Relations and functions of gas interacting with solid particle in real production.
Abstract
After the centrifugation stage, refined salt particles have rather high moisture content; therefore, the moist salt particles in contact with each other will stick together in a short time. In particular, the moist salt particles will stick together faster and tighter and form a larger unit when they are exposed to drying hot air. For this reason, the refined salt was dried by rotary drum dryers with vibrating balls distributed along the drum or a vibrating fluidized bed dryers. These drying methods make poor product sensory quality, low product recovery efficiency, while also lead to an increase of heat and electricity energy consumption. In order to increase the efficiency of refined salt drying technology by conventional continuous fluidized bed dryers, the chapter focuses on the study of aerodynamic properties of refined salt grains in the continuous fluidized particle layer. The content of the chapter presents theoretical and empirical methods to determine fluidization velocity types in designing a continuous fluidized bed dryer.
Keywords
 refined salt
 solid particles
 aerodynamic
 minimum fluidization velocity
 homogeneous fluidization
 bed fraction
 fluidized bed dryer
1. Introduction
1.1 Preface
The phenomenon in which solid particles float in a gas stream and have a liquidlike property is called a fluidized bed. This phenomenon of fluidization in gas or liquid flow was discovered by Fritz Winkler in the 1920s [1]. This one was investigated by Lewis et al. and had been raised to fluidized theory [2]. The first commercial fluidized bed dryer was installed in USA in 1948 [3]. The fluidized bed technology is used for drying of bulk materials, includes examples such as: vibrating fluidized bed dryer, normal fluidized bed dryer without vibrating device and pulsed fluidized bed dryer.
Mathematical modeling and computer simulation of grain drying are now widely used and become an important tool for designing new dryers, for analyzing existing drying systems and for identifying drying conditions [4]. Identifying the drying conditions is necessary to establish the optimal protocol for ensuring seed quality [5]. To solve the simulation models, equations concerning aerodynamic properties such as the gas stream velocity and particle velocity are the most important components. The aerodynamic properties are affected by shape, density and size of particles [6].
In recent years, the fluidized bed technology has been concerned in the application in the sugar drying and refined salt drying in Vietnam. In the scope of this chapter, we discuss the issues related to the hydrodynamics of refined salt particles in the gas stream at ambient temperature and temperature equivalent to that of drying particle. The focus of this chapter is to determine the velocity values of the gas through the particle layer to form the minimum, homogeneous and critical fluidized layers.
In industrial manufacturing practice, we often encounter the contact, interaction between solidparticle materials and gases. These interaction phenomena are described in Table 1.
Order  Function of gases  Function of solid materials  Equipment in practice 

1  Heat carrier  Materials do not react to gases 

2  Loading and transportation of particle materials  Materials do not react to gases  Pneumatic solid particle carrier 
3  Heat carrier and material loading and transportation  Materials do not react to gases  Aerodynamic dryers 
4  Chemical agents 


5  Agitation  Materials do not react to gases  Mixer of different materials in the tank 
1.2 Applied materials in fluidized bed drying technology
According to Abrahamsen and Geldart [7], the two most important factors affecting the fluidization characteristic of the particle layer are particle size and particle density.
Geldart [8] visually observed the various conditions and classified fluidizable particles into four groups: A, B, C and D. As a result, the classification was related to the influence of the average particle size and particle density on the properties of the fluidized layer, as depicted in Figure 1 and Table 2.
Particle group characteristics  C group  A group  B group  D group 

Particle size (μm)  0–3  30 ≤ d_{p} ≤ 100  100 ≤ d_{p} ≤ 1000  ≥ 1000 
Density (kg/m^{3})  Smallest  1400  400–4500  Lower than other materials 
The most obvious characteristics of group 




Typical granulars 




Particle layer expansion 

 Medium  Difficult to fluidize evenly (low) 
Properties of air bubbles 




Property of mixed solid particles  Very low  High  Solids’ recirculation rates are smaller  Low 
Spaying  None  None  Only occurs in the upper layer 

According to the content of this chapter, we focus on approaching, researching and experimenting on the mechanism and principle of interaction between air and the applied material in fluidized bed drying. The approach method is to arrange a stream of heatcarrying air blowing from the bottom of the particle chamber through a gas distributor (the holes arranged at an angle to the cross section of the tank). Hot air stream is evenly distributed and touches the surface of particles in tank (the particle layer was on the gas distributor). The continuous air stream ensures that the contact of particle surfaces with the gas flow is consecutive. The nature of the gas flowing through the particle layer may be laminar, turbulent, or transition flow at the material contact surface. The inflow of hot air affects the velocity of the interaction between the gas stream and the material.
1.3 Basic concept of fluidized particle layer and principle of fluidized particle layer creation
When the material layer is fluidized, its state is converted from a fixed bed to a dynamic state. The particle layer has liquidlike properties. The surface area of the particles contacting with the fluid increases, and therefore the heat transfer ability from fluid to particles rapidly rises.
