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Ind. Eng. Chem. Res. 2009, 48, 7624–7630
PROCESS DESIGN AND CONTROL Effect of Geometry of the Plenum Chamber on Gas Distribution in a Fluidized Bed Ali Mohammadkhah and Navid Mostoufi* Department of Chemical Engineering, UniVersity of Tehran, PO Box 11155/4563, Tehran, Iran
The computational fluid dynamics (CFD) technique was used to simulate a fluidized bed with eight different plenum chambers of different design. The effect of the geometry of the plenum chamber on the velocity profile on the distributor and the pressure drop across the distributor was investigated. The plenums were selected such that the influence of characteristics such as body shape, direction and location of gas entrance, entrance type, and existence and shape of the internal baffle could be studied. The results indicate that the geometry of the body and the existence of the baffle are the most important characteristics that affect the flow uniformity above the distributor. It was shown that the shape of the baffle does not have a remarkable impact on the velocity profile. The direction and location of the gas entrance each has a significant effect on the distribution quality. The downward injection of gas and placement of the gas entrance far enough from the distributor increases the uniformity of flow over the distributor. It was shown that the geometry of the plenum chamber affects the total pressure drop across the distributor. A correction factor was introduced to quantify the effect of the geometry of the plenum on the pressure drop of the perforated plate distributor. 1. Introduction Fluidized beds play an important role in many industries such as oil, gas, petrochemicals, and power plants, because of their multifunctional applications, such as mixing, drying, coating, granulation, separation, combustion, etc. The hydrodynamic properties and mixing pattern in gas-solid fluidized beds are dependent on many parameters, such as gas properties, solid properties, gas entrance conditions, and distributor geometry. The complexity of hydrodynamics and development of efficient numerical methods have led researchers to employ computational fluid dynamics (CFD) to study the hydrodynamics of fluidized beds.1-10 Most researchers who used CFD to investigate the hydrodynamics of fluidized beds did not take the effect of the plenum into account. Taghipour et al.10 assumed a uniform entry for gas in simulations, and they reported that nonuniformity causes the differences between experiments and simulations. However, researchers such as Depypere et al.5 and Peirano et al.,11 who considered the plenum chamber in their simulation, found that the plenum has a significant impact on the bed behavior. Peirano et al.11 found that a constant gas velocity profile on the distributor is not a reasonable assumption. As mentioned in their research, if the gas supply system and the bed are coupled, a transient effect and spatial effects can be expected. They indicated that, when the pressure drop of the distributor is low, the air-supply system and especially the plenum chamber affects the bed. In most industrial cases, the pressure drop across the distributor is low, because of the high cost of the gas-supply systems. Therefore, the optimum design of the plenum chamber is the one that provides uniform gas distribution above the grid while offering a low pressure drop. There are some other studies on the effect of plenum volume on the dominant frequency of the bed and intensity of pressure fluctuations, as well as studies * To whom correspondence should be addressed. Tel.: (98-21)66967797. Fax: (98-21) 6640-1024. E-mail address:
[email protected].
on the observed behavior of the bed, relating to its inlet boundary conditions.11-18 Uniformity of the flow over the distributor is extremely important for the proper performance of fluidized-bed reactors. There is little information about the effect of plenum chamber on the gas velocity distribution at the bottom of fluidized beds. Therefore, in this work, an effort was made to investigate the effect of the characteristics of the plenum chamber on the pressure drop across the distributor and velocity profile of the gas above the distributor. The effect of factors such as body shape, baffles, gas entrance location, and gas entrance direction were investigated in this work. 2. Modeling In this section, required equations and information for modeling the flow of gas in the plenum chamber are presented. Single-phase flow of gas in the plenum was modeled by writing mass and momentum balance equations. 2.1. Governing Equations. Conservations of mass and momentum under steady-state condition for the flow of gas can be written as ∇ · (FV b) ) 0
(1)
∇ · (FV bb V ) ) -∇p + ∇ · τ + Fg b
(2)
2.2. Turbulency. As mentioned in the Introduction, although the fluidized beds operate in multiphase mode, the simulations of this study were conducted in the single-phase mode, because the plenum volume below the grid was investigated. Neglecting grid leakage, this region can be considered only as a single phase. Many researchers have adopted either a k-ε model or a LES model for taking turbulency into account.19-22 The k-ε model has been used for the simulation of fluidized beds23,24 and has shown good agreement with experimental results. There are three versions for the k-ε model, i.e., standard, renormal-
10.1021/ie9001684 CCC: $40.75 2009 American Chemical Society Published on Web 07/23/2009
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typical 500-µm solid with a density of 2500 kg/m and an initial solids aspect ratio of 2. Eight different plenum chambers were considered in the simulations. These plenums were selected based on their application in industry. Figure 2 shows schematics of the plenums considered in this work. 4. Simulation
Figure 1. Schematic of a simulated fluidized bed.
ization group theory (RNG), and realizable. The realizable version is a relatively recent development of the k-ε model,25 which is different from the standard k-ε model in the formulation of k and the transport equation for ε. In the present study, simulations were done using the k-ε realizable model. 2.3. Boundary Conditions. The uniform inlet velocity was used for the entrance to the plenum. The direction of air coming into the plenum chamber was considered normal to the boundary. The turbulent kinetic energy (k) was calculated from the turbulent intensity (I), 3 k ) (UI)2 2
(3)
and the turbulent dissipation rate was calculated from the hydraulic diameter of the entrance:
( )
ε ) C3/4
k3/2 DH
(4)
At the outlet (i.e., the top of the column), the pressure was considered constant and set to the atmospheric pressure. 3. Geometry Figure 1 shows a schematic of the fluidized bed considered in this study. The bed diameter was considered to be 150 mm. Because of the prevalent use of perforated plate distributors in industry and research activities, this type of distributor was used in the present study. The distributor considered in this work has 375 orifices, each with a diameter of 2 mm and a triangular pitch of 6.84 mm (corresponding to an open area ratio of 6.7%). This distributor was used for all different plenums considered in this investigation. Note that this distributor was designed based on the recommendations of Kunii and Levenspiel26 for a
4.1. Gas. Air with a constant density of 1.225 kg/m3 and viscosity of 1.7894 × 10-5 kg/(m s) flows through the plenum. Since the pressure drop is
