. Air properties: density = 1.137 kg/m3 viscosity = 1.90x10-5 Pa-s Ans: 0.1372m/s

Hindered settling Particles of sphalerite (S.G 4) are settling under the force of gravity in CCl4 (S.G 1.594) @ 20ºC. The dia of sphalerite particles is 0.004”. The volume fraction of sphalerite in CCl4 is 0.2. What is the settling velocity of sphalerite? Assume Stoke’s law is valid. Richardson zaki index is = 4.1. Take viscosity is 1.03 cP ut=0.0131m/s us=5.2mm/s