In order for the fluidization phenomena to occur in the bulk material layer, the air stream must have sufficient pressure and velocity. The air stream flows upward, passes through the particle materials (follow the linear increment) through uncountable air holes of the distributor, which are arranged at the bottom of the particle material layer. When the velocity of air stream is small, pressure exerted on particles is small, the particle layer maintains its original fixed bed (the state from 0 before point A, Figure 2). As the air velocity is increased further, the aerodynamic traction appears, which has opposite effect of the gravitational force of the particles, causing the expansion of particle layers in a volume, and the particles begin to move apart from each other (at point A, Figure 1).
By further raising the velocity of air stream to the critical value, the friction force between the particles and air is equal to the weight of particles. At this time, the vertical component of the compression pressure is eliminated, the upwardpulling force equals the downward gravity, causing the particle material to be suspended in the air stream. When the gas velocity reaches the critical value, the particle material layer will be converted to complete fluidization state, called the fluidization particle layer and having the liquidlike properties (position from A to B in Figure 2).
By further increasing the velocity of the gas, the bulk density of the particle layers continues to decrease, its fluidization becomes more violent, until the particles no longer form a bed and are swept up and fallen down in the fluidization motion (position from B to C, Figure 2). At this time, each particle material is covered with gas flow, the intensity of the heat and material transfer occurs violently. When granular material is fully fluidized, the bed will conform to the volume of the chamber, its surface remaining perpendicular to gravity; objects with a lower density than the bed density will float on its surface, bobbing up and down, while objects with a higher density sink to the bottom of the bed.
Fluidization has many applications in many technologies of manufacturing practice, such as mixing different types of granular materials; fluidized bed drying; cooling grain after drying; supporting interaction between chemicals in the fluidized bed; granulation technology; film coating technology of medicine and pharmacy; manufacturing technology through the combined use of organic and inorganic fertilizers; and biomass fuel combustion technology in fluidized bed.
To clarify the dynamics of the fluidized beds for application in refined salt drying in the fluidized bed, the theoretical and experimental issues determining the velocity of gas through the particle layers to form different fluidized layers are described as follows.
2. Methodology
2.1 Determination of the minimum fluidization velocity from publications
2.1.1 Determination of V_{mf} using the Ergun equation
When the air stream having sufficient pressure and velocity passes through the static spherical particle layers, they begin to expand (the particles become “flexible”). In this condition, it is called the minimum particulate fluidization state and is described by the modified equation of Ergun (see position A in Figure 1) [12].
For particles of arbitrary shapes, the pressure drop of air stream at the minimum fluidization state is represented by Eq. (2). The spherical value of particle material got in the Eq. (1) [10] is given by:
For the particle layer to be converted from a fixed state to a fluidization state, the pressure of air stream must be large enough to overcome the weight of the particle layers and it is determined by Eq. (3) [10].
In Eq. (3), it is considered that there was no interaction force between particles in layer and no interaction between particles and the wall of the tank. So, that did not cause the pressure increasing effect. Thus, the pressure drop of the air stream was constant while increasing the gas velocity from the smallest fluidization velocity to the value when the entrainment process of particles occurred (position C, Figure 2).
In Eqs. (1) and (2), it is also shown that the pressure drop of the gas stream that is generated through the fluidized particle layer is depended on the particle size (d_{p}), the bed voidage (ε) and the gas temperature (t^{°}C). According to Eq. (3), the pressure drop of the gas stream through the particle layers is dependent upon the material mass (m), the gas distributor grate area (A), particle density (ρ_{p}) and gas density (ρ_{f}). Thus, we could calculate the minimum fluidization velocity value (V_{mf}), which was based on Eqs. (1)–(3) for nonspherical particles by solving Eq. (4).
The minimum fluidization velocity (V_{mf}) is the root of Eq. (4), which is based on available parameters, such as the height of minimum fluidization bed (H_{mf}), the mass of particles in the air distributor (m), the area for gas distribution or called crosssectional area of the bed (A), particle density (ρ_{p}), air density (ρ_{f}), mean particle diameter (d_{p}), spherical degree of particles (ϕ) and void fraction at minimum fluidization particle layer (ε_{mf}).
Commonly, the sphere degree of particles (ϕ) must be determined in experiments [10]. The spherical degree of refined salt particles was found out by Bui [13, 14, 15]. Theoretically, in order to fluidize the particle layer, the actual weight of the solid particles must be equal to the force exerted on the particle layers and that is equal to the pressure drop across the bed (ΔP) multiplied by the crosssectional area of the chamber (A). A minimum fluidization layer which must have determined layer thickness (H_{mf}), void fraction (ε_{mf}), then the expanded volume of the fluidized particles (U) has the value of the Eq. (5):
And the actual gravity of the particle mass has a value of:
The balance of the real gravity components of the particle mass and the upward force exerted on the particle mass of the gas flow was calculated according to
Substituting Eq. (8) into Eq. (1) or Eq. (2) yields Eq. (9).
