E~E~ER
Two-Phase Flow Patterns for Evaporating Flow D. P. Frankum V. V. Wadekar HTFS, AEA Technology, Harwell, Oxfordshire, 0 X l l ORA, England B. J. Azzopardi Department of Chemical Engineering, University of Nottingham, Nottingham, NG7 2RD, England
• Results of the analysis of empirical flow-pattern maps and theoretical models are presented. The flow-pattern maps are examined against available nonadiabatic data under flow boiling conditions, and modification of the flow-pattem transitions due to evaporating flow are discussed. Theoretical models are generally found to be better than the empirical flow-pattern maps, with good agreement obtained against the data. © Elsevier Science Inc., 1997
Keywords: fluid dynamics, two-phase, evaporation~boiling, data (experimental), velocity
INTRODUCTION Two-phase vapor-liquid flow in a tube can adopt many geometrical configurations of the distribution between the liquid and the vapor phases, which are commonly known as "flow patterns" or "flow regimes." The many different types of flow patterns that may develop have been described by Hewitt and Hall-Taylor [1]. The flow regimes in a vertical tube may be broadly divided into the following four different types: (1) bubble flow, where the vapor phase is in the form of bubbles distributed within the liquid continuum; (2) plug flow, where the vapor bubbles have a cross-sectional area closely approaching that of the tube and, in smaller-diameter tubes, are "bullet" shaped, with the bubbles separated by a length of liquid that may contain a dispersion of smaller bubbles; (3) churn flow, where the structure is unstable, with the vapor plugs becoming narrower and irregular while the liquid slug is destroyed by regions of vapor bubbles; (4) annular flow, where a liquid film layer is present on the tube wall, with a vapor core in the center of the tube, which may or may not contain entrained droplets. In most of the reported experimental and modeling work, the transition of flow patterns is performed for adiabatic (no heat addition) two-phase flow. However, in industrial processes, in many c.ases, two-phase flow develops under nonadiabatic conditions--for example, during boiling or condensation in the petrochemical, chemical processing, and refrigeration industries. In this paper, current methods available for flow-pattern transition and flow-pattern maps for adiabatic flow will be examined and compared with the available data for evaporating flows. Possible modifications to the adiabatic methods, to account for the effect of heat addition, will then be described. F L O W - P A T t E R N MAPS Most of the work published for empirical as well as theoretical two-phase flow-pattern maps has been per-
formed with adiabatic air-water systems. This work, along with other work covering evaporating flows, is described here. Empirical Flow-Pattern Maps Data collected from flow-pattern observations may be presented as a flow-pattern map, a two-dimensional plot attempting to separate the flow patterns into particular areas. The simplest types of flow-pattern maps present the data for a particular type of fluid and geometry only. Bennett et al. [2], Bergles et al. [3], and Mayinger and Zetzmann [4] plotted total mass flux against quality. However, these flow-pattern maps may not be reliable when used for fluids or tube geometries other than those from which they were obtained. Mayinger and Zetzmann [4] generalized total mass flux against quality plots by plotting the total mass flux against a dimensionless number, Z: z
Xg
(1)
where Xg is the mass quality, m an empirical exponent, and P/Pc is the reduced pressure--that is, the ratio of the system to critical pressure of the fluid. Three fluids systems (steam-water, Refrigerant-ll, and Refrigerant-12) were considered, with the transitions being approximately represented by the same line on the flow-pattern map for these three different fluids. Fair [5] plotted the total mass flux against the reciprocal of the Lockhart-Martinelli parameter (l/Xtt). This coordinate was chosen following the success of Lockhart and Martinelli [6] in correlating their adiabatic two-phase data for pressure drop and void fraction by the LockhartMartinelli parameter. Hewitt and Roberts [7] presented a generalized flowpattern map for vertical upward flows in round tubes, Data from air-water mixtures and steam-water mixtures in
Address correspondence to D. Frankum, AEA Technology, B404 Harwell, Didcot, Oxfordshire, OX11 ORA, England.
