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Ind. Eng. Chem. Res. 2008, 47, 7934–7939
Flow Patterns: Does Gas/Solids Flow Pattern Correspond to Churn Flow in Gas/Liquid Flow B. J. Azzopardi* School of Chemical and EnVironmental Engineering, UniVersity of Nottingham, UniVersity Park, Nottingham NG7 2RD, United Kingdom
The output of electrical capacitance tomography measurements of gas/solids flow in a vertical pipe have been analyzed to extract flow pattern information. Two approaches already used for gas/liquid flows were employed. One uses the shape of the probability density functions of the cross-sectionally averaged gas fraction time series. The other considered the velocities of periodic structures, i.e., pulses of particles. The results from both techniques showed that a flow pattern similar to churn flow in gas/liquid flow was indicated. When the gas/solids flow rates are plotted on a gas/liquid flow pattern map, they fell in the churn flow region. Introduction Gas/liquid and gas/solids flows in pipes have been observed to exhibit similar behavior. In particular, it is the variation in time and space that makes them such an interesting subject for study. On the whole, research into each phase combination has developed separately. However, there have been some publications examining links. For example, some1-4 have looked at the correlations for void fraction and pressure drop in gas/liquid flows and applied versions of them to gas/solids flows. Gas slugs in fluidized beds have been shown to be analogous to slug flow in gas/liquid flows in vertical pipes.5 The analogy has been extended to slug flow in horizontal pipes.6 For vertical upflow, Bi and Grace7 have gathered data, particularly for flow pattern transition for gas/liquid flow, and considered analogies to gas/ solids flows. In industrial applications, such as boiler tubes or the feed lines to solids fueled gasifier plants, typical flow rates can be in the range 1000-3000 kg/m2 s. These are much higher than those studies in many research papers. It is recognized that lower flow rates are important in other pieces of equipment. In assessing similarities between the two two-phase combinations, it might be helpful to start by considering the flow patterns in gas/liquid flows. Here, let us confine ourselves to upward flow in vertical pipes. In 1970, Hewitt and Hall-Taylor8 proposed five flow patterns: bubbly, slug, churn, annular, and wispy annular. Bubbly flow consists of a liquid continuum with small bubbles dispersed within it. However, the bubbles are only uniformly dispersed at very low gas flow rates. There are waves of void fraction giving spatiotemporal variation in concentration. In slug flow, the gas travels either in large gas bubbles of nearly the pipe diameter or as small bubbles in the liquid bodies that divide the large bubbles. The voidage within the liquid sections can be zero for very small pipe diameters9,10 but it increases systematically with pipe diameter. For pipe diameters >100 mm, conventional slug flow is not observed.11 There is not a consensus about the nature of churn flow. However, it is recognized that there are large structures (waves) present that carry the liquid upward. The film between these waves could flow backward at low liquid flow rates. At higher liquid flow rates, the film travels upward but at velocities lower than those of the waves, thus giving the strong impression of oscillation * To whom correspondence should be addressed: Tel: +44 115 951 4160. Fax: +44 115 951 4115. E-mail: barry.azzopardi@ nottingham.ac.uk.
that usually characterizes this flow pattern. In annular flow, part of the liquid travels as a film on the pipe walls with the rest being conveyed as drops in the gas core. There is constant interchange of liquid between film and drops. Atomization from the film only occurs from disturbance waves that occur on the film interface. Flow pattern identification was originally carried out using maps, graphical plots of superficial velocities, momentum fluxes,12 or Froude numbers. Later work proposed a physical basis for each transition and developed a mathematical model for each. The bubble/slug transition is taken to depend on bubble coalescence; beyond a critical void fraction, collisions would occur at a high frequency and lead to the large bubbles characterizing slug flow.13 A critical (and constant) void fraction was assumed at the transition. Allowing for a drift velocity resulted in the simple equation ulsc )
( )
1 - εg ugs + (1 - εg)u∞ εg
(1)
where ulsc is the liquid superficial velocity at transition, ugs is the corresponding gas superficial velocity, u∞ is the drift velocity (usually taken as a function of the phase velocities and surface tension), and εg is the void fraction. Later work showed that the critical void fraction at transition depended on the bubble/ pipe diameter ratio. The slug/churn transition has been attributed to the occurrence of flooding of the film around the large bubble.14 Flooding is the reversal of direction at critical gas velocities. The churn/annular transition is linked to flow reversal, when all of the liquid in the film travels upward.8 Identification of flow patterns was originally achieved using direct visual observation or via high speed cine film. However, it was not always clear which flow pattern was being seen, and in one instance a panel’s votes were used to fix the flow pattern. More objective methods using probability density function (PDF) plots of pressure, pressure drop, or void fraction are now being employed. Costigan and Whalley15 identified the PDF signature for bubbly flow as a narrow peak at low void fraction, slug flow had two peaks at high and low void fractions, and churn was epitomized by a single peak at high void fraction with a tail to lower fractions, while annular flow was characterized by a narrow peak at high void fraction. A different approach was employed by Sekoguchi and Mori.16 They instrumented their pipe with several probes from which they could determine void fraction time histories. A distance/