Giving physical parameters of particle and gas into the Eq. (8), velocity (V_{mf}) was found out. In case of very small particles, the gas stream regime through the particle layer was laminar flow and the minimum fluidization velocity should be calculated by the Ergun equation [12]. In case of Re_{mf} < 1, we use Eq. (9) to calculate the minimum fluidization velocity of gas.
2.1.2 Determination of V_{mf} by the correlation of Re_{mf} and Archimeter (Ar)
When gas passes through the particle bulk, which can have any shape, the minimum fluidization Reynolds coefficient (Re_{mf}) is determined by Eq. (10).
Eq. (11) describes the correlation between Ar and Re_{mf} with void fraction at minimum fluidization particle layer (V_{mf})
Archimeter (Ar) is determined by Eq. (12) for particles of any shape.
Set up Eq. (13):
Substituting physical parameters into the Eq. (12), which includes the particle density (ρ_{p}), the gas density at the temperature of minimum fluidization velocity (ρ_{f}), the air dynamic viscosity (μ_{f}), spherical degree of particle (ϕ), void fraction at the minimum fluidization velocity (ε_{mf}), mean particle diameter (d_{m}) [13, 14, 15] and getting Ar number value into the Eq. (13). Then, we solved the quadratic equation to find out the root of equation Re_{mf} in Eq. (10), we got only the positive value. Thus, we calculated the minimum fluidization velocity (V_{mf}) from Eq. (10).
2.1.3 Determination of V_{mf} by the KozenyCarman correlation
KozenyCarman gave the formula of calculation of the minimum fluidization velocity for a very small particle size with the Re_{mf} < 10 in Eq. (14) described in Yates [16].
For spherical particles or sphericity equivalent, the bed voidage of the minimum fluidization ε_{mf} = 0.4 ÷ 0.45.
2.1.4 Determination of V_{mf} by correlation of Wen and Yu
In case of the unavailability of the sphericity of particles, we determine the minimum fluidization velocity (V_{mf}) by using of the experimental correlation of Wen and Yu [17]. An empirical formula of calculation of the void fraction at minimum fluidization particle layers in Eq. (15) or Eq. (16) with the available sphericity degree of particle (ϕ) or the calculation of the sphericity degree of particle (ϕ) in case void fraction (ε_{mf}) at minimum fluidization particle layer is available, which was also described by Wen and Yu equation (cited in Howard, 1989) [10].
We can use the calculation of the void fraction at minimum fluidization particle layers from the other correlation, which is also converted from Wen and Yu.
It is based on the calculation of the void fraction (ε_{mf}) (at position A in Figure 2) of Eq. (15) or Eq. (16) and substituting the obtained ε_{mf} value into the Ergun Eq. (2), we have Eq. (17).
Using the calculated Ar number from Eq. (12) and substituting the Ar value into Eq. (17), we obtain Eq. (18) to calculate the particle Reynolds number at the minimum fluidization velocity (Re_{mf}).
Taking the positive square root, we get Eq. (19):
It was applied to calculate for solid particles with size larger than 100 μm [10]. From the Re_{mf} value that was found out in the Eq. (19), V_{mf} is calculated according to Eq. (10). In case of solid particles with small size (C group of Geldart, 1973) in the specified temperature conditions, the V_{mf} value is calculated in Eq. (20) by Wen and Yu.
2.1.5 Determination of V_{mf} by the correlation of Beayens and Geldart
For solid spherical particles with diameters ranging from 0.05 to 4 mm (0.05 mm < d_{p} < 4 mm) and particle density ranging from 850 to 8810 kg/m^{3} (850 kg/m^{3} < ρ_{p} < 8810 kg/m^{3}), the method of calculation of V_{mf} was proposed by Beayens and Geldart as shown in Eq. (21) [18].
Then the V_{mf} can be calculated from Eq. (22) in case of available solid particle and gas parameters.
2.1.6 Determination of V_{mf} by correlation of Goroshko
The minimum fluidization velocity of spherical particles was determined by correlation shown in Eq. (23) by Goroshko described in Howard [10, 19].
where
We get ϕ is 1.0 (ϕ = 1) then solving the Eq. (23) take the spherical degree value, we have the Eq. (25).
Multiplying
And its value was determined by Eq. (27) by Goroshko:
Eq. (27) is different from Eq. (26) by the added value
2.1.7 Determination of V_{mf} following Goroshko and Todes equation
The minimum fluidization velocity (V_{mf}) of sphericity particles was defined from the Re_{mf} by Goroshko et al. in Eq. (29) [19].
In case of nonspherical particles with different sizes, the Re_{pmf} value was error from 15–20% in case we use the Eq. (29) of calculation described in [20]. In the case of rapid calculation, we considered the bed voidage of the minimum fluidization state to be equal to the bed voidage at static particle layers (ε_{o} = ε_{mf} = 0.4), and the Re_{mf} is calculated in Eq. (30) [21].
2.1.8 Determination of V_{mf} following Leva
From the formula of CarmanKozan
The Leva formula is used in case of Reynolds to be smaller than 10 (Re_{mf} < 10). In case of Reynolds to be larger than 10 (Re_{mf} > 10), there is an adjustment factor added into this formula.