Experimental Thermaland Fluid Sciehce 1997; 15:183-192 © Elsevier Science Inc., 1997 655 Avenue of the Americas, New York, NY 10010
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D.P. Frankum et al.
a 23.5-m-long, 31.8-mm-diameter vertical tube was used to develop a map where the flow regimes were plotted in terms of the superficial momentum flux of the two phases (pL/, 2 and pgb2). Duns and Ros [8] collected flow-pattern information in a vertical column 10-m long. Different tube diameters between 32 and 142 mm were used with different fluids to encompass a wide spread in the density, viscosity, and surface tension of the flowing fluids. The resulting flowpattern map was a plot of the dimensionless liquid velocity number iq(pl/go') 1/4 against the vapor velocity number /,g(pl/gtr) 1/4. Gould [9] used the same axes, and, because the same physical property group was used in both coordinates, the map represented principally the superficial velocity of each phase.
Theoretical Flow-Pattern Maps for Adiabatic Flows To construct a theoretical map, the mechanisms that cause the transition between the successive flow patterns need to be identified. Taitel et al. [10] examined these physical mechanisms to produce a series of equations to account for both physical properties and tube geometry. Mishima and Ishii [11], McQuillan and Whalley [12], Bilicki and Kestin [13], and Barnea [14] have all presented flow-pattern maps based on physical modeling of the transition boundaries• The transition mechanisms proposed between the four basic flow patterns (bubble, plug, churn, and annular) are discussed here. Bubble-Plug Transition In bubble flow, two opposing processes are acting on the bubbles: (1) coalescence of the smaller bubbles by impact to form larger bubbles and (2) breakup of the larger bubbles into smaller ones caused by turbulence in the liquid phase.
Nondispersed bubble to plug flow. If bubble coalescence dominates over the breakup forces, then large vapor pockets may appear and lead to plug flow. The coalescence of the bubbles depends on both the rate of impact and the number of bubbles in the flow. Therefore, increasing the vapor flow rate will cause the bubble flow to become unstable at a critical value of the void fraction. This critical void fraction has been determined both theoretically and experimentally. Radovcich and Moissis [15] considered the individual bubble fluctuations within a cubic lattice structure and determined a relation between frequency of bubble collision and void fraction that indicated that the collision frequency became very high at a void fraction of 0.3. This value agrees with the experimental results obtained by Griffith and Synder [16]. Taitel et al. [10] modeled the transition for bubble-toplug flow by considering the relative rise velocity of a single bubble in an infinite liquid, assuming a maximum void fraction of 0.25, to give i,, = 3.0i~g - 1.15I g°-( P-l -- Pg) }l/4 t~
.
(2)
Nondi~persed to dispersed bubble flow. In this case, where turbulence forces dominate over the coalescence forces, the bubbles will break up to give dispersed bubble flow.
Taitel et al. [10] claimed that, provided the bubbles produced were small enough to remain spherical, the transition from bubble flow to plug flow would be suppressed for void fractions in excess of the critical value, eg, of 0.25. Sevik and Park [17] assumed that the breakup of bubbles was due to pressure forces causing the bubbles to oscillate at their natural frequency and established the maximum stable bubble size in a turbulent liquid field. Taitei et al. [10] assumed that turbulent breakup could prevent coalescence only if the bubble size produced were small enough to remain spherical. Equating the bubble size with the maximum spherical bubble size, as determined by Brodkey [18], produced the following equation: vl + /'g >->-
4D°'429(or/pl)°'°89[g(pl pg)]°'4-46 0.072
vl
--
. (3)
/91
Using the equation of Weisman et al. [19], which was developed for horizontal tubes with diameters in the range of 0.01 to 0.127 m, McQuillan and Whalley [12] proposed >
[go-(.,- .2]
.
(4)
McQuillan and Whalley assumed that, at the high liquid velocities under consideration, the effect of slip between the two phases is negligible, such that turbulence is caused by bulk flow alone and therefore should not be affected by tube inclination.
