The vibro fluidized bed was discussed when dealing with various types of dryers in the beginning of this section. Vibration in combination with fluidization enables the drying particle to fluidize smoothly. The gentle action of vibration helps the fluidization of fragile materials. Vibro fluidization is widely used for drying abrasive and heat-sensitive materials. The agglomerate which forms during the fluidization of a sticky material is kept in a mobile state, thereby enabling effective fluidization throughout the drying process. The amount of drying gas required to fluidize is reduced considerably. In a conventional fluidized bed, low gas velocity can fluidize fine particles, thereby reducing elutriation. The larger particles remain defluidized, causing partial fluidization of fine and partial defluidization of coarse or large particles. However, in a vibro fluidized bed, fines remain in a fluidized state with less gas, and coarse particles remain in a mobile state due to vibration. Drying of granitic particles ranging in size from 3 to 38 mm in a vibro fluidized bed was reported by Pye.21 Wet particles near the feed are well distributed in the vibrated
state, and even sticky or pasty materials in granulated or extruded form can be successfully processed in vibro fluidized beds. The gentle fluidization in a vibro fluidized bed creates an erosion-free environment for the fluidization vessel even when abrasive materials are handled.
1. Basics
The aerodynamics and thermal characteristics of vibrated fluidized beds were reviewed by Gupta and Mujumdar.22 Studies on the drying of granular products in
a vibro fluidized bed were reported by Strumillo and Pakowski.23 The additional
parameters in a vibro fluidized bed compared to conventional fluidized beds are those pertaining to the amplitude (a) of vibration and the vibration frequency (ω), which is applicable in general for angular motion. The product aω2 is termed angular
or vibrational acceleration and is used to characterize vibro fluidization. When the ratio aω2/g < 1, the bed of solids is in contact with the distributor plate and the
solids are kept away or levitated when the ratio is greater than unity. Hence, in vibro fluidization, solids can be brought into an incipient state of fluidization at a low drag force. The incipient velocity for a vibro fluidized bed (Umvf) is smaller than the
unvibrated bed velocity (Umf). Umvf can be determined by a conventional plot of bed
pressure drop (∆Pb) versus superficial fluid velocity. The difference between Umf
and Umvf depends on the operating conditions. Details regarding the pressure
drop–velocity curve were given as a map by Gupta and Mujumdar.24 The difference
between Umf and Umvf is small for deep beds vibrated at small amplitudes and is
wide for shallow beds vibrated at high amplitudes. Beds operated between these two extremes correspond to a transition from fixed to fluidized bed. Gupta and Mujumdar24 defined a new incipient vibro fluidized bed velocity (U
mm) for a visually
(2.15)
Equation 2.15 is valid for aω2/g < 1. In general, it is observed that U
mm > Umf > Umvf.
The bed pressure drop (∆Pb,mvf) at Umvf was also presented by Gupta and Mujumdar24 as:
∆Pb,mvf/∆Pb,mf = 1 – 0.0935 (dp/H)0.946 (aω2/g)0.606 (φv)1.657 (2.16)
This relationship is valid for 25 < ω < 40 s–1, where φ
v is the equivalent volume
shape factor. Equation 2.16 contains the bed height whereas Equation 2.15 does not. The difference in ∆Pb,mvf and ∆Pb,mf for H > 0.05 m was found to be negligible.24
Heat transfer in a vibro fluidized bed in general is enhanced, and as a result the heat transfer coefficient in a vibro fluidized bed is much higher even for gas velocities far below the minimum fluidization velocity. Studies by Yamazaki et al.25 showed
that the difference in the heat transfer coefficients of a vibrated and an unvibrated fluidized bed for smaller particles (Ý114 µm) increases, and this difference shows a declining effect for larger particles. Heat transfer during constant rate drying can take place near the distributor, and hence the surface area available for heat transfer is lower than the total surface area of the bed. Hence, heat transfer coefficient calculations based on the total surface area of the particulate solid in the bed can result in lower values.26 In a vibrated fluidized bed, the fraction of gas that passes
through the emulsion phase is increased due to the fact that the number of bubbles and their size and frequency are reduced by vibration.27 Because thermal equilibrium
between the gas and the solid particles is achieved quickly, heat transfer between hot gas and solid in the emulsion phase is predominant.
2. Vibro Inclined Fluidized Bed a. Gas Velocity
A vibro fluidized bed, in conjunction with an inclined distributor plate, can be used conveniently for drying and transportation of solids on a continuous basis. Such a class of vibro fluidized beds, called vibro inclined fluidized beds, was investigated in detail by Arai and Hasatani.28 Their investigations mainly focused on the effect
of vibration acceleration (aω2) on the linear velocity of the solid particles, particle-
to-gas heat transfer, and the drying of moist particles. The angle of inclination (θ) of the distributor plate ranged from 3 to 5°. Their investigation of transportation of solids by vibration revealed that particulate solids like sand require a certain mini- mum velocity to achieve solid transfer, and the linear velocity for transfer is enhanced by the intensity of the vibration acceleration. However, for particulate solids such as polystyrol, the vibration acceleration has no effect in enhancing the linear velocity. A correlation to predict the gas velocity ratio,
U U a g a g mm mf =1 952. – .0 275
(
ω2)
– .0 686(
ω2)
2 Ug+Ug Ug(
*)
was porposed as:
(2.17)
where
(2.18)
αΓ = 1 for Γ < 3,5, Γ = 0.285 for 3.5 < Γ < 15, and Ug* is the difference in gas
velocity between the unvibrated and the vibrated inclined fluidized bed for the same linear velocity of the particulate solid in both systems.
b. Heat Transfer
The heat transfer rate between the particle and gas in a vibrated fluidized bed was predicted by the correlation28
(2.19)
where
(2.20)
The mechanical vibration added vertically is found to enhance the heat transfer rate, and this would increase the drying rate. The distribution of moisture and temperature along the length of an inclined fluidized bed was predicted by a model which assumes the solid to be in a perfectly mixed state along the height of the bed and plug flow in its flow path. The gas flow is assumed to be in a plug flow state and the interparticle resistance for fine-sized particles is assumed to be negligible. This model28 can fit well with experimental findings. However, the mathematical
equations developed through the model must be solved by numerical methods. A vibro fluidized bed can give an enhanced drying rate uniformly as the linear velocity of the particle is evenly distributed and the velocity of the wet particles can be accelerated by mechanical vibration.