2.1.9 Determination of V_{mf} according to KuniiLevenspiel
The formula of KuniiLevenspiel was simplified from the Ergun formula and it gave out two cases of calculation of the minimum fluidization velocity. In the first case for solid particles of small size with Re_{mf} < 20, we have to use Eq. (32).
We have to use Eq. (33) for the larger particle size with Reynolds number larger than 1000 (Re_{mf} > 1000).
2.1.10 Determination of V_{mf} based on the bed voidage problem
There is a correlation equation of particle mass balance at the minimum fluidization state (fluidization without bubbles), which was created by Kunii and Levenspiel as shown in Eq. (34).
Thus, we can obtain a correlation as shown in Eq. (35).
According to Ginzburg, described in [18], the bed voidage of minimum fluidization and height of particle layer are calculated by Eq. (36) and Eq. (37).
McCabe et al. proposed ε_{mf} = 0.4 ÷ 0.45 for the spherical particle [24]. The bed voidage of minimum fluidization particle layers was 0.5 (ε_{mf} = 0.5) for larger particle size. The bed voidage is equal to 1.0 (ε_{t} = 1.0) when the particle layers are attracted to the gas stream (see position C in Figure 2).
2.2 Physical model of experiment
Experimental arrangement of determining the minimum fluidization velocity is shown in Figure 3.
In order to gradually increase the bed surface velocity of hot air via the particle layers, the air fan (1) is equipped with an inverter to change the rotation of the fan motor.
2.3 Experimental equipment
The instruments in experiments include a moisture analyzer (Axis AGS100, Germany), measurement error ± 0.01%; a digital electronic scale (Satorius MA45, Germany), measurement error ± 0.001 g; an air velocity meter (Extech SDL350 Taiwan), measurement error ± 0.01 m/s and a digital thermometer (WIKA CTH6300, Germany), measurement accuracy 0.001°C. This instrument has two measuring rate modes including fast at 4/s and slow at 1/s; an inclined manometer (T10, UK), measured range is 0–280 mmwg with error ± 0.1% and a pitot pipe (PT6300, 304 Germany), measurement range is 0–400 mmwg with error ± 0.1%. For measurement on the bulk density and density of refined salt particles, we used instruments such as Graduated pipet, buret, graduated cylinder, all of them made in Germany with error measurement ± 0.01 ml. The HCl acid is used for density measurement of refined salt particles.
2.4 The materials of refined salt particles
The material of refined salt particles was supplied by a combined hydraulic separatingwashinggrinding machine in the saturated saltwater condition and which was dried by a continuous centrifugal machines. Samples of refined salt were randomly taken at different sizes at Vinh Hao salt company in Binh Thuan Province, Bac Lieu salt company and Sea salt Research Center of Vietnam for analysis (Table 3) [14].
No.  Equipment/parts  Technical parameter 

1  Drying air fan  Flow: 0.63 m^{3}/s; total pressure: 1244 Pa; motor power: 2.2 kW 
2  Electrical heater  Overall dimension (L × W × H): 600 × 630 × 275 mm; heating power: 1.0 kW; number of heater bars: 6 
3  Drying chamber  Overall dimension (L × W × H): 1750 × 300 × 350 mm Fabrication material: SUS304 
4  Salt dust settling chamber  Overall dimension (L × W × H): 1750 × 450 × 350 mm Fabrication material: SUS304 
3. Results and discussions
The above section presented nine methods to calculate minimum fluidization velocity based on the physical parameters of particles and physical thermal parameters of gas stream. These parameters were obtained from experiments in combination with the correlation calculation or empirical formulas.
In order to have the basis of comparison and accuracy evaluation of each calculating method in comparison with the empirical method, the theoretical calculation was carried out for refined salt particles with diameters of 1.5 mm, 1.2 mm, 0.9 mm, 0.6 mm and 0.3 mm. On the other hand, to achieve empirical result, samples of dried refined salt particles (of which meandiameter was determined) were taken randomly from a combined hydraulicseparatingwashingcrushing machine, presenting various particle sizes of the raw material that was put in the dryer.
3.1 Results of theoretical and empirical calculations for determining V_{mf} of refined salt particles
3.1.1 Some primary conditions for determining the V_{mf} by theoretical calculations
When calculating the pressure drop across a refined salt particle layer, we relied on the empirical results of physical parameters of particles and air (summarized in Table 4). Specific notes for each calculating method are as follows:
Calculation based on Ergun equations and correlations of pressure
Applying to calculate the minimum fluidization velocity (V_{mf}) for refined salt particles with the fixed bed height (H_{0}) is 30 mm, the bed voidage (ε_{0}) is 0.5 using Eqs. (35) and (36) to find out the minimum fluidization state including H_{mf} = 1.1 × H_{0} = 33 mm; bed voidage ε_{mf} = 1.1 × ε_{0} = 0.56. Using the spherical degree value of refined salt particle is 0.71 (ϕ = 0.71) and other parameters were taken from the Table 5 which described in Bui (2009). Then we use the Ergun equations to calculate the minimum fluidization velocity. It is recommended that Re_{mf} had no limit [13, 14, 15].