Dispersed bubble flow to plug. The void fraction in dispersed flow can increase beyond the critical value, e., of 0.25. The upper hmit for the void fraction was taken by Taitel et al. [10] as 0.52, indicating a cubic lattice of bubbles. McQuillan and Whalley [12] used a value of 0.74 for a true hexagonal or cubic close-packed lattice. Both then performed a similar analysis, as described in the section on nondispersed bubble to plug flow. Mishima and Ishii [11] used a critical void fraction value of 0.3 for the transition between dispersed bubble flow to plug flow but made no allowance for turbulence. Plug-Churn Transition Because the definition of churn flow itself is a subject of considerable debate [20, 21], plug-to-churn-flow transition is not as well defined and as well characterized as are other transitions. Moreover, as will be discussed in the section on practical significance, from the heat-transfer point of view, plug and churn flow can be grouped together as intermittent two-phase flow. A number of transition models have been reviewed by Jayanti and Hewitt [22], who investigated transition mechanisms due to entrance effects, flooding, wake effects, and bubble mechanisms. They concluded that the flooding mechanism proposed by McQuillan and Whalley [12] and the bubble entrainment model of Brauner and Barnea [23] were based on phenomena normally associated with plug flow and showed good agreement with experimental results. Subsequently video imaging by Jayanti et al. [24] of a vertical tube with cocurrent flow showed flooding waves within the Taylor bubble in plug flow as the transition to churn flow was approached. The model of McQuillan and Whalley [12] was further improved by Jayanti and Hewitt [22], who applied a film thickness correlation over a wider range of film Reynolds
Two-Phase Flow Patterns numbers and modeled the effect of length of the falling film on the flooding velocity. Plug-Churn to Annular Transition Haberstroh and Griffith [25] studied slug-annular transition in various fluid systems and tube diameters. They found that the transition occurred for a void fraction of between 0.8 and 0.9. Taitel et al. [10] proposed that annular flow occurs when the vapor flow rate becomes sufficiently high to entrain liquid droplets. The minimum vapor velocity was determined from a balance between the gravity and the drag forces acting on the droplet. The droplet size was evaluated by equating the impact force of the vapor that tends to shatter the droplet to the surface tension force that holds the droplet together to give • 1/2 = 3.1. (5) [ o ' g ( p , - pg)] 1/4 The preceding dimensionless group is recognized as the Kutataladze number. This number was found to be 3.2 by Pushkina and Sorokin [26], who empirically determined the gas velocity necessary to lift a liquid film during flooding experiments. McQuillan and Whalley [12] suggested that the assumption of Taitel et al. [10] of the entrained droplet being accelerated by the gas core was incorrect and proposed the following inequality: Fr* > 1, (6) which was first suggested by Wallis [27], where Fr* is the modified Froude number, the ratio of the inertial to gravitational forces, and is given by • 0.5 Fr* = Vgpg (7) [up( 0, - pg)]05 • This value was confirmed experimentally by Bennett et al.