10.1021/ie800868b CCC: $40.75 2008 American Chemical Society Published on Web 09/24/2008
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time void fraction plot helped them identified those structures that has coherence, i.e., which persisted over a long distance. These they classified by their velocity/amplitude/axial extent characteristics. Slugs occupied the entire pipe cross section. For those individual lumps that do not occupy the whole crosssection, it is seen that, for some, there is little increase in lump velocity with increasing width, while for others, the velocity increases significantly with width. These were identified as disturbance waves from annular flow and huge waves from churn flow, respectively. They found that more than one type of the above structures could occur at given gas and liquid flow rates. They determined the frequency of each of the three structures and identified boundaries when the frequencies were equal. These areas can be mapped onto slug, churn, and annular flows. Note that the churn region of Sekoguchi and Mori covers both the churn and wispy-annular regions of the flow pattern map of Hewitt and Roberts.12 This lends credence to the observation by Azzopardi et al.17 of large continuous liquid structures in the gas core at flow conditions corresponding to churn flow. These are presumably wisps and are partially atomized liquid where the gas velocity is not sufficiently high to break it down into small drops. Another way that flow patterns can be differentiated is through the trends in the velocity of the structure with mixture velocity (the sum of the superficial velocities of the gas and liquid).10,11,18 For slug flow the gradient of such a plot is positive and is well predicted by the equation of Nicklin et al.19 ust ) A(ugs + uls) + u∞
Figure 1. Phase diagram for vertical gas/solids flow (data from Lippert;21 pipe diameter ) 40 mm, particles ) alumina, diameter ) 75 µm.
(2)
where ust is the velocity of slugs, ugs is the gas superficial velocity, uls is the liquid superficial velocity, and u∞ is the drift velocity of the gas bubbles, which is usually taken to be 0.35(gD). In that expression g is the gravitational acceleration and D is the pipe diameter. A is a constant whose value is usually set to 1.2. The transition to churn flow was characterized by a deviation of the structure velocity from the Nicklin curve with the gradient changing to take a negative value. The gradient reverted to a positive value when the flow pattern changed to annular flow. In considering gas/solids flow, an added complication is that the particle size is an independent variable unlike bubble or drop sizes in gas/liquid flows, which are dependent variables. Here the classification suggested by Geldart20 for fluidization will be used to group different sizes of particles. Flow pattern maps are used in gas/solids as well as gas/liquid flows. In many cases, the pipes were opaque so that there was no opportunity to identify the flow pattern. Moreover, the solids themselves are opaque, so it is not possible to see into the center of the pipe and flow patterns have more often than not been inferred. Early work used plots called phase diagrams, essentially pressure drop versus gas superficial velocity. An example is given in Figure 1 using the data of Lippert.21 A similar plot is presented by Zenz and Othmer.22 For each solids flow rate the chart can be divided in to regions according to the pressure drop/gas velocity gradient. Mass lift is described as an upward constrained packed bed type of flow. Dense and dilute phases are differentiated more on their concentration than any detailed mechanism relating to the flow. Other flow pattern maps are plots of solids fraction against gas superficial velocity.23 In some cases, e.g., Leung24 and Bi and Grace,25 the transition boundaries are defined by simple correlational equations. An example of these is illustrated in Figure 2. In that, the flow patterns identified were homogeneous dilute phase flow, core-annular dilute phase flow, fast fluidization, and a region where “practical operation was very difficult if not impossible”. Leung24 proposed an
Figure 2. Flow pattern transition lines of Bi and Grace25 for gas/solids flow.
equation for the transition between packed bed and slugging flow. This can be written as ussc )
(
) (
)
1 - εmf 1 - εmf ugs umf εmf εmf
(3)
where ussc is the superficial velocity of the solids at the transition and εmf and umf are the void fraction and velocity at the inception of fluidization, respectively. Obviously, there are similarities between eqs 1 and 3. The difference in sign is logically relating to relative density of the phases. It is noted that the range of the Bi and Grace map is limited to low gas and solids flow rates and so excludes high flow rate data.21,26-30 Understanding the behavior within the different flow patterns of gas/solids flows requires information about the disposition of solids in space (about the cross-section) and time. Bhusarapu et al.31 have presented methods to give time-averaged, crosssectionally resolved information. Electrical capacitance tomography (ECT) is a technique that has been employed by a number of researchers30,32-36 to obtain information of the type required. It employs a number of electrodes (6, 8, or 12) mounted around the outside of a nonconducting pipe. Rapid measurements (up to 200 cross-sections per second) of the capacitance between each pair of electrodes yield a matrix of capacitances that can be used to determine the spatial distribution of solids. Use of two rings of electrodes allows velocities and hence mass flow rates to be determined. Azzopardi et al.30 have shown that this approach can measure mass flow rates with errors of