Calculation based on the correlation between (Re_{mf}), (Ar) and KozenyCarman
In these two calculation methods, the parameters in the calculations are taken from the empirical results according to Table 5.
Determination of the (V_{mf}) value according to Wen and Yu
According to Wen and Yu methods, the bed voidage of the refined salt particle layer at minimum fluidization state (ε_{mf}) was unknown, but we had the value of spherical degree particle from experiments (see Table 5). We put the value of spherical degree into Eq. (5) or Eq. (16) and found out the value of bed voidage (ε_{mf}) from which the velocity value of gas passing through the minimum fluidization particle layer (V_{mf}) was calculated.
Determination of V_{mf} according to GroshkoTodes
In this method, we also used the results of physical parameters of refined salt particles and air supplied to the dryer from Table 5 to calculate Ar number. The Re_{mf} is determined by using Eq. 2 and the obtained result was multiplied by the error coefficient k = 1.2 and it was considered as the result of calculation of Re_{mf} for nonspherical salt particles (described by Lebedev, [21]).
In addition, in Todes method there was another calculation by using Eq.(29) based on the available results of the minimum fluidization velocity (ε_{mf} = 0.4). We put this value into Eq. (15) and we found out the spherical degree of salt particles according to correlation given by Wen and Yu. Then we put this value into Eq. (12) to determine Ar number. By replacing Eq. (29) with the value of Ar number, we found out Re_{mf,} from which we could calculate V_{mf} value by using Eq. (10).
Determination of V_{mf} by the formula of BeayensGeldart, Goroshko, Leva, and KuniiLevenspiel
The minimum fluidization bed velocity (V_{mf}) was determined by using theoretical calculation of formulas of BeayensGeldart, Goroshko, Leva, and KuniiLevenspiel with the available physical parameters of refined salt particles and gas given in Table 5 [18, 19, 22, 25, 26]. Table 4 shows the calculated results from the formulas of authors published last time.
Determination of the minimum fluidization velocity according to theoretical and empirical methods  

No  d_{h} (mm)  Minimum fluidization velocity  
Ergun  Re andAr  Ko and Ca  Wen and Yu  Gedar  Go  Todes  Leva  Kunii and Levenspiel  Empirical methods  
1  1.65  1.327  0.939  3.149  0.5414  0.45  1.1223  1.122  2.362  3.149  0.8 
2  1.35  1.094  0.736  2.108  0.4002  0.331  0.9022  0.902  1.581  2.108  0.6 
3  1.05  0.826  0.518  1.275  0.2625  0.219  0.6653  0.665  0.956  1.275  0.58 
7  
4  0.75  0.522  0.298  0.651  0.1416  0.123  0.4188  0.419  0.488  0.651  0.42 
5  0.45  0.22  0.115  0.234  0.0524  0.05  0.1863  0.186  0.176  0.234  0.2 
6  0.225  0.058  0.029  0.059  0.0132  0.014  0.0537  0.054  0.044  0.059  0.15 
Technical parameter  Symbol  Unit  Value  Ref. 

Refined salt particle diameter  d_{p}  mm  1.65; 1.35; 1.05; 0.75; 0.45; 0.225  [13, 14] [15] 
Average diameter of particle  d_{m}  mm  0.953  
Static bed voidage  ε_{0}  0.51  
Bed voidage in minimum fluidization velocity  ε_{mf}  0.56  
Particle density  ρ_{p}  kg/m^{3}  2138  
Bulk density  ρ_{b}  kg/m^{3}  982  
Spherical degree of particle  ϕ  0.71  
Gas density (at 160°C)  ρ_{f}  kg/m^{3}  0.815  
Dynamic viscosity (at 160°C)  μ_{f}  kg/m.s  2.45 × 10^{−5}  
Fixed refined salt particle bed height  H_{0}  m  30 
3.1.2 Primary conditions for determining V_{mf} by experimental method
A model in Figure 3 and the other of fluidized bed dryer in Figure 4 was designed by authors to define the minimum fluidization velocity of refined salt particles in experiment. The dryer model was designed with its capacity of 48 kg/hour, the height of salt particle layer at the static bed was 30 mm (H_{0} ≥ 30 mm). In the experiments, the authors determined the minimum fluidization velocity (V_{mf}) for refined salt particles with diameter 1.65, 1.35, 1.05, 0.9, 0.65, 0.4 and 0.3 mm. The experimental results of determination of the minimum fluidization velocity of the particle layers with the different particle sizes are shown in Table 4. Besides, these experimental minimum fluidization velocity values were also compared with results of theoretical models that were published by authors presented in the methodology part above (Figure 5).
3.2 Discussions
The obtained values of minimum fluidization velocity (V_{mf}) calculated by the Ergun equation and the correlation between Re_{mf} number and Ar number for all particle sizes agreed well with the experimental values. The value of Re_{mf} number varies from 0.3 to 51.7. Particles with sizes d_{p} = 0.225; 0.45 and 0.75 had the tendency for laminar flow.