[2] for steam-water systems. Mishima and Ishii [11] suggested that annular flow transition occurred as a result of either flooding of the falling liquid film or destruction of the liquid slugs or large waves by entrainment or deformation. N O N A D I A B A T I C FLOW-PAT'FERN DATA Flow-pattern determinations have been recorded by Bennett et al. [2], Hosler [28], and Celata et al. [29] for boiling inside vertical channels. Data have also been reported by Tippetts [30] and Lu and Zhang [31], although these data are in a less-accessible form. Observations have also been recorded by Kattan et al. [32] for flow boiling in horizontal channels, but this topic is outside the scope of the present discussion. Bennett et al. [2] examined flow patterns for steam-water mixtures inside a 3.65-m vertical titanium tube of 12.6-mm diameter. Resistive heating to as much as 1200 k W / m 2 was used to heat water at pressures as high as 68.9 bar. A glass section through which photographs could be taken of the flow pattern was placed at the exit of the test section. A panel adjudicated the prevailing flow pattern from the photographs, with some disagreement among the members. Hosler [28] noted flow patterns for steam-water mixtures inside a rectangular channel at pressures as high as 137.9 bar. Three walls of the channel were made from
185
glass, with the remaining wall consisting of a resistively heated metal strip. The channel dimensions were 25•4 mm by 3•43 mm and 610 mm long• The flow pattern was determined from visual observation of the glass channel. Celata et al. [29] determined flow-pattern information for Refrigerant 12 inside a 2.3-m-long, 7.72-mm-diameter tube by using an optical probe, at pressures of 12-27 bar. Only the transition between intermittent flow to annular was studied in detail• Papers dealing with nonadiabatic data present them in the form of total mass flux against quality. Therefore, the following conversion is used to reproduce the data on superficial velocity plots: rh = i,g Og + i~j Pl,
(8)
/'g P~ (9) Xg rh Hosler's [28] data presented actual quality rather than thermodynamic equilibrium quality. Therefore, provided that the subcooling is not very large, Eqs. (8) and (9) should give a good approximation of the actual superficial velocities. C o m p a r i s o n s with Empirical Flow-Pattern Maps
The observed flow-pattern data for the water and Refrigerant 12 vapor-liquid two-phase flow are compared in Tables 1 and 2, respectively, against the different empirical flow-pattern maps. The flow pattern are separated into bubble flow, intermittent flow, and annular flow for steam-water. For Refrigerant 12, because the data are biased toward the intermittent-to-annular transition, the flow patterns listed in Table 2 are intermittent, transitional, and annular flow. A number of the flow-pattern points for the Refrigerant 12 data were noted as transitional. These data were not included in the calculation of the percentage of the data points correctly predicted. The data of Bennett et al. [2] at 34.5 bar are shown in Figs. 1-4 for the various experimental flow-pattern maps. In Fig. 1, for the flow-pattern map of Fair [5], the annular-flow data are predicted well. However, the plugflow data are predicted generally as bubble flow, whereas the bubble flow is predicted well. Similar conclusions may be drawn from Table 1 for Fair's empirical flow-pattern map. A total of 80% of all data points were correctly determined. This method also predicts the Refrigerant 12 data of Celata et al. [29] well, at 96%, with the transitional data being predicted as either intermittent or annular. The flow-pattern map of Duns and Ros [8] is shown in Fig. 2. The map does not adequately predict the annularflow transition, with a general tendency of predicting the data as pertaining to intermittent flow, whereas intermittent-flow data are determined as bubble-flow data. A total of 59% of the water data points were correctly predicted, but this percentage was primarily due to a majority of the data being in the bubble-flow region• Not surprisingly, the agreement with the data of Celata et al. [29], as shown in Table 2, is poor, with all the annular-flow data being predicted as either bubble or intermittent flow. The flow-pattern map of Hewitt and Roberts [7] showed very good agreement with the data of Bennett et al. [2] for all the different types of flow patterns, as can be observed in Fig. 3. This good agreement is not surprising, because
186
D . P . Frankum et al.
