Recent Researches in Applied Mechanics
Modes of Flow in Pneumatic Conveying Systems ALPEREN TOZLU, EMRAH ÖZAHĐ, AHMET ĐHSAN KUTLAR, MELDA ÖZDĐNÇ ÇARPINLIOĞLU Department of Mechanical Engineering University of Gaziantep 27310 Gaziantep TURKEY
[email protected] http://www.gantep.edu.tr Abstract: - Pneumatic conveying systems are used widely to convey different types of materials in a variety of industrial settings. The knowledge on flow modes is particularly important in the design stage of pneumatic conveying lines in terms of energy requirements. There are some classifications of flow modes valid for both powders and bulk solid particles based on mean particle size, particle and gas density and loose poured bulk density considering also air/particle interactions. In this paper, the available literature on classifications of flow modes for pneumatic conveying are summarized. The material and flow parameters which are defined separately with different symbols are also presented on a common base. The results are tabulated in terms of proposed critical equations in order to provide ease and understanding in practice.
Key-Words: - Pneumatic conveying, Modes of flow, Two-phase flow, Powder, Granular particle.
1 Introduction
density and shape. Loose-poured bulk density, ρ blp ,
In gas-solid flow structure, the combined flow nature plays an important role in terms of effective transport and energy consumption, which are called as modes of flow in two-phase flow concept. In practice, non-suspension or dense phase flow is desirable for effective conveying in terms of the ratio of conveyed material in amount to the amount of air supply whereas the suspension or dilute phase flow is not. However, many products are/have to be conveyed in dilute phase conveying system. It is more convenient to determine the modes of flow using some predictive techniques instead of experimentally conveying the material in a pipeline at the start of design stage providing a considerable benefit in terms of cost. In literature, there are two distinct classifications in order to form generalized charts in terms of flow modes; i) based on physical properties of particles conveyed [1-3], and ii) based on particle/air interaction of gas-solid phase [4-7]. Moreover improvements to the classifications based on physical properties of particles are carried out taking into account a loose-poured bulk density parameter [8-10] and inter particle cohesion forces [11]. Air/particle interactions such as permeability, air retention and de-aeration are also dependent on the physical properties such as: particle size, size distribution, density of particle, loose-poured bulk
of bulk materials is the weight per unit volume that is measured when the particle is in a loose, noncompacted or poured condition, expressed as follows;
ISBN: 978-1-61804-078-7
ρ blp = (1 − ε )( ρ s − ρ g ) ≈ (1 − ε ) ρ s
(1)
where ρs is the density of particle, ρg is the fluid density and ε is the bulk voidage. Permeability, Pf is a measure of how the air flows through the material under a motive force and can be expressed as the ratio of the superficial velocity of the gas, Vmf to the pressure drop per unit pipe length, ∆P / L occurred in the direction of the flow as; Pf = A∆P LQ = Vmf (∆P / L)
(2)
Superficial gas velocity is given as; Vmf = Q A
(3)
where Q is the volumetric gas flow rate and A is the cross-sectional area of the bed/pipe. Air retention is the ability of a material to retain air in the void spaces of the material after the air supply has been terminated. De-aeration, A f is a measure
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Recent Researches in Applied Mechanics
1.4 g / cm 3 ≤ ρ s ≤ 4 g / cm 3 , respectively. Sand is the typical example for this group. 3) Powders in Group C are difficult to fluidize at all due to interparticle cohesive forces. The powder lifts as a plug in small diameter tubes, or channels (rat-holes) badly. The interparticle forces are greater than the fluid forces exerted on particle. These generally occur for the materials that have very small particle size, strong electrostatic force and for very wet or sticky materials. Pulverized powders are exampled for this group. 4) The materials in Group D have large and/or very dense particles. The materials in this group can be spouted if gas is admitted only through a centrally positioned hole. The flow regime among the particles may be turbulent. Geldart [1] proposed a criterion to determine the boundary between the powders in Groups A and B according to being whether the superficial gas velocity at minimum bubbling, Vmb is greater than superficial gas velocity at minimum fluidization, Vmf or not. In Group A,
of how the air naturally escapes from the material and can be expressed as; A f = t ( ∆P L )
(4)
where t is the time related to the pressure drop decay plot from fluidization pressure to atmospheric pressure. Minimum fluidization velocity at the onset of fluidization is commonly given as; Vmf = Pf (∆P / L) crit
(5)
Fluidization defined as the aerated state of the material. Saltation is the process of deposition of particles along the horizontal pipeline which occurs when the air velocity falls below the minimum conveying value. Dense phase (non-suspension) is defined as a state which occurs when the gas velocity below the saltation velocity of particle conveyed. Dilute phase (suspension) is a state when the gas velocity equal to or above the saltation velocity of particle. Slug flow is described by the presence of liquid rich slugs that span the entire channel or pipe diameter. This type of flow is proper for friable and/or granular products. When the air mass flow rate is reduced further, some particles conveyed accumulate at the bottom of the pipeline and form long plugs. This type of flow is described as plug flow. In plug flows, high fluctuations in pressure and vibration occur due to being long plug structures. This region is referred as unstable zone.