The obtained values of minimum fluidization velocity (v_{mf}) determined by the KozenyCarman and Kunii equations for particles with diameter greater than 1 mm (d_{p} > 1 mm) were much larger than experimental values (V_{tmf} > > V_{emf}). While, with particles having diameter smaller than 1 mm (d_{p} < 1 mm), the result of calculation was nearly equal to the experimental values. Notably, the void fraction value of the minimum fluidization state from 0.4 to 0.5 (ε_{mf} = 0.4–0.5) the calculation result matches the experimental value.
By using the correlation of Wen and Yu to calculate void fraction at (ε_{mf}) knowing the spherical properties of particle, we obtained values that were much smaller than the experimental value. The Re_{mf} number varied from 0.07 to 21.1.
When using the correlation between Re_{mf} and Ar, the obtained values of minimum fluidization velocity fit quite well to experimental results. Reynolds values vary from 0.16 to 36.6.
The minimum fluidization velocity that was calculated according the correlation between Re_{mf} and Ar number of Beayens and Geldart (Eq. (19)) gave reasonable results.
The obtained values by using the Goroshko and Todes formula in Eq. (28) were nearly equal to the experimental values.
The calculated value of V_{mf} according to Beayens and Geldart was the lowest in comparison to other methods.
The difference between the values of Re_{mf} calculated according to Goroshko and Ergun was lower than 10–20% for particles that lie in the range of Re_{mf} number from 0.28 to 43.7 (Re_{mf} = 0.28–43.7). The obtained values of velocity value (V_{mf}) for particles with diameter smaller than 0.9 mm (d_{p} < 0.9 mm) were closer to the experimental value in comparison with particles with diameter larger than 0.9 mm (d_{p} > 0.9 mm).
The minimum fluidization velocity that was calculated by Leva formula was only suitable for particles with diameter smaller than 0.75 mm (d_{p} < 0.75 mm) and value of Re_{mf} number smaller than 10 (Re_{mf} < 10). The regime of air flow through the particle layer is laminar flow.
The calculation method of the minimum fluidization velocity according to the Kunii and Levenspiel equations was suitable for particle with diameter d_{p} = (0.225; 0.45; 0.75 mm) and the results were appropriate under the conditions Re_{mf} < 20, and the calculation result was close to the experimental value.
3.3 Determination of air velocity through the particle layer at the optimum fluidization regime (V_{of})
The optimal fluidization velocity V_{of} was in the region from A to C (Figure 2). It meets the conditions:
The air superficial velocity value from A to C (Figure 2) was determined by the two standard equations as follows:
The air velocity through the solid particle layer at the optimum fluidization regime (V_{of}) was calculated according to Fedorov standard (Fe) by Eq. (39) (as cited in Lebedev [21]), with refined salt particles and drying air parameters taken from Table 5 (t_{f} = 160°C) [13, 15].
According to Ginzburg (1973), Re_{hf2} was calculated by Eq. (40) [20, 27].
The homogeneous fluidization velocity (V_{hf1}) was calculated by Eq. (41).
Reynolds value at homogeneous fluidization velocity (V_{hf1}) was measured according to Archimedes standard by Eq. (42) [20].
where Ar was calculated by Eq. (12):
Substituting parameters of air and refined salt particles into the Eq. (12),
The Ar value is 8818.4
Therefore, Re_{hf1} = 0.275 × (8818.4)^{0.52} = 66.917 = 31.53.
The homogeneous fluidization velocity (V_{hf1}) was calculated by Eq. (43).
Recalculating the homogeneous fluidization velocity (V_{hf1}) by using the experimental equation Eq. (44) [27].
From Table 4 for the specific case: V_{mf} = 0.55 m/s and particle diameter was 0.953 mm.
Both V_{hf1} and V_{hf2} met the conditions of the Eq. (38). Selecting the optimum velocity V_{of}:
Recalculating the standard Reynolds number at reasonable fluidization state (Re_{of}) under the condition of optimum fluidization velocity (V_{of} = 1.33 m/s)
or
The value of optimum Reynolds number (Re_{of}) was 30 (Re_{of} = 30).
The void fraction of the particle layer at the reasonable fluidization state was determined by the Zabrodski formula (Eq. 46) (described in Lebedev, [21]).
Re_{hf2} could be recalculated according to the correlation between Re_{hf2} and Ar Eq. (47).
Substituting value of Re_{hf2} into Eq. (46), we recalculated the homogeneous fluidization void fraction (ε_{hf}) by Eq. (48).
These two calculation methods generated almost identical results.
3.4 Calculation of the critical air velocity flowing through the fluidization particle layer
In order to have a basis for determining the reasonable dimension of separating chamber of fluidized bed dryer (the chamber was located above the fluidization particle drying tank) and to limit removal of materials from the drying chamber, we defined the theoretical critical velocity (also called the final velocity).
From the calculation result of Re_{mf} of the minimum fluidization state (Re_{mf} = 10.032), this parameter of the air stream through the particle layer in the transition flow was in range 1 < Re_{mf} < 500.