Table 1. Observed Flow-Pattern Data Against Predicted Flow Pattern for Various Empirical Flow-Pattern Maps for Water Data (Observed Pattern) Model
Predicted Pattern
Fair [5]
Bubble Intermittent Annular Duns and Ros Bubble [8] Intermittent Annular Hewitt and Bubble Roberts [7] Intermittent Annular Owen [33] Bubble Intermittent Annular Mayinger and Bubble Zetzmann [4] Intermittent Annular
Bubble
Bennett et al. [2] Intermittent Annular % Correct Bubble
17 7 0 24 0 0 12 10 2 16 6 2 14 1 9
17 21 0 27 11 0 1 34 3 16 19 3 13 22 3
2 14 45 10 48 3 2 0 59 2 0 59 0 2 59
these data were used to develop the transition boundaries. However, the Hosler d a t a are not as well predicted. The annular transition b o u n d a r y was accurately determined, but a majority of the bubble-flow data are predicted as intermittent flow. The overall n u m b e r of water data points correctly predicted was 44%. The Refrigerant-12 data were predicted with 85% of the points correct. Owen [33] r e c o r d e d adiabatic-flow-pattern information for air-water in a vertical tube of 32-ram diameter. The data were plotted by using the same coordinate system as that of Hewitt and R o b e r t s [7] and led to new transition boundaries, as shown in Fig. 4. F r o m Table 1, for ease of comparison, the churn-annular flow was included in the annular region, where it may be observed that the agreement for the Hosler [28] data is 83%, which is significantly
67
31
85
76
77
Hosler [28] % Total Intermittent Annular % Correct Correct
360 50 3 394 19 0 21 376 16 351 46 16 316 86 11
19 90 3 55 57 0 4 81 27 16 69 27 14 65 33
1 45 121 3 164 0 0 11 156 1 10 156 1 12 154
83
80
65
59
37
44
83
82
77
77
greater than that of Hewitt and Roberts [7] of 37%. The agreement with the Refrigerant-12 data was 83%, similar to that of Hewitt and R o b e r t s [7]. Figure 5, shows the flow m a p of Mayinger and Zetzmann [4]. The value of the exponent, m, used in Eq. (1) was set at 1.45. This value compares well with the range 0.95 < m < 1.7 given by Mayinger and Z e t z m a n n [4] for water. W i t h this value, the data of Bennett et al. [2] and Hosler [28] were predicted correctly at 77% of data points and the refrigerant data at 89%. Unfortunately, this value does not compare favorably with the value of 0.85 suggested by Mayinger and Z e t z m a n n [4]. O f the empirical flow-pattern maps evaluated, for the data of water and Refrigerant 12, the m a p of Fair [5] p r o d u c e d the best overall results. This map, in reality, is
Table 2. Observed Flow-Pattern Data Against Predicted Flow Pattern for Various Empirical Flow-Pattern Maps for Refrigerant 12 Data (Observed Pattern) Model Fair [5]
Duns and Ros [8]
Hewitt and Roberts [7] Owen [33]
Mayinger and Zetzmann [4]
Predicted Pattern
Intermittent
Bubble Intermittent Annular Bubble Intermittent Annular Bubble Intermittent Annular Bubble Intermittent Annular Bubble Intermittent Annular
1 30 0 31 0 0 0 19 12 1 18 12 6 25 0
Celata et al. [29] Transitional 0 20 11 9 22 11 0 6 25 0 6 25 0 17 14
Annular 0 2 46 1 47 0 0 0 48 0 0 48 0 3 45
% Total Correct 96
0
85
83
89
Two-Phase Flow Patterns
A
From Table 3, it can be observed that the models predict the water data correctly between the range 7881%. For the Refrigerant 12 data, Table 4, the range was 62-86%, with the lowest being the model of Taitel et al. [10], which predicted a number of the transitional points as bubble flow. McQuiUan and Whalley [12] produced a statistical analysis similar to that presented in this paper for their model. They analyzed 1399 points covering adiabatic and boiling flows for systems consisting of air-water, steam-water, nitrogen-water, and Refrigerants R l l , R12, and 113. They found 84% of the points to be correctly predicted, which is close to the prediction noted here for boiling data only.
iA
,= 0 0 512 i i
!
'
'
DISCUSSION
11111 0.Ol
0.1
1
10
100
Effect of Heat A d d i t i o n o n F l o w - P a t t e r n T r a n s i t i o n
1IX= Figure 1. Empirical flow-pattern map of Fair [5] for the data of Bennett et al. [2] at 34.5 bar. an extension of the common mass flux versus quality plots, using the reciprocal of the Lockhart-Martinelli parameter instead of quality. Comparisons
187
w i t h A d i a b a t i c Theoretical Models
The data of Bennett are compared in Fig. 6 with the flow-pattern-transition methods of Taitel et al. [10], Weisman and Kang [34], Mishima and Ishii [11], and McQuillan and Whalley [12]. For evaporating flow, as the quality increases, the superficial gas velocity increases with a corresponding reduction of the liquid superficial velocity. The observed flow patterns for water and Refrigerant 12 are shown in Tables 3 and 4, respectively, against the predicted flow patterns for the different theoretical flowpattern maps.