Vmb Vmf ≥ 1
Geldart [1] used three different low density powder of Diakon, fresh and spent catalyst in his experiment. He proposed a linear equation representing the relationship between mean particle size, d p and minimum bubbling velocity, Vmb , and compared it with the equation of Davies and Richardson [2] for the superficial gas velocity at minimum fluidization, respectively as follows;
2 Flow Mode Approaches 2.1 Classification based on properties on particles conveying
physical
The behavior of gas-solid flow was classified into four categories by Geldart [1] in terms of mean particle size and density difference. According to his classification based on gas fluidization; 1) Powders in Group A in which material has a small mean size and/or a low particle density (less than about 1.4 g/cm3) behave as dense phase expansion after minimum fluidization. When the superficial gas velocity is high enough in order to form slugging conditions, the slugs are axisymmetric, while the superficial gas velocity is increased further, slug flow tends to transition to turbulent. Some cracking catalysts can be given as typical examples. 2) Powders in Group B bubble at the minimum fluidization velocity contrary to powders in Group A. The materials in this group have the mean size and density ranges of 40 µm ≤ d p ≤ 500 µm and
ISBN: 978-1-61804-078-7
(6)
Vmb = 100 d p
(7)
Vmf = 0.0008 gd p2 ( ρ s − ρ g ) µ
(8)
where g is the gravitational acceleration and µ is the dynamic viscosity. The equation describing the border of Group A and B is derived by Geldart [1] inserting Eqs. (7) and (8) into Eq. (6) (see Table 1). The boundary between Group B and D is not so clear as that between Group A and B. However, the proposed criterion by Geldart [1] is available in Table 1. There is no exact criterion describing the boundary between Group A-C. Dixon [3] classified gas-solid flow into three groups as i) axisymmetric slugs, ii) weak asymmetric slugs (dunes) and iii) no slugs at all. He considered the relationship between the gas slug velocity, Vsp , terminal velocity, Vt , and minimum fluidization velocity, Vmf
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using the following
Recent Researches in Applied Mechanics
22µm ≤ d p ≤
equations; Vsp = 0.35( K sp gD)1 2
kg/m3, and i.e., air mass flow rate 5 g/s < mɺ air < 100 g/s for conveying of pulverized coal, 2 g/s < mɺ air < 20 g/s for conveying of 1000 µm sand. Mainwaring and Reed [4] proposed the line separating two modes of fluidized dense phase and plug flow by introducing a parameter denoted as X = t ρ s = 0.001 m3s/kg. Fargette et al. [5] classified the powders conveyed in a dense phase, which are especially used for the manufacture of steel, according to the permeability factor, air retention and cohesion of powders. They defined the pneumatic flow parameter, Ω as follows;
(9)
where D is the pipe diameter and K sp =1 for axisymmetric slugs; K sp =2 for asymmetric slugs. Vt = 0.152d 1p.14 g 0.714 ( ρ s − ρ g ) 0.714 µ 0.428 ρ g0.258 (10) 2 (1 − ε ) 2 µVmf (1 − ε ) ρ g Vmf ρ s (1 − ε ) = 150 + 1.75 3 gd p ε3 gd p2 ε
(11) where ε is voidage which is the ratio of the space volume among the particles/powders in a bed to the total volume of bed. According to Dixon [3], there is no stable slug formation if Vt < Vsp hence the boundary between
Ω = tda Pf ρblp
hence the boundary between axisymmetric slug and asymmetric slugs is given as Vmf = Vsp .
air/particle
N c = ρs Pf t da
Mainwaring and Reed [4] developed two diagrams in terms of permeability and de-aeration factors of material with respect to steady state fluidization pressure drop per unit length for dense phase conveying at minimum fluidization. According to permeability factor, two different areas were defined with respect to the constant minimum fluidization velocity of 50 mm/s. The data above this critical line specifies the conveying in a dense phase plug flow in which the materials have a high permeability factors. On the other hand, the other data below the line illustrates those conveyed in dilute phase or fluidized dense phase. In terms of classification with respect to the specified parameter of the de-aeration factor divided by the particle density, they found the materials having the high values of the specified parameter (above the demarcation line) can be conveyed in fluidized dense phase while other materials below the demarcation line can be conveyed in a dilute phase or plug flow. A conventional pressure vessel system (blow tank) was used in their experiment. A wide range of products were conveyed at low velocity in dense phase. The fine powders such as cement, pulverized coal etc. and coarse granular materials such as mustard seed, plastic pellets etc. were conveyed in the range of 990 kg/m3 ≤ ρs ≤ 4610 kg/m3,
ISBN: 978-1-61804-078-7
(12)
If Ω >4000, the mode of flow becomes fluidized dense phase; plug flow if Ω 1000 µm
PC2-PC3 ρblp = 1000
-
Geldart's A-
A/C-B ρblp d p = 121x10−3
Geldart's B- Dilute phase Geldart's C-
B-D ρblp d 2p = 539 x10−6
Geldart's D- Plug flow Dixon's Axisymmetric slugs- Plug type
Asymmetric slugs - axisymmetric slugs d p ρblp
Williams & Jones [10]
Dixon's Weak asymmetric slugs- Dilute only
D 0.5
Loose poured bulk density-Mean particle diameter 3 (kg/m ) - ( µm )
=
0.885x10−3 dp
+ 1.44 D0.5
No slugging-asymmetric slugs d1p.14 ρblp 0.714 D 0.5
Dixon's no slugging- Fluidized dense-phase Molerus's A-
ρblpd 3p = 1.27 x10−9
Molerus's C-
B-D ρblp d p = 0.841
Molerus's D- Plug flow -4
Nc(mod)