According to the equation of Haider and Levenspiel (described in WenChingYang) [28, 29], the critical velocity was calculated by Eq. (49).
With resistance coefficient (C_{D}) (described in WenChingYang) [27, 28] given by
So, the critical velocity at position C (Figure 2) in the specific case had the value:
In fact, during the drying process, to ensure the drying productivity and quality, the dryer operator must observe the fluidization particle layer and adjust the inlet doors of drying air capacity at appropriate the air velocity value in the range from A to C (Figure 2) and the correlation of velocity types V_{mf} < V_{hf} < V_{cf}.
We recalculated the void fraction of particle layer with average particle diameter d_{p} = ϕd_{m} = 0.953 mm at the theoretical critical velocity in fluidization particle layer condition.
Substituting the above value into Eq. (52), we get:
Using Eq. (46) to recalculate the void fraction of particle layer at the complete fluidization state:
When the void fraction of particle layer was 1 (ε = 1), the fluidization particle layer turned to the transport regime in the air stream (called pneumatic transportation).
4. Conclusions
Most of the used correlations in the calculations and the formulas given by the authors, as mentioned above, were derived from the experiments with temperature close to the ambient temperature. So, when we use them in calculations in specific cases, they should consider the accuracy. The extrapolation should be used in the cases of the states at the temperature higher than the ambient temperature.
The mentioned theoretical calculations show the necessity for the determining of the minimum fluidization velocity of the solid particle layer with high accuracy. The sphericity of particle and void fraction of the particle layer were often not known, therefore it is required to get their values from the range of experimental variables. Empirically, the void fraction of the particles in the minimum fluidization layer at the ambient temperature is not the same as that in the increasing gas temperature.
The best method to determine the minimum fluidization velocity is to conduct the experiments. Firstly, we directly measured the pressure drop across the particle layer when the air velocity gradually decreased. Secondly, we built the graphs and read the results of the minimum fluidization velocity value.
However, if we were forced to find out the fluidization velocity without carrying out experiments to measure the pressure drop across the particle layer, the best way would be to determine the void fraction at the minimum fluidization velocity. Then we calculated the spherical property of the particle using the Ergun equations or correlation between Ar and Re_{mf} in Eqs. (10)–(12) to count out the minimum air velocity through the particle fluidization layer. This velocity value also had accuracy close to the experimental one.
The average particle diameter considered spherical degree of the particles of different sizes was 953 μm (d_{m} = 953 μm). This diameter represented the size of the particles in dry grinding technology with the hammer crusher. It is also in the common size distribution range of the combined washinggrinding hydraulicseparation technology in Vietnam’s market. Besides, the particle diameter of 953 μm (d_{p} = 953 μm) is also used in calculating the value of all types of velocity, characterized for the medium particle size of the refined salt production technology in Vietnam.
We calculated the values of three characteristic velocity types of fluidized bed drying for particles with average size d_{m} = d_{p} = 953 μm, including the minimum fluidization velocity V_{mf} = 0.55 m/s with void fraction ε_{mf} = 0.56; reasonable fluidization velocity V_{hf} = 1.33 m/s corresponding to the void fraction of particle layer ε_{hf} = 0.615; and the critical velocity of the air flow through the particle bulk V_{cf} = 2.3 m/s with the void fraction value of fluidization particle layer ε_{cf} = 0.73.
In fact, during the drying process, to ensure the drying productivity and quality, the dryer operator must observe the fluidization particle layer and adjust the inlet doors of drying air capacity at appropriate air velocity value in the range from A to C (Figure 2) to make sure the correlation of velocity types V_{mf} < V_{hf} < V_{cf}.
Nomenclature
cross sectional area of the bed
area for gas distribution
height of the bed, m
Archimedes number, dimensionless
initial bed height, m
void fraction at static particle layer
minimum fluidization bed height, m
void fraction at minimum fluidization particle layer
pressure drop across the bed, N/m^{2}
void fraction at homogeneous fluidization particle layer
Reynolds number
terminal void fraction
Reynolds number at the minimum fluidization velocity
Reynolds number at the homogeneous fluidization velocity
spherical particle diameter, m
equivalent spherical mean diameters, m
Reynolds number at the fluidization terminal velocity
sphericity degree, dimensionless
Reynolds number at the optimum fluidization velocity
Fedorov standard, dimensionless
bed surface velocity or superficial velocity, m/s
acceleration due to gravity, m/s^{2}
minimum fluidization velocity, m/s
solid particle density, kg/m^{3}
theoretical minimum fluidization velocity, m/s
particle bulk density, kg/m^{3}
experimental minimum fluidization velocity, m/s
air density, kg/m^{3}
homogeneous fluidization velocity, m/s
KozenyCarman coefficient
optimum homogeneous fluidization velocity, m/s
mass of particles, kg
terminal velocity or critical velocity, m/s
mass of particles bulk, kg
air dynamic viscosity, kg/ms
specific surface area, cm^{−1}, cm^{2}/g
cubic volume of particle layer, m^{3}
weight of particle, mass, N
References
 1.