1=[
i "
10
From earlier sections, it appears that the adiabatic flowpattern maps and flow-transition models are performing reasonably well with the flow boiling data. This is broadly in agreement with conclusions drawn by other workers-for example, Celata et al. [29] and Lu and Zhang [31]. One of the reasons may be that it is difficult to observe flow patterns under truly flow boiling conditions. Moreover, owing to the difficult and subjective nature of flow-pattern observations, a high accuracy verification of a given method may not be possible. Nevertheless, there appears to be less incentive for developing flow-pattern-transition methods for nonadiabatic flows to improve predictive capability. As will be discussed in the next section, heat-transfer experiments, which provide a less-subjective method of a broader classification of flow patterns, indicate that the adiabatic methods of flow-pattern predictions may not be accurate. Moreover, the objective of basing our methods on more realistic physical models is always worth pursuing. In this section, therefore, we delineate various factors, arising from the differences between nonadiabatic and
i °°
~"/
I "
"
°
1
"
0.1 1
10
100
8kay)
1000 Figure 2. Empirical flow-pattern map of Duns and Ros [8] for the data of Bennett et al. [2] at 34.5 bar.
188 D.P. Frankum et al. 10 5 AA
lo' ,
l
ZX
,
I
................................ + .............................. ° ............................ x ............................ ..................................
(kg/s~)
.
{'~.-Z~. {
,.
~
i c~j
!
i:,',u=
[ f
"
---bb,y
101 .loo lO o
Figure 3. Empirical flow-pattern map of Hewett and Roberts [7] for the data of Bennett et al. [2] at 34.5 bar.
10'
10
10 2
10 4
10 s
p,0,~ (k~s~m)
adiabatic flows, that could affect the adiabatic flow-pattern transition mechanisms. Bubble-Plug Transition In a flow boiling situation, the bubble flow region is characterized by uneven void fraction distribution because of the vapor bubble generation at the wall. This feature is well documented for subcooled flow boiling by Hahne et al. [35]. The void fraction profile, under boiling conditions, is expected to be much flatter for similar quality conditions than in adiabatic flow, owing to bubble generation at the tube wall. This flatter void profile may reduce bubble coalescence, leading to a delay in transition until a higher void fraction is reached. However, there is no conclusive evidence to prove it. In addi-
tion, the temperature gradient between the bulk and near-tube-wall fluid may lower the viscosity and reduce the wall shear stress, affecting the local turbulence that may cause bubbles to either coalesce or remain dispersed. Plug-Churn to Annular Transition This transition may be best examined by considering the two boiling mechanisms individually.
Convective heat transfer dominated region. The falling liquid film associated with vapor plugs can be expected to have significantly better convective heat transfer than the liquid slugs. Therefore it is likely that there is preferential vapor generation from the liquid films directly into the
10 s
I (kg/s2m) 101
Figure 4. Empirical flow-pattern map of
Owen [33] for the data of Hosler [28] at 55.2 bar.
: lool lO o
o 10 ~
10 2
o
o 10 3
ptO~ (kg/s2m)
10 4
,O s
Two-Phase Flow Patterns
189
5O(2O
4OO0
o Churn ,-/nlular
iN
E
300O °
.
iy _
Ek.a l31
X :3
i
2OOO oo
1000
,~
r~
0 .....0
0
Annular
\ ...............
0
. . m . ~ ....... d . . . . . . . . . . . . . . .
0
¢
I
0 0.5
1.5
2
Z
Figure 5. Empirical flow-pattern map of Mayinger and Zetzmann [4] for the data of Bennett et al. [2] at 34.5 bar.
(b) Weisman and Kang [34]
(a)Taitel eta 1110] 10
1 f
l
A O0~a A 0 •. a . A ~ A
* o
i
ol
t
I
0
,~A aAala
i nl
....... ]
0.1
(11
0.01
1
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(101
I nn
~
~,,pmlk;~mOmvwciy (m/~)
10
10 A : O0
~Q
i
~
|
a 4,,
"i,
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I AA
A ! OC
• o i1~ 1
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~
I11 0.01
0.1
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,"7"
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1
0== v , , ~ t y {m/s)
(d) McQuillan and Whalley [ 12]
(c) Mishima and Ishii [11]
*
0.1
:
111
Figure 6. Theoretical flow-pattern maps against the data of Bennett et al. [2] at 34.5 bar.
lOO
190
D.P. Frankum et al.
Table 3. Observed Flow-Pattern Data Against Predicted Flow Pattern for Various Adiabatic Theoretical Models for Water Data (Observed Pattern) Model
Predicted Pattern
Taitel et al. Bubble [10] Intermittent Annular Weisman Bubble et al. [34] Intermittent Annular Mishima Bubble et al. [11] Intermittent Annular McQuillan Bubble et al. [12] Intermittent Annular
Bubble
23 0 1 20 1 3 23 1 0 22 1 1
Bennett et al. [2] Intermittent Annular
23 13 2 12 24 2 14 24 0 11 25 2
%Correct
9 0 58 2 1 58 2 10 49 2 0 59
76
83
78
86
vapor plugs rather than the liquid slug. This preference can affect the transition to annular flow by accelerating and increasing the size of the vapor plug.
Nucleate boiling dominated region. Nucleate boiling can dominate the flow boiling heat transfer at high wall superheats. Owing to higher convective-heat-transfer coefficients associated with vapor plugs, the local wall superheat will be lower than that in the liquid slug region. This implies that nucleate boiling can be more pronounced in the liquid slugs that in the vapor plugs. Thus, potentially nucleate boiling could lead to higher vapor generation into the liquid slug rather than the vapor plug, causing the size of the liquid slug to increase in relation to that of the vapor plug. Because nucleate boiling heat transfer and convective heat transfer slow opposite trends with respect to pressure, the uneven generation of vapor into liquid slug or vapor plug can go in the opposite direction with an increase in the operating pressure. To verify these specu-
Bubble
Hosler [28] Intermittent Annular
338 56 19 320 66 27 348 50 15 315 65 33
41 52 19 9 53 50 23 82 7 9 48 55
2 16 149 1 7 159 6 25 136 1 1 165
%Correct
% Total Correct
78
78
77
78
82
81
76
78
lations, we will need more systematic experiments at different pressures. At present, indirect evidence indicates that adiabatic transition criteria for the transition from plug-churn flow to annular flow may not be as accurate for flow boiling. This particular point is discussed in detail in the next section.
Flow Patterns f r o m T h e r m a l Measurements To our knowledge, the only reported work that covers the effect of flow patterns on vertical flow boiling heat transfer is that of Wadekar and Kenning [36], who analyzed the results obtained by Kenning and Cooper [37]. Kenning and Cooper conducted experiments essentially for flow boiling in electrically heated tubes; no observations of flow pattern were made. Along with other variables, they measured local wall temperatures at a number of points along the length of the test section. These thermal measurements obtained from a 14.4-mm-diameter tube show two distinct regions of heat-transfer behavior. Wadekar
Table 4. Observe Flow-Pattern Data Against Predicted Flow Pattern for Various Adiabatic Theoretical Models for Refrigerant 12 Data (Observed Pattern) Model
Taitel et al. [10]
Weisman et al. [34]
Mishima et al. [11]
McQuillan et al. [12]
Predicted Pattern
Intermittent
Bubble Intermittent Annular Bubble Intermittent Annular Bubble Intermittent Annular Bubble Intermittent Annular
11 1 19 7 20 4 7 5 19 6 8 17
Celata et al. [29] Transitional
2 0 29 0 10 21 0 4 27 0 5 26
Annular
0 0 48 0 0 48 0 0 48 0 0 48
% Total Correct
62
86
67
71
Two-Phase Flow Patterns and Kenning [36] related these two different behaviors to a broad classification of intermittent two-phase flow and nonintermittent two-phase flow. They included slug and churn flow in the intermittent category and annular flow in the nonintermittent category. They showed that it was possible to predict the boiling data in the intermittent flow region by a slug flow heat-transfer model. Importantly, Wadekar and Kenning noted that transition from the intermittent and nonintermittent region as deduced from heat-transfer characteristics does not coincide with the standard adiabatic criteria [e.g., Eq. (6)] used for the transition to annular flow. They have raised a possibility that, under flow boiling conditions, the normal mechanism for transition to annular flow is likely to be different. More systematic experimental work is indeed necessary in this direction.