Tavoulareas S. Fluidizedbed combustion technology. Annual Reviews. 1991; 16 :2527  2.
Lewis WK, Gilliland ER, Bauer WC. Characteristics of fluidized particles. Industrial and Engineering Chemistry. 1949; 41 :11041117. DOI: 10.1021/ie50497a059  3.
Zahed AH, Zhu JX, Grace JR. Modelling and simulation of batch and continuous fluidized bed dryers. Drying Technology. 1995; 13 :128. DOI: 10.1080/07373939508916940  4.
Han JW, Keum DH, Kim W, Duc LA, Cho SH, Kim H. Circulating concurrentflow drying simulation of rapeseed. Journal of Biosystems Engineering. 2010; 35 (6):401407. DOI: 10.5307/JBE.2010.35.6.401  5.
Hong SJ, Duc LA, Han JW, Kim H, Kim YH, Keum DH. Physical properties of rapeseed (II). Journal of Biosystems Engineering. 2008; 33 (3):173178. DOI: 10.5307/JBE.2008.33.3.173  6.
Duc LA, Han JW. The effects of drying conditions on the germination properties of rapeseed. Journal of Biosystems Engineering. 2009; 34 (1):3036. DOI: 10.5307/JBE.2009.34.1.030  7.
Abrahamsen AR, Gedart D. Behaviour of gasfluidized beds of fine powders part I. Homogeneous expansion. Powder Technology. 1980; 26 :4755. DOI: 10.1016/00325910(80)850066  8.
Geldart D. The effect of particle size and size distribution on the behaviour of gasfluidized beds. Powder Technology. 1972; 6 :201215  9.
Geldart D. Types of gas fluidization. Powder Technology. 1973; 7 :285292. DOI: 10.1016/00325910(73)800373  10.
Howard JR. Fluidized Bed Technology: Principles and Application. Publisher Taylor and Francis Group; 1989. p. 214  11.
Rhodes M. Fluidization of particles by fluids. In: Educational Resources for Particles Technology. Melbourne, Australia: Monash University; 2001. pp. 139  12.
Ergun S. Fluid flow through packed columns. Chemical Engineering Progress. 1952; 48 :994  13.
Bui TT. Determination on geometrical parameters of refined salt particle applying of fluidized particle lay drying. Journal of Heat Science and Technology. 2009; 86 :1013  14.
Bui TT. Determination on hydrodynamic parameters in fine salt drying in a model of fluidized bed dryer. Journal of Heat Science and Technology. 2009; 90 :1317  15.
Bui TT. Researching and determining on basic physical parameters of refined salt particles to apply in the calculation and designing of continuous fluidized bed. Journal of Vietnam Mechanical Engineering. 2009; 146 :831 and 48  16.
Yates JG. Fundamentals of FluidizedBed Chemical Processes. 1st ed. Oxford: ButterworthHeinemann; 1983. p. 236  17.
Wen CY, Yu YH. A generalized method for predicting the minimum fluidized velocity. AICHE Journal. 1966; 12 :610612  18.
Baeyens J, Geldart D. Predictive calculations of flow parameters in gas fluidized bed and fluidization behavior of various powders. In: Proceedings of the International Symposiu on Fluidization and its Applications; 1973  19.
Goroshko VD, Rozenbaum RB, Todes OM. Approximate laws of fluidized bed hydraulics and restrained fall. Izvestiya Vysshikh Uchebnykh Zavedenii, Neft i Gaz. 1958; 1 :125131  20.
Tran VP. Calculation and Designing on the Drying System. Hanoi: Education Publishing House; 2002  21.
Lebedev PD. Calculation and Design of Drying Equipmet. Moscow, Leningrad: Gosenergoizdat; 1963. p. 320 (in Russian)  22.
Leva M. Fluidization. New York: McGrawHill; 1959. p. 281  23.
Carman PC. Fluid flow through granular beds. Transactions, Institution of Chemical Engineers. 1937; 15 :150166  24.
McCabe WE, Smith JC, Harriott P. Unit Operations of Chemical Engineering. 6th ed. New York: McGraw Hill; 2001. p. 1132  25.
Kunii D, Levenspiel O. Various kinds of contacting of a batch of solids by fluid. In: Fluidized Engineering. Huntington, NY: Robert E. Krieger Publishing Co.; 1977. pp. 2456  26.
Kunii D, Levenspiel O. Fluidization engineering. 2nd ed. Boston: ButterworthHeinemann; 1991. p. 49  27.
Ginzburg AS. Theoretical and Technical Basis of Drying Food Products. Moscow: Pishchevaya Promyshlennost; 1973. p. 528 (in Russian)  28.
Yang WC. Particle characterization and dynamics. In: Yang WC, editor. Handbook of Fluidization and FluidParticle System. New York: Marcel Dekker; 2003. pp. 129  29.
Yang WC. Flow through fixed beds. In: Yang WC, editor. Handbook of Fluidization and FluidParticle System. New York: Marcel Dekker; 2003. pp. 2953