191
hence flow-pattern boundaries. Further information would be desirable for different systems, with, for example, surface tension, to examine the forces holding bubbles together; latent heat, to investigate the effect of the rate of change of the developing flow; or changes in the system pressure, to investigate the effect of the dominance of the nucleate boiling or convective mechanisms. This is especially important because the present methods do not correctly predict the flow pattern as judged from the thermal measurements. In addition to the flow patterns at different flow conditions, local heat-transfer coefficients and pressure-drop measurements are required to determine how they are affected by the flow regimes. This authors gratefully acknowledge the permission given by the Heat Transfer and Fluid Flow Service (HTFS) for publication of this work.
PRACTICAL SIGNIFICANCE / USEFULNESS Empirical as well as theoretical methods for flow-pattern prediction are based on an adiabatic approach. A question therefore is always asked about their validity for evaporating flow because it occurs in practical equipment such as reboilers of vaporizers. The work carried out in the present paper demonstrates that the methods based on an adiabatic approach essentially perform satisfactorily in predicting the currently available evaporating flow data. This is encouraging for design engineers needing to predict the local flow patterns in industrial heat exchangers. Although the agreement between the predictive methods and the observed data is satisfactory, the paper also draws attention to the inadequacy of present methods in predicting the flow patterns judged from the thermal measurements. This is an area for further work and is discussed later.
NOMENCLATURE D diameter, m g gravitational acceleration, 9.81 m / s 2 m constant rh mass flux (mass velocity), kg/(m z s) p pressure, bar /'i superficial velocity of a phase (i.e., that if other phase absent) where i is 1 or g, m / s Xg quality of gas-phase mass flow fraction Greek Symbols % void fraction 7/ dynamic viscosity, N s / m z v kinematic viscosity, m2/s p mass density, k g / m 3 o- surface tension, N / m Subscripts
CONCLUSIONS The empirical flow-pattern map of Fair [5], using the Lockhart-Martinelli parameter, was found to have the best performance for these types of maps. The LockhartMartinelli parameter as a correlating parameter for the pressure drop was noted by Holt et al. [38] to perform as well as most other pressure drop correlations. The theoretical models were generally found to perform better than the empirical flow-pattern maps. In general, there was little difference in the reported level of agreement between the various models. The level of agreement between the nonadiabatic data with the flow-pattern models is similar to that found by McQuillan and Whalley [12] for their model, with predominantly adiabatic data. RECOMMENDATIONS AND FUTURE W O R K The analysis presented herein shows that the theoretical flow-pattern maps, based on adiabatic flow-pattern-transition mechanisms, are adequate in predicting the flow patterns for evaporating flow. The performances of all the theoretical models are comparable to one another. Among the empirical methods, that of Fair [5] can be recommended. Further work is required to determine the effect that evaporating flow has on the transition mechanisms and
c critical g gas phase (including vapor phase) 1 liquid phase Dimensionless numbers
Fr* Xtt
modified Froude number, given by Eq. (7) Martinelli parameter, [(1 -- Xg)/Xg]0"9(pg/Pl)0"5('Fll/T~g)
Z
0"1
Mayinger and Zetzmann parameter, given by Eq. (1) REFERENCES
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Received January 15, 1996; revised July 1, 